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arXiv:0810.3372 · Physical Review A

Conditions for vanishing central-well population in triple-well adiabatic transport

Tomáš Opatrný, Kunal K. Das

Published Jan 26, 2009• 46 citations
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Abstract

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.

DOI
10.1103/physreva.79.012113

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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 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.
Coherent control of quantum tunneling is investigated for a single atom held in a driven triple-well potential without tight-binding approximation. In the high-frequency regime within or without multiphoton resonance, we find the analytical solutions and their numerical correspondences, including the special Floquet states of invariant populations and the non-Floquet states of slowly varying populations. The Floquet quasienergy spectrum exhibits anticrossings and crossings for different values of the driving parameters, which are associated with different tunneling properties described by the non-Floquet states. Applying the presented results, we suggest a scheme for transporting a single atom between nonadjacent wells or between adjacent wells.
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 report on an experimental demonstration of light transfer in an engineered triple-well optical waveguide structure which provides a classic analog of coherent tunneling by adiabatic passage (CTAP) recently proposed for coherent transport in space of neutral atoms or electrons among tunneling-coupled optical traps or quantum wells [A. D. Greentree et al., Phys. Rev. B 70, 235317 (2004); K. Eckert et al., Phys. Rev. A 70, 023606 (2004)]. The direct visualization of CTAP wave-packet dynamics enabled by our simple optical system clearly shows that in the counterintuitive passage scheme light waves tunnel between the two outer wells without appreciable excitation of the middle well.
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.
A solid-state analog of stimulated Raman adiabatic passage can be implemented in a triple-well solid-state system to coherently transport an electron across the wells with exponentially suppressed occupation in the central well at any point of time. Termed coherent-tunneling adiabatic passage (CTAP), this method provides a robust way to transfer quantum information encoded in the electronic spin across a chain of quantum dots or donors. Using large-scale atomistic tight-binding simulations involving over $3.5\ifmmode\times\else\texttimes\fi{}{10}^{6}$ atoms, we verify the existence of a CTAP pathway in a realistic solid-state system: gated triple donors in silicon. Realistic gate profiles from commercial tools were combined with tight-binding methods to simulate gate control of the donor to donor tunnel barriers in the presence of crosstalk. As CTAP is an adiabatic protocol, it can be analyzed by solving the time-independent problem at various stages of the pulse justifying the use of time-independent tight-binding methods to this problem. This work also involves the first atomistic treatment to translate the three-state-based quantum-optics type of modeling into a solid-state description beyond the ideal localization assumption. Our results show that a three-donor CTAP transfer, with interdonor spacing of 15 nm can occur on time scales greater than 23 ps, well within experimentally accessible regimes. The method not only provides a tool to guide future CTAP experiments but also illuminates the possibility of system engineering to enhance control and transfer times.