Quantum dynamics intervened by repeated nonselective measurements (original) (raw)
Unitary dynamics and finite-time measurements: a case study
Physica Scripta, 2015
The inhibition of the decay of a quantum system by frequent measurements is known as quantum Zeno effect. Beyond the limit of projective measurements, the interplay between the unitary dynamics of the system and the coupling to a measurement apparatus becomes relevant. We explore this interplay by considering a quantum particle moving on a one-dimensional chain. A local measurement by coupling to an apparatus with a two-dimensional Hilbert space detects the presence of the particle on a specific chain site. The decay of the population is studied analytically for a two-site chain and numerically for a larger system as a function of the measurement time and the time between subsequent measurements. Particular attention is given to the shift of the energy of the measured site due to the coupling to the apparatus. The decay of the initial population can be hindered or accelerated, depending on the chosen system and the coupling parameters.
Quantum measurements in continuous time, non-Markovian evolutions and feedback
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012
In this article we reconsider a version of quantum trajectory theory based on the stochastic Schrödinger equation with stochastic coefficients, which was mathematically introduced in the '90s, and we develop it in order to describe the non Markovian evolution of a quantum system continuously measured and controlled thanks to a measurement based feedback. Indeed, realistic descriptions of a feedback loop have to include delay and thus need a non Markovian theory. The theory allows to put together non Markovian evolutions and measurements in continuous time in agreement with the modern axiomatic formulation of quantum mechanics. To illustrate the possibilities of such a theory, we apply it to a two-level atom stimulated by a laser. We introduce closed loop control too, via the stimulating laser, with the aim to enhance the "squeezing" of the emitted light, or other typical quantum properties. Note that here we change the point of view with respect to the usual applications of control theory. In our model the "system" is the two-level atom, but we do not want to control its state, to bring the atom to a final target state. Our aim is to control the "Mandel Q-parameter" and the spectrum of the emitted light; in particular the spectrum is not a property at a single time, but involves a long interval of times (a Fourier transform of the autocorrelation function of the observed output is needed).
Physical Review A, 2015
A one-dimensional quantum oscillator is monitored by taking repeated position measurements. As a first contribution, it is shown that, under a quantum nondemolition measurement scheme applied to a system initially at the ground state: i) the observed sequence of measurements (quantum tracks) corresponding to a single experiment converges to a limit point, and that ii) the limit point is random over the ensemble of the experiments, being distributed as a zero-mean Gaussian random variable with a variance at most equal to the ground state variance. As a second contribution, the richer scenario where the oscillator is coupled with a frozen (i.e., at the ground state) ensemble of independent quantum oscillators. A sharply different behavior emerges: under the same measurement scheme, here we observe that the measurement sequences are essentially divergent. Such a rigorous statistical analysis of the sequential measurement process might be useful for characterizing the main quantities that are currently used for inference, manipulation and monitoring of many quantum systems. Several interesting properties of the quantum tracks evolution, as well as of the associated (quantum) threshold crossing times are discussed, and the dependence upon the main system parameters (e.g., the choice of the measurement sampling time, the degree of interaction with the environment, the measurement device accuracy) are elucidated. At a more fundamental level, it is seen that, as an application of basic Quantum Mechanics principles, a sharp difference exists between the intrinsic randomness unavoidably present in any quantum system, and the extrinsic randomness arising from the environmental coupling, i.e., the randomness induced by an external source of disturbance.
Recovering classical dynamics from coupled quantum systems through continuous measurement
We study the role of continuous measurement in the quantum to classical transition for a system with coupled internal ͑spin͒ and external ͑motional͒ degrees of freedom. Even when the measured motional degree of freedom can be treated classically, entanglement between spin and motion causes strong measurement back action on the quantum spin subsystem so that classical trajectories are not recovered in this mixed quantumclassical regime. The measurement can extract localized quantum trajectories that behave classically only when the internal action also becomes large relative to ប.
Equilibration by quantum observation
New Journal of Physics, 2010
We consider an unexplored regime of open quantum systems that relax via coupling to a bath while being monitored by an energy meter. We show that any such system inevitably reaches an equilibrium (quasi-steady) state controllable by the effective rate of monitoring. In the non-Markovian regime, this approach suggests the possible 'freezing' of states, by choosing monitoring rates that set a non-thermal equilibrium state to be the desired one. For measurement rates high enough to cause the quantum Zeno effect, the only steady state is the fully mixed state, due to the breakdown of the rotating wave approximation. Regardless of the monitoring rate, all the quasi-steady states of an observed open quantum system live only as long as the Born approximation holds, namely the bath entropy does not change. Otherwise, both the system and the bath converge to their fully mixed states.
Exact master equation and general non-Markovian dynamics in open quantum systems
The European Physical Journal Special Topics, 2019
Investigations of quantum and mesoscopic thermodynamics force one to answer two fundamental questions associated with the foundations of statistical mechanics: (i) how does macroscopic irreversibility emerge from microscopic reversibility? (ii) how does the system relax in general to thermal equilibrium with its environment? The answers to these questions rely on a deep understanding of nonequilibrium dynamics of systems interacting with their environments. Decoherence is also a main concern in developing quantum information technology. In the past two decades, many theoretical and experimental investigations have devoted to this topic, most of these investigations take the Markov (memory-less) approximation. These investigations have provided a partial understanding to several fundamental issues, such as quantum measurement and the quantum-to-classical transition, etc. However, experimental implementations of nanoscale solidstate quantum information processing makes strong non-Markovian memory effects unavoidable, thus rendering their study a pressing and vital issue. Through the rigorous derivation of the exact master equation and a systematical exploration of various non-Markovian processes for a large class of open quantum systems, we find that decoherence manifests unexpected complexities. We demonstrate these general non-Markovian dynamics manifested in different open quantum systems.
Decoherence of an Open System under Continuous Quantum Measurement of Energy
International Journal of Theoretical Physics, 2009
We study continuous quantum measurements (CQM) of energy of an open quantum system by Lindblad master equation. It turns out that the time-dependence of decoherence is identified. We conclude that the CQM of energy accelerate quantum decoherence. Keywords Continuous quantum measurements • Decoherence • Master equation • Density matrix elements The simplest description of a measurement in quantum physics was provided by von Neumann [1]. When quantum measurement was first introduced to quantum mechanics, it was invariably treated by ignoring the time the measurement takes. However, it is not sufficient to describe continuously monitored system. Usually, one wants to understand what happens to the system while the measurement takes place continuously. This is the subject of continuous quantum measurement [2]. Recently, continuous or repeated measurements of quantum system has been actively discussed due to its implication in feedback control [3], metrology [4-7], quantum information [8], quantum computing [9-11] and its importance in understanding the quantum to classical transition [12-15]. When a quantum system is measured, its state is changed which may be described as decoherence. Decoherence is a basic idea in the theory of CQM which plays a decisive role in the dynamics of a system subject to repeated or continuous quantum measurement. The interest in decoherence is widespread, due to the fact that it is the main limiting factor for quantum information processing [16]. Sponsored by K.C. Wong Magna Fund in Ningbo University.
Conditional measurements as probes of quantum dynamics
Physical Review A, 2003
We discuss conditional measurements as probes of quantum dynamics and show that they provide different ways to characterize quantum fluctuations. We illustrate this by considering the light from a subthreshold degenerate parametric oscillator. Analytic results and curves are presented to illustrate the behavior.
Theory of temporal fluctuations in isolated quantum systems
International Journal of Modern Physics B, 2015
When an isolated quantum system is driven out of equilibrium, expectation values of general observables start oscillating in time. This paper reviews the general theory of such temporal fluctuations. We first survey some results on the strength of such temporal fluctuations. For example temporal fluctuations are exponentially small in the…