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Fortschritte der Physik

Detector's quantum backaction effects on a mesoscopic conductor and fluctuation‐dissipation relation

Luca Magazzù, Davide Valenti, Bernardo Spagnolo, Thierry Martin, G. Falci, Elisabetta Paladino

Published Oct 10, 2016• 0 citations
Publisher

Abstract

When measuring quantum mechanical properties of charge transport in mesoscopic conductors, backaction effects occur. We consider a measurement setup with an elementary quantum circuit, composed of an inductance and a capacitor, as detector of the current flowing in a nearby quantum point contact. A quantum Langevin equation for the detector variable including backaction effects is derived. Differences with the quantum Langevin equation obtained in linear response are pointed out. In this last case, a relation between fluctuations and dissipation is obtained, provided that an effective temperature of the quantum point contact is defined.

DOI
10.1002/prop.201600059

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When measuring quantum mechanical properties of charge transport in mesoscopic conductors, backaction effects occur. We consider a measurement setup with an elementary quantum circuit, composed of an inductance and a capacitor, as detector of the current flowing in a nearby quantum point contact. A quantum Langevin equation for the detector variable including backaction effects is derived. Differences with the quantum Langevin equation obtained in linear response are pointed out. In this last case, a relation between fluctuations and dissipation is obtained, provided that an effective temperature of the quantum point contact is defined.
We propose a setup for a quantitative test of the quantum fluctuation theorem. It consists of a quantum conductor, driven by an external voltage source, and a classical inductor-capacitor circuit. The work done on the system by the voltage source can be expressed by the classical degrees of freedom of the LCLCLC circuit, which are measurable by conventional techniques. In this way, the circuit acts as a classical detector to perform measurements of the quantum conductor. We prove that this definition is consistent with the work fluctuation theorem. The system under consideration is effectively described by a Langevin equation with non-Gaussian white noise. Our analysis extends the proof of the fluctuation theorem to this situation.
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.
We study theoretically transitions of a double quantum-dot qubit caused by nonequilibrium charge fluctuations in a nearby quantum point contact (QPC) used as a detector. We show that these transitions are related to the fundamental Heisenberg backaction associated with the measurement, and use the uncertainty principle to derive a lower bound on the transition rates. We also derive simple expressions for the transition rates for the usual model of a QPC as a mesoscopic conductor, with screening treated at the RPA level. Finally, numerical results are presented which demonstrate that the charge noise and shot noise backaction mechanisms can be distinguished in QPCs having nonadiabatic potentials. The enhanced sensitivity of the charge noise to the QPC potential is explained in terms of interference contributions similar to those which cause Friedel oscillations.
Using the quantum theory for a mesoscopic circuit based on the discretenes of electric charges, the finite-difference Schrödinger equation of the non-dissipative mesoscopic inductance and capacity coupling circuit is achieved. The Coulomb blockade effect, which is caused by the discreteness of electric charges, is studied. Appropriately choose the components in the circuits, the finite-difference Schrödinger equation can be divided into two Mathieu equations in representation. With the WKBJ method, the currents quantum fluctuations in the ground states of the two circuits are calculated. The results show that the currents quantum zero-point fluctuations of the two circuits are exist and correlated.
We consider the measurement of higher current moments with a dissipative resonant circuit, which is coupled inductively to a mesoscopic device in the coherent regime. Information about the higher current moments is coded in the histograms of the charge on the capacitor plates of the resonant circuit. The role of dissipation is shown to be essential for the measured noise to remain finite. We also identify which combination of current correlators enters the measurement of the third moment. The results are illustrated for a quantum point contact.