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...
We apply the Bose-Hubbard Hamiltonian to a three-well system and show analytically that coherent transport via adiabatic passage (CTAP) of N non-interacting particles across the chain is possible. We investigate the effect of detuning the middle well to recover CTAP when on-site interparticle interactions would otherwise disrupt the transport. The case of small interactions is restated using first-order perturbation theory to develop criteria for adibaticity that define the regime where CTAP is possible. Within this regime we investigate restricting the Hilbert space to the minimum necessary basis needed to demonstrate CTAP, which dramatically increases the number of particles that can be efficiently considered. Finally, we compare the results of the Bose-Hubbard model to a mean-field three-mode Gross-Pitaevskii analysis for the equivalent system.
We numerically demonstrate an optical waveguide structure for the coherent tunnelling adiabatic passage of photons. An alternative coupling scheme is used compared to earlier work. We show that a three rib optical waveguide structure is robust to material loss in the intermediate waveguide and variations to the waveguide parameters. We also present a five rib optical waveguide structure that represents a new class of octave spanning power divider.
We theoretically examine three-well interferometry in Bose-Einstein condensates (BECs) using adiabatic passage. Specifically, we demonstrate that a fractional coherent transport adiabatic passage protocol enables stable spatial splitting in the presence of nonlinear interactions. A reversal of this protocol produces a coherent recombination of the BEC with a phase-dependent population of the three wells. The effect of nonlinear interactions on the interferometric measurement is quantified and is found to lead to an enhancement in sensitivity for moderate interaction strengths.
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