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Physical Review A

Suppression of elastic scattering loss for slowly colliding Bose-Einstein condensates

Y. B. Band, John H. Burke, Andrea Simoni, Paul S. Julienne

Published Jul 1, 2001• 11 citations
Publisher

Abstract

Superfluid suppression of the elastic scattering loss in atomic Bose condensed systems can be significant when the ratio of the relative velocity of the wave packets to the critical velocity is $\ensuremath{\sim}1.$ We show how to incorporate the effect of such losses and their suppression into the time-dependent dynamics of two colliding condensate wave packets. We illustrate the magnitude of the effect through three-dimensional simulations of the collision dynamics of an $|F=2,{M}_{F}=2〉$ with an $|F=2,{M}_{F}=1〉{}^{87}\mathrm{Rb}$ condensate in a harmonic trap, as studied in a recent experiment [Maddaloni et al., Phys. Rev. Lett. 85, 2413 (2000)]. These calculations show that the effect of elastic scattering and its suppression should be seen in the oscillatory center-of-mass amplitude of the ${M}_{F}=1$ wave packet for suitable experimental conditions.

DOI
10.1103/physreva.64.023607

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Superfluid suppression of the elastic scattering loss in atomic Bose condensed systems can be significant when the ratio of the relative velocity of the wave packets to the critical velocity is \ensuremath∼1.\ensuremath{\sim}1.\ensuremath∼1. We show how to incorporate the effect of such losses and their suppression into the time-dependent dynamics of two colliding condensate wave packets. We illustrate the magnitude of the effect through three-dimensional simulations of the collision dynamics of an ∣F=2,MF=2〉|F=2,{M}_{F}=2〉∣F=2,MF​=2〉 with an ∣F=2,MF=1〉87Rb|F=2,{M}_{F}=1〉{}^{87}\mathrm{Rb}∣F=2,MF​=1〉87Rb condensate in a harmonic trap, as studied in a recent experiment [Maddaloni et al., Phys. Rev. Lett. 85, 2413 (2000)]. These calculations show that the effect of elastic scattering and its suppression should be seen in the oscillatory center-of-mass amplitude of the MF=1{M}_{F}=1MF​=1 wave packet for suitable experimental conditions.
Bragg diffraction of atoms by light waves can create high momentum components in a Bose-Einstein condensate. Collisions between atoms from two distinct momentum wave packets cause elastic scattering that can remove a significant fraction of atoms from the wave packets and cause the formation of a spherical shell of scattered atoms. We develop a slowly varying envelope technique that includes the effects of this loss on the condensate dynamics described by the Gross-Pitaevski equation. Three-dimensional numerical calculations are presented for two experimental situations: passage of a moving daughter condensate through a nonmoving parent condensate, and four-wave mixing of matter waves.
Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently, Zi\ifmmode \acute{n}\else \'{n}\fi{} et al. [Phys. Rev. Lett. 94, 200401 (2005)] introduced a model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first-order approximation, we derive analytical expressions for the density matrix and anomalous density that provide excellent insight into correlation properties of scattered atoms.
Dynamics of fluctuations in unstable Bose-Einstein condensates is analyzed by the solution of approximate operator equations. In the case of a condensate with a negative scattering length the present treatment describes a delay of collapse, in agreement with recent experiments. In the case of a collision of two condensate wave packets it is shown that quantum effects lead to a Bose enhancement of elastic-scattering losses. In both cases the noncondensate atoms are formed as entangled pairs in squeezed states.
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 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 experimentally and theoretically investigate the dynamics of two trapped condensates in a magnetostatic trap. The two condensates, being in different internal Zeeman state (/F = 2, m = 2) and /F = 2,m = i]), experience external parabolic potentials that differ by both curvature and equilibrium position. The dynamics of the system, exhibiting large amplitude oscillations of the /F = 2,nt = 1] condensate, is affected in a profound manner by the periodical inter condensates collisions. In particular, we show that both an amplitude damping and a frequency shift occur. Measuring the former allows to study the elastic scattering, whose suppression is a manifestation of the Bose condensates superfluidity, while the latter gives access to the cross scattering length alpha.