scholarly journals Extractable quantum work from a two-mode Gaussian state in a noisy channel

2021 ◽  
Author(s):  
Marina Cuzminschi ◽  
Isar Aurelian ◽  
Alexei Zubarev
Keyword(s):  
Master Equation ◽  
Time Evolution ◽  
Open System ◽  
Thermal State ◽  
Second Order ◽  
Heterodyne Detection ◽  
Gaussian State ◽  
Noisy Channel ◽  
Initial State ◽  
Lindblad Master Equation

Abstract We study a Szilard engine based on a Gaussian state of a system consisting of two bosonic modes placed in a noisy channel. As the initial state of the system is taken an entangled squeezed thermal state, and the quantum work is extracted by performing a measurement on one of the two modes. We use the Markovian Kossakowski-Lindblad master equation for describing the time evolution of the open system and the quantum work definition based on the second order R\'{e}nyi entropy to simulate the engine. We show that the extractable quantum work increases with the temperature of the reservoir and the squeezing between the modes, average numbers of thermal photons and frequencies of the modes. The work increases also with the strength of the measurement, attaining the maximal values in the case of a heterodyne detection. As well the extractable work is decreasing by increasing the squeezing parameter of the noisy channel and it oscillates with the phase of the squeezed thermal reservoir.

scholarly journals Extractable quantum work from a two-mode Gaussian state in a noisy channel

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Marina Cuzminschi ◽  
Alexei Zubarev ◽  
Aurelian Isar
Keyword(s):  
Open System ◽  
Thermal State ◽  
Heterodyne Detection ◽  
Gaussian State ◽  
Noisy Channel ◽  
Work Efficiency ◽  
Initial State ◽  
System Parameters ◽  
Information Work ◽  
Lindblad Master Equation

AbstractWe study a Szilard engine based on a Gaussian state of a system consisting of two bosonic modes placed in a noisy channel. As the initial state of the system is taken an entangled squeezed thermal state, and the quantum work is extracted by performing a measurement on one of the two modes. We use the Markovian Kossakowski-Lindblad master equation for describing the time evolution of the open system and the quantum work definition based on the second order Rényi entropy to simulate the engine. We also study the information-work efficiency of the Szilard engine as a function of the system parameters. The efficiency is defined as the ratio of the extractable work averaged over the measurement angle and the erasure work, which is proportional to the information stored in the system. We show that the extractable quantum work increases with the temperature of the reservoir and the squeezing between the modes, average numbers of thermal photons and frequencies of the modes. The work increases also with the strength of the measurement, attaining the maximal values in the case of a heterodyne detection. The extractable work is decreasing by increasing the squeezing parameter of the noisy channel and it oscillates with the phase of the squeezed thermal reservoir. The efficiency mostly has a similar behavior with the extractable quantum work evolution. However information-work efficiency decreases with temperature, while the quantity of the extractable work increases.

SOLVING THE MASTER EQUATION FOR AN ATTENUATED OR AMPLIFIED NONLINEAR OSCILLATOR VIA A SUPEROPERATOR METHOD

2002 ◽  
Vol 16 (15n16) ◽  
pp. 595-600 ◽  
Author(s):  
HUAI-XIN LU ◽  
ZENG-BING CHEN ◽  
YONG-DE ZHANG
Keyword(s):  
Master Equation ◽  
Time Evolution ◽  
Explicit Solution ◽  
Density Operator ◽  
Nonlinear Oscillator ◽  
Initial State

Using the decomposition theorm of superoperators, an explicit solution of the master equation for an attenuated or amplified nonlinear oscillator is presented. It is found that the time evolution of the density operator can be easily obtained from an arbitary initial state using this method.

scholarly journals On non-Markovian Time Evolution in Open Quantum Systems

2007 ◽  
Vol 14 (03) ◽  
pp. 265-274 ◽  
Author(s):  
Andrzej Kossakowski ◽  
Rolando Rebolledo
Keyword(s):  
Time Evolution ◽  
Open System ◽  
Open Quantum Systems ◽  
Vacuum State ◽  
Quantum Systems ◽  
Initial State ◽  
Completely Positive ◽  
Open Quantum

Non-Markovian reduced dynamics of an open system is investigated. In the case when the initial state of the reservoir is the vacuum state, an approximation is introduced which makes it possible to construct a reduced dynamics which is completely positive.

scholarly journals Application of Perturbation Theory to a Master Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
B. M. Villegas-Martínez ◽  
F. Soto-Eguibar ◽  
H. M. Moya-Cessa
Keyword(s):  
Perturbation Theory ◽  
Perturbation Method ◽  
Master Equation ◽  
Analytic Solution ◽  
Second Order ◽  
Exact Analytic Solution ◽  
Kerr Medium ◽  
Matrix Perturbation ◽  
Density Matrices ◽  
Lindblad Master Equation

We develop a matrix perturbation method for the Lindblad master equation. The first- and second-order corrections are obtained and the method is generalized for higher orders. The perturbation method developed is applied to the problem of a lossy cavity filled with a Kerr medium; the second-order corrections are estimated and compared with the known exact analytic solution. The comparison is done by calculating theQ-function, the average number of photons, and the distance between density matrices.

scholarly journals Quantum correlations for two coupled oscillators interacting with two heat baths

2020 ◽  
Vol 98 (4) ◽  
pp. 327-331
Author(s):  
I.V. Dudinetc ◽  
V.I. Man’ko
Keyword(s):  
Equilibrium State ◽  
Coupled Oscillators ◽  
Thermal State ◽  
Heat Bath ◽  
Quantum Correlations ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Gaussian State ◽  
Initial State ◽  
Dependent State

We study a system of two coupled oscillators (A oscillators), each of which linearly interact with their own heat bath consisting of a set of independent harmonic oscillators (B oscillators). The initial state of the A oscillator is taken to be coherent while the B oscillator is in a thermal state. We analyze the time-dependent state of the A oscillator, which is a two-mode Gaussian state. By making use of Simon’s separability criterion, we show that this state is separable for all times. We consider the equilibrium state of the A oscillator in detail and calculate its Wigner function.

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

Time evolution of structural changes and second‐order optical nonlinearity of hemicyanine doped silica film

1996 ◽  
Vol 69 (25) ◽  
pp. 3791-3793 ◽  
Author(s):  
Lei Xu ◽  
Liying Liu ◽  
Jing Yu ◽  
Wencheng Wang ◽  
Fuming Li
Keyword(s):  
Time Evolution ◽  
Structural Changes ◽  
Optical Nonlinearity ◽  
Silica Film ◽  
Second Order

scholarly journals Stimulated emission of relic gravitons and their super-Poissonian statistics

2019 ◽  
Vol 34 (23) ◽  
pp. 1950185 ◽  
Author(s):  
Massimo Giovannini
Keyword(s):  
Coherent State ◽  
Second Order ◽  
Stimulated Emission ◽  
Initial State ◽  
Einstein Distribution ◽  
Hubble Radius ◽  
Initial States ◽  
Bose Einstein ◽  
Final Degree ◽  
Poissonian Statistics

The degree of second-order coherence of the relic gravitons produced from the vacuum is super-Poissonian and larger than in the case of a chaotic source characterized by a Bose–Einstein distribution. If the initial state does not minimize the tensor Hamiltonian and has a dispersion smaller than its averaged multiplicity, the overall statistics is by definition sub-Poissonian. Depending on the nature of the sub-Poissonian initial state, the final degree of second-order coherence of the quanta produced by stimulated emission may diminish (possibly even below the characteristic value of a chaotic source) but it always remains larger than one (i.e. super-Poissonian). When the initial statistics is Poissonian (like in the case of a coherent state or for a mixed state weighted by a Poisson distribution) the degree of second-order coherence of the produced gravitons is still super-Poissonian. Even though the quantum origin of the relic gravitons inside the Hubble radius can be effectively disambiguated by looking at the corresponding Hanbury Brown–Twiss correlations, the final distributions caused by different initial states maintain their super-Poissonian character which cannot be altered.

scholarly journals Tracking Control of Variable Structure System Using Variable Boundary Layer

2001 ◽  
Vol 5 (6) ◽  
pp. 338-345
Author(s):  
Heejin Lee ◽  
Keyword(s):  
Boundary Layer ◽  
Tracking Control ◽  
Linear Time ◽  
Variable Structure ◽  
Second Order ◽  
Initial State ◽  
Variable Boundary ◽  
Variable Structure Systems ◽  
Variable Structure System ◽  
Arbitrary Initial State

In this paper, a new scheme is presented for the accurate tracking control of the second-order variable structure systems using the variable boundary layer. Up to now, variable structure controller(VSC) applying the variable boundary layer did not remove chattering from an arbitrary initial state of the system trajectory because VSC has used the fixed sliding surface. But, by using the linear time-varying sliding surfaces, the scheme has the robustness against chattering from all states. The suggested method can be applied to the second-order nonlinear systems with parameter uncertainty and extraneous disturbances, and have better tracking performance than the conventional method.To demonstrate the advantages of the proposed algorithm, it is applied to a two-link manipulator.

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