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arXiv:1407.2803 · Physical Review B

Monitoring quantum transport: Backaction and measurement correlations

Robert Hussein, Jorge Gómez-García, Sigmund Kohler

Published Oct 14, 2014• 9 citations
arXivHTMLPDF

Abstract

We investigate a tunnel contact coupled to a double quantum dot (DQD) and employed as a charge monitor for the latter. We consider both the classical limit and the quantum regime. In the classical case, we derive measurement correlations from conditional probabilities, yielding quantitative statements about the parameter regime in which the detection scheme works well. Moreover, we demonstrate that not only the DQD occupation but also the corresponding current may strongly correlate with the detector current. The quantum-mechanical solution, obtained with a Bloch-Redfield master equation, shows that the backaction of the measurement tends to localize the DQD electrons, and thus significantly reduces the DQD current. Moreover, it provides the effective parameters of the classical treatment. It turns out that already the classical description is adequate for most operating regimes.

DOI
10.1103/physrevb.90.155424

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We investigate a tunnel contact coupled to a double quantum dot (DQD) and employed as a charge monitor for the latter. We consider both the classical limit and the quantum regime. In the classical case, we derive measurement correlations from conditional probabilities, yielding quantitative statements about the parameter regime in which the detection scheme works well. Moreover, we demonstrate that not only the DQD occupation but also the corresponding current may strongly correlate with the detector current. The quantum-mechanical solution, obtained with a Bloch-Redfield master equation, shows that the backaction of the measurement tends to localize the DQD electrons, and thus significantly reduces the DQD current. Moreover, it provides the effective parameters of the classical treatment. It turns out that already the classical description is adequate for most operating regimes.
Quantum measurements disturb the quantum system being measured, and this is known as measurement-induced backaction. In this paper, we consider a double quantum dot monitored by a nearby quantum point contact, where the measurement-induced backaction plays an important role. Taking advantage of the quantum master equation approach, we calculate the tunneling current and propose a simple feedback-control law to realize and stabilize the tunneling current. Theoretical analysis and numerical simulations show that the feedback control law can make the current quickly convergent to the desired value.
We consider the counting statistics of electron transport through a double quantum dot with special emphasis on the dephasing induced by a nearby charge detector. The double dot is embedded in a dissipative enviroment, and the presence of electrons on the double dot is detected with a nearby quantum point contact. Charge transport through the double dot is governed by a non-Markovian generalized master equation. We describe how the cumulants of the current can be obtained for such problems, and investigate the difference between the dephasing mechanisms induced by the quantum point contact and the coupling to the external heat bath. Finally, we consider various open questions of relevance to future research.
Quantum measurement always disturbs the quantum system being measured, which is known as measurement-induced backaction. We consider a specific model, a double quantum dot charge qubit measured by a nearby quantum point contact. We explore the evolution by deriving a master equation. The advantages of this master equation are (i) it has the Lindblad form and the non-Markovian effects are embodied in the time-dependent coefficients, (ii) the tunnelling and decay effect can be clearly understood in the master equation, and (iii) it can be further easily controlled by manipulate the Hamiltonian.
A detailed understanding of the full measurement statistics in experiments is the basis for thorough device characterization and advanced applications such as quantum metrology. In this spirit, we investigate the conditional counting statistics of an electron-spin-resonance pumped quantum dot (QD), which is tunnel-coupled to a side electrode and continuously monitored by a quantum point contact (QPC). For such a noninvasive detector, we find that the spin current through the QD and its related cumulants exhibit intriguing features and system parameter dependences when conditioned on the QPC current, which are in strong contrast to the unconditional cumulants. By turning the perspective around and considering the counting statistics of the QPC current conditioned on the QD current, we reveal an anomalous conditional QPC current noise, which is surprisingly suppressed for increasing coupling to the environment. Our results show that information backaction can substantially render statistical transport fluctuations. This unique advantage of the conditional counting statistics in probing the underlying correlations between system and detector, even for noninvasive measurements, can thus be employed for improving measurement protocols in quantum metrology.
We propose to continuously monitor a charge qubit by utilizing a T-shaped double quantum dot detector, in which the qubit and double dot are arranged in such a unique way that the detector turns out to be particularly susceptible to the charge states of the qubit. Special attention is paid to the regime where acquisition of qubit information and backaction upon the measured system exhibit nontrivial correlation. The intrinsic dynamics of the qubit gives rise to dynamical blockade of tunneling events through the detector, resulting in a super-Poissonian noise. However, such a pronounced enhancement of the detector's shot noise does not necessarily produce a rising dephasing rate. In contrast, an inhibition of dephasing is entailed by the reduction of information acquisition in the dynamically blockaded regimes. We further reveal the important impact of the charge fluctuations on the measurement characteristics. Noticeably, under the condition of symmetric junction capacitances the noise pedestal of the circuit current is completely suppressed, leading to a divergent signal-to-noise ratio, and eventually to a violation of the Korotkov-Averin bound in quantum measurement. Our study offers the possibility for a double dot detector to reach the quantum limited effectiveness in a transparent manner.
We present the conditional quantum dynamics of an electron tunneling between two quantum dots subject to a measurement using a low transparency point contact or tunnel junction. The double dot system forms a single qubit and the measurement corresponds to a continuous in time readout of the occupancy of the quantum dot. We illustrate the difference between conditional and unconditional dynamics of the qubit. The conditional dynamics is discussed in two regimes depending on the rate of tunneling through the point contact: quantum jumps, in which individual electron tunneling current events can be distinguished, and a diffusive dynamics in which individual events are ignored, and the time-averaged current is considered as a continuous diffusive variable. We include the effect of inefficient measurement and the influence of the relative phase between the two tunneling amplitudes of the double dot/point contact system.