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arXiv:0802.2398 · Physical Review B

Spatial adiabatic passage in a realistic triple well structure

Jared H. Cole, Andrew D. Greentree, Lloyd C. L. Hollenberg, S. Das Sarma

Published Jun 13, 2008• 52 citations
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Abstract

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.

DOI
10.1103/physrevb.77.235418

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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.
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.
Incoherent quantum charge tunneling forms the basis of semiconductor devices. However it is well known from atomic and optical work, that coherent tunneling can be significantly faster and in principle, coherent transfer is dissipationless, i.e. the charge being transferred does not exchange heat with the environment. Furthermore, adiabatic controls are inherently robust provided the adiabaticity criterion is satisfied. Adiabatic control methods are therefore preferable to ensure high-fidelity operation despite increased operating time. We describe recent work towards understanding charge transfer mechanisms based on adiabatic passage techniques with all-electrical controls in three-, five- and seven-dot systems based on Coherent Tunneling Adiabatic Paassage (CTAP). We derive analytical values for the important eigenstates and the adiabaticity criteria for these schemes. These analytical results allow us to make comments regarding the scalability of these schemes to realistic quantum networks.
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.
Qubit transport has been identified as vital in improving quantum error correction thresholds in scalable quantum computer architectures. Introducing practical transport in the solid-state is problematic, but in phosphorus in silicon implementations we have shown an interesting adiabatic protocol for qubit transfer, coherent tunneling adiabatic passage (CTAP). Here we review the role of CTAP as a quantum wire, highlighting the protocol and the temporal scaling as the length of the transport chain is increased. We also highlight an extension of CTAP to generate spatial superposition states which demonstrates some of the flexibility of quantum electronic structures over quantum optical systems.
We study the backaction of a nearby measurement device on electrons undergoing coherent transfer via adiabatic passage (CTAP) in a triple-well system. The measurement is provided by a quantum point contact capacitively coupled to the middle well. We account for this continuous measurement by treating the whole {triple-well+detector} as a closed quantum system. This leads to a set of coupled differential equations for the density matrix of the enlarged system which we solve numerically. This approach allows us to study a single realization of the measurement process while keeping track of the detector output, which is especially relevant for experiments. In particular, we find the emergence of a new peak in the distribution of electrons inside the detector, accompanied by a drop in the fidelity of the protocol.