Spatial coherent transport of interacting dilute Bose gases

Classically it is impossible to have transport without transit, i.e., if the points 1, 2, and 3 lie sequentially along a path then an object moving from 1 to 3 must, at some point in time, be located at 2. For a quantum particle in a three-well system it is possible to transport the particle between wells 1 and 3 such that the probability of finding it at any time in the classically accessible state in well 2 is negligible. We consider theoretically the analogous scenario for an interacting Bose-Einstein condensate BEC . Specifically, the adiabatic transportation of a condensate of 2000 Li atoms from well 1 to well 3 without a macroscopic occupation of the classically allowed intermediate well is predicted. Such a protocol paves the way for a robust method of control for atom-optical devices. The ideas underpinning the protocol for macroscopic matter-wave transport without transit TWT stem from stimulated Raman adiabatic passage STIRAP 1–4 . STIRAP is a robust technique for transferring population between two atomic states, 1 and 3 , via an intermediate excited state, 2 . Using electromagnetic pulses to couple states 1 to 2 and 2 to 3 , characterized by coupling parameters K12 and K23. When K23 precedes and overlaps K12, the population is 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 4–7 and have been proposed 8 , and recently demonstrated 9 , in three channel optical waveguides. Recently this protocol has been proposed to transport single atoms 10,11 , Cooper pairs 12 , spin states 13 , and electrons 14–18 and is referred to as coherent tunneling adiabatic passage CTAP . Here we consider transport of dilute gas BECs containing thousands of interacting atoms, thus distinguishing our treatment from the previous single particle cases. 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 initially in well 1, we show how, through adiabatic changes to the tunneling rates between the wells, to transport it into well 3 with minimal occupation of the intervening well. This effect is shown in Fig. 1 b , where a BEC of 2000 Li atoms is transported from well 1 to well 3 over a timescale of 1 s, with less than 1% of the atoms occupying well 2 at any time. As such it appears that the BEC is transported from well 1 to well 3 without macroscopically transiting through well 2. Here we elucidate the properties of the three-well system by first considering a three-mode approximation 19–21 , where the form of the potential is not important. We then employ the mean-field Gross-Pitaevskii equation GPE to quantitatively describe the BEC dynamics and consider experimental scenarios in which to realize macroscopic matterwave TWT. Reducing our three-well system, shown in Fig. 1 a , such that each well is described by a single mode basis 19–21 , i, gives