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arXiv:1802.08629 · Physical Review A

Gaussian ancillary bombardment

Daniel Grimmer, Eric Brown, Achim Kempf, Robert B. Mann, Eduardo Martín-Martínez

Published May 18, 2018• 10 citations
arXivHTMLPDF

Abstract

We analyze in full detail the time evolution of an open Gaussian quantum system rapidly bombarded by Gaussian ancillae. As a particular case this analysis covers the thermalization (or not) of a harmonic oscillator coupled to a thermal reservoir made of harmonic oscillators. We derive general results for this scenario and apply them to the problem of thermalization. We show that only a particular family of system-environment couplings will cause the system to thermalize to the temperature of its environment. We discuss that if we want to understand thermalization as ensuing from the Markovian interaction of a system with the individual microconstituents of its (thermal) environment then the process of thermalization is not as robust as one might expect.

DOI
10.1103/physreva.97.052120

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We analyze in full detail the time evolution of an open Gaussian quantum system rapidly bombarded by Gaussian ancillae. As a particular case this analysis covers the thermalization (or not) of a harmonic oscillator coupled to a thermal reservoir made of harmonic oscillators. We derive general results for this scenario and apply them to the problem of thermalization. We show that only a particular family of system-environment couplings will cause the system to thermalize to the temperature of its environment. We discuss that if we want to understand thermalization as ensuing from the Markovian interaction of a system with the individual microconstituents of its (thermal) environment then the process of thermalization is not as robust as one might expect.
We consider a particle in the harmonic approximation coupled linearly to an environment modeled by an infinite set of harmonic oscillators. The system (particle environment) is considered in a cavity at thermal equilibrium. We employ the recently introduced notion of renormalized coordinates to investigate the time evolution of the particle occupation number. For comparison, we first present this study in bare coordinates. For a long elapsed time, in both approaches, the occupation number of the particle becomes independent of its initial value. The value of the occupation number of the particle is the physically expected one at the given temperature. So we have a Markovian process, describing the particle thermalization with the environment. With renormalized coordinates, no renormalization procedure is required, leading directly to a finite result.
We generally study whether or not the information of open quantum systems would be totally erased by their surrounding environments in thermalization processes. A complex system composed of a harmonic oscillator and its environment is studied. When the interaction spectral density contains zero-value regions, there is a threshold of system-bath coupling, ${\ensuremath{\eta}}_{c}$, above which the initial information of the system partially remains. We estimated this threshold by the properties of the system and its bath, i.e., the density of the environment states. Thus, its long-time stabilization deviates from the usual thermalization. This nonthermal stabilization happens as a non-Markovian effect.
Abstract Quantum collision models normally consist of a system interacting with a set of ancillary units representing the environment. While these ancillary systems are usually assumed to be either two level systems or harmonic oscillators, in this work we move further and represent each ancillary system as a structured system, i.e. a system made out of two or more subsystems. We show how this scenario modifies the kind of master equation that one can obtain for the evolution of the open systems. Moreover, we are able to consider a situation where the ancilla state is thermal yet has some coherence. This allows the generation of coherence in the steady state of the open system and, thanks to the simplicity of the collision model, this allows us to better understand the thermodynamic cost of creating coherence in a system. Specifically, we show that letting the system interact with the coherent degrees of freedom requires a work cost, leading to the natural fulfillment of the first and second law of thermodynamics without the necessity of ad hoc formulations.
The study of thermal operations allows one to investigate the ultimate possibilities of quantum states and of nanoscale thermal machines. Whilst fairly general, these results typically do not apply to continuous variable systems and do not take into account that, in many practically relevant settings, system-environment interactions are effectively bilinear. Here we tackle these issues by focusing on Gaussian quantum states and channels. We provide a complete characterization of the most general Gaussian thermal operation acting on an arbitrary number of bosonic modes, which turn out to be all embeddable in a Markovian dynamics, and derive necessary and sufficient conditions for state transformations under such operations in the single-mode case, encompassing states with nonzero coherence in the energy eigenbasis (i.e., squeezed states). Our analysis leads to a no-go result for the technologically relevant task of algorithmic cooling: We show that it is impossible to reduce the entropy of a system coupled to a Gaussian environment below its own or the environmental temperature, by means of a sequence of Gaussian thermal operations interspersed by arbitrary (even non-Gaussian) unitaries. These findings establish fundamental constraints on the usefulness of Gaussian resources for quantum thermodynamic processes.
We consider a particle in the approximation of a harmonic oscillator, coupled linearly to a field modeling an environment. The field is described by an infinite set of harmonic oscillators, and the system (particle--field) is considered in a cavity at thermal equilibrium. We employ the notions of bare and dressed coordinates to study the time evolution of the occupation number. With dressed coordinates no renormalization procedure is required, leading directly to a finite result. In particular, for a large time, the occupation number of the particle becomes independent of its initial value. So we have a Markovian process, describing the particle thermalization with the environment.
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of "classicalizing" behavior in the approach to thermal equilibrium are briefly considered.