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arXiv:0710.2842

Coherence and Correlations in Atom Lasers

P. D. Drummond, Timothy G. Vaughan, Joel Frederick Corney, Gerd Leuchs, Piotr Deuar

Published Oct 15, 2007• 0 citations
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Abstract

We review and characterize the quantum coherence measures that are most useful for quantum gases, including Bose-Einstein condensates (BEC) and ultra-cold fermions, and outline how to calculate these in the typically dynamical environment of an interacting multi-mode quantum gas.
DOI
10.48550/arxiv.0710.2842

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One of the seminal advances in quantum optics was the understanding that a quantised description of ensembles of photons is best characterised by correlation functions. Correlations are also a fundamental property of matter waves, and the single wavefunction that describes a Bose-Einstein condensate (BEC) is in principle characterised by long range coherence to all orders (i.e. a universal correlation value of unity). Here we measure the higher order correlation properties of ultra-cold matter waves and use them to probe the coherence of the gas.
One of the seminal advances in quantum optics was the understanding that a quantised description of ensembles of photons is best characterised by correlation functions. Correlations are also a fundamental property of matter waves, and the single wavefunction that describes a Bose-Einstein condensate (BEC) is in principle characterised by long range coherence to all orders (i.e. a universal correlation value of unity). Here we measure the higher order correlation properties of ultra-cold matter waves and use them to probe the coherence of the gas.
Since the achievement of Bose-Einstein condensation (BEC), the progress in matterwave \nphysics has been immense. Among the many recent achievements there is \nthe miniaturization of atom traps, demonstration of the superfluid-Mott insulator \nquantum-phase transition in optical lattices and the experimental demonstration of \nthe BEC-BCS crossover in ultra-cold gases. \nMiniaturization of atom traps using micro-structured wires on a chip is one important \nstep towards an on-chip cold-atom device. These so-called \\atom chips" provide \nhigh control and versatility for trapping and guiding the ultra-cold atomic clouds. \nParticularly interesting is the use of these microchips to build mesoscopic devices \nfor cold atomic clouds as, for instance, in the case of an atom-cloud interferometer. \nHowever, these mesoscopic devices require coherent transport of the atom cloud. A \ngeneral method to treat decoherence due to current fluctuations in multi-wire atomchip \ntraps is presented in the rst part of this thesis. The decoherence rate Γ shows a \nstrong dependence on the distance between the wire and the atom cloud, r0, scaling \nas Γ ~ r-4 0 for a single atom waveguide. Considering an interferometer device, a \nstrong dependence of the decoherence rate on the trap geometry is found. \n \nStudying many-body eects in ultra-cold quantum gases is another important \nresearch eld. Experiments using ultra-cold quantum gases in optical lattices have \ndemonstrated the superuid-Mott insulator quantum phase transition and manybody \nentanglement. Optical lattices are based on a periodic modulation of the light \nintensity, generated by retro-reected laser beams. Correlations of the atomic cloud \nbetween dierent lattice sites of the optical lattice play a central role in these manybody \nexperiments. The dierent phases of the superuid-Mott insulator system can \nbe characterized by the dierent behavior of the inter-lattice site correlations. There \nare several numerical methods such as Quantum Monte Carlo (QMC) simulations, \nDensity Matrix Renormalization Group (DMRG) simulations, exact-diagonalization, \nor the Gutzwiller ansatz, to investigate the dynamics of an ultra-cold gas in an optical \nlattice theoretically. The Gutzwiller method, corresponding to the mean-eld solution, \nallows for the treatment of large lattice sizes. Mean-eld approaches have proven \nto be very useful to describe many-body physics. However, diculties arise in the correct \ndescription of the behavior of the decay of inter-lattice site correlations. Based on \nthe Gutzwiller approach, we have developed a method which allows the successive inclusion \nof inter-lattice site correlations. Comparing the results for the particle-number \nuctuations and the correlation function obtained from pure Gutzwiller calculations, \nto calculations which perturbatively include short-range correlations and calculations \n \nusing \\quasi-exact methods", showed a considerable improvement relative to the pure \nGutzwiller results due to the inclusion of short-range correlations. \nMany-body eects do not only arise in periodic potentials, but become increasingly \nimportant at ultra-low temperatures. The formation of Bose-Einstein condensates \nrequires an overlap of the atom wavefunctions and, hence, the formation of \na single condensate wavefunction. Another example of a many-body state is the \nsuperuid-BCS state, commonly used as a description of superconductivity. Here, \nfermions in dierent hyperne states form Cooper pairs. Experiments with ultracold \nquantum gases enable a variation of the interparticle interaction, e.g. , by using \na Feshbach resonance. Using Feshbach resonances to tune the interaction strength \nhas enabled the experimental observation of the crossover from a superuid-BCS \nstate to a Bose-Einstein condensate of molecules. A useful way to characterize the \ndierent states of ultra-cold quantum gases is to investigate the particle-number uctuations. \nIn this thesis we suggest to divide the atomic cloud into bins and consider \nthe atom-number uctuations in these bins. We calculate the full counting statistics \nfor dierent physical systems of ultra-cold gases (e.g. bosonic gases, fermionic gases, \nand spin mixtures). In particular, we consider the BCS-state as a rst trial example \nto show that there is a strong variation in the particle-number statistics at the \ncrossover from a superuid-BCS state to a Bose-Einstein condensate of molecules.