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Physical Review A

Nonclassical dynamics induced by a quantum meter

J. Clausen, J. Salo, V. M. Akulin, Stig Stenholm

Published Dec 5, 2005• 3 citations
Publisher

Abstract

Conventionally, the effect of measurements on a quantum system is assumed to introduce decoherence, which renders the system classical-like. We consider here a microscopic meter, that is, an auxiliary essentially quantum system whose state is measured repeatedly, and show that it can be employed to induce transitions from classical states into inherently quantumlike states. The meter state is assumed to be lost in the environment and we derive a non-Markovian master equation for the dynamic system in the case of nondemolition coupling to the meter; this equation can be cast in the form of an $({N}_{a})$th-order differential equation in time, where ${N}_{a}$ is the dimension of the meter basis. We apply the approach to a harmonic oscillator coupled to a spin-$\frac{1}{2}$ meter and demonstrate how it can be used to engineer effective Hamiltonian evolution, subject to decoherence induced by the projective meter measurements.

DOI
10.1103/physreva.72.062104

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•Feb 22, 2018•0 citations
Conventionally, the effect of measurements on a quantum system is assumed to introduce decoherence, which renders the system classical-like. We consider here a microscopic meter, that is, an auxiliary essentially quantum system whose state is measured repeatedly, and show that it can be employed to induce transitions from classical states into inherently quantumlike states. The meter state is assumed to be lost in the environment and we derive a non-Markovian master equation for the dynamic system in the case of nondemolition coupling to the meter; this equation can be cast in the form of an (Na)({N}_{a})(Na​)th-order differential equation in time, where Na{N}_{a}Na​ is the dimension of the meter basis. We apply the approach to a harmonic oscillator coupled to a spin-12\frac{1}{2}21​ meter and demonstrate how it can be used to engineer effective Hamiltonian evolution, subject to decoherence induced by the projective meter measurements.
A specific measurement model based on quantum nondemolition monitoring of oscillator quanta is used to illustrate the essential elements of the quantum theory of measurement, viz., state reduction and existence of a ``pointer basis,'' recently discussed by Zurek. The form of the interaction between the meter and its environment determines the system observable recorded by the meter. In our model this quantity is the square of the oscillator's quanta. The corresponding pointer basis states are the meter coherent states. The more accurate the measurement the more excited (and classical) these states become. We show explicitly that the state reduction of the system during measurement is due to nonunitary evolution resulting from the meter-environment coupling. A particular realization of the environment as a photoelectron counter is discussed.
We address the dynamics of nonclassicality for a quantum system interacting with a noisy fluctuating environment described by a classical stochastic field. As a paradigmatic example, we consider a harmonic oscillator initially prepared in a maximally nonclassical state, e.g., a Fock number state or a Schr\"odinger-cat-like state, and then coupled to either a resonant or a nonresonant external field. Stochastic modeling allows us to describe the decoherence dynamics without resorting to approximated quantum master equations and to introduce non-Markovian effects in a controlled way. A detailed comparison among different nonclassicality criteria and a thorough analysis of the decoherence time reveal a rich phenomenology whose main features may be summarized as follows: (i) Classical memory effects increase the survival time of quantum coherence and (ii) a detuning between the natural frequency of the system and the central frequency of the classical field induces revivals of quantum coherence.
One of the main goals of the theory of open quantum systems is to devise methods which help preserve the quantum properties of a system interacting with its environment.One possible pathway to achieve this goal is to use non-Markovian reservoirs, characterized by information backflows and revivals of certain quantum properties.These reservoirs usually require advanced engineering techniques, which may turn their implementation impractical.In this dissertation we propose an alternative technique: the injection of a classical colored noise, which induces the desired quantum non-Markovianity.In order to do that, we investigate the dynamics of a quantum system interacting with its surrounding environment and under the injection of a classical stochastic colored noise.A time-local master equation for the system is derived by using the stochastic wave function formalism and functional calculus.Afterwards, the non-Markovianity of the evolution is detected by using the Andersson, Cresser, Hall and Li measure, which is based on the decay rates of the master equation in canonical Lindblad-like form.Finally, we evaluate the measure for three different colored noises and study the interplay between environment and noise pump necessary to induce quantum non-Markovianity, as well as the energy balance of the system.
The precise characterization of dynamics in open quantum systems often presents significant challenges, leading to the introduction of various approximations to simplify a model. One commonly used strategy involves Markovian approximations, assuming a memoryless environment. In this study, such approximations are not used and an analytical dynamical depiction of an open quantum system is provided. The system under consideration is an oscillator that is surrounded by a bath of oscillators. The resulting dynamics are characterized by a second-order complex coefficient linear differential equation, which may be either homogeneous or inhomogeneous. Moreover, distinct dynamical regions emerge, depending on certain parameter values. Notably, the steady-state average excitation number (AEN) of the system shows rapid escalation with increasing non-Markovianity, reflecting the intricacies of real-world dynamics. In cases where there is detuning between the system frequency and the environmental central frequency within a non-Markovian regime, the AEN maintains its initial value for an extended period. Furthermore, the application of pulse control can effectively protect the quantum system from decoherence effects without using approximations. The pulse control can not only prolong the relaxation time of the oscillator, but can also be used to speed up the relaxation process, depending on the specifications of the pulse. By employing a kick pulse, the Mpemba effect can be observed in the non-Markovian regime in a surprisingly super-cooling-like effect.
We study nonclassical effects in the dynamics of an open quantum system. The model involves a harmonic oscillator coupled to a reservoir of non-interacting harmonic oscillators. Different system-bath interaction schemes as well as reservoir states are considered. Particularly, the squeezed reservoirs coupled to the system through single and two quanta exchange processes are put in the spotlight. We investigate the quantumness conveyed to the system through the bath by computing a nonclassicality measure for different bath properties and when the memory effects are appreciable. The measure of nonclassicality is calculated for projective measurements both in the number state basis and a basis formed by a set of coherent states. Our results show that in both bases the measure exhibits characteristic features for each bath state and the form of its interaction with the system. Some of those features are independent from the measurement scheme (number or coherent), and thus, emergent from the bath and its interaction with the probe system. This allows for fingerprinting and identifying the environmental effects by tracking a given probe with appropriate measurements. Hence, may prove useful for distinguishing different sources of decoherence.
This thesis investigates two thematic lines of research, both underpinned by non-Markovian system-reservoir interactions in quantum optics. The overarching focus is on modelling the open system dynamics in a non-perturbative fashion, broadly on - though not restricted to - instances when the environment is structured. A theory is developed by means of enlarging the open system over environmental degrees of freedom to include memory effects in its dynamics. This is achieved using an established technique that involves mapping a bosonic environment onto a 1D chain of harmonic oscillators. Within this setting, we apply a Heisenberg equation-of-motion approach to derive an exact set coupled differential equations for the open system and a single auxiliary oscillator of the chain. The combined equations are shown to have their interpretation rooted in a quantum Markov stochastic process. Including the auxiliary chain oscillator as part of the original system then enables us to obtain an exact master equation for the enlarged system, avoiding any need for the Born-Markov approximations. Our method is valid for a dissipative two-state system, with cases of multiple excitations and added driving discussed. Separately, we apply the framework of quantum Darwinism to an atom-cavity system, and, subsequently, to a more general multiple-environment model. In both cases, the time-dependent spread of correlations between the open system and fractions of the environment is analysed during the course of the decoherence process. The degree to which information is redundant across different fractions is checked to infer the emergence of classicality. In the second case, we go further and present a decomposition of information in terms of its quantum and classical correlations. A quantitative measure of redundancy is also studied with regard to its ability to witness non-Markovian behaviour. Besides fundamental interest, our results have application to quantum information processing and quantum technologies, keeping in mind the potential beneficial use of non-Markovian effects in reservoir engineering.