Strong dissipation inhibits losses and induces correlations in cold molecular gases
N. Syassen, D. M. Bauer, M. Lettner, T. Volz, D. Dietze, J. J. García-Ripoll, J. I. Cirac, G. Rempe, S. Dürr
Science 320, 1329 (2008)

Atomic quantum gases in the strong-correlation regime offer unique possibilities to explore a variety of many-body quantum phenomena. Reaching this regime has usually required both strong elastic and weak inelastic interactions because the latter produce losses. We show that strong inelastic collisions can actually inhibit particle losses and drive a system into a strongly correlated regime. Studying the dynamics of ultracold molecules in an optical lattice confined to one dimension, we show that the particle loss rate is reduced by a factor of 10. Adding a lattice along the one dimension increases the reduction to a factor of 2000. Our results open the possibility to observe exotic quantum many-body phenomena with systems that suffer from strong inelastic collisions. (Science, free access)

Nonlinear spectroscopy of photons bound to one atom
I. Schuster, A. Kubanek, A. Fuhrmanek, T. Puppe, P.W.H. Pinkse, K. Murr, G. Rempe
Nature Physics 4, 382-385 (2008)

Optical nonlinearities typically require macroscopic media, thereby making their implementation at the quantum level an outstanding challenge. Here, we demonstrate a nonlinearity for one atom enclosed by two highly reflecting mirrors. We send laser light through the input mirror and record the light from the output mirror of the cavity. For weak laser intensity, we find the vacuum-Rabi resonances. But for higher intensities, we observe an extra resonance, which originates from the fact that the cavity can accommodate only an integer number of photons and that this photon number determines the characteristic frequencies of the coupled atom–cavity system. We selectively excite such a frequency by depositing two photons at once into the system and find a transmission that increases with the laser intensity squared. The nonlinearity differs from classical saturation nonlinearities and is direct spectroscopic proof of the quantum nature of the atom–cavity system. It provides a photon–photon interaction by means of one atom, and constitutes a step towards a two-photon gateway or a singlephoton transistor. (Nat. Phys., quant-ph/0803.2712v1)

Internal-state thermometry by depletion spectroscopy in a cold guided beam of formaldehyde
M. Motsch, M. Schenk, L.D. van Buuren, M. Zeppenfeld, P.W.H. Pinkse, G. Rempe
Physical Review A 76, 061402(R) (2007)

We present measurements of the internal state distribution of electrostatically guided formaldehyde. Upon excitation with continuous tunable ultraviolet laser light the molecules dissociate, leading to a decrease in the molecular flux. The population of individual guided states is measured by addressing transitions originating from them. The measured populations of selected states show good agreement with theoretical calculations for different temperatures of the molecule source. The purity of the guided beam as deduced from the entropy of the guided sample using a source temperature of 150 K corresponds to that of a thermal ensemble with a temperature of about 30 K. (PRA, chem-ph/0710.3316v1)

Doppler-Free Spectroscopy of Weak Transitions:An Analytical Model Applied to Formaldehyde
M. Zeppenfeld, M. Motsch, P.W.H. Pinkse, G. Rempe
Applied Physics B 89(4), 475-481 (2007).

Experimental observation of Doppler-free signals for weak transitions can be greatly facilitated by an estimate for their expected amplitudes. We derive an analytical model which allows the Doppler-free amplitude to be estimated for small Doppler-free signals. Application of this model to formaldehyde allows the amplitude of experimentally observed Doppler-free signals to be reproduced to within the experimental error. (APB, optics/0708.0784)

Cavity cooling of translational and ro-vibrational motion of molecules: ab initio-based simulations for OH and NO
Markus Kowalewski, Giovanna Morigi, Pepijn W. H. Pinkse, Regina de Vivie-Riedle
Applied Physics B 89(4), 459-467 (2007).

We present detailed calculations at the basis of our recent proposal for simultaneous cooling the rotational, vibrational and external molecular degrees of freedom [Morigi et al., accepted for publication in Phys. Rev. Lett. (2007)]. In this method, the molecular rovibronic states are coupled by an intense laser and an optical cavity via coherent Raman processes enhanced by the strong coupling with the cavity modes. For a prototype system, OH, we showed that the translational motion is cooled to few µK and the molecule is brought to the internal ground state in about a second. Here, we investigate numerically the dependence of the cooling scheme on the molecular polarizability, selecting NO as a second example. Furthermore, we demonstrate the general applicability of the proposed cooling scheme to initially vibrationally and rotationally hot molecular systems. (APB, quant-ph/0704.2155)

Cavity cooling of internal molecular motion
Giovanna Morigi, Pepijn W.H. Pinkse, Markus Kowalewski, Regina de Vivie-Riedle
Phys. Rev. Lett. 99, 073001 (2007)

We predict that it is possible to cool rotational, vibrational and translational degrees of freedom of molecules by coupling a molecular dipole transition to an optical cavity. The dynamics is numerically simulated for a realistic set of experimental parameters using OH molecules. The results show that the translational motion is cooled to few µK and the internal state is prepared in one of the two ground states of the two decoupled rotational ladders in few seconds. Shorter cooling times are expected for molecules with larger polarizability. (PRL, quant-ph/0703157)

Trapping of Neutral Rubidium with a Macroscopic Three-Phase Electric Trap
T. Rieger, P. Windpassinger, S.A. Rangwala, G. Rempe, P.W.H. Pinkse
Phys. Rev. Lett. 99, 063001 (2007)

We trap neutral ground-state rubidium atoms in a macroscopic trap based on purely electric fields. For this, three electrostatic field configurations are alternated in a periodic manner. The rubidium is precooled in a magneto-optical trap, transferred into a magnetic trap and then translated into the electric trap. The electric trap consists of six rod-shaped electrodes in cubic arrangement, giving ample optical access. Up to 10^5 atoms have been trapped with an initial temperature of around 20 microkelvin in the three-phase electric trap. The observations are in good agreement with detailed numerical simulations. (PRL, atom-ph/0707.1703v1)

Single-Atom Single-Photon Quantum Interface
T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe.
Science 317, 488 (2007).

Free access to abstract and full text.

Atom-molecule Rabi oscillations in a Mott insulator
N. Syassen, D. M. Bauer, M. Lettner, D. Dietze, T. Volz, S. Dürr, G. Rempe
Physical Review Letters 99, 033201 (2007).

We observe large-amplitude Rabi oscillations between an atomic and a molecular state near a Feshbach resonance. The experiment uses 87Rb in an optical lattice and a Feshbach resonance near 414 G. The frequency and amplitude of the oscillations depend on magnetic field in a way that is well described by a two-level model. The observed density dependence of the oscillation frequency agrees with the theoretical expectation. We confirmed that the state produced after a half-cycle contains exactly one molecule at each lattice site. In addition, we show that for energies in a gap of the lattice band structure, the molecules cannot dissociate. (cond-mat/0704.2155)

Collisional relaxation of Feshbach molecules and three-body recombination in 87Rb Bose-Einstein condensates
G. Smirne, R. M. Godun, D. Cassettari, V. Boyer, C. J. Foot, T. Volz, N. Syassen, S. Dürr, G. Rempe, M. D. Lee, K. Goral, T. Köhler
Physical Review A 75, 020702 (2007)

We determine the magnetic field dependence of three-body recombination and atom-dimer collision rates in a 87Rb Bose-Einstein condensate (BEC) close to 1007 G. Our exact treatments of three-particle scattering explicitly include the dependence of the interactions on the Zeeman levels of each atom. The weakly coupled Feshbach resonance distorts the entire diatomic energy spectrum causing interferences in both loss phenomena. Our two independent experiments confirm the predicted resonance-enhanced recombination loss over a range of rate constants that spans four orders of magnitude. (pdf, cond-mat/0604183)

Trapping and Observing Single Atoms in a Blue-Detuned Intracavity Dipole Trap
T. Puppe, I. Schuster, A. Grothe, A. Kubanek, K. Murr, P.W.H. Pinkse, and G. Rempe.
Physical Review Letters 99, 013002 (2007).

A single atom strongly coupled to a cavity mode is stored by three-dimensional confinement in bluedetuned cavity modes of different longitudinal and transverse order. The vanishing light intensity at the trap center reduces the light shift of all atomic energy levels. This is exploited to detect a single atom by means of a dispersive measurement with 95% confidence in 10 µs, limited by the photon-detection efficiency. As the atom switches resonant cavity transmission into cavity reflection, the atom can be detected while scattering about one photon. (pdf, quant-ph/0702162 )

A Single-Photon Server with Just One Atom
M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and Gerhard Rempe.
Nature Physics 3, 253 (2007).

Neutral atoms are ideal objects for the deterministic processing of quantum information. Entanglement operations have been carried out by photon exchange or controlled collisions, and atom–photon interfaces have been realized with single atoms in free space or strongly coupled to an optical cavity. A long-standing challenge with neutral atoms, however, is to overcome the limited observation time. Without exception, quantum effects appeared only after ensemble averaging. Here, we report on a single-photon source with one, and only one, atom quasi-permanently coupled to a high-finesse cavity. 'Quasi-permanent' refers to our ability to keep the atom long enough to, first, quantify the photon-emission statistics and, second, guarantee the subsequent performance as a single-photon server delivering up to 300,000 photons for up to 30 s. This is achieved by a unique combination of single-photon generation and atom cooling. Our scheme brings deterministic protocols of quantum information science with light and matter closer to realization. (quant-ph/0702034 )

Light force fluctuations in a strongly coupled atom-cavity system
T. Puppe, I. Schuster, P. Maunz, K. Murr, P.W.H. Pinkse, G. Rempe
Journal of Modern Optics 54, 1927-1937 (2007)

Between mirrors, the density of electromagnetic modes differs from the one in free space. This changes the radiation properties of an atom as well as the light forces acting on an atom. It has profound consequences in the strong-coupling regime of cavity quantum electrodynamics. For a single atom trapped inside the cavity, we investigate the atom-cavity system by scanning the frequency of a probe laser for various atom-cavity detunings. The avoided crossing between atom and cavity resonance is visible in the transmission of the cavity. It is also visible in the loss rate of the atom from the intracavity dipole trap. On the normal-mode resonances, the dominant contribution to the loss rate originates from dipole-force fluctuations which are dramatically enhanced in the cavity. This conclusion is supported by Monte-Carlo simulations. (Journal of Modern Optics, quant-ph/0702087 )

Polarization-controlled single photons
T. Wilk, S. C. Webster, H. P. Specht, G. Rempe, and A. Kuhn.
Physical Review Letters 98, 063601 (2007).

Vacuum-stimulated Raman transitions are driven between two magnetic substates of a rubidium-87 atom strongly coupled to an optical cavity. A magnetic field lifts the degeneracy of these states, and the atom is alternately exposed to laser pulses of two different frequencies. This produces a stream of single photons with alternating circular polarization in a predetermined spatio-temporal mode. MHz repetition rates are possible as no recycling of the atom between photon generations is required. Photon indistinguishability is tested by time-resolved two-photon interference. (pdf, quant-ph/0610227 )

The Phase of a Bose-Einstein Condensate
Stephan Dürr.
Physics & Philosophy, 4 (2006)

If two Bose-Einstein condensates are prepared independently and then overlapped, a spatial interference pattern is observed. This prompts the question what determines the phase of the fringe pattern, and whether a condensate has a well-defined value of the phase. This problem has been studied in the literature in detail. The objective of this article is, to present an introduction to the subject and to summarize the discussion for a wider audience.
(link to online journal)

Light Forces In Cavity QED
Gerhard Rempe and Karim Murr.
Proceedings of the 20th International Conference on Atomic Physics, edited by C. Roos, H. Häffner, and R. Blatt (AIP, Melville, 2006), pp. 136-143.

Mirrors are ideal tools for controlling the optical and motional properties of an atom. To understand the physics of the light force in a cavity, and to explain why this force can be so much larger than in free space, we present an intuitive corpuscular picture based on the notion of cavity-enhanced photon scattering. We also discuss a nonintuitive phenomenon that finds no simple explanation in terms of photon scattering and that we attribute to the wave aspect of light. Both particle and wave picture provide a complementary description of the main features of atomic motion in a cavity, in particular in the strong-coupling regime.

A Mott-like State of Molecules
S. Dürr, T. Volz, N. Syassen, D. M. Bauer, E. Hansis, and G. Rempe.
Proceedings of the 20th International Conference on Atomic Physics, edited by C. Roos, H. Häffner, and R. Blatt (AIP, Melville, 2006), pp. 278-283.

We prepare a quantum state where each site of an optical lattice is occupied by exactly one molecule. This is the same quantum state as in a Mott insulator of molecules in the limit of negligible tunneling. Unlike previous Mott insulators, our system consists of molecules which can collide inelastically. In the absence of the optical lattice these collisions would lead to fast loss of the molecules from the sample. To prepare the state, we start from a Mott insulator of atomic 87Rb with a central region, where each lattice site is occupied by exactly two atoms. We then associate molecules using a Feshbach resonance. Remaining atoms can be removed using blast light. Our method does not rely on the molecule-molecule interaction properties and is therefore applicable to many systems. (cond-mat/0612148)

Collisional decay of 87Rb Feshbach molecules at 1005.8 G
N. Syassen, T. Volz, S. Teichmann, S. Dürr, and G. Rempe.
Physical Review A 74, 062706 (2006).

We present measurements of the loss-rate coefficients K_am and K_mm caused by inelastic atom-molecule and molecule-molecule collisions. A thermal cloud of atomic 87Rb is prepared in an optical dipole trap. A magnetic field is ramped across the Feshbach resonance at 1007.4 G. This associates atom pairs to molecules. A measurement of the molecule loss at 1005.8 G yields K_am=2 10^-10 cm^3/s. Additionally, the atoms can be removed with blast light. In this case, the measured molecule loss yields K_mm=3 10^-10 cm^3/s. (pdf, cond-mat/0611047 )

Momentum diffusion for coupled atom-cavity oscillators
K. Murr, P. Maunz, P.W.H. Pinkse, T. Puppe, I. Schuster, D. Vitali, and G. Rempe.
Physical Review A 74, 043412 (2006).

It is shown that the momentum diffusion of free-space laser cooling has a natural correspondence in optical cavities when the internal state of the atom is treated as a harmonic oscillator. We derive a general expression for the momentum diffusion which is valid for most configurations of interest: The atom or the cavity or both can be probed by lasers, with or without the presence of traps inducing local atomic frequency shifts. It is shown that, albeit the (possibly strong) coupling between atom and cavity, it is sufficient for deriving the momentum diffusion to consider that the atom couples to a mean cavity field, which gives a first contribution, and that the cavity mode couples to a mean atomic dipole, giving a second contribution. Both contributions have an intuitive form and present a clear symmetry. The total diffusion is the sum of these two contributions plus the diffusion originating from the fluctuations of the forces due to the coupling to the vacuum modes other than the cavity mode (the so called spontaneous emission term). Examples are given that help to evaluate the heating rates induced by an optical cavity for experiments operating at low atomic saturation. We also point out intriguing situations where the atom is heated although it cannot scatter light. (pdf, quant-ph/0512001 )

Preparation of a quantum state with one molecule at each site of an optical lattice
T. Volz, N. Syassen, D. M. Bauer, E. Hansis, S. Dürr and G. Rempe.
Nature Physics 2, 692-695 (2006).

Ultracold gases in optical lattices are of great interest, because these systems bear great potential for applications in quantum simulations and quantum information processing, in particular when using particles with a long-range dipole­dipole interaction, such as polar molecules. Here we show the preparation of a quantum state with exactly one molecule at each site of an optical lattice. The molecules are produced from an atomic Mott insulator with a density profile chosen such that the central region of the gas contains two atoms per lattice site. A Feshbach resonance is used to associate the atom pairs to molecules. The remaining atoms can be removed with blast light. The technique does not rely on the molecule­molecule interaction properties and is therefore applicable to many systems. (Nature Physics, cond-mat/0605184 )

Water Vapour at a Translational Temperature of 1 K
T. Rieger, T. Junglen, S.A. Rangwala, G. Rempe P.W.H. Pinkse, and J. Bulthuis.
Physical Review A 73, 061402 (2006).

We report the creation of a confined slow beam of heavy-water (D2O) molecules with a translational temperature around 1 K. This is achieved by filtering slow D2O from a thermal ensemble with inhomogeneous static electric fields exploiting the quadratic Stark shift of D2O. All previous demonstrations of electric-field manipulation of cold dipolar molecules rely on a predominantly linear Stark shift. Further, on the basis of elementary molecular properties and our filtering technique we argue that our D2O beam contains molecules in only a few rovibrational states. (pdf)

Large Velocity Capture Range and Low Temperatures with Cavities
Karim Murr.
Physical Review Letters 96, 253001 (2006).

There are interesting modifications to the Doppler force when atoms strongly couple to an optical cavity. In particular, there is the possibility to increase the velocity capture range while maintaining a final temperature close to the Doppler limit. The mechanism is based on the multiple absorption emissions of each cavity photon. A previously reported counterintuitive Doppler effect is clarified. (pdf)

Three-dimensional cavity cooling and trapping in an optical lattice
Karim Murr, Stefan Nußmann, Thomas Puppe, Markus Hijlkema, Bernhard Weber, Simon C. Webster, Axel Kuhn, and Gerhard Rempe.
Physical Review A 73, 063415 (2006).

A robust scheme for trapping and cooling atoms is described. It combines a deep dipole-trap which localizes the atom in the center of a cavity with a laser directly exciting the atom. In that way one obtains three-dimensional cooling while the atom is dipole-trapped. In particular, we identify a cooling force along the large spatial modulations of the trap. A feature of this setup, with respect to a dipole trap alone, is that all cooling forces keep a constant amplitude if the trap depth is increased simultaneously with the intensity of the probe laser. No strong coupling is required, which makes such a technique experimentally attractive. Several analytical expressions for the cooling forces and heating rates are derived and interpreted by analogy to ordinary laser cooling. (pdf)

Scheme for generating a sequence of single photons of alternating polarisation
T. Wilk, H. P. Specht, S. C. Webster, G. Rempe, and A. Kuhn
Journal of Modern Optics 54, 1569-1580 (2007)

Single-photons of well-defined polarisation that are deterministically generated in a single spatio-temporal field mode are the key to the creation of multi-partite entangled states in photonic networks. Here, we present a novel scheme to produce such photons from a single atom in an optical cavity, by means of vacuum-stimulated Raman transitions between the Zeeman substates of a single hyperfine state. Upon each transition, a photon is emitted into the cavity, with a polarisation that depends on the direction of the Raman process. (quant-ph/0603083)

Time-resolved and state-selective detection of single freely falling atoms
Torsten Bondo, Markus Hennrich, Thomas Legero, Gerhard Rempe, and Axel Kuhn
accepted for publication in Optics Communications (2006)

We report on the detection of single, slowly moving Rubidium atoms using laser-induced fluorescence. The atoms move at 3m/s while they are detected with a time resolution of 60 µs. The detection scheme employs a near-resonant laser beam that drives a cycling atomic transition, and a highly efficient mirror setup to focus a large fraction of the fluorescence photons to a photomultiplier tube. It counts on average 20 photons per atom. (quant-ph/0512006, pdf)

Characterization of single photons using two-photon interference
T. Legero, T. Wilk, A. Kuhn, and G. Rempe
Advances in Atomic, Molecular and Optical Physics 53, (2006)
(quant-ph/0512023)

Continuous Loading of an Electrostatic Trap for Polar Molecules
T. Rieger, T. Junglen, S.A. Rangwala, P.W.H. Pinkse, and G. Rempe
Physical Review Letters 95, 173002 (2005).

A continuously operated electrostatic trap for polar molecules is demonstrated. The trap has a volume of 0.6 ccm and holds molecules with a positive Stark shift. With deuterated ammonia from a quadrupole velocity filter, a trap density of 10^8 / ccm is achieved with an average lifetime of 130ms and a motional temperature of 300mK. The trap offers good starting conditions for high-precision measurements, and can be used as a first stage in cooling schemes for molecules and as a "reaction vessel" in cold chemistry. (physics/0505039, pdf)

Dissociation of Feshbach Molecules into Different Partial Waves
Stephan Dürr, Thomas Volz, Niels Syassen, Gerhard Rempe, Eric van Kempen, Servaas Kokkelmans, Boudewijn Verhaar, and Harald Friedrich
Phys. Rev. A 72, 052707 (2005)

Ultracold molecules can be associated from ultracold atoms by ramping the magnetic field through a Feshbach resonance. A reverse ramp dissociates the molecules. Under suitable conditions, more than one outgoing partial wave can be populated. A theoretical model for this process is discussed here in detail. The model reveals the connection between the dissociation and the theory of multichannel scattering resonances. In particular, the decay rate, the branching ratio, and the relative phase between the partial waves can be predicted from theory or extracted from experiment. The results are applicable to our recent experiment in 87Rb, which has a d-wave shape resonance. (pdf, cond-mat/0507580)

Vacuum-stimulated cooling of single atoms in three dimensions
Stefan Nußmann, Karim Murr, Markus Hijlkema, Bernhard Weber, Axel Kuhn, and Gerhard Rempe.
Nature Physics 1,122-125 (2005).

Controlling quantum dynamical processes is the key to practical applications of quantum physics, for example in quantum information science. The manipulation of light–matter interactions at the single-atom and single-photon level can be achieved in cavity quantum electrodynamics, in particular in the regime of strong coupling in which atom and cavity form a single entity. In the optical domain, this requires a single atom at rest inside a microcavity. Here we show that an orthogonal arrangement of a cooling laser, trapping laser and cavity vacuum gives rise to a unique combination of friction forces that act along all three directions. This combination of cooling forces is applied to catch and cool a single atom in a high-finesse cavity. The high cooling efficiency leads to a low temperature and an average single-atom trapping time of 17 s, during which the strongly coupled atom can be observed continuously. (pdf, quant-ph/0506067)

Submicron Positioning of Single Atoms in a Microcavity
Stefan Nußmann, Markus Hijlkema, Bernhard Weber, Felix Rohde, Gerhard Rempe, and Axel Kuhn.
Physical Review Letters 95, 173602 (2005).

The coupling of individual atoms to a high-finesse optical cavity is precisely controlled and adjusted using a standing-wave dipole-force trap, a challenge for strong atom-cavity coupling. Ultracold Rubidium atoms are first loaded into potential minima of the dipole trap in the center of the cavity. Then we use the trap as a conveyor belt that we set into motion perpendicular to the cavity axis. This allows us to repetitively move atoms out of and back into the cavity mode with a repositioning precision of 135 nm. This makes possible to either selectively address one atom of a string of atoms by the cavity, or to simultaneously couple two precisely separated atoms to a higher mode of the cavity. (quant-ph/0506088, pdf)

Feshbach Spectroscopy of a Shape Resonance
Thomas Volz, Stephan Dürr, Niels Syassen, Gerhard Rempe, Eric van Kempen, and Servaas Kokkelmans.
Physical Review A 72, 010704(R) (2005).

We present a new spectroscopy technique for studying cold-collision properties. The technique is based on the association and dissociation of ultracold molecules using a magnetically tunable Feshbach resonance. The energy and lifetime of a shape resonance are determined from a measurement of the dissociation rate. Additional spectroscopic information is obtained from the observation of a spatial interference pattern between an outgoing s wave and d wave. The experimental data agree well with the results from a new model, in which the dissociation process is connected to a scattering gedanken experiment, which is analyzed using a coupled-channels calculation. (pdf, cond-mat0410083)

Transition from antibunching to bunching in cavity QED
M. Hennrich, A. Kuhn, and G. Rempe
Physical Review Letters 94, 053604 (2005).

The photon statistics of the light emitted from an atomic ensemble into a single field mode of an optical cavity is investigated as a function of the number of atoms. The light is produced in a Raman transition driven by a pump laser and the cavity vacuum, and a recycling laser is employed to repeat this process continuously. For weak driving, a smooth transition from antibunching to bunching is found for about one intra-cavity atom. Remarkably, the bunching peak develops within the antibunching dip. The observed behavior is well explained by a model describing an ensemble of independent emitters. (pdf)

Normal-mode spectroscopy of a single bound atom-cavity system
P. Maunz, T. Puppe, I. Schuster, N. Syassen, P.W.H. Pinkse, and G. Rempe
Physical Review Letters 94, 033002 (2005).

The energy-level structure of a single atom strongly coupled to the mode of a high-finesse optical cavity is investigated. The atom is stored in an intracavity dipole trap and cavity cooling is used to compensate for inevitable heating. Two well-resolved normal modes are observed both in the cavity transmission and the trap lifetime. The experiment is in good agreement with a Monte Carlo simulation, demonstrating our ability to localize the atom to within lambda/10 at a cavity antinode. (pdf)

Slow ammonia molecules in an electrostatic quadrupole guide
T. Junglen, T. Rieger, S.A. Rangwala, P.W.H. Pinkse, and G. Rempe
Eur. Phys. J. D 31, 365–373 (2004)

An electrostatic quadrupole is used to filter slow dipolar ND3 molecules from an effusive source and to guide them into ultrahigh vacuum. The molecules in the electrostatic quadrupole experience a Stark interaction which allows filtering of small velocities in the linear and bent sections of the quadrupole. With this technique we demonstrate a flux of ~10^10/s with a longitudinal temperature of a few K. The technique and the set-up are discussed in detail, and the guided gas as well as the output beam are characterized. Improvements in the set-up are highlighted, as for instance cooling of the effusive source to below 150 K. (pdf)

Quantum Beat of Two Single Photons
Thomas Legero, Tatjana Wilk, Markus Hennrich, Gerhard Rempe, and Axel Kuhn
Physical Review Letters 93, 070503 (2004).

The interference of two single photons impinging on a beam splitter is measured in a time-resolved manner. Using long photons of different frequencies emitted from an atom-cavity system, a quantum beat with a visibility close to 100% is observed in the correlation between the photodetections at the output ports of the beam splitter. The time dependence of the beat amplitude reflects the coherence properties of the photons. Most remarkably, simultaneous photodetections are never observed, so that a temporal filter allows one to obtain perfect two-photon coalescence even for non-perfect photons. (quant-ph/0406096, pdf)

Photon Statistics of a Non-Stationary Periodically Driven Single-Photon Source
M. Hennrich, T. Legero, A. Kuhn, and G. Rempe
New Journal of Physics 6, 86 (2004).

We investigate the photon statistics of a single-photon source that operates under non-stationary conditions. The photons are emitted by shining a periodic sequence of laser pulses on single atoms falling randomly through a high-finesse optical cavity. Strong antibunching is found in the intensity correlation of the emitted light, demonstrating that a single atom emits photons one-by-one. However, the number of atoms interacting with the cavity follows a Poissonian statistics so that, on average, no sub-Poissonian photon statistics is obtained, unless the measurement is conditioned on the presence of single atoms. (quant-ph/0406034, pdf)

Dissociation of ultracold molecules with Feshbach resonances
S. Dürr, T. Volz, and G. Rempe
Physical Review A, 70, 031601(R) (2004).

Ultracold molecules are associated from an atomic Bose-Einstein condensate by ramping a magnetic field across a Feshbach resonance. The reverse ramp dissociates the molecules. The kinetic energy released in the dissociation process is used to measure the widths of 4 Feshbach resonances in 87Rb. This method to determine the width works remarkably well for narrow resonances even in the presence of significant magnetic-field noise. In addition, a quasi-mono-energetic atomic wave is created by jumping the magnetic field across the Feshbach resonance. (cond-mat/0405606, pdf )

Cavity cooling of a single atom
P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe
Nature 428, 50-52 (2004). 

All conventional methods to laser-cool atoms rely on repeated cycles of optical pumping and spontaneous emission of a photon by the atom. Spontaneous emission in a random direction provides the dissipative mechanism required to remove entropy from the atom. However, alternative cooling methods have been proposed for a single atom strongly coupled to a high-finesse cavity; the role of spontaneous emission is replaced by the escape of a photon from the cavity. Application of such cooling schemes would improve the performance of atom–cavity systems for quantum information processing. Furthermore, as cavity cooling does not rely on spontaneous emission, it can be applied to systems that cannot be laser-cooled by conventional methods; these include molecules (which do not have a closed transition) and collective excitations of Bose condensates, which are destroyed by randomly directed recoil kicks. Here we demonstrate cavity cooling of single rubidium atoms stored in an intracavity dipole trap. The cooling mechanism results in extended storage times and improved localization of atoms. We estimate that the observed cooling rate is at least five times larger than that produced by free-space cooling methods, for comparable excitation of the atom. (pdf)

Two-dimensional trapping of dipolar molecules in time-varying electric fields
T. Junglen, T. Rieger, S.A. Rangwala, P.W.H. Pinkse, and G. Rempe
Physical Review Letters 92, 223001 (2004) . 

Simultaneous two-dimensional trapping of neutral dipolar molecules in low- and high-field seeking states is analyzed. A trapping potential of the order of 10 mK can be produced for molecules like ND3 with time-dependent electric fields. The analysis is in agreement with our experiment where slow molecules with longitudinal velocities of the order of 10 m/s are guided between four 50 cm long rods driven by an alternating electric potential at a variable frequency of a few kHz. (physics/0310046, pdf )

Observation of molecules produced from a Bose-Einstein condensate
S. Dürr, T. Volz, A. Marte, and G. Rempe
Physical Review Letters 92, 020406 (2004). 

Molecules are created from a Bose-Einstein condensate of atomic ⁸⁷Rb using a Feshbach resonance. A Stern-Gerlach field is applied, in order to spatially separate the molecules from the remaining atoms. For detection, the molecules are converted back into atoms, again using the Feshbach resonance. The measured position of the molecules yields their magnetic moment. This quantity strongly depends on the magnetic field, thus revealing an avoided crossing of two bound states at a field value slightly below the Feshbach resonance. This avoided crossing is exploited to trap the molecules in one dimension. (cond-mat/0307440, pdf)

Single-Atom Trajectories in Higher-Order Transverse Modes of a High-Finesse Optical Cavity
T. Puppe, P. Maunz, T. Fischer, P.W.H. Pinkse, and G. Rempe
Physica Scripta T112, p 7-12 (2004).

Transits of single atoms through higher-order Hermite-Gaussian transverse modes of a high-finesse optical cavity are observed. Compared to the fundamental Gaussian mode, the use of higher-order modes increases the information on the atomic position. The experiment is a first experimental step towards the realisation of an atomic kaleidoscope. (quant-ph/0310084, pdf)

Single atoms and single photons in cavity quantum electrodynamics.
G. Rempe, T. Fischer, M. Hennrich, A. Kuhn, T. Legero, P. Maunz, P. Pinkse, and T. Puppe.
"Coherence and Quantum Optics VIII", N. P. Bigelow, J. H. Eberly, C. R. Stroud, and I. A. Walmsley, editors, pages 241-248.
Kluwer Academic / Plenum Publishers, New York, 2003.

We review some recent work performed with single moving atoms strongly coupled to high-finesse optical cavities, emphasizing cavity mediated light forces and vacuum-stimulated generation of single photons.

Time-Resolved Two-Photon Quantum Interference
T. Legero, T. Wilk, A. Kuhn, and G. Rempe
Applied Physics B 77(8), 797-802 (2003).

The interference of two independent single-photon pulses impinging on a beam splitter is analysed in a generalised time-resolved manner. Different aspects of the phenomenon are elaborated using different representations of the single-photon wave packets, like the decomposition into single-frequency field modes or spatio-temporal modes matching the photonic wave packets. Both representations lead to equivalent results, and a photon-by-photon analysis reveals that the quantum-mechanical two-photon interference can be interpreted as a classical one-photon interference once a first photon is detected. A novel time-dependent quantum-beat effect is predicted if the interfering photons have different frequencies. The calculation also reveals that full two-photon fringe visibility can be achieved under almost any circumstances by applying a temporal filter to the signal. (quant-ph/0308024, pdf)

Filtering Slow Polar Molecules from a Thermal Gas
P.W.H. Pinkse, T. Junglen, T. Rieger, S.A. Rangwala, and G. Rempe
"Interactions in Ultracold Gases", M. Weidemüller, C. Zimmermann (Eds). Wiley-VCH, Weinheim , 2003.
(pdf.)

Characterization of elastic scattering near a Feshbach resonance in ⁸⁷Rb
T. Volz, S. Dürr, S. Ernst, A. Marte, and G. Rempe
Physical Review A 68, 010702(R) (2003). 

The s-wave scattering length for elastic collisions between ⁸⁷Rb atoms in the state |f,m_f>=|1,1> is measured in the vicinity of a Feshbach resonance near 1007 G. Experimentally, the scattering length is determined from the mean-field driven expansion of a Bose-Einstein condensate in a homogeneous magnetic field. The scattering length is measured as a function of the magnetic field and agrees with the theoretical expectation. The width of the resonance is determined to be 0.20(3) G, the position of the zero crossing of the scattering length is found at 1007.60(3) G. ( pdf)

Continuous source of translationally cold dipolar molecules
S. A. Rangwala, T. Junglen, T. Rieger, P. W. H. Pinkse, and G. Rempe
Physical Rewiew A 67, 043406 (2003). 

The Stark interaction of polar molecules with an inhomogeneous electric field is exploited to select slow molecules from a room-temperature reservoir and guide them into an ultrahigh vacuum chamber. A linear electrostatic quadrupole with a curved section selects molecules with small transverse and longitudinal velocities. The source is tested with formaldehyde (H₂CO) and deuterated ammonia (ND₃). With H₂CO a continuous flux is measured of 10⁹/s and a longitudinal temperature of a few kelvin. The data are compared with the result of a Monte Carlo simulation. ( pdf )

Emission pattern of an atomic dipole in a high-finesse optical cavity
P. Maunz, T. Puppe, T. Fischer, P. W. H. Pinkse, and G. Rempe
Optics Letters 28(1), 46 (2003). 

An atom placed in a small high-finesse optical cavity will dominantly emit into modes sustained by the cavity. If the cavity supports many frequency-degenerate modes, the radiation pattern depends strongly on the position of the atom. These patterns can be used to detect the position of the atom with high sensitivity. ( pdf )

Counter-Intuitive Vacuum-Stimulated Raman Scattering
Markus Hennrich, Thomas Legero, Axel Kuhn, and Gerhard Rempe 
Journal of Modern Optics, 50(6-7), 935-942 (2003).

Vacuum-stimulated Raman scattering in strongly coupled atom-cavity systems allows one to generate free-running single photon pulses on demand. Most properties of the emitted photons are well defined, provided spontaneous emission processes do not contribute. Therefore, electronic excitation of the atom must not occur, which is assured for a system adiabatically following a dark state during the photon-generation process. We experimentally investigate the conditions that must be met for adiabatic following in a time-of-flight driven system, with atoms passing through a cavity and a pump beam oriented transverse to the cavity axis. From our results, we infer the optimal intensity and relative pump-beam position with respect to the cavity axis. ( pdf )

Strongly Coupled Atom-Cavity Systems
Axel Kuhn, Markus Hennrich, and Gerhard Rempe
"Quantum Information Processing", G. Leuchs and T. Beth (Eds.),
Wiley-VCH, Weinheim, 182-195 (2003).

Single Atoms Moving in a High-Finesse Cavity
P.W.H. Pinkse and G. Rempe 
"Cavity-Enhanced Spectroscopies", Roger van Zee and Patrick Looney (Eds.)
Experimental methods in the physical sciences 40, 255-295 Elsevier Science, (2002). (pdf)

Feshbach Resonances in Rubidium 87: Precision Measurement and Analysis
A. Marte, T. Volz, J. Schuster, S. Dürr , G. Rempe, E.G.M. van Kempen, and B. J. Verhaar 
Physical Review Letters 89, 283202 (2002). 

More than 40 Feshbach resonances in rubidium 87 are observed in the magnetic field range between 0.5 and 1260 gauss for various spin mixtures in the lower hyperfine ground state. The Feshbach resonances are observed by monitoring the atom loss, and their positions are determined with an accuracy of 30 mG. In a detailed analysis, the resonances are identified and an improved set of model parameters for the rubidium interatomic potential is deduced. The elastic width of the broadest resonance at 1007 G is predicted to be significantly larger than the magnetic field resolution of the apparatus. This demonstrates the potential for applications based on tuning the scattering length and for experimental studies of inelastic three-body collisions. ( pdf )

Deterministic Single-Photon Source for Distributed Quantum Networking
A. Kuhn, M. Hennrich and G. Rempe 
Physical Review Letters 89, 067901 (2002). 

A sequence of single photons is emitted on demand from a single three-level atom strongly coupled to a high-finesse optical cavity. The photons are generated by an adiabatically driven stimulated Raman transition between two atomic ground states, with the vacuum field of the cavity stimulating one branch of the transition, and laser pulses deterministically driving the other branch. This process is unitary and therefore intrinsically reversible, which is essential for quantum communication and networking, and the photons should be appropriate for all-optical quantum information processing. ( pdf )

Feedback on the Motion of a Single Atom in an Optical Cavity
T. Fischer, P. Maunz, P. W. H. Pinkse, T. Puppe and G. Rempe
Physical Review Letters 88, 163002 (2002). 

We demonstrate feedback on the motion of a single neutral atom trapped in the light field of a high-finesse cavity. Information on the atomic motion is obtained from the transmittance of the cavity. This is used to implement a feedback loop in analog electronics that influences the atom's motion by controlling the optical dipole force exerted by the same light that is used to observe the atom. In spite of intrinsic limitations, the time the atom stays within the cavity could be extended by almost 30% beyond that of a comparable constant-intensity dipole trap. ( pdf )

An optical kaleidoscope using a single atom
P. Horak, H. Ritsch,  T. Fischer,  P. Maunz, T. Puppe, P.W.H. Pinkse and G. Rempe 
Physical Review Letters 88, 043601 (2002). 

A new method to track the motion of a single particle in the field of a high-finesse optical resonator is analyzed. It exploits sets of near-degenerate higher-order Gaussian cavity modes, whose symmetry is broken by the position dependent phase shifts induced by the particle. Observation of the spatial intensity distribution outside the cavity allows direct determination of the particle's position. This is demonstrated by numerically generating a realistic atomic trajectory using a semiclassical simulation and comparing it to the reconstructed path. The path reconstruction itself requires no knowledge about the forces on the particle. Experimental realization strategies are discussed. ( pdf )

Optical Cavity QED: Fundamentals and Application as a Single-Photon Light Source
Axel Kuhn and Gerhard Rempe 
"Experimental Quantum Computation and Information", F. de Martini and C. Monroe (Eds.),
Proc. Int. School of Physics Enrico Fermi, course CXLVIII, IOS Press, Amsterdam, 37-66 (2002).

Quantitative wave-particle duality in multibeam interferometers
S. Dürr 
Physical Review A 64, 042113 (2001). 

We propose quantitative measures of the wave properties and particle properties for multibeam interferometers. We show that these quantities are connected by a few fundamental inequalities which are expressing wave-particle duality. Our analysis includes which-way detection schemes and quantum erasure. The inequalities derived here are a generalization of similar limits which have been studied previously in the special case of two-beam interferometers. In addition, we propose alternative measures that express the available information more efficiently and we show that these measures fulfill similar inequalities. ( pdf )

Avalanches in a Bose-Einstein condensate
J. Schuster, A. Marte, S. Amtage, B. Sang, G. Rempe, H.C.W. Beijerinck 
Physical Review Letters 87, 170404 (2001). 

Collisional avalanches are identified to be responsible for an 8-fold increase of the initial loss rate of a large ⁸⁷Rb condensate. We show that the collisional opacity of an ultracold gas exhibits a critical value. When exceeded, losses due to inelastic collisions are substantially enhanced. Under these circumstances, reaching the hydrodynamic regime in conventional Bose-Einstein condensation experiments is highly questionable. ( pdf )

Collective light forces on atoms in a high-finesse cavity
T. Fischer, P. Maunz, T. Puppe, P.W.H. Pinkse and G. Rempe 
New Journal of Physics 3, 11.1-11.20 (2001). 

We solve the quantum Langevin equations of motion for N point-like two-level atoms moving in an externally pumped cavity field. In the limit of the low saturation of the atoms, we obtain analytical expressions for the dipole force, the velocity-dependent force and the momentum diffusion coefficient for each atom in the presence of other atoms. The expressions show that in general the forces on each atom depend on the position and the velocity of all the other atoms. ( pdf )

Interference of a Bose-Einstein condensate in a hard-wall trap: From nonlinear Talbot effect to formation of vorticity
J. Ruostekoski, B. Kneer, W. P. Schleich, G. Rempe 
Physical Review A 63, 043613 (2001). 

We theoretically study the coherent expansion of a Bose-Einstein condensate in the presence of a confining impenetrable hard-wall potential. The nonlinear dynamics of the macroscopically coherent matter field results in rich and complex spatiotemporal self-interference patterns demonstrating a nonlinear Talbot effect, and the formation of vorticity and solitonlike structures. ( pdf )

Quantum Physics of Entangled Systems: Wave-Particle-Duality and Atom-Photon Molecules
G. Rempe 
Annalen der Physik (Leipzig)9, 843-850 (2000). 

One of the cornerstones of quantum physics is the wave nature of matter. It explains experimentally observed effects like interference and diffraction, occurring when an object moves from one place to another along several indistinguishable ways simultaneously. The wave nature disappears when the individual ways are distinguishable. In this case, the particle nature of the object becomes visible. To determine the particle nature quantitatively, the way of the object has to be measured. Here, large progress has been made recently with new techniques, enabling one to investigate single moving atoms in a controlled manner. Two examples are discussed in the following two sections. The first experiment describes an atom interferometer, where the way of the atom is entangled with its internal state. This allows one to explore the origin of wave-particle duality and perform a quantitative test of this fundamental principle. The second experiment reports on the observation of an atom-photon molecule, a bound state between an atom and a single photon. A fascinating aspect of this system is that it makes possible to monitor the motion of a single neutral atom in real time.

How to catch an atom with single photons
P.W.H. Pinkse,  T. Fischer, P. Maunz, T. Puppe, and G. Rempe 
Journal of Modern Optics 47, 2769-2787 (2000). 

We report on trapping a single neutral atom in the standing wave light field of a high-finesse optical cavity containing one photon on average, a single-photon optical trap, or SPOT for short. This trap has the novel feature that the light field is also used to observe the atom in real time. The oscillatory motion of the trapped atom induces well-resolved oscillations of the light intensity. Periodic structure is visible in the fourth-order intensity correlation function, attributed to long-distance flights of the atom along the standing wave. The finite duration of those flights provide evidence for cavity-mediated cooling of atoms. We discuss the various mechanisms determining the trapping time and compare the results with a quantum-jump Monte Carlo simulation to interpret the observed signals. ( pdf )

Vacuum-Stimulated Raman Scattering based on Adiabatic Passage in a High-Finesse Optical Cavity
M. Hennrich, T. Legero, A. Kuhn and G. Rempe,
Phys. Rev. Lett. 85, 4872-4875 (2000).

We report on the first observation of stimulated Raman scattering from a Lambda-type three-level atom, where the stimulation is realized by the vacuum field of a high-finesse optical cavity. The scheme produces one intracavity photon by means of an adiabatic passage technique based on a counter-intuitive interaction sequence between pump laser and cavity field. This photon leaves the cavity through the less-reflecting mirror. The emission rate shows a characteristic dependence on the cavity and pump detuning, and the observed spectra have a sub-natural linewidth. The results are in excellent agreement with numerical simulations. ( pdf )

Observation of cavity-mediated long-range light forces between strongly coupled atoms
P. Münstermann, T. Fischer, P. Maunz, P.W.H. Pinkse, and G. Rempe
Physical Review Letters 84, 4068-4071 (2000).

We report on the observation of long-range forces between ultracold rubidium atoms that are mutually coupled by the field of a driven high-finesse optical cavity. Even for much less than one photon in the cavity on average, the forces strongly influence the spatial distribution of the atoms. This manifests itself as an asymmetric normal-mode spectrum of the strongly coupled atoms-cavity system. Expressions are given for the dipole force and the diffusion coefficient for the atoms in presence of the other atoms. The data agree well with calculated spectra, which include the full motional dynamics of the many-atom system. ( pdf )

Trapping an atom with single photons
P.W.H. Pinkse, T. Fischer, P. Maunz, and G. Rempe
Nature 404, 365-368 (2000).

The prediction that it should be possible to trap an atom with a single photon has long defied experimental verification. We have trapped a neutral atom in the standing-wave light field of a high-finesse optical cavity containing one photon on average. The field is also used to observe the atom continuously in real time. The oscillatory motion of the trapped atom induces well-resolved oscillations of the light intensity. Periodic structure is visible in the fourth-order intensity correlation function, attributed to ``long-distance'' flights of the atom along the standing wave. We compare the results with a quantum jump Monte Carlo simulation to interpret the observed signals.

Wave-particle duality in an atom interferometer
S. Dürr and G. Rempe
"Advances in Atomic, Molecular and Optical Physics", 42 B. Bedersen, H. Walther (Eds.), Academic Press, San Diego, 29-71 (2000).

Complementarity and Quantum Erasure in an Atom Interferometer
Stephan Dürr and Gerhard Rempe
"Marlan O. Scully Festschrift", Optics Communications 179, 323-335 (2000)

We report on experiments with an atom interferometer, where the atom's spin is used as a marker for the atom's way through the interferometer. A measurement on this which-way marker allows us to acquire which-way knowledge. The choice of the measured observable determines how much which-way knowledge is obtained. In a quantum eraser, in particular, the observable is chosen so that no which-way knowledge is obtained. This allows us to regain interference fringes in subensembles of atoms, which are sorted according to the result of the measurement on the which-way marker. Here we focus on intermediate situations where the which-way information is only partially erased. We quantitatively compare the which-way knowledge obtained in such a measurement with the visibilities of the resulting interference patterns. The experimental data are in good agreement with two fundamental inequalities, one recently derived by Björk and Karlsson [1], the other introduced here. ( pdf )

Can wave-particle duality be based on the uncertainity relation?
S. Dürr, G. Rempe,
American Journal of Physics 68, 1021-1024 (2000)

Wave and particle properties of a quantum object cannot be observed simultaneously. In particular, the fringe visibility in an interferometer is limited by the amount of which-way information which can be obtained. This limit is set by the recently discovered duality relation. So far, all derivations of the duality relation are independent of Heisenberg's uncertainty relation. Here we demonstrate that it is alternatively possible to derive the duality relation in the form of an uncertainty relation for some suitably chosen observables. ( pdf )

Single atoms observed one by one in a high-finesse optical cavity
G. Rempe, T. Fischer, P. Maunz, P. Münstermann, P.W.H. Pinkse
"Laser Spectroscopy IX", R. Blatt, J. Eschner, D. Leibfried, F. Schmidt-Kaler (Eds.), World Scientific, Singapore, 150-159(1999).

We report on real-time experiments with single atoms slowly moving through a high-finesse optical cavity. Typically, the cavity contains less than one photon on average. The photon statistics of the light transmitted through the cavity exhibits distinct features attributed to the dipole force, diffusion and a new cavity-mediated Sysiphus force. Quantitatively, our data agree with the results of a Monte Carlo simulation. Finally we show that an external feed-back mechanism controlling the intra-cavity intensity allows us to significantly extend the atom-cavity interaction time.

Atom Interferometric Tests of Complementarity
S. Dürr, T. Nonn, G. Rempe,
Proceedings of the "Sixth International Conference on Squeezed States and Uncertainty Relations", Naples, Italy (1999), D. Han, Y. S. Kim and S. Solimeno (Eds). NASA Conference Publications 2000-209899.

We report on several which-way experiments performed with an atom interferometer. The internal atomic state serves as a which-way marker. With which-way information stored, the interference fringes are lost. It is a peculiarity of this experiment that Heisenberg's position-momentum uncertainty relation cannot explain the loss of spatial interference fringes. In addition, we can vary the parameters of the experiment such that only incomplete which-way information is stored. In this case, a reduced fringe visibility is observed. For a given fringe visibility, the amount of which-way information which can be obtained is limited by the recently discovered duality relation. With this atom interferometer, we have performed the first experimental test of the duality relation. ( pdf)

Controlled generation of single photons from a strongly coupled atom-cavity system
A. Kuhn, M. Hennrich, T. Bondo, and G. Rempe,
Applied Physics B 69, 373-377 (1999).

We propose a new method for the generation of single photons. Our scheme will lead to the emission of one photon into a single mode of the radiation field in response to a trigger event. This photon is emitted from an atom strongly coupled to a high-finesse optical cavity, and the trigger is a classical light pulse. The device combines cavity-QED with an adiabatic transfer technique. We simulate this process numerically and show that it is possible to control the temporal behaviour of the photon emission probability by the shape and the detuning of the trigger pulse. An extension of the scheme with a reloading mechanism will allow one to emit a bit-stream of photons at a given rate. ( pdf 178 kB )

Adiabatic Following in Standing Wave Diffraction of Atoms
Claudia Keller, Jörg Schmiedmayer, Anton Zeilinger, Thomas Nonn, Stephan Dürr, and Gerhard Rempe
Applied Physics B 69, 303-309 (1999).

We report experiments on the diffraction of atoms from a standing light wave in the channeling regime, characterized by long interaction time and large potential height. The observed far-field diffraction patterns depend specifically on the way, in which the potential is switched on and off. For fast switching, the evolution is non-adiabatic and many diffraction orders are populated. For slow switching, however, the evolution is adiabatic and the number of populated diffraction orders decreases dramatically. The experiments are performed in two different setups employing rubidium and argon atoms, respectively. In one of the setups, we study the dependence of the diffraction pattern on the interaction time, in the other setup that on the incidence angle. ( pdf 503 kB )

Dynamics of single-atom motion observed in a high-finesse cavity
P. Münstermann, T. Fischer, P. Maunz, P.W.H. Pinkse, and G. Rempe
Physical Review Letters 82, 3791-3794 (1999)

We investigate mechanical forces on single atoms in a high-finesse optical cavity containing less than one photon on average. We count the number of atoms strongly coupled to the cavity mode close to an antinode and measure the intensity autocorrelation function of the pump light transmitted through the cavity. Distinct features are observed and attributed to the dipole force, diffusion and velocity-dependent force, as predicted by the work of Horak et al. Our data agree well with the results of a Monte Carlo simulation. ( pdf 268 kB)

Single Slow Atoms from an Atomic Fountain Observed in a High-Finesse Optical Cavity
P. Münstermann, T. Fischer, P.W.H. Pinkse, and G. Rempe
Optics Communications, 159, 63-67 (1999).

A novel setup for investigations in cavity quantum electrodynamics is described, which combines an optical microcavity (finesse 4.3x10⁵) with an atomic ⁸⁵Rb fountain, allowing full control over density and velocity of atoms entering the optical cavity. To demonstrate this point we study the temporal width of the transmission drops if slow single atoms pass through the cavity. We observe absorptive and dispersive single atom signals in the cavity transmission in real time. ( pdf 119 kB )

Acceptance angle for Bragg reflection of atoms from a standing light wave
S. Dürr and G. Rempe
Physical Review A 59, 1495 (1999).

We experimentally investigate Bragg reflection of atoms from a standing light wave. We focus on the influence of small angular deviations from the exact Bragg resonance onto the reflection probability. The Bragg resonance has a finite acceptance angle, which depends on the light intensity. Within this acceptance angle, an oscillatory behavior of the reflection probability as a function of the angle is observed. ( pdf 104 kB )

Free expansion of a Bose-Einstein condensate from a Ioffe-Pritchard magnetic trap
U. Ernst, J. Schuster, F. Schreck, A. Marte, A. Kuhn, and G. Rempe,
Applied Physics B, 67, 719-722 (1998).

The free expansion of a Bose-Einstein condensate of about 10⁵ rubidium-87 atoms released from an Ioffe-Pritchard magnetic trap is investigated experimentally. The expansion dynamics depend only on the trap frequencies, which are determined independently. The data are in good agreement with the expected expansion of a condensate, and are clearly distinct from the behaviour of a classical gas in the hydrodynamic regime. ( pdf 241 kB)

Fringe visibility and Which-Way Information in an Atom Interferometer
S. Dürr, T. Nonn, and G. Rempe
Physical Review Letters 81, 5705-5709 (1998)

We experimentally investigate the reduction of the fringe visibility in an atom interferometer due to the storage of which-way information. We focus on the case of incomplete which-way information and use the distinguishability D to quantify how much information is stored. For a given value of D, the fringe visibility V is limited by the duality relation D²+V²<=1. We have measured D and V independently. Combining the results, we find good agreement with the duality relation. ( pdf 171 kB )

Origin of quantum-mechanical complementarity probed by a `which-way' experiment in an atom interferometer
S.Dürr, T.Nonn, and G.Rempe
Nature, 395, 33-37 (1998).

The principle of complementarity refers to the ability of quantum-mechanical entities to behave as particles or waves under different experimental conditions. For example, in the famous double-slit experiment, a single electron can apparently pass through both apertures simultaneously, forming an interference pattern. But if a `which-way' detector is employed to determine the particle's path, the interference pattern is destroyed. This is usually explained in terms of Heisenberg's uncertainty principle, in which the acquisition of spatial information increases the uncertainty in the particle's momentum, thus destroying the interference. Here we report a which-way experiment in an atom interferometer in which the `back action' of path detection on the atom's momentum is too small to explain the disappearance of the interference pattern. We attribute it instead to correlations between the which-way detector and the atomic motion, rather than to the uncertainty principle. ( pdf 273 kB )

Bose-Einstein condensation in a pure Ioffe-Pritchard field configuration
U. Ernst, A. Marte, F. Schreck, J. Schuster, and G. Rempe
Europhysics Letters, 41, 1-6 (1998).

A glass-cell apparatus and a dc magnetic trap with radial gradient of 275 G/cm and axial curvature of 365 G/cm² were used to capture and evaporatively cool rubidium 87 atoms. Below a critical temperature of 550 nK, Bose-Einstein condensation was observed with 10⁶ atoms in the trap. Pure condensates with more than 10⁵ atoms and peak densities exceeding 4x10¹⁴cm^-3 were produced. ( pdf 350 kB )

Standing Wave Diffraction with a Beam of Slow Atoms
S.Kunze, S.Dürr, K.Dieckmann, M.Elbs, U.Ernst, A.Hardell, S.Wolf, and G.Rempe
Journal of Modern Optics, 44, 1863-1881 (1997).

We report on atom optical experiments employing a magneto-optical trap as a source of a pulsed beam of slow atoms. After turning off the trap, experiments are performed on the cloud of atoms in free fall over a distance of 45 cm. We give a detailed description of the apparatus and discuss experimental results on the diffraction of atoms from a standing light wave in the regime of short, intermediate an long interaction times. (pdf)

Atom localization via Ramsey interferometry: A coherent field provides a better resolution
Fam Le Kien, G.Rempe, W.P.Schleich, and M.S.Zubairy
Physical Review A 56, 2972-2977 (1997)

We investigate the position localization of a polarized atom interacting with an off-resonant quantized standing-wave field. We show that a coherent field achieves a higher resolution than a classical field. An almost perfect localization is possible when the atom passes through several identically prepared cavities. ( pdf 144 kB )

Diffraction of Atoms from a Measurement Induced Grating
S.Kunze, K.Dieckmann, and G.Rempe
Physical Review Letters 78, 2038-2041 (1997).

We report on an experiment with polarized atoms passing a standing light wave, where the atom's position is encoded (entangled) with the excitation amplitude of two long lived electronic states. Position information can be obtained a posteriori by measuring the electronic state. If this measurement is performed, the atom is localized in an array of virtual slits. This gives rise to diffraction of the atomic de Broglie waves from a measurement induced amplitude grating, thus showing the back action onto the momentum due to localization. We further demonstrate experimentally that the encoding can be totally erased. ( pdf 125 kB )

Ramsey-Experiments with Slow Atoms
K.Dieckmann, S.Kunze, G.Rempe, and S.Wolf
Frequency Standards Based on Laser-Manipulated Atoms and Ions, J.Helmcke, S.Penselin (Ed.),
Physikalisch Technische Bundesanstalt, Braunschweig, Germany, PTB-Opt-51, 115-123 (1996).

We report on three experiments: First, fast frequency fluctuations of a 780 nm grating-stabilized diode laser are characterized by means of the Allan variance. Time intervals as short as 10 ns are realized by means of two independent time interval counters. This diode laser is used in a second experiment, where hyperfine transitions of slow Rubidium atoms are excited by Ramsey's method of separated oscillatory fields. Two microwave pulses are used while the atoms fall through a resonant microwave cavity. Finally, we give an outlook by reporting first results of a new position measurement scheme for free atoms which employs a standing wave light field between the two Ramsey pulses. With a resolution possible of lambda/20, the back-action onto the atomic momentum leads to unique far-field diffraction patterns.

Towards Cavity Quantum Electrodynamics with Slow Atoms
S.Dürr, S.Kunze, S.Wolf, and G.Rempe
Symposium on Frequency Standards and Metrology, J.C.Bergquist (Ed.), World Scientific, Singapore, 251-258 (1996).

We report on two experiments: first, fast frequency fluctuations of a 780 nm grating-stabilized diode laser are directly observed by measurement of the Allan variance. Time intervals as short as 10 ns are realized by means of two independent time-interval counters. In a second experiment, the momentum distribution of atomic matter waves is controlled with high precision by means of a non resonant light grating. In particular, Pendellösung oscillations are observed in Bragg scattering of slow atoms. Finally, we address the implications of this experiment on possible applications in cavity QED.

Position Measurement of Cold Atoms
S.Kunze and G.Rempe
Laser Spectroscopy XII, M. Inguscio, M.Allegrini, and A.Sasso (Ed.), World Scientific, Singapore, 138-139 (1996).

Using a standard CCD-camera we have measured the temperature of a cloud of laser-cooled atoms by time resolved observation of the cloud's free expansion. We also propose a new position measurement scheme which employs coherent excitation of internal atomic states. For example, by monitoring the phase of the atomic dipole moment the position of polarized atoms passing through a standing-wave light field can be localized better than lambda/20. The back-action onto the atomic momentum leads to unique far-field diffraction patterns.

Measurement of fast frequency fluctuations: Allan variance of a grating stabilized diode laser
S.Kunze, S.Wolf, and G.Rempe
Optics Communications 128, 269-274 (1996).

Fast frequency fluctuations of a 780 nm grating-stabilized diode laser are directly observed by the measurement of the Allan variance. Time intervals as short as 10 ns and up to 1 s are realized by means of two independent time interval counters. Frequency fluctuations with the laser locked to a Doppler-free resonance transition of atomic rubidium are examined in detail.

Pendellösung oscillations in second-order Bragg scattering of atoms from a standing light wave
S.Dürr, S.Kunze, and G.Rempe
Quantum and Semiclasscal Optics 8, 531-539 (1996).

Bragg scattering of atoms from a standing light wave exhibits Pendellösung oscillations in the scattering probability. For second-order scattering, we have recently observed significant deviation of the oscillation frequency from the prediction for a pure four-photon type process. To give a quantitative explanation for this behaviour, we present an analytical calculation which takes into account lowest energy momentum states. Our calculation suggests that a transition between a four-photon type process at low light intensity to a two-photon type process at higher light intensity is responsible for this behaviour. ( pdf 108 kB )

Bragg scattering of slow atoms from a standing light wave
S.Kunze, S.Dürr, and G.Rempe
Europhysics Letters 34, 343-348 (1996).

Slow atoms from a magneto-optical trap are used to study diffraction from a near-resonant standing wave light field. Long interaction times make possible to observe unidirectional Bragg scattering. In particular, the Pendellösung interference effect between two resonant momentum states is demonstrated for first- and second-order diffraction. The oscillation frequency of second-order scattering shows a transition from a four-photon type process at low light intensity to a two-photon type process at higher intensity. The data are in quantitative agreement with a theoretical description which takes into account lowest energy momentum states. ( pdf 962 kB )

One atom in an optical cavity: Spatial resolution beyond the standard diffraction limit
G.Rempe
Applied Physics B 60, 233-237 (1995).

The position of a slow atom passing through a standing-wave light field in an ultrahigh-finesse optical resonator can be measured by observing either the intensity of the light transmitted through the cavity or its phase. Apart from the periodicity of the standing wave, both techniques allow to determine the position of the particle with a resolution much better than the standard classical diffraction limit dx >= lambda/2. Position measurements whith uncernity < lambda/20 seem to be possible whith all-optical techniques.

Atomic-position measurement via Internal State Encoding
S.Kunze, G.Rempe, and M.Wilkens
Europhysics Letters 27, 115-121 (1994)

The position of a polarized atom passing through a standing light wave can be localized by observing the phase of the atomic dipole moment in a Ramsey-type experiment. Depending on the outcome of the measurement, the diffraction pattern in the far field corresponds to atoms with their momentum changed by integer multiples four times the photon recoil. Position measurements with standard deviation of approx. lambda/40 seem to be possible with optical techniques.

Atoms in an Optical Cavity: Quantum Electrodynamics in Confined Space
G. Rempe
Contemporary Physics, 34, 119-129 (1993).

Cavity quantum electrodynamics studies the behaviour of atoms inside a low-loss cavity. The composite atom-cavity system constitutes a new "molecule" with radiative properties which differ radically from those of individual components. For example, spontaneous emission becomes reversible, the spectrum splits into several peaks and the intensity fluctuations of the light transmitted by this novel "molecule" are below the classical shot noise limit. In terms of practical applications, the system renders possible, first, the detection of single atoms with a high sensitiviy and, second, optical bistability for a few atoms and photons only.

last modified: 10-Oct-2006