共查询到20条相似文献,搜索用时 312 毫秒
1.
We analyze the unravelling of the quantum optical master equation at finite temperature due to direct, continuous, general-dyne detection of the environment. We first express the general-dyne Positive Operator Valued Measure (POVM) in terms of the eigenstates of a non-Hermitian operator associated to the general-dyne measurement. Then we derive the stochastic master equation obtained by considering the interaction between the system and a reservoir at thermal equilibrium, which is measured according to the POVM previously determined. Finally, we present a feasible measurement scheme, which reproduces general-dyne detection for any value of the parameter characterizing the stochastic master equation. 相似文献
2.
Philippe Lewalle Sreenath K. Manikandan Cyril Elouard Andrew N. Jordan 《Contemporary Physics》2020,61(1):26-50
We review the continuous monitoring of a qubit through its spontaneous emission, at an introductory level. Contemporary experiments have been able to collect the fluorescence of an artificial atom in a cavity and transmission line, and then make measurements of that emission to obtain diffusive quantum trajectories in the qubit's state. We give a straightforward theoretical overview of such scenarios, using a framework based on Kraus operators derived from a Bayesian update concept; we apply this flexible framework across common types of measurements including photodetection, homodyne, and heterodyne monitoring and illustrate its equivalence to the stochastic master equation formalism throughout. Special emphasis is given to homodyne (phase-sensitive) monitoring of fluorescence. The examples we develop are used to illustrate basic methods in quantum trajectories, but also to introduce some more advanced topics of contemporary interest, including the arrow of time in quantum measurement, and trajectories following optimal measurement records derived from a variational principle. The derivations we perform lead directly from the development of a simple model to an understanding of recent experimental results. 相似文献
3.
We derive a master equation describing the evolution of a quantum system subjected to a sequence of observations. These measurements occur randomly at a given rate and can be of a very general form. As an example, we analyse the effects of these measurements on the evolution of a two-level atom driven by an electromagnetic field. For the associated quantum trajectories we find Rabi oscillations, Zeno-effect type behaviour and random telegraph evolution spawned by mini quantum jumps as we change the rates and strengths of measurement. 相似文献
4.
Fluctuation relations establish rigorous identities for the nonequilibrium averages of observables. Starting from a general transport master equation with time-dependent rates, we employ the stochastic path integral approach to study statistical fluctuations around such averages. We show how under nonequilibrium conditions, rare realizations of transport observables are crucial and imply massive fluctuations that may completely mask such identities. Quantitative estimates for these fluctuations are provided. We illustrate our results on the paradigmatic example of a mesoscopic RC circuit. 相似文献
5.
In recent years, quantum collision models, sometimes dubbed repeated interaction models, have gained much attention due to their simplicity and their capacity to convey ideas without resorting to technical complications typical of many approaches and techniques used in the field of open quantum systems. In this tutorial, we show how to use these models, highlighting their strengths and some technical subtleties often overlooked in the literature. We do this by deriving the Markovian master equation and comparing the standard collisional derivation with the standard microscopic one. We then use the collision model to derive the master equation of a two-level system interacting with either a bosonic or fermionic bath to give the reader a flavour of the real use of the model. 相似文献
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7.
A quantum system \({\mathcal S}\) undergoing continuous time measurement is usually described by a jump-diffusion stochastic differential equation. Such an equation is called a quantum filtering equation (or quantum stochastic master equation) and its solution is called a quantum filter (or quantum trajectory). This solution describes the evolution of the state of \({\mathcal S}\) . In the context of quantum non demolition measurement, we investigate the large time behavior of this solution. It is rigorously shown that, for large time, this solution behaves as if a direct Von Neumann measurement has been performed at time 0. In particular the solution converges to a random pure state which can be directly linked to the wave packet reduction postulate. Using the theory of Girsanov transformation, we obtain the explicit rate of convergence towards this random state. The problem of state estimation (used in experiment) is also investigated. 相似文献
8.
Esteban Calzetta Albert Roura Enric Verdaguer 《International Journal of Theoretical Physics》2001,40(12):2317-2332
The master equation for a linear open quantum system in a general environment is derived using a stochastic approach. This is an alternative derivation to that of Hu, Paz, and Zhang, which was based on the direct computation of path integrals, or to that of Halliwell and Yu, based on the evolution of the Wigner function for a linear closed quantum system. We first show by using the influence functional formalism that the reduced Wigner function for the open system coincides with a distribution function resulting from averaging both over the initial conditions and the stochastic source of a formal Langevin equation. The master equation for the reduced Wigner function can then be deduced as a Fokker-Planck equation obtained from the formal Langevin equation. 相似文献
9.
Joseph W. Baron Antonio F. Peralta Tobias Galla Raúl Toral 《Entropy (Basel, Switzerland)》2022,24(10)
The conventional voter model is modified so that an agent’s switching rate depends on the ‘age’ of the agent—that is, the time since the agent last switched opinion. In contrast to previous work, age is continuous in the present model. We show how the resulting individual-based system with non-Markovian dynamics and concentration-dependent rates can be handled both computationally and analytically. The thinning algorithm of Lewis and Shedler can be modified in order to provide an efficient simulation method. Analytically, we demonstrate how the asymptotic approach to an absorbing state (consensus) can be deduced. We discuss three special cases of the age-dependent switching rate: one in which the concentration of voters can be approximated by a fractional differential equation, another for which the approach to consensus is exponential in time, and a third case in which the system reaches a frozen state instead of consensus. Finally, we include the effects of a spontaneous change of opinion, i.e., we study a noisy voter model with continuous ageing. We demonstrate that this can give rise to a continuous transition between coexistence and consensus phases. We also show how the stationary probability distribution can be approximated, despite the fact that the system cannot be described by a conventional master equation. 相似文献
10.
Z. Haba 《International Journal of Theoretical Physics》1996,35(12):2461-2473
We consider a class of models describing a quantum oscillator in interaction with an environment. We show that models of continuous spontaneous localization based on a stochastic Schrödinger equation can be derived as an approximation to purely deterministic Hamiltonian systems. 相似文献
11.
During a continuous measurement, quantum systems can be described by a stochastic Schrödinger equation which, in the appropriate limit, reproduces the von Neumann wave-function collapse. The average behavior on the ensemble of all measurement results is described by a master equation obtained from a general model of measurement apparatus consisting of an infinite set of degrees of freedom linearly interacting with the measured system and in contact with a reservoir at high temperature. 相似文献
12.
The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test
the effect, Itanoet al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of
short laser pulses. Using dynamical considerations, we give an explanation why the projection postulate can be applied in
good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss
how far the experiment of Itanoet al. can be considered as a test of the quantum Zeno effect. We also analyze a new possible experiment on a single atom where
stochastic light and dark periods can be interpreted as manifestation of the quantum Zeno effect. We show that the measurement
point of view gives a quick and intuitive understanding of experiments of the above type, although a finer analysis has to
take the corrections into account. 相似文献
13.
E. D. Vol 《International Journal of Theoretical Physics》2009,48(2):392-402
In the present paper we propose the way of passage from quantum theory of continuous measurements based on the Lindblad equation
to its “classical” analog. The last one describes the influence of continuous measurement on the behavior of macroscopical
Markov system. Such theory can be represented in the form of the Fokker-Planck equation for the distribution function of measured
system. The diffusion tensor of this equation is uniquely determined by a type of the measured quantity. As the example of
using of the approach proposed we describe the stationary states of linear dissipative systems induced by measurements in
them. We consider possible qualitative effects connected with measurements also. In particular we demonstrate on the simple
example, how in the macroscopic system, consisting of noninteracting parts, measurement of global integral of motion results
in relaxation to the quasi-thermodynamic equilibrium between parts of the system. The “temperature” of such state is determined
by the total energy of the system and by mean value of measured quantity.
相似文献
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Summary In this paper we formualte a master equation approach describing a D+T thermonuclear plasma in a lumped phase space. From
the first moments of this master equation and performing the pass to the continuous limit the evolution equations for the
expected phase space ion densities emerge. Also we have obtained the evolution equations of the equal time correlation and
covariance functions. Finally we have deduced the hydrodynamic equations that arise from a master equation approach. 相似文献
16.
We show how the quantum analog of the Fokker-Planck equation for describing
Brownian motion can be obtained as the diffusive limit of the quantum linear
Boltzmann equation. The latter describes the quantum dynamics of a tracer
particle in a dilute, ideal gas by means of a translation-covariant master
equation. We discuss the type of approximations required to obtain the
generalized form of the Caldeira-Leggett master equation, along with their
physical justification. Microscopic expressions for the diffusion and
relaxation coefficients are obtained by analyzing the limiting form of the
equation in both the Schr?dinger and the Heisenberg picture. 相似文献
17.
Recent fluorescence spectroscopy measurements of single-enzyme kinetics have shown that enzymatic turnovers form a renewal stochastic process in which the inverse of the mean waiting time between turnovers follows the Michaelis-Menten equation. We study enzyme kinetics at physiologically relevant mesoscopic concentrations using a master equation. From the exact solution of the master equation we find that the waiting times are neither independent nor identically distributed, implying that enzymatic turnovers form a nonrenewal stochastic process. The inverse of the mean waiting time shows strong departure from the Michaelis-Menten equation. The waiting times between consecutive turnovers are anticorrelated, where short intervals are more likely to be followed by long intervals and vice versa. Correlations persist beyond consecutive turnovers indicating that multiscale fluctuations govern enzyme kinetics. 相似文献
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19.
C. van den Broeck 《Physics letters. A》1982,90(3):119-122
We derive the multivariate master equation describing reaction diffusion systems from a discrete form master equation in phase space, assuming that the elastic collisions of the chemically active substances with the inert carrier gas have relaxed. In this state of collisional equilibrium the stochastic operator modelling the displacement of the particles between spatial cells reduces to the random wall operator and the reactive collision term yields the usual birth and death operator. Correlation functions are derived and their validity is discussed. 相似文献
20.
A. Barchielli 《International Journal of Theoretical Physics》1993,32(12):2221-2233
In recent years a consistent theory describing measurements continuous in time in quantum mechanics has been developed. The result of such a measurement is atrajectoryfor one or more quantities observed with continuity in time. Applications are connected especially with detection theory in quantum optics. In such a theory of continuous measurements one can ask what is the state of the system given that a certain trajectory up to timet has been observed. The response to this question is the notion ofa posteriori states and afilteringequation governing the evolution of such states: this turns out to be a nonlinear stochastic differential equation for density matrices or for pure vectors. The driving noise appearing in such an equation is not an external one, but its probability law is determined by the system itself (it is the probability measure on the trajectory space given by the theory of continuous measurements). 相似文献