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arXiv:1003.5743 · Physical Review Letters

Effect of Measurement Backaction on Adiabatic Coherent Electron Transport

Jérôme Rech, Stefan K. Kehrein

Published Mar 31, 2011• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.106.136808

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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.
We study the detection of electrons undergoing coherent transfer via adiabatic passage (CTAP) in a triple quantum-dot system with a quantum point contact sensing the charge of the middle dot. In the ideal scenario, the protocol amounts to perfect change transfer between the external dots with vanishing occupation of the central dot at all times, rendering the measurement and its backaction moot. Nevertheless, even with minor corrections to the protocol, a small population builds up in the central dot. We study the measurement backaction using a Bayesian formalism simulation of an instantaneous detection at the time of maximal occupancy of the dot. We show that the interplay between the measurement backaction and the nonadiabatic dynamics induces a change in the success probability of the protocol, which quantitatively agrees with a continuous detection treatment. We introduce a correlated measurement signal to certify the nonoccupancy of the central dot for a successful CTAP protocol, which, in the weak-measurement limit, confirms a vanishing occupation of the central dot. Our proposed correlated signal purports the proper experimental method by which to confirm CTAP.
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 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.
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 consider the continuous measurement of a double quantum dot by a weakly coupled detector (tunnel point contact nearby). While the conventional approach describes the gradual system decoherence due to the measurement, we study the situation when the detector output is explicitly recorded that leads to the opposite effect: gradual purification of the double-dot density matrix. The nonlinear Langevin equation is derived for the random evolution of the density matrix which is reflected and caused by the stochastic detector output. Gradual collapse, gradual purification, and the quantum Zeno effect are naturally described by the equation. We also discuss the possible experiments to confirm the theory.
We investigate experimentally the quantum coherence of an electronic two-level system in a double quantum dot under continuous charge detection. The charge state of the two-level system is monitored by a capacitively coupled single quantum dot detector that imposes a backaction effect on the system. The measured backaction is well described by an additional decoherence rate, approximately linearly proportional to the detector electron tunneling rate. We provide a model for the decoherence rate arising due to level detuning fluctuations induced by detector charge fluctuations. The theory predicts a factor of 2 lower decoherence rates than observed in the experiment, suggesting the need for a more elaborate theory accounting for additional sources of decoherence.