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arXiv:1107.4276 · Physical Review A

Need for relativistic corrections in the analysis of spatial adiabatic passage of matter waves

Albert Benseny, Joan Bagudà, Xavier Oriols, J. Mompart

Published May 15, 2012• 19 citations
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Abstract

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.

DOI
10.1103/physreva.85.053619

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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.
Analytical expressions are derived for coherent tunneling via adiabatic passage in a triple-well system with negligible central-well population at all times during the transfer. It is shown that a manipulation of the depths of the extreme wells, correlated with the time variation of the nonadjacent barriers, is essential for maintaining the vanishing population of the central well. The validity of our conditions is demonstrated with a numerical solution of the time-dependent Schr\"odinger equation. The transfer process is interpreted in terms of a current through the central well.
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 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.
By using a close similarity between multi-photon and tunneling population transfer schemes, we propose robust adiabatic methods for the transport of Bose-Einstein condensate (BEC) in double- and triple-well traps. The calculations within the mean-field approximation (Gross-Pitaevskii equation) show that irreversible and complete transport takes place even in the presence of the non-linear effects caused by interaction between BEC atoms. The transfer is driven by adiabatic time-dependent monitoring the barriers and well depths. The proposed methods are universal and can be applied to a variety of systems and scenarios.
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 evolution of an electron undergoing coherent tunneling via adiabatic passage (CTAP) using the solution of the one-dimensional Schr\"odinger equation in both space and time for a triple well potential. We find the eigenspectrum and complete time evolution for a range of different pulsing schemes. This also provides an example of a system that can be described with the tools from both quantum optics and condensed matter. We find that while the quantum optics description of the process captures most of the key physics, there are important effects that can only be correctly described by a more complete representation. This is an important point for applications such as quantum information processing or quantum control where it is common practice to use a reduced state space formulation of the quantum system in question.