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Physical Review A

Interference of two Bose-Einstein condensates with collisions

Thomas G. Wong, Matthew J. Collett, Daniel F. Walls

Published Nov 1, 1996• 99 citations
Publisher

Abstract

We extend the work of Javanainen and Yoo [Phys. Rev. Lett. 76, 161 (1996)] on the interference between two Bose-Einstein condensates to include the effects of collisions. The competing effects of the atomic detections that establish phase coherence and the decohering effects of the collisions are computed using the Monte Carlo wave-function method. Limits to the tolerance of the condensate phase to atomic collisions are established.

DOI
10.1103/physreva.54.r3718

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We extend the work of Javanainen and Yoo [Phys. Rev. Lett. 76, 161 (1996)] on the interference between two Bose-Einstein condensates to include the effects of collisions. The competing effects of the atomic detections that establish phase coherence and the decohering effects of the collisions are computed using the Monte Carlo wave-function method. Limits to the tolerance of the condensate phase to atomic collisions are established.
We study the interference of two Bose-Einstein condensates within an elementary model. The detection of the atoms is modeled by adapting the standard theory of photon detection. Even though the condensates are taken to be in number states with no phases whatsoever, our stochastic simulations of atom detection produce interference patterns as would also be predicted on the basis of the phases of the macroscopic wave functions describing the condensates. In statistical mechanics terms, we have devised a method to analyze spontaneous symmetry breaking for an arbitrary (not necessarily larger) number of particles.
We study the collision dynamics of two Bose-Einstein condensates with their dynamical wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective one-dimensional system, we identify regimes characterized by the relationship between inter- and intra-atomic interactions and the initial configuration of the system, akin to the equilibrium phase diagram of two interacting Bose condensates. We consider a dynamical setup in which two wave packets are initially at rest with a small separation about the center of an asymmetric harmonic trap. Upon release, we observe a rapid approach to dynamical equilibrium in the limits of very large and very small inter-particle repulsion, characterized by periodic transmission or reflection of the condensates as distinguishable units, whereas the intermediate, critical regime is characterized by extended transient dynamics, density fracturing, and dynamical mixing. We therefore have reason to believe that non-trivial behavior may exist during the collisions of Bose-Einstein condensates as a result of their non-linear interactions, and these effects may be observable in a suitable laboratory environment.
We propose a method for simulating a single realization of a collision of two Bose-Einstein condensates. Recently [Phys. Rev. Lett. 94, 200401 (2005)], we introduced a quantum model of incoherent elastic scattering in a collision of two counterpropagating atomic Gaussian wave packets. Here we show that this model is capable of generating data that can be interpreted as results of a single collisional event. We find a range of parameters, including relative velocity, population, and the size of colliding condensates, where the structure of the halo of scattered atoms in a single realization strongly differs from that averaged over many realizations.
We propose a method for simulating a single realization of a collision of two Bose--Einstein condensates. Recently in Ziń {\it et al.} (Phys. Rev. Lett. {\bf 94}, 200401 (2005)) we introduced a quantum model of an incoherent elastic scattering in a collision of two counter-propagating atomic Gaussian wavepackets. Here show that this model is capable of generating the data that can be interpreted as results of a single collision event. We find a range of parameters, including relative velocity, population and the size of colliding condensates, where the structure of hallo of scattered atoms in a single realization strongly differs from that averaged over many realizations.
Summary form only given. According to the conventional argument, Bose-Einstein condensate (BEG) has a macroscopic wave function with a definite phase. This phase is analogous to the phase of laser light. Here we describe a novel theoretical approach to the study of phase, coherence, and potential of interference of a BEG. We consider a thought experiment in which two BECs are dropped on top of each other. We adapt the standard theory of photon counting to atom detection, and calculate the joint probability density for atom detection.