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arXiv:cond-mat/0401103 · Physical Review B

Noise and measurement efficiency of a partially coherent mesoscopic detector

Aashish A. Clerk, A. Douglas Stone

Published Jun 8, 2004• 27 citations
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Abstract

We study the noise properties and efficiency of a mesoscopic resonant-level conductor which is used as a quantum detector, in the regime where transport through the level is only partially phase coherent. We contrast models in which detector incoherence arises from escape to a voltage probe, versus those in which it arises from a random time-dependent potential. Particular attention is paid to the back-action charge noise of the system. While the average detector current is similar in all models, we find that its noise properties and measurement efficiency are sensitive both to the degree of coherence and to the nature of the dephasing source. Detector incoherence prevents quantum limited detection, except in the nongeneric case where the source of dephasing is not associated with extra unobserved information. This latter case can be realized in a version of the voltage-probe model.

DOI
10.1103/physrevb.69.245303

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We study the noise properties and efficiency of a mesoscopic resonant-level conductor which is used as a quantum detector, in the regime where transport through the level is only partially phase coherent. We contrast models in which detector incoherence arises from escape to a voltage probe, versus those in which it arises from a random time-dependent potential. Particular attention is paid to the back-action charge noise of the system. While the average detector current is similar in all models, we find that its noise properties and measurement efficiency are sensitive both to the degree of coherence and to the nature of the dephasing source. Detector incoherence prevents quantum limited detection, except in the nongeneric case where the source of dephasing is not associated with extra unobserved information. This latter case can be realized in a version of the voltage-probe model.
We study charge detection and controlled dephasing of a mesoscopic system via a quantum dot detector (QDD), where the mesoscopic system and the QDD are capacitively coupled. The QDD is considered to have coherent resonant tunnelling via a single level. It is found that the dephasing rate is proportional to the square of the conductance of the QDD for the Breit-Wigner model, showing that the dephasing is completely different from the shot noise of the detector. The measurement rate, on the other hand, shows a dip near the resonance. Our findings are peculiar especially for a symmetric detector in the following aspect: The dephasing rate is maximum at resonance of the QDD where the detector conductance is insensitive to the charge state of the mesoscopic system. As a result, the efficiency of the detector shows a dip and vanishes at resonance, in contrast to the single-channel symmetric non-resonant detector that has always a maximum efficiency. We find that this difference originates from a very general property of the scattering matrix: The abrupt phase change exists in the scattering amplitudes in the presence of the symmetry, which is insensitive to the detector current but {\em stores} the information of the quantum state of the mesoscopic system.
We investigate the effects of dephasing on the current statistics of mesoscopic conductors with a recently developed statistical model, focusing, in particular, on mesoscopic cavities and Aharonov-Bohm rings. For such devices, we analyze the influence of an arbitrary degree of decoherence on the cumulants of the current. We recover known results for the limiting cases of fully coherent and totally incoherent transport and are able to obtain detailed information on the intermediate regime of partial coherence for a varying number of open channels. We show that dephasing affects the average current, shot noise, and higher order cumulants in a quantitatively and qualitatively similar way, and that consequently shot noise or higher order cumulants of the current do not provide information on decoherence additional or complementary to what can be already obtained from the average current.
Quantum mechanics can strongly influence the noise properties of mesoscopic devices. To probe this effect we have measured the current fluctuations at high-frequency (5-90G Hz) using a superconductor-insulator-superconductor tunnel junction as an on-chip spectrum analyzer. By coupling this frequency-resolved noise detector to a quantum device we can measure the high-frequency, non-symmetrized noise as demonstrated for a Josephson junction. The same scheme has been used to detect the current fluctuations arising from coherent charge oscillations in a two-level system, a superconducting charge qubit. A narrow band peak was observed in the spectral noise density at the frequency of the coherent charge oscillations.
Quantum transport in mesoscopic conductors is essentially governed by the laws of quantum mechanics. One of the major open questions of quantum mechanics is what happens if noncommuting observables are measured simultaneously. Since current operators at different times do not commute, the high-frequency correlation functions of the current are realization of this fundamental quantum question. We formulate this problem in the context of measurements of finite-frequency current cumulants in a general quantum point contact, which are the subject to ongoing experimental effort. To this end, we present two models of detectors that correspond to a weak time-resolved measurement of the electronic current in a mesoscopic junction. In both cases, the backaction of the detector leads to observable corrections to the current correlations functions involving the so-called noise susceptibilities. As a result, we propose a reinterpretation of environmental corrections to the finite-frequency cumulants as inevitable effect resulting from basic quantum mechanical principles. Finally we make concrete predictions for the temperature, voltage, and frequency dependence of the third cumulant, which could be verified directly using current experimental techniques.
Quantum point contact (QPC), one of the typical mesoscopic transport devices, has been suggested to be an efficient detector for quantum measurement. In the context of two-state charge qubit, our previous studies showed that the QPC's measurement back-action cannot be described by the conventional Lindblad quantum master equation. In this work, we study the measurement problem of a multistate system, say, an electron in disordered potential, subject to the quantum measurement of the mesoscopic detector QPC. The effect of measurement back-action and the detector's readout current are analyzed, where particular attention is focused on some new features and the underlying physics associated with the measurement-induced delocalization versus the measurement voltages.
We present simulations of the effects of dephasing on the shot noise properties of mesoscopic coherent devices, such as chaotic cavities and Aharonov-Bohm rings. We adopt a phenomenological model that exploits the statistical nature of the dephasing mechanism and is able to cover the intermediate regime between a fully coherent and completely incoherent (i.e., semiclassical) transport. By investigating conductance and noise properties as a function of the dephasing length, we conclude that decoherence has no specific effect on shot noise which can be distinguished from the one it has on conductance. In addition, when a large number of conducting channels is considered, semiclassical and quantum behavior must converge, yielding as a consequence the independence of DC and noise properties from dephasing.