Spatial coherence and density correlations of trapped Bose gases

Optics Express, 1997

For a dilute, interacting Bose gas of magnetically-trapped atoms at temperatures below the critical temperature T 0 for Bose-Einstein condensation, we determine the second-order coherence function g (2) (r 1 , r 2) within the framework of a finite-temperature quantum field theory. We show that, because of the different spatial distributions of condensate and thermal atoms in the trap, g (2) (r 1 , r 2) does not depend on |r 1 − r 2 | alone. This means that the experimental determinations of g (2) reported to date give only its spatial average. Such an average may underestimate the degree of coherence attainable in an atom laser by judicious engineering of the output coupler.

1998

For a dilute, interacting Bose gas of magnetically-trapped atoms at temperatures below the critical temperature T 0 for Bose-Einstein condensation, we determine the second-order coherence function g (2) (r 1 , r 2) within the framework of a finite-temperature quantum field theory. We show that, because of the different spatial distributions of condensate and thermal atoms in the trap, g (2) (r 1 , r 2) does not depend on |r 1 − r 2 | alone. This means that the experimental determinations of g (2) reported to date give only its spatial average. Such an average may underestimate the degree of coherence attainable in an atom laser by judicious engineering of the output coupler.

Nature, 2007

Low-dimensional systems are beautiful examples of many-body quantum physics . For onedimensional systems the Luttinger liquid approach provides insight into universal properties. Much is known of the equilibrium state, both in the weakly and strongly interacting regime. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached . Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1d Bose gases. Dynamic splitting is used to create two 1d systems in a phase coherent state . The time evolution of the coherence is revealed in local phase shifts of the subsequently observed interference patterns. Completely isolated 1d Bose gases are observed to exhibit a universal subexponential coherence decay in excellent agreement with recent predictions by Burkov et al. . For two coupled 1d Bose gases the coherence factor is observed to approach a non-zero equilibrium value as predicted by a Bogoliubov approach . This coupled-system decay to finite coherence is the matter wave equivalent of phase locking two lasers by injection. The non-equilibrium dynamics of superfluids plays an important role in a wide range of physical systems, such as superconductors, quantum-Hall systems, superfluid Helium, and spin systems . Our experiments studying coherence dynamics show that 1d Bose gases are ideally suited for investigating this class of phenomena.

New Journal of Physics, 2014

We describe the relaxation dynamics of a coherently split one-dimensional (1D) Bose gas in the harmonic approximation. A dephased, prethermalized state emerges in a light-cone-like evolution which is connected to the spreading of correlations with a characteristic velocity. In our description we put special emphasis on the influence of the longitudinal trapping potential and the finite size of the system, both of which are highly relevant in experiments. In particular, we quantify their influence on the phase correlation properties and the characteristic velocity with which the prethermalized state is established. Finally, we show that the trapping potential has an important effect on the recurrences of coherence which are expected to appear in a finite size system.

Physical Review A, 2004

We calculate the dynamic single-particle and many-particle correlation functions at non-zero temperature in one-dimensional trapped repulsive Bose gases. The decay for increasing distance between the points of these correlation functions is governed by a scaling exponent that has a universal expression in terms of observed quantities. This expression is valid in the weak-interaction Gross-Pitaevskii as well as in the strong-interaction Girardeau-Tonks limit, but the observed quantities involved depend on the interaction strength. The confining trap introduces a weak center-of-mass dependence in the scaling exponent. We also conjecture results for the density-density correlation function.

2010

The low energy properties of a trapped bose gas split by a potential barrier are determined over the whole range of barrier heights. We derive a self-consistent two-mode model which reduces, for large N , to a Bogoliubov model for low barriers and to a Josephson model for any (asymmetric) double well potential, with explicitly calculated tunneling and pair interaction parameters. We compare the numerical results to analytical results that precisely specify the role of number squeezing and finite temperatures in the loss of coherence.

Journal of Mathematical Sciences

Multi-particle correlation functions at nonzero temperatures in a trapped Bose gas for D = 3, 2, 1 dimensions are considered. It is shown that, at relatively large distances, the multi-particle correlators are expressed in terms of one-particle ones. Bibliography: 13 titles.

Nature Physics, 2012

Hanbury Brown and Twiss correlations-correlations in farfield intensity fluctuations-yield fundamental information on the quantum statistics of light sources, as demonstrated after the discovery of photon bunching 1-3 . Drawing on the analogy between photons and atoms, similar measurements have been performed for matter-wave sources, probing density fluctuations of expanding ultracold Bose gases 4-8 . Here we use two-point density correlations to study how coherence is gradually established when crossing the Bose-Einstein condensation threshold. Our experiments reveal a persistent multimode character of the emerging matter-wave as seen in the non-trivial spatial shape of the correlation functions for all probed source geometries, from nearly isotropic to quasi-onedimensional, and for all probed temperatures. The qualitative features of our observations are captured by ideal Bose gas theory 9 , whereas the quantitative differences illustrate the role of particle interactions.

Physical Review A, 2005

We study the effects of many-body correlations in trapped ultracold atomic Bose gases. We calculate the ground state of the gas using a ground-state auxiliary-field quantum Monte Carlo (QMC) method [Phys. Rev. E 70, 056702 (2004)]. We examine the properties of the gas, such as the energetics, condensate fraction, real-space density, and momentum distribution, as a function of the number of particles and the scattering length. We find that the mean-field Gross-Pitaevskii (GP) approach gives qualitatively incorrect result of the kinetic energy as a function of the scattering length. We present detailed QMC data for the various quantities, and discuss the behavior of GP, modified GP, and the Bogoliubov method under a local density approximation.

2003

We investigate the long-range phase coherence of homogeneous and trapped Bose gases as a function of the geometry of the trap, the temperature, and the mean-field interactions in the weakly interacting limit. We explicitly take into account the (quasi)condensate depletion due to quantum and thermal fluctuations, i.e., we include the effects of both phase and density fluctuations. In particular, we determine the phase diagram of the gas by calculating the off-diagonal one-particle density matrix and discuss the various crossovers that occur in this phase diagram and the feasibility of their experimental observation in trapped Bose gases.