11 research outputs found
Thermodynamics of a continuously monitored double quantum dot heat engine in the repeated interactions framework
Understanding the thermodynamic role of measurement in quantum mechanical
systems is a burgeoning field of study. In this article, we study a double
quantum dot (DQD) connected to two macroscopic fermionic thermal reservoirs. We
assume that the DQD is continuously monitored by a quantum point contact (QPC),
which serves as a charge detector. Starting from a minimalist microscopic model
for the QPC and reservoirs, we show that the local master equation of the DQD
can alternatively be derived in the framework of repeated interactions and that
this framework guarantees a thermodynamically consistent description of the DQD
and its environment (including the QPC). We analyze the effect of the
measurement strength and identify a regime in which particle transport through
the DQD is both assisted and stabilized by dephasing. We also find that in this
regime the entropic cost of driving the particle current with fixed relative
fluctuations through the DQD is reduced. We thus conclude that under continuous
measurement a more constant particle current may be achieved at a fixed
entropic cost.Comment: 11 pages, 7 figures; comments are welcom
First Passage Times for Continuous Quantum Measurement Currents
The First Passage Time (FPT) is the time taken for a stochastic process to
reach a desired threshold. It finds wide application in various fields and has
recently become particularly important in stochastic thermodynamics, due to its
relation to kinetic uncertainty relations (KURs). In this letter we address the
FPT of the stochastic measurement current in the case of continuously measured
quantum systems. Our approach is based on a charge-resolved master equation,
which is related to the Full-Counting statistics of charge detection. In the
quantum jump unravelling we show that this takes the form of a coupled system
of master equations, while for quantum diffusion it becomes a type of quantum
Fokker-Planck equation. In both cases, we show that the FPT can be obtained by
introducing absorbing boundary conditions, making their computation extremely
efficient. The versatility of our framework is demonstrated with two relevant
examples. First, we show how our method can be used to study the tightness of
recently proposed KURs for quantum jumps. Second, we study the homodyne
detection of a single two-level atom, and show how our approach can unveil
various non-trivial features in the FPT distribution.Comment: 8 pages, 2 figure
Powering an autonomous clock with quantum electromechanics
We theoretically analyse an autonomous clock comprising a
nanoelectromechanical system, which undergoes self-oscillations driven by
electron tunnelling. The periodic mechanical motion behaves as the clockwork,
similar to the swinging of a pendulum, while induced oscillations in the
electrical current can be used to read out the ticks. We simulate the dynamics
of the system in the quasi-adiabatic limit of slow mechanical motion, allowing
us to infer statistical properties of the clock's ticks from the current
auto-correlation function. The distribution of individual ticks exhibits a
tradeoff between accuracy, resolution, and dissipation, as expected from
previous literature. Going beyond the distribution of individual ticks, we
investigate how clock accuracy varies over different integration times by
computing the Allan variance. We observe non-monotonic features in the Allan
variance as a function of time and applied voltage, which can be explained by
the presence of temporal correlations between ticks. These correlations are
shown to yield a precision advantage for timekeeping over the timescales that
the correlations persist. Our results illustrate the non-trivial features of
the tick series produced by nanoscale clocks, and pave the way for experimental
investigation of clock thermodynamics using nanoelectromechanical systems.Comment: 10 pages, 8 figure
Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics
Continuously measured quantum systems are characterized by an output current,
in the form of a stochastic and correlated time series which conveys crucial
information about the underlying quantum system. The many tools used to
describe current fluctuations are scattered across different communities:
quantum opticians often use stochastic master equations, while a prevalent
approach in condensed matter physics is provided by full counting statistics.
These, however, are simply different sides of the same coin. Our goal with this
tutorial is to provide a unified toolbox for describing current fluctuations.
This not only provides novel insights, by bringing together different fields in
physics, but also yields various analytical and numerical tools for computing
quantities of interest. We illustrate our results with various pedagogical
examples, and connect them with topical fields of research, such as
waiting-time statistics, quantum metrology, thermodynamic uncertainty
relations, quantum point contacts and Maxwell's demons.Comment: This is a tutorial paper, submitted to PRX Quantu
Measurement based estimator scheme for continuous quantum error correction
Canonical discrete quantum error correction (DQEC) schemes use projective von
Neumann measurements on stabilizers to discretize the error syndromes into a
finite set, and fast unitary gates are applied to recover the corrupted
information. Quantum error correction (QEC) based on continuous measurement,
known as continuous quantum error correction (CQEC), in principle, can be
executed faster than DQEC and can also be resource efficient. However, CQEC
requires meticulous filtering of noisy continuous measurement data to reliably
extract error syndromes on the basis of which errors could be detected. In this
paper, we show that by constructing a measurement-based estimator (MBE) of the
logical qubit to be protected, which is driven by the noisy continuous
measurement currents of the stabilizers, it is possible to accurately track the
errors occurring on the physical qubits in real time. We use this MBE to
develop a continuous quantum error correction (MBE-CQEC) scheme that can
protect the logical qubit to a high degree, surpassing the performance of DQEC,
and also allows QEC to be conducted either immediately or in delayed time with
instantaneous feedbacks.Comment: 10 pages, 4 figures, journal articl
Measurement-Based Feedback Quantum Control with Deep Reinforcement Learning for a Double-Well Nonlinear Potential
Closed loop quantum control uses measurement to control the dynamics of a quantum system to achieve either a desired target state or target dynamics. In the case when the quantum Hamiltonian is quadratic in x and p, there are known optimal control techniques to drive the dynamics toward particular states, e.g., the ground state. However, for nonlinear Hamiltonian such control techniques often fail. We apply deep reinforcement learning (DRL), where an artificial neural agent explores and learns to control the quantum evolution of a highly nonlinear system (double well), driving the system toward the ground state with high fidelity. We consider a DRL strategy which is particularly motivated by experiment where the quantum system is continuously but weakly measured. This measurement is then fed back to the neural agent and used for training. We show that the DRL can effectively learn counterintuitive strategies to cool the system to a nearly pure “cat” state, which has a high overlap fidelity with the true ground state
Measurement-based estimator scheme for continuous quantum error correction
Canonical discrete quantum error correction (DQEC) schemes use projective von Neumann measurements on stabilizers to discretize the error syndromes into a finite set, and fast unitary gates are applied to recover the corrupted information. Quantum error correction (QEC) based on continuous measurement, known as continuous quantum error correction (CQEC), in principle, can be executed faster than DQEC and can also be resource efficient. However, CQEC requires meticulous filtering of noisy continuous measurement data to reliably extract error syndromes on the basis of which errors could be detected. In this paper, we show that by constructing a measurement-based estimator (MBE) of the logical qubit to be protected, which is driven by the noisy continuous measurement currents of the stabilizers, it is possible to accurately track the errors occurring on the physical qubits in real time. We use this MBE to develop a continuous quantum error correction (MBE-CQEC) scheme that can protect the logical qubit to a high degree, surpassing the performance of DQEC, and also allows QEC to be conducted either immediately or in delayed time with instantaneous feedbacks
Powering an autonomous clock with quantum electromechanics
We theoretically analyse an autonomous clock comprising a nanoelectromechanical system, which undergoes self-oscillations driven by electron tunnelling. The periodic mechanical motion behaves as the clockwork, similar to the swinging of a pendulum, while induced oscillations in the electrical current can be used to read out the ticks. We simulate the dynamics of the system in the quasi-adiabatic limit of slow mechanical motion, allowing us to infer statistical properties of the clock’s ticks from the current auto-correlation function. The distribution of individual ticks exhibits a tradeoff between accuracy, resolution, and dissipation, as expected from previous literature. Going beyond the distribution of individual ticks, we investigate how clock accuracy varies over different integration times by computing the Allan variance. We observe non-monotonic features in the Allan variance as a function of time and applied voltage, which can be explained by the presence of temporal correlations between ticks. These correlations are shown to yield a precision advantage for timekeeping over the timescales that the correlations persist. Our results illustrate the non-trivial features of the tick series produced by nanoscale clocks, and pave the way for experimental investigation of clock thermodynamics using nanoelectromechanical systems