Spatial coherent transport of interacting dilute Bose gases

Abstract

Classically it is impossible to have transport without transit, i.e., if the points one, two and three lie sequentially along a path then an object moving from one to three must, at some point in time, be located at two. However, for a quantum particle in a three-well system it is possible to transport the particle between wells one and three such that the probability of finding it at any time in the classically accessible state in well two is negligible. We consider theoretically the analogous scenario for a Bose-Einstein condensate confined within a three well system. In particular, we predict the adiabatic transportation of an interacting Bose-Einstein condensate of 2000 7 Li atoms from well one to well three without transiting the allowed intermediate region. To an observer of this macroscopic quantum effect it would appear that, over a timescale of the order of 1s, the condensate had transported, but not transited, a macroscopic distance of ∼ 20µm between wells one and three.The system under consideration is schematically shown in Fig. 1(a), where a three-dimensional harmonic trap is split into three regions via the addition of two parallel repulsive Gaussian potentials. With the Bose-Einstein condensate (BEC) [blue object in Fig. 1(a)], initially in well 1, we show how it is possible, through adiabatic changes to the tunneling rates between the wells, to transport it into well 3 with minimal (ideally zero) occupation of the intervening well. This effect as a function of time is shown in Fig. 1(b), where an interacting BEC of 2000 7 Li atoms is transported from well 1 to well 3 over a timescale of ∼ 1s, with less than 1% atoms occupying well 2 at any particular time. As such it appears that the BEC is transported from well 1 to well 3 without transiting through well 2.This effect of transport without transit (TWT) can be likened to the lay concept of teleportation. However, although TWT relies on quantum control of the global BEC state and associated tunneling matrix elements, it is quite distinct from the quantum definition of teleportation [1]. In the TWT of a BEC we describe the many body system in a time dependent mean-field approximation. As such the wavefunction used to describe the condensed state is a classical field and can not describe such properties as entanglement and hence quantum teleportation.The ideas underpinning the protocol for TWT stem from Stimulated Raman Adiabatic Passage (STIRAP) [2,3,4,5]. STIRAP is a robust optical technique for transferring population between two atomic states, |1 and |3 , via an intermediate excited state, |2 . Using off-resonant pulses to couple states |1 to |2 and |2 to |3 , characterised by coupling parameters K 12 and K 23 , and such that K 23 precedes and overlaps K 12 , the population can be adiabatically transferred from state |1 to |3 . Population transfer is achieved via a superposition of states |1 and |3 with the occupation of state |2 strongly suppressed. These techniques are used in quantum optics for coherent internal state transfer [5,6,7,8] and h...

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