Continuous stochastic Schrödinger equations and localization

Rigo, M.; Mota-Furtado, F.; O’Mahony, Patrick

doi:10.1088/0305-4470/30/21/026

Cited by 28 publications

(43 citation statements)

References 37 publications

(89 reference statements)

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“…Fortunately, if the Hamiltonian for the mechanical dynamics is no more than quadratic in the position and momentum, and the initial state of the system is Gaussian, the SME may be solved analytically, since it remains Gaussian at all times [27]. Taking the initial state to be Gaussian is also sensible, because there is reason to believe that non-classical states evolve rapidly to Gaussians due to environmental interactions, of which the measurement process is one example [28,29]. A quantum mechanical Gaussian state is uniquely determined by its mean values and covariance matrix (see for example [30]), just as is the case for classical probability distributions and so we only need to find equations for these variables in order to fully describe the evolution of the conditioned state.…”

Section: Estimation and Feedbackmentioning

confidence: 99%

Feedback control of quantum systems using continuous state estimation

1999

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We present a formulation of feedback in quantum systems in which the best estimates of the dynamical variables are obtained continuously from the measurement record, and fed back to control the system. We apply this method to the problem of cooling and confining a single quantum degree of freedom, and compare it to current schemes in which the measurement signal is fed back directly in the manner usually considered in existing treatments of quantum feedback. Direct feedback may be combined with feedback by estimation, and the resulting combination, performed on a linear system, is closely analogous to classical LQG control theory with residual feedback. 42.50.Lc,03.65.Bz,42.50.Ct

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Section: Estimation and Feedbackmentioning

confidence: 99%

Feedback control of quantum systems using continuous state estimation

1999

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“…In this case the measurement current is white noise. In [21] it was noted that where a Lindblad operator is hermitian there exists an unravelling of the master equation which does not localize the conditioned state. The reason for this is clear in this context, such an unravelling corresponds to a measurement in which the observer obtains no information about the system state.…”

Section: B Steady State Conditioned Variancesmentioning

confidence: 99%

State determination in continuous measurement

et al. 1999

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The possibility of determining the state of a quantum system after a continuous measurement of position is discussed in the framework of quantum trajectory theory. Initial lack of knowledge of the system and external noises are accounted for by considering the evolution of conditioned density matrices under a stochastic master equation. It is shown that after a finite time the state of the system is a pure state and can be inferred from the measurement record alone. The relation to emerging possibilities for the continuous experimental observation of single quanta, as for example in cavity quantum electrodynamics, is discussed.42.50. Lc,03.65.Bz,42.50.Ct

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“…An unraveling consists of a stochastic dynamics for the pure states |ψ of the system, which reproduces the ME under stochastic average. Here, we focus on the case of a diffusive unraveling, associated to a Stochastic Differential Equation (SDE) in the form [19][20][21][22][23][24] …”

Section: Unraveling Of Cp Semigroupsmentioning

confidence: 99%

Stochastic unraveling of positive quantum dynamics

2017

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Stochastic unravelings represent a useful tool to describe the dynamics of open quantum systems, and standard methods, such as quantum state diffusion (QSD), call for the complete positivity of the open-system dynamics. Here, we present a generalization of QSD, which also applies to positive, but not completely positive evolutions. The rate and the action of the diffusive processes involved in the unraveling are obtained by applying a proper transformation to the operators which define the master equation. The unraveling is first defined for semigroup dynamics and then extended to a definite class of time-dependent generators. We test our approach on a prototypical model for the description of exciton transfer, keeping track of relevant phenomena, which are instead disregarded within the standard, completely positive framework.

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Continuous stochastic Schrödinger equations and localization

Cited by 28 publications

References 37 publications

Feedback control of quantum systems using continuous state estimation

Feedback control of quantum systems using continuous state estimation

State determination in continuous measurement

Stochastic unraveling of positive quantum dynamics

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