Spatial pair correlations of atoms in molecular dissociation

We perform first-principles quantum simulations of dissociation of trapped, spatially inhomogeneous Bose-Einstein condensates of molecular dimers. Specifically, we study spatial pair correlations of atoms produced in dissociation after time of flight. We find that the observable correlations may significantly degrade in systems with spatial inhomogeneity compared to the predictions of idealized uniform models. We show how binning of the signal can enhance the detectable correlations and lead to the violation of the classical Cauchy-Schwartz inequality and relative number squeezing.Comment: Final published versio

Proposal for demonstrating the Hong-Ou-Mandel effect with matter waves

The Hong-Ou-Mandel (HOM) effect is a striking demonstration of destructive quantum interference between pairs of indistinguishable bosons, realised so far only with massless photons. Here we propose an experiment which can realise this effect in the matter-wave regime using pair-correlated atoms produced via a collision of two Bose-Einstein condensates and subjected to two laser induced Bragg pulses. We formulate a novel measurement protocol appropriate for the multimode matter-wave field, which---unlike the typical two-mode optical case---bypasses the need for repeated measurements under different displacement settings of the beam-splitter, thus dramatically reducing the number of experimental runs required to map out the interference visibility. The protocol can be utilised in related matter-wave schemes; here we focus on condensate collisions and by simulating the entire experiment we predict a HOM-dip visibility of ~69%. By being larger than 50%, such a visibility highlights strong quantum correlations between the atoms and paves the way for a possible demonstration of a Bell inequality violation with massive particles in a related Rarity-Tapster setup.Comment: Essentially the same version as v2, except in Nature Communications style; for Supplementary Information see the source fil

First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with non-opposite momenta. The net effect of this process -- which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion -- is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode-mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.Comment: Final published version, with updated references and minor modification

Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps

We analyze free expansion of a trapped one-dimensional Bose gas after a sudden release from the confining trap potential. By using the stationary phase and local density approximations, we show that the long-time asymptotic density profile and the momentum distribution of the gas are determined by the initial distribution of Bethe rapidities (quasimomenta) and hence can be obtained from the solutions to the Lieb-Liniger equations in the thermodynamic limit. For expansion from a harmonic trap, and in the limits of very weak and very strong interactions, we recover the self-similar scaling solutions known from the hydrodynamic approach. For all other power-law traps and arbitrary interaction strengths, the expansion is not self-similar and shows strong dependence of the density profile evolution on the trap anharmonicity. We also characterize dynamical fermionization of the expanding cloud in terms of correlation functions describing phase and density fluctuations.Comment: Final published version with modified title and a couple of other minor changes. 5 pages, 2 figures, and Supplemental Materia

Quantum atom optics with fermions from molecular dissociation

We study a fermionic atom optics counterpart of parametric down-conversion with photons. This can be realized through dissociation of a Bose-Einstein condensate of molecular dimers consisting of fermionic atoms. We present a theoretical model describing the quantum dynamics of dissociation and find analytic solutions for mode occupancies and atomic pair correlations, valid in the short time limit. The solutions are used to identify upper bounds for the correlation functions, which are applicable to any fermionic system and correspond to ideal particle number-difference squeezingComment: Changes in response to referees' comments, updated reference

Role of spatial inhomogeneity in dissociation of trapped molecular condensates

We theoretically analyze dissociation of a harmonically trapped Bose-Einstein condensate of molecular dimers and examine how the spatial inhomogeneity of the molecular condensate affects the conversion dynamics and the atom-atom pair correlations in the short-time limit. Both fermionic and bosonic statistics of the constituent atoms are considered. Using the undepleted molecular-field approximation, we obtain explicit analytic results for the asymptotic behavior of the second-order correlation functions and for the relative number squeezing between the dissociated atoms in one, two, and three spatial dimensions. Comparison with the numerical results shows that the analytic approach employed here captures the main underlying physics and provides useful insights into the dynamics of dissociation for conversion efficiencies up to 10%. The results show explicitly how the strength of atom-atom correlations and relative number squeezing degrade with the reduction of the size of the molecular condensate. © 2010 The American Physical Society

Exact steady-state Wigner function for a nondegenerate parametric oscillator

We consider the model of a nondegenerate parametric oscillator, in the adiabatic limit of strongly damped pump mode, and find an exact analytic solution for the joint two-mode Wigner function in the steady-state regime. The one-mode Wigner functions for the individual signal and idler modes are derived as well. This gives an explicit and complete phase-space representation of this two-mode nonequilibrium quantum system. Simple examples are given illustrating the phase-space images of optical bistability and the phase diffusion effect

Coherent molecular bound states of bosons and fermions near a Feshbach resonance

We analyze molecular bound states of atomic quantum gases near a Feshbach resonance. A simple, renormalizable field theoretic model is shown to have exact solutions in the two-body sector, whose binding energy agrees well with observed experimental results in both Bosonic and Fermionic cases. These solutions, which interpolate between BEC and BCS theories, also provide a more general variational ansatz for resonant superfluidity and related problems.Comment: Minor changes -- to match the final published versio

Atom-atom correlations and relative number squeezing in dissociation of spatially inhomogeneous molecular condensates

We study atom-atom correlations and relative number squeezing in the dissociation of a Bose-Einstein condensate (BEC) of molecular dimers made of either bosonic or fermionic atom pairs. Our treatment addresses the role of the spatial inhomogeneity of the molecular BEC on the strength of correlations in the short time limit. We obtain explicit analytic results for the density-density correlation functions in momentum space, and show that the correlation widths and the degree of relative number squeezing are determined merely by the shape of the molecular condensate.Comment: Minor corrections, final published versio