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arXiv:1209.2037 · Physical Review B

Decoherence effects on weak value measurements in double quantum dots

Mark Thomas, Alessandro Romito

Published Dec 12, 2012• 7 citations
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Abstract

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.

DOI
10.1103/physrevb.86.235419

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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.
We study theoretically the process of a weak measurement of charge states in a double quantum dot performed by coupling to a quantum point contact.We focus on the interplay of the measurement process with phonon-induced dephasing of delocalized superpositions of electron states and compare the time scales relevant for the dynamics of the open system and for the measurement process: the decoherence rate, the localization rate of the state conditioned on the measurement outcome and the time scale on which information on the system state is gained in the process of the measurement.
We propose a protocol for a controlled experiment to measure a weak value of the electron's spin in a solid state device. The weak value is obtained by a two step procedure--weak measurement followed by a strong one (postselection), where the outcome of the first measurement is kept provided a second postselected outcome occurs. The setup consists of a double quantum dot and a weakly coupled quantum point contact to be used as a detector. Anomalously large values of the spin of a two electron system are predicted, as well as negative values of the total spin. We also show how to incorporate the adverse effect of decoherence into this procedure.
We consider evolution of a double quantum dot (DQD) two-electron spin qubit which is continuously weakly measured with a linear charge detector (quantum point contact). Since the interaction between the spins of two electrons depends on their charge state, the charge measurement affects the state of two spins, and induces non-trivial spin dynamics. We consider the regimes of strong and weak coupling to the detector, and investigate the measurement-induced spin dynamics both analytically and numerically. We observe emergence of the negative-result evolution and the system stabilization due to an analog of quantum Zeno effect. Moreover, unitary evolution between the triplet and a singlet state is induced by the negative-result measurement. We demonstrate that these effects exist for both strong and weak coupling between the detector and the DQD system.
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.
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.