Ergodicity of quantum trajectory detection records

JD Cresser

Ergodicity of quantum trajectory detection records

JD Cresser^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

Abstract

An examination is made of the conditions under which the detection record generated by the quantum trajectory simulation of the output of a detector continuously monitoring an open Markovian system is ergodic, i.e. where the time averages of a single realization of such a record will yield the same result as an ensemble average over many such realizations. It is shown, in the case of discrete counting, that ergodicity holds in the mean and to first order if the long time steady state of the system is independent of the initial state of the system. A two-photon dissipative process is used as an example of a situation in which ergodicity does not hold.

Original language	English
Title of host publication	DIRECTIONS IN QUANTUM OPTICS
Editors	HJ Carmichael, RJ Glauber, MO Scully
Place of Publication	Berlin; Heidelberg
Publisher	Springer, Springer Nature
Pages	358-369
Number of pages	12
ISBN (Print)	3540411879
Publication status	Published - 2001
Event	TAMU-ONR Workshop on Quantum Optics - JACKSON Duration: 26 Jul 1999 → 30 Jul 1999

Publication series

Name	LECTURE NOTES IN PHYSICS
Publisher	SPRINGER-VERLAG BERLIN
Volume	561
ISSN (Print)	0075-8450

Conference

Conference	TAMU-ONR Workshop on Quantum Optics
City	JACKSON
Period	26/07/99 → 30/07/99

Keywords

STOCHASTIC DIFFERENTIAL-EQUATIONS
LIGHT

Cite this

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title = "Ergodicity of quantum trajectory detection records",

abstract = "An examination is made of the conditions under which the detection record generated by the quantum trajectory simulation of the output of a detector continuously monitoring an open Markovian system is ergodic, i.e. where the time averages of a single realization of such a record will yield the same result as an ensemble average over many such realizations. It is shown, in the case of discrete counting, that ergodicity holds in the mean and to first order if the long time steady state of the system is independent of the initial state of the system. A two-photon dissipative process is used as an example of a situation in which ergodicity does not hold.",

keywords = "STOCHASTIC DIFFERENTIAL-EQUATIONS, LIGHT",

author = "JD Cresser",

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pages = "358--369",

editor = "HJ Carmichael and RJ Glauber and MO Scully",

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T1 - Ergodicity of quantum trajectory detection records

AU - Cresser, JD

PY - 2001

Y1 - 2001

N2 - An examination is made of the conditions under which the detection record generated by the quantum trajectory simulation of the output of a detector continuously monitoring an open Markovian system is ergodic, i.e. where the time averages of a single realization of such a record will yield the same result as an ensemble average over many such realizations. It is shown, in the case of discrete counting, that ergodicity holds in the mean and to first order if the long time steady state of the system is independent of the initial state of the system. A two-photon dissipative process is used as an example of a situation in which ergodicity does not hold.

AB - An examination is made of the conditions under which the detection record generated by the quantum trajectory simulation of the output of a detector continuously monitoring an open Markovian system is ergodic, i.e. where the time averages of a single realization of such a record will yield the same result as an ensemble average over many such realizations. It is shown, in the case of discrete counting, that ergodicity holds in the mean and to first order if the long time steady state of the system is independent of the initial state of the system. A two-photon dissipative process is used as an example of a situation in which ergodicity does not hold.

KW - STOCHASTIC DIFFERENTIAL-EQUATIONS

KW - LIGHT

M3 - Conference proceeding contribution

SN - 3540411879

T3 - LECTURE NOTES IN PHYSICS

SP - 358

EP - 369

BT - DIRECTIONS IN QUANTUM OPTICS

A2 - Carmichael, HJ

A2 - Glauber, RJ

A2 - Scully, MO

PB - Springer, Springer Nature

CY - Berlin; Heidelberg

T2 - TAMU-ONR Workshop on Quantum Optics

Y2 - 26 July 1999 through 30 July 1999

ER -

Ergodicity of quantum trajectory detection records

Abstract

Publication series

Conference

Keywords

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Cite this