The Calculation of Correlation Functions in the Quantum-state Diffusion Model

Sondermann, Dirk G

doi:10.1080/09500349514551451

Cited by 6 publications

(11 citation statements)

References 4 publications

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“…This algorithm and its generalizations are quite popular in the quantum optics community, where they have been applied to a variety of problems, see Refs. [1][2][3][4][5][6].…”

Section: Propagation Of Proper State Operatorsmentioning

confidence: 99%

Stochastic wave-function simulation of two-time correlation functions

Felbinger

Wilkens

1999

Journal of Modern Optics

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“…This algorithm and its generalizations are quite popular in the quantum optics community, where they have been applied to a variety of problems, see Refs. [1][2][3][4][5][6].…”

Section: Propagation Of Proper State Operatorsmentioning

confidence: 99%

Stochastic wave-function simulation of two-time correlation functions

Felbinger

Wilkens

1999

Journal of Modern Optics

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“…(31) to determine the time evolution of the probability distribution of the total system if the initial probability distribution is given by Eq. (21). For the propagated distribution P [Ψ, t 0 + τ ] we simply obtain…”

Section: Time Evolution Of the Total System In Second Order Perturbatmentioning

confidence: 99%

Stochastic wave-function approach to the calculation of multitime correlation functions of open quantum systems

1997

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Within the framework of probability distributions on projective Hilbert space, a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave-function description of an open quantum system coupled to an environment consisting of an ensemble of harmonic oscillators in arbitrary pure or mixed states. It is shown that matrix elements of reduced Heisenberg picture operators and general time-ordered correlation functions can be expressed by time-symmetric expectation values of extended operators in a doubled Hilbert space. This representation allows the construction of a stochastic process in the doubled Hilbert space which enables a determination of arbitrary matrix elements and correlation functions. The numerical efficiency of the resulting stochastic simulation algorithm is investigated and compared with an alternative Monte Carlo wave function method proposed first by Dalibard, Castin, and Mo "lmer ͓Phys. Rev. Lett. 68, 580 ͑1992͔͒. By means of a standard example the suggested algorithm is shown to be more efficient numerically and to converge faster. Finally, some specific examples from quantum optics are presented in order to illustrate the proposed method, such as the coupling of a system to a vacuum, a squeezed vacuum within a finite solid angle, and a thermal mixture of coherent states.

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“…Since unravelings of the master equation do not generically preserve the trace, this feature will arise in any similar derivation. This might be one argument for using an unraveling specifically chosen to preserve the trace, such as that used by Gisin in his discussion of a Heisenberg picture for QSD [7,8]. In any case, the desired relation does hold in the mean:…”

Section: Spectra and Time Correlations In Qsdmentioning

confidence: 99%

“…Sondermann [8], using the same stochastic equations, has suggested another definition for time correlation functions. In both cases it is difficult to relate this to the usual QSD formalism.…”

Section: Introductionmentioning

confidence: 99%

Quantum state diffusion and time correlation functions

Brun

Gisin

1996

Journal of Modern Optics

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In computing the spectra of quantum mechanical systems one encounters the Fourier transforms of time correlation functions, as given by the quantum regression theorem for systems described by master equations. Quantum state diffusion (QSD) gives a useful method of solving these problems by unraveling the master equation into stochastic trajectories; but there is no generally accepted definition of a time correlation function for a single QSD trajectory. In this paper we show how QSD can be used to calculate these spectra directly; by formally solving the equations which arise, we arrive at a natural definition for a two-time correlation function in QSD, which depends explicitly on both the stochastic noise of the particular trajectory and the time of measurement, and which agrees in the mean with the ensemble average definition of correlation functions.

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The Calculation of Correlation Functions in the Quantum-state Diffusion Model

Cited by 6 publications

References 4 publications

Stochastic wave-function simulation of two-time correlation functions

Stochastic wave-function simulation of two-time correlation functions

Stochastic wave-function approach to the calculation of multitime correlation functions of open quantum systems

Quantum state diffusion and time correlation functions

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