Bose Einstein Condensation (BEC)
Single-Photon Switch Based on Rydberg Blockade
An atomic ensemble can serve not only as a quantum memory but also as a processing unit for single photons. We realized an all-optical switch in which the presence or absence of a gate light pulse determines whether a target light pulse is transmitted or not. Our experiment takes this to the quantum regime, where the incoming gate pulse contains only one photon on average. This pulse is stored in the atomic gas in the form of a Rydberg excitation with principal quantum number 100 using a slow-light technique based on electromagnetically induced transparency (EIT). If a gate photon is stored, Rydberg blockade suppresses the transmission of the subsequent target pulse by a factor of 20. If no gate photon is stored, the transmission of the target pulse is high due to Rydberg EIT. We manage to retrieve the gate excitation after the target pulse passed the medium. This retrieved signal shows that phase coherence was preserved and it serves as a herald to indicate successful storage.
Quantum memory and remote entanglement
Entanglement between stationary systems at remote locations is a key resource for quantum networks. We experimentally generated such remote entanglement between a single atom inside an optical cavity and a BEC. To this end, two laboratories joined forces. In one lab, a triggered single photon was created in an atom-cavity system, thereby generating entanglement between the internal state of the single atom and the polarization of the photon. The photon was transported in a 30 meter long optical fiber to the BEC in the other lab. Electromagnetically induced transparency was used to store this photon in the BEC in the form of a collective excitation. Here, the BEC served as a quantum memory for the photonic polarization qubit. The storage in the BEC established matter-matter entanglement. After a variable delay, the single photon was retrieved from the quantum memory. In addition, a second photon was generated from the single atom in the cavity, thereby mapping the internal state of the single atom onto the polarization of the single photon. These steps converted the entanglement onto the polarization states of two single photons. Finally the polarization of both photons was detected to determine how well the entanglement survived the storage in the quantum memory. In the experiment, we found a total fidelity of all concatenated operations of 95 %. We observed a lifetime of the matter-matter entanglement of 100 µs, exceeding the photon duration by two orders of magnitude. The fidelity of the entangled state is limited by the properties of the single atom inside the cavity. The performance of the memory was independently measured using attenuated laser pulses, yielding an average process fidelity of unity with an error of only 0.004.
Optical Control of a Magnetic Feshbach Resonance
The capability to tune the strength of the elastic interparticle interaction is crucial for many experiments with ultracold gases. Magnetic Feshbach resonances are widely used for this purpose, but future experiments would benefit from extra flexibility, in particular from the capability to spatially modulate the interaction strength on short length scales. Optical Feshbach resonances offer this possibility in principle, but in alkali atoms they induce rapid loss of particles due to light-induced inelastic collisions. We conceived and experimentally demonstrated a scheme in which light near-resonant with a molecular bound-to-bound transition in 87Rb is used to shift the magnetic field at which a magnetic Feshbach resonance occurs. This enables us to tune the interaction strength with laser light, but with considerably less loss than using an optical Feshbach resonance.
Strong Dissipation Inhibits Losses and Induces Correlations in Cold Molecular Gases
Reaching the strongly correlated regime usually requires strong elastic interactions and weak inelastic interactions, as the latter produce losses. We showed that strong inelastic interactions can actually inhibit the particle losses and drive the system into a strongly-correlated regime. Molecules associated from bosonic atoms, such as the 87Rb atoms in our experiment, have large rate coefficients for inelastic molecule-molecule collisions. We load our optical lattice with exactly one molecule per site. We then lower the lattice along one spatial dimension, thus allowing the molecules to tunnel between different sites and explore their inelastic interactions. The resulting one-dimensional gas closely resembles a Tonks-Girardeau gas, where strong elastic interactions prevent particles from being at the same position. In our experiment, the strong inelastic interactions lead to a reflection of the particles off each other, creating a state that is described by the same wave function as a Tonks-Girardeau gas. The physical origin of this reflection can be understood from an analogy to Fresnel's formulas in classical optics or as a manifestation of the continuous quantum Zeno effect.
Atom-Molecule Oscillations in a Mott Insulator
The association of ultracold molecules with a Feshbach resonance can be used to obtain full quantum control of this chemical reaction. To this end, we first load the atoms into an optical lattice in such a way that a large number of lattice sites contains exactly two atoms. We then jump the magnetic field quickly to resonance, in contrast to the majority of previous experiments where the magnetic field is ramped slowly across the resonance. We thus induce coherent oscillations between the unbound atom pair state and the bound molecular state. The oscillations have large amplitude and are only weakly damped. We observe up to 29 oscillations. We study the dependence of the oscillation frequency on atomic density and magnetic field and find good agreement with theory. This experiment demonstrates full quantum mechanical control over a chemical reaction.
A Mott-Like State of Molecules in an Optical Lattice
An optical lattice is a periodic potential created with laser light. We use three retro-reflected laser beams to create a simple-cubic lattice potential. When an atomic gas at zero temperature is loaded into a shallow lattice, the ground state is superfluid and there is a macroscopic phase across the whole sample. The number-phase uncertainty relation implies that the number of particles at a particular lattice site has shot noise. If the lattice depth is increased, a quantum phase transition occurs. For a deep lattice, the ground state has a fixed number of particles per lattice site, and the relative phase between lattice sites is smeared out. This state is called a Mott insulator. The transition between the superfluid and the Mott insulator can be observed in time-of-flight images, where diffraction of atoms from the lattice is seen in the superfluid phase, while such diffraction peaks are absent in the Mott phase. Additional information can be obtained from the excitation spectrum. It characterizes the response of the system to an external perturbation and is fundamentally different for the two phases.
We performed an experiment, where the central region of the optical lattice contains exactly two atoms at each lattice site. Next, molecules are associated from the atom pairs using the Feshbach resonance at 1007G. The molecules cannot move between lattice sites because of their low tunneling amplitude. When dissociating the molecules, the atomic Mott insulator is reestablished (see image), thus showing that the association-dissociation sequence is adiabatic and that the intermediate state contained exactly one molecule at each lattice site. This state is interesting for various proposals concerning quantum simulations and quantum computing in optical lattices.
Magnetic-field Dependent Losses
We measured inelastic collision rates near the Feshbach resonance at 1007.4 G. Inelastic collision rates for atom-molecule, molecule-molecule, and three-atom collisions yield valuable input for theoretical models on the three-atom and four-atom system.
Dissociation into d-Wave Atom Pairs
Most Feshbach resonances in ultracold collisions are pure s-wave phenomena. The only significant incoming and outgoing atomic waves are s waves and the molecular bound state often is an s-wave state, too. We used a Feshbach resonance at 632 G to create molecules in a d-wave molecular state. These molecules can dissociate into the atomic s wave and d wave. This creates a spatial interference pattern between the two partial waves (see image). This is particularly interesting in 87Rb, because here the atomic d wave features a shape resonance. The Feshbach resonance can be tuned through this shape resonance by varying the magnetic field, at which the molecules dissociate. Thus the properties of the shape resonance can be studied.
Dissociation of Molecules
The ultracold molecules can be dissociated by ramping the magnetic field in the opposite direction through the Feshbach resonance. Once above the Feshbach resonance, the molecules dissociate spontaneously with a finite rate. The internal energy of a molecule is released in form of kinetic energy of the dissociated atom pair. A fast ramp drags the population far above the resonance before dissociation becomes significant and therefore produces hotter atoms. The width of the Feshbach resonance can be determined from a measurement of the kinetic energy released. We used this technique to measure the widths of the four broadest Feshbach resonances in 87Rb. When jumping (instead of ramping) the magnetic field across the Feshbach resonance, a mono-energetic wave of atoms is created (see image).
Creation of Ultracold Molecules
A Feshbach resonance offers an intriguing possibility to create ultracold molecules. To this end, the magnetic field is slowly ramped across the Feshbach resonance in the proper direction. We use a Stern-Gerlach technique to separate the molecules from the atoms. The magnetic moment of the molecules can be measured with this technique and gives a clear proof that molecules are created in the expected ro-vibrational state. An avoided crossing between two molecular states creates a minimum of the internal energy of the molecules at a magnetic field of 1001.7 G. The molecules can therefore be trapped by applying a magnetic field gradient. This is very different from a normal magnetic trap, where particles are trapped at a local minimum of the magnetic field. We demonstrated this trapping in one spatial dimension by offsetting the molecule cloud from the trap center and monitoring the resulting spatial oscillation (see image).
Feshbach Resonances in Rb-87
Magnetically tunable Feshbach resonances make it possible to control the elastic collision properties of ultracold dilute gases. Such collisions determine many properties of a BEC, such as shape, stability, collective excitations, etc. Feshbach resonances in 87Rb are especially interesting, because this isotope is used by far more than 50% of all BEC experiments worldwide. In our experiment, the positions of more than 40 Feshbach resonances in 87Rb have been observed by monitoring enhanced atom loss at the resonances. All these resonances are very narrow and can easily be washed out in the experiment by magnetic-field noise. The broadest resonance, located near 1007 G, is therefore most interesting for applications. The collision properties are quantitatively described by the s-wave scattering length. We measured the variation of the scattering length as a function of magnetic field in the vicinity of the 1007 G resonance. The exact position and width of this Feshbach resonance were extracted from the measurement.
Investigating the loss of atoms from a BEC, it was found that the usual rate-equation models including single-, two-, and three-body losses could not account for the fast losses that are found in a BEC at high density. This is because the usual loss models are based on the assumption that the products of inelastic collisions simply leave the trap. But at high density the collision products often undergo an elastic collision with a cold atom before leaving the BEC. Such a secondary collision accelerates the previously cold atom. The thus heated atom can either leave the trap or collide again before leaving the BEC and so forth. Above a certain critical density, such higher-order collisions can create a collisional avalanche, which results in a dramatically increased number of atoms being lost due to one initial three-body inelastic collision. Such collisional avalanches were modeled in detail and quantitative agreement with the observed data was achieved.
What is Bose-Einstein Condensation?
The indistinguishability of identical particles has interesting consequences for statistical mechanics at low temperatures. The most prominent example is Bose-Einstein condensation (BEC). This refers to the fact that in a gas of non-interacting identical bosons a surprisingly large fraction of the particles occupies the absolute ground state of the system at low temperatures. This phenomenon predicted by Albert Einstein in 1924 is related to superfluidity in liquid helium and superconductivity in solids, but the properties of these liquid or solid-state systems are drastically modified by the relatively strong interactions between the particles. Ultracold dilute gases are experimental systems that are much closer to Einstein's original proposal. BEC in dilute gases was experimentally achieved in 1995 and the Nobel prize in physics 2001 was awarded for this achievement. Meanwhile, there are more than 100 BEC experiments worldwide and the investigation of properties and applications of BEC is one of the most rapidly developing fields in present-day atomic physics.
In September 1997, our group was the first to produce a BEC outside the USA. Our first experiment with the BEC investigated collisional avalanches. Since 2001, our work is focused on Feshbach resonances and the creation of ultracold molecules. Since 2006, we combine this with an optical lattice to study quantum states that are strongly correlated and related to solid state systems.
Creating a Bose-Einstein Condensate
An excellent interactive introduction into the experimental techniques for non-experts can be found on the University of Colorado's Physics 2000 website (in their upper left frame, scroll down to the Bose-Einstein condensation link). A brief summary is given here: To achieve BEC in a dilute atomic gas, extremely low temperatures are required. Our experimental setup employs a combination of laser cooling and evaporative cooling to produce cold and dense atomic clouds in a vacuum system. A double magneto-optical trap system captures and cools up to 6x 109 87Rb atoms using laser light. Although responsible for achieving temperatures as low as 0.03 mK, the light sets a lower limit for the temperature. To overcome this limitation, the gas is transferred into a magnetic trap, where it is further cooled by radio-frequency evaporation. This method selectively removes the hottest atoms from the trap, so that the ones left behind are colder and denser on average. After 5 s of evaporative cooling, a temperature of 500 nK is reached and a Bose-Einstein condensate forms in the center of the trap.