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arXiv:1712.04791 · IEEE Transactions on Control Systems Technology

Modeling and Control of Quantum Measurement-Induced Backaction in Double Quantum Dots

Wei Cui, Daoyi Dong

Published Oct 8, 2018• 8 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/tcst.2018.2871790

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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.
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.
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.
A controllable low noise current lies at the heart of high-precision measurements in quantum transport and metrology. While the previous research dealt with the suppression of noise in transport through a tunneling junction or a single quantum dot (QD) device, the present work investigates noise inhibition of a double quantum dot (DQD) transport system based on closed-loop feedback control. The unique advantage of a DQD device is that bidirectional transport at low bias can be measured by a nearby quantum point contact. However, the continuous monitoring of the DQD states inevitably leads to a measurement-induced dephasing. To appropriately characterize its transport properties in the presence of feedback action, we here develop a numerical method dubbed auxiliary density matrix approach, motivated by the hierarchical expansion of the moment-generating function in the hierarchy equations of motion [J. Cerrillo et al., Phys. Rev. B 94, 214308 (2016)]. This generic method has no restriction on the system structure and parameters and is able to evaluate the feedback current cumulants to an arbitrary order. It is revealed that the feedback control of the tunnel coupling between the two dots is the most effective to suppress the noise under various tunnel coupling configurations. The influence of interdot Coulomb interaction, measurement-induced dephasing, and finite time delay on feedback is also analyzed in detail.
The current revolution in quantum technologies relies on the ability to isolate, coherently control, and measure the state of quantum systems. The act of measurement in quantum mechanics, however, is naturally invasive as the measurement apparatus becomes entangled with the system that it observes. Even for ideal detectors, the measurement outcome always leads to a disturbance in the observed system, a phenomenon called quantum measurement backaction. Here we report a profound change in the many-body properties of the measured system due to quantum measurements. We observe this backaction-induced transition in a mesoscopic double quantum-dot in the Coulomb-blockade regime, where we switch the electron population through measurement with a charge sensor dot. Our finding showcases the important changes in behaviour that can arise due to quantum detectors, which are ubiquitous in quantum technologies.
We study the effect of decoherence on a weak value measurement in a paradigm system consisting of a double quantum dot continuously measured by a quantum point contact. Fluctuations of the parameters controlling the dot state induce decoherence. We find that, for measurements longer than the decoherence time, weak values are always reduced within the range of the eigenvalues of the measured observable. For measurements at shorter time scales, the measured weak value strongly depends on the interplay between the decoherence dynamics of the system and the detector backaction. In particular, depending on the postselected state and the strength of the decoherence, a more frequent classical readout of the detector might lead to an enhancement of weak values.
Quantum information processing is a key technology in the ongoing second quantum revolution, with a wide variety of hardware platforms competing toward its realization. An indispensable component of such hardware is a measurement device, i.e., a quantum detector that is used to determine the outcome of a computation. The act of measurement in quantum mechanics, however, is naturally invasive as the measurement apparatus becomes entangled with the system that it observes. This always leads to a disturbance in the observed system, a phenomenon called quantum measurement backaction, which should solely lead to the collapse of the quantum wave function and the physical realization of the measurement postulate of quantum mechanics. Here we demonstrate that backaction can fundamentally change the quantum system through the detection process. For quantum information processing, this means that the readout alters the system in such a way that a faulty measurement outcome is obtained. Specifically, we report a backaction-induced population switching, where the bare presence of weak, nonprojective measurements by an adjacent charge sensor inverts the electronic charge configuration of a semiconductor double quantum dot system. The transition region grows with measurement strength and is suppressed by temperature, in excellent agreement with our coherent quantum backaction model. Our result exposes backaction channels that appear at the interplay between the detector and the system environments, and opens new avenues for controlling and mitigating backaction effects in future quantum technologies.