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arXiv:1810.10452 · Physical Review A

Optimal conditions for spatial adiabatic passage of a Bose-Einstein condensate

J. L. Rubio, V. Ahufinger, Thomas Busch, J. Mompart

Published Nov 8, 2016• 4 citations
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Abstract

We investigate spatial adiabatic passage of a Bose-Einstein condensate in a triple-well potential within the three-mode approximation. By rewriting the dynamics in the so-called time-dependent dark-dressed basis, we analytically derive the optimal conditions for the nonlinear parameter and the on-site energies of each well to achieve a highly efficient condensate transport. We show that the nonlinearity yields a high-efficiency plateau for the condensate transport as a function of the on-site energy difference between the outermost wells, favoring the robustness of the transport. We also analyze the case of different nonlinearities in each well, which, for certain parameter values, leads to an increase of the width of this plateau.

DOI
10.1103/physreva.94.053606

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We investigate spatial adiabatic passage of a Bose-Einstein condensate in a triple-well potential within the three-mode approximation. By rewriting the dynamics in the so-called time-dependent dark-dressed basis, we analytically derive the optimal conditions for the nonlinear parameter and the on-site energies of each well to achieve a highly efficient condensate transport. We show that the nonlinearity yields a high-efficiency plateau for the condensate transport as a function of the on-site energy difference between the outermost wells, favoring the robustness of the transport. We also analyze the case of different nonlinearities in each well, which, for certain parameter values, leads to an increase of the width of this plateau.
We show that the adiabatic dynamics of a Bose-Einstein condensate (BEC) in a double-well potential can be described in terms of a dark variable resulting from the combination of the population imbalance and the spatial atomic coherence between the two wells. By means of this dark variable, we extend, to the nonlinear matter-wave case, the recent proposal by Vitanov and Shore [Phys. Rev. A 73, 053402 (2006)] on adiabatic passage techniques to coherently control the population of two internal levels of an atom or molecule. We investigate the conditions to adiabatically split or transport a BEC as well as to prepare an adiabatic self-trapping state by the optimal delayed temporal variation of the tunneling rate via either the energy bias between the two wells or the BEC nonlinearity. The emergence of nonlinear eigenstates and unstable stationary solutions of the system as well as their role in the breaking down of the adiabatic dynamics is investigated in detail.
We investigate the dynamics of a Bose-Einstein condensate in a triple-well trap in a three-level approximation. The interatomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. Additional eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three-level Landau-Zener model and the stimulated Raman adiabatic passage (STIRAP) scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning.
We investigate the coherent transport of a single particle and a Bose-Einstein condensate between the two extreme traps of a triple-well potential by means of the spatial adiabatic passage technique. This matter wave transport technique consists of adiabatically following an energy eigenstate of the system that only populates the vibrational ground states of the two extreme wells and presents at all times a node in the central region. Unraveling the (nonlinear) time-dependent Schr\"odinger equation in terms of Bohmian quantum trajectories, we show that by slowing down the total time duration of the transport process, Bohmian velocities in the central region are orders of magnitude larger than the mean atomic velocities. This leads to a very counterintuitive effect: in the regime of almost perfect adiabaticity, these velocities require relativistic corrections to properly address the transfer process and avoid superluminal propagation.
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.
We investigate coherent atomic tunneling of a dilute gas Bose-Einstein condensate (BEC) in a three-well system. In particular, we generalize stimulated Raman adiabatic passage (STIRAP) to adiabatically transport a BEC of 2000 7Li^{7}\mathrm{Li}7Li atoms between two wells with minimal occupation in the intervening well. This protocol paves the way for a robust method of control in atom-optical devices.
We investigate the energy structures and the dynamics of a Bose-Einstein condensates (BEC) in a triple-well potential coupled a high finesse optical cavity within a mean field approach. Due to the intrinsic atom-cavity field nonlinearity, several interesting phenomena arise which are the focuses of this work. For the energy structure, the bistability appears in the energy levels due to this atoms-cavity field nonlinearity, and the same phenomena can be found in the intra-cavity photons number. With an increase of the pump-cavity detunings, the higher and lower energy levels show a loop structure due to this cavity-mediated effects. In the dynamical process, an extensive numerical simulation of localization of the BECs for atoms initially trapped in one-, two-, and three-wells are performed for the symmetric and asymmetric cases in detail. It is shown that the the transition from oscillation to the localization can be modified by the cavity-mediated potential, which will enlarge the regions of oscillation. With the increasing of the atomic interaction, the oscillation is blocked and the localization emerges. The condensates atoms can be trapped either in one-, two-, or in three wells eventually where they are initially uploaded for certain parameters. In particular, we find that the transition from the oscillation to the localization is accompanied with some irregular regime where tunneling dynamics is dominated by chaos for this cavity-mediated system.