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arXiv:cond-mat/0301409 · Physical Review Letters

Relaxation and the Zeno Effect in Qubit Measurements

S. A. Gurvitz, Leonid Evgenevich Fedichkin, Dmitry Mozyrsky, G. P. Berman

Published Aug 5, 2003• 103 citations
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Abstract

We consider a qubit interacting with its environment and continuously monitored by a detector represented by a point contact. Bloch-type equations describing the entire system of the qubit, the environment, and the detector are derived. Using these equations we evaluate the detector current and its noise spectrum in terms of the decoherence and relaxation rates of the qubit. Simple expressions are obtained that show how these quantities can be accurately measured. We demonstrate that due to interaction with the environment, the measurement can never localize a qubit even for infinite decoherence rate.

DOI
10.1103/physrevlett.91.066801

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We consider a qubit interacting with its environment and continuously monitored by a detector represented by a point contact. Bloch-type equations describing the entire system of the qubit, the environment, and the detector are derived. Using these equations we evaluate the detector current and its noise spectrum in terms of the decoherence and relaxation rates of the qubit. Simple expressions are obtained that show how these quantities can be accurately measured. We demonstrate that due to interaction with the environment, the measurement can never localize a qubit even for infinite decoherence rate.
We employ a quantum Langevin-equation approach to establish Bloch-type dynamical equations, on a fully microscopic basis, to investigate the measurement of the state of a coupled quantum dot qubit by a nearby quantum point contact. The ensuing Bloch equations allow us to analyze qubit relaxation and decoherence induced by measurement, and also to determine the noise spectrum of the meter output current with the help of a quantum regression theorem, at arbitrary bias voltage and temperature. Our analyses attempt to provide a clear resolution of a recent debate concerning the occurrence of a quantum oscillation peak in the noise spectrum.
During measurement, information is transferred from the measured quantum system to the detector via their coupling. The same coupling that extracts information from the quantum system transmits noise from the detector's environment to the system as well. In this paper, we derive the limit to the measurement efficiency of a superconducting persistent-current qubit measured by a dc superconducting quantum interference device (SQUID) and calculate the noise transmitted to the qubit from the environment of the dc SQUID. The method, with simple linear circuitry correspondence, can be applied to calculate the noise transferred to a quantum system from the environment of an arbitrary external system that interacts with it. The relaxation and decoherence induced by this noise are also estimated.
We investigated the electron tunneling out of a quantum dot in the presence of continuous monitoring by a detector. It is shown that the Schrodinger equation for the whole system can be reduced to new Bloch-type rate equations describing the time development of the detector and the measured system at once. Using these equations we find that the continuous measurement of the unstable system does not affect its exponential decay, exp(-gammat), contrary to expectations based on the quantum Zeno effect. However, the width of the energy distribution of the tunneling electron is no longer gamma, but increases due to the decoherence, generated by the detector.
We theoretically study the quantum measurement of a double quantum dot coupled to environments by Bloch equations with an additional vector. Using a quantum point contact as a detector, we accurately calculate the current, the Fano factor, and the waiting time, respectively, to characterize the dynamical properties in two kinds of environments. In the dissipative case, the asymmetrical Fano factor is enhanced with the increase in deocoherence rates and suppressed as the growth of relaxation rates, and the super-Poissonian noise is mainly due to the effects of a dynamical channel blockade and quantum coherence. In the pure dephasing case, the symmetrical Fano factor is magnified, which can be attributed to the quantum Zeno effect. Moreover, we show that the distribution of the average waiting time exhibits good agreement with the variation tendency of the current. Our paper provides an effective method in handling quantum measurement.