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arXiv:1711.09892

Measurement time in double quantum dots

Heber R. da Cruz

Published Nov 27, 2017• 0 citations
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Abstract

In this letter, we have considered an electron in a double quantum dot system interacting with a detector represented by a point contact. We present a dynamical model for the gradual decoherence of the density matrix due to the interaction with the detector. The interaction of the qubit (quantum system) on the quantum point contact (environment) leads to a discrete set of pointer states of the double quantum dot (apparatus). The necessary time for the qubit decoherence process (measurement time) has been calculated through this model. The existence of a minimum time for the quantum measurement has been obtained.

DOI
10.48550/arxiv.1711.09892

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In this letter, we have considered an electron in a double quantum dot system interacting with a detector represented by a point contact. We present a dynamical model for the gradual decoherence of the density matrix due to the interaction with the detector. The interaction of the qubit (quantum system) on the quantum point contact (environment) leads to a discrete set of pointer states of the double quantum dot (apparatus). The necessary time for the qubit decoherence process (measurement time) has been calculated through this model. The existence of a minimum time for the quantum measurement has been obtained.
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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 study the effect of decoherence on a weak value measurement in a paradigm system consisting of a double quantum dot continuously measured by a quantum point contact. Fluctuations of the parameters controlling the dot state induce decoherence. We find that, for measurements longer than the decoherence time, weak values are always reduced within the range of the eigenvalues of the measured observable. For measurements at shorter time scales, the measured weak value strongly depends on the interplay between the decoherence dynamics of the system and the detector backaction. In particular, depending on the postselected state and the strength of the decoherence, a more frequent classical readout of the detector might lead to an enhancement of weak values.
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Entanglement between a particle and a detector is known to be inherent in the measurement process. Gurvitz recently analyzed the coupling of an electron in a double dot (DD) to a quantum point contact (QPC) detector. In this paper we examine the dynamics of entanglement that result between the DD and QPC. The rate of entanglement is optimized as a function of coupling when the electron is initially in one of the dots. It decreases asymptotically towards zero with increased coupling. The opposite behavior is observed when the DD is initially in a superposition: the rate of entanglement increases unboundedly as the coupling is increased. The possibility that there are conditions for which measurement occurs versus entanglement is considered.