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arXiv:cond-mat/9706074 · Physical review. B, Condensed matter

Measurements with a noninvasive detector and dephasing mechanism

S. A. Gurvitz

Published Dec 15, 1997• 350 citations
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Abstract

We study the dynamics of the measurement process in quantum-dot systems, where a particular state out of coherent superposition is observed. The ballistic point contact placed near one of the dots is taken as a noninvasive detector. We demonstrate that the measurement process is fully described by the Bloch-type equations applied to the whole system. These equations clearly reproduce the collapse of the density matrix into the statistical mixture in the course of the measurement process. The corresponding dephasing width is uniquely defined. We show that the continuous observation of one of the states in a coherent superposition may accelerate decay from this state---in contradiction with rapidly repeated observations, which slow down the transitions between quantum states (the quantum Zeno effect).

DOI
10.1103/physrevb.56.15215

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We study the dynamics of the measurement process in quantum-dot systems, where a particular state out of coherent superposition is observed. The ballistic point contact placed near one of the dots is taken as a noninvasive detector. We demonstrate that the measurement process is fully described by the Bloch-type equations applied to the whole system. These equations clearly reproduce the collapse of the density matrix into the statistical mixture in the course of the measurement process. The corresponding dephasing width is uniquely defined. We show that the continuous observation of one of the states in a coherent superposition may accelerate decay from this state---in contradiction with rapidly repeated observations, which slow down the transitions between quantum states (the quantum Zeno effect).
We show that a noninvasive,``negative-result measurement'' can be realized in quantum dot systems. The measurement process is studied by applying the Schrödinger equation to the whole system (including the detector). We demonstrate that the possibility of observing a particular state out of coherent superposition leads to collapse of the corresponding nondiagonal density-matrix elements of the measured system. No additional reduction postulate is needed. Experimental consequences of the collapse time and the relativistic requirement are discussed for mesoscopic and optical systems.
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 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 consider a continuous measurement of a two-level system (double-dot) by weakly coupled detector (tunnel point contact nearby). While usual treatment leads to the gradual system decoherence due to the measurement, we show that the knowledge of the measurement result can restore the pure wavefunction at any time (this can be experimentally verified). The formalism allows to write a simple Langevin equation for the random evolution of the system density matrix which is reflected and caused by the stochastic detector output. Gradual wavefunction ``collapse'' and quantum Zeno effect are naturally described by the equation.
We investigate the quantum Zeno effect in the case of electron tunneling out of a quantum dot in the presence of continuous monitoring by a detector. It is shown that the Schr\"odinger equation for the whole system can be reduced to Bloch-type rate equations describing the combined time development of the detector and the measured system. Using these equations we find that continuous measurement of the unstable system does not affect its exponential decay to a reservoir with a constant density of states. The width of the energy distribution of the tunneling electron, however, is not equal to the inverse lifetime---it increases due to the decoherence generated by the detector. We extend the analysis to the case of a reservoir described by an energy-dependent density of states, and we show that continuous measurement of such quantum systems affects both the exponential decay rate and the energy distribution. The decay does not always slow down, but might be accelerated. The energy distribution of the tunneling electron may reveal the lines invisible before the measurement.
We consider a continuous measurement of a two-level system (double-dot) by weakly coupled detector (tunnel point contact nearby). While usual treatment leads to the gradual system decoherence due to the measurement, we show that the knowledge of the measurement result can restore the pure wavefunction at any time (this can be experimentally verified). The formalism allows to write a simple Langevin equation for the random evolution of the system density matrix which is reflected and caused by the stochastic detector output. Gradual wavefunction ``collapse'' and quantum Zeno effect are naturally described by the equation.