Coherent tunneling via adiabatic passage in a three-well Bose-Hubbard system

Abstract

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.

Interferometry using adiabatic passage in dilute-gas Bose-Einstein condensates

“…The D 0 eigenstate has no population in the center well for all and, in the limit of 12 / 23 1, the atomic population is confined entirely to well 1.…”

“…This scheme can be used to generate any preselected coherent superposition of two atomic states, |1 and |3 , via an intermediate excited state, |2 . Electromagnetic pulses are used to couple states |1 to |2 and |2 to |3 , characterized by coupling parameters 12 and 23 . As in STIRAP, 23 precedes 12 , but unlike STIRAP where 23 vanishes first, here, the two pulses vanish simultaneously while maintaining a constant ratio of amplitudes.…”

“…Electromagnetic pulses are used to couple states |1 to |2 and |2 to |3 , characterized by coupling parameters 12 and 23 . As in STIRAP, 23 precedes 12 , but unlike STIRAP where 23 vanishes first, here, the two pulses vanish simultaneously while maintaining a constant ratio of amplitudes. The ratio of probability amplitudes of the resulting coherent superposition of states |1 and |3 is proportional to the ratio 23 / 12 .…”

“…In three-well atomic [21] and electronic quantum dot [22] systems, the coherent spatial transport of single-particle quantum states is known as coherent tunneling adiabatic passage (CTAP). Recent papers have shown that this principle can be extended to interacting manybody quantum systems, such as BECs, both in the quantum [23] and in the semiclassical mean-field limits [24][25][26][27][28][29][30].…”

Quantification of the memory effect of steady-state currents from interaction-induced transport in quantum systems

“…The zero-temperature Bose-Einstein condensate and its dynamics may be studied by the mean-field Gross-Pitaevskii equation (GPE) [69,70]. It can be generalized to describe timedependent systems [71][72][73] and has been previously implemented in modeling coherent transport [74,75]. In one dimension, the time-dependent GPE can be written as…”