We can not translate quantum behaviour arising with superposition states or entanglement efficiently into the classical language of conventional computers. A universal quantum computer could describe and help to understand complex quantum systems. But it is envisioned to become functional only within the next decade(s). A shortcut was proposed via simulating the quantum behaviour of interest in another quantum system, where all relevant parameters and interactions can be controlled and observables of interest detected sufficiently well. Instead of translating quantum dynamics into an algorithm of stroboscopic quantum gate operations to run them on a universal quantum computer, we want to continuously control and manipulate the spins, equivalent to the way nature evolves the system of our interest.
Already a comparably small amount of simulation-spins, of the order of 30-50, are supposed to be sufficient to outperform classical computers. In addition, the fidelities of the proposed operations are predicted to be sufficiently high in state of the art experiments and do not have to be performed within very demanding fault tolerant limits for universal quantum computation.
Our system comprises magnesium ions, confined in a linear Paul trap. It can simulate Quantum spin Hamiltonians, describing many solid-state systems like magnets, high-Tc superconductors, quantum Hall ferromagnets, ferroelectrics, etcetera. For our feasibility study we aim for the simulation of the Quantum Ising Hamiltonian realizing the proposal of Porras and Cirac.
Two electronic levels of each ion span a two-level system that can be interpreted (simulates) a spin ½ particle. Those are very well isolated from external disturbances. To provide controlled interaction with and between the simulated spins we apply rf- and laser-fields respectively.
For the first time we are able to trap an ion in an optical dipole trap. This opens up new perspectives for quantum simulations, combined atom-ion systems and ultracold collision experiments.
We are able to cool up to five ions close to the radial ground state of motion.
To pave the way towards larger scale simulations, we have to use the radial modes of motion to transfer/simulate interactions. We implement a (radial) geometric phase gate and prepare an entangled Bell state of two ions with a fidelity exceeding 95%.
We implement the proof of principle for the quantum walk of one ion in our linear ion trap[9,10]. With a single-step fidelity exceeding 0.99, we perform three steps of an asymmetric walk on the line. We clearly reveal the differences to its classical counterpart (random walk) if we allow the walker/ion to take all classical paths simultaneously. Quantum interferences enforce asymmetric, non-classical distributions in the highly entangled degrees of freedom (of coin and position states). We theoretically study and experimentally observe the limitation in the number of steps of our approach, that is imposed by motional squeezing. We propose an altered protocol based on methods of impulsive steps to overcome these restrictions, in principal allowing to scale the quantum walk to several hundreds of steps.
We experimentally simulate the adiabatic evolution of the smallest non-trivial spin system from the paramagnetic into the (anti-) ferromagnetic order with a quantum magnetisation for two spins of 98%. We prove that the observed transition is not driven by thermal-fluctuations but of quantum mechanical origin, the source of quantum-fluctuations in quantum phase transitions. We observe a final superposition state of the two degenerate spin configurations for the ferromagnetic (+) and the anti-ferromagnetic (+) order, respectively. These correspond to deterministically entangled states achieved with a fidelity up to 88%. Our work demonstrates the building blocks for simulating quantum spin-Hamiltonians with trapped ions.
To calibrate our operational fidelities, we implement a (axial) geometric phase gate and prepare an entangled Bell state of two ions with a fidelity exceeding 95%.
We will explore the limits of our one dimensional approach by investigating the dynamics for an increased amount of spins, simulating larger spins and altering the duration of the simulation.
Our experimental setup provides us with the necessary tools to approach a set of additional simulation problems we will try to access, like the strong correlation between Bosons, the quantum-walk of entangled ions, the particle production in our early universe[13,14] or relativistic effects described by the Dirac equation.
Based on new ion-trap technology it seems to become feasible to scale the ion simulator to a larger amount of spins and into two dimensions in surface trap arrays. Here we could investigate quantum simulations on two dimensional spin-grids, e.g. spin-frustration.
Experts in the field allow us to hope, starting from arrays spanned by 10x10 ions, to provide new insight into quantum dynamics. We aim to observe effects that represent Quantum-Phase Transitions for many-particle systems.
The possibility to control all the parameters of the system individually by switching laser beams and/or trap voltages and to address each single spin on each single lattice site turn it into a versatile system offering tools for analysis overcoming the access in experiments on solid-state systems.
In January 2006 we had trapped our first ions and Doppler cooled them via our two times frequency doubled fibre-laser system. Subsequently, we setup two additional fibre laser systems for coherent control of +Mg25 spins and realized the detection of the ions with a spatial resolution < 1m.We set up a real time coherent experimental control and data acquisition. In December 2006 we achieved state-sensitive detection (fidelity > 99%), coherent transitions in +Mg25 (fidelity > 99%) and motional ground state cooling of the axial motion (
Letzte Änderung: 05.05.2010, 13.40