Correlation evolution in dilute Bose-Einstein condensates after quantum quenches

Pietraszewicz, Joanna; Stobińska, Magdalena; Deuar, P.

doi:10.1103/physreva.99.023620

Cited by 8 publications

(9 citation statements)

References 42 publications

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“…Its speed is approximately 2J, twice the tunnelling rate. Correlation waves often travel at twice the characteristic speed for single particles [25,97,114], so this is not unexpected. However, the speed is clearly not related to the superfluid speed of sound, here ∼ U n j , which is far lower.…”

Section: Correlation Dynamics In the Stationary Statementioning

confidence: 94%

“…appearing in the X j are calculated just once at the beginning of the entire procedure for making the full ∆t step. Other noise input can change the expressions (114).…”

Section: A1 Integration Algorithmmentioning

confidence: 99%

“…Sumarizing, the algorithm used for the simulations of Sec. 7 consists of (108), ( 109), ( 112)- (114).…”

Section: A1 Integration Algorithmmentioning

confidence: 99%

“…The weak variant is more commonly used in practice and sufficient to obtain overall stable and accurate integration. It is what is applied in (114) and the calculations of Sec. 7.…”

Section: A2 Timestep Autocorrelation Correctionmentioning

confidence: 99%

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Multi-time correlations in the positive-P, Q, and doubled phase-space representations

Deuar

2021

Quantum

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A number of physically intuitive results for the calculation of multi-time correlations in phase-space representations of quantum mechanics are obtained. They relate time-dependent stochastic samples to multi-time observables, and rely on the presence of derivative-free operator identities. In particular, expressions for time-ordered normal-ordered observables in the positive-P distribution are derived which replace Heisenberg operators with the bare time-dependent stochastic variables, confirming extension of earlier such results for the Glauber-Sudarshan P. Analogous expressions are found for the anti-normal-ordered case of the doubled phase-space Q representation, along with conversion rules among doubled phase-space s-ordered representations. The latter are then shown to be readily exploited to further calculate anti-normal and mixed-ordered multi-time observables in the positive-P, Wigner, and doubled-Wigner representations. Which mixed-order observables are amenable and which are not is indicated, and explicit tallies are given up to 4th order. Overall, the theory of quantum multi-time observables in phase-space representations is extended, allowing non-perturbative treatment of many cases. The accuracy, usability, and scalability of the results to large systems is demonstrated using stochastic simulations of the unconventional photon blockade system and a related Bose-Hubbard chain. In addition, a robust but simple algorithm for integration of stochastic equations for phase-space samples is provided.

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Section: Correlation Dynamics In the Stationary Statementioning

confidence: 94%

“…appearing in the X j are calculated just once at the beginning of the entire procedure for making the full ∆t step. Other noise input can change the expressions (114).…”

Section: A1 Integration Algorithmmentioning

confidence: 99%

“…Sumarizing, the algorithm used for the simulations of Sec. 7 consists of (108), ( 109), ( 112)- (114).…”

Section: A1 Integration Algorithmmentioning

confidence: 99%

“…The weak variant is more commonly used in practice and sufficient to obtain overall stable and accurate integration. It is what is applied in (114) and the calculations of Sec. 7.…”

Section: A2 Timestep Autocorrelation Correctionmentioning

confidence: 99%

See 2 more Smart Citations

Multi-time correlations in the positive-P, Q, and doubled phase-space representations

Deuar

2021

Quantum

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show abstract

“…Its speed is approximately 2J, twice the tunnelling rate. Correlation waves often travel at twice the characteristic speed for single particles [84][85][86], so this is not unexpected. However, the speed is clearly not related to the superfluid speed of sound, here ∼ U n j , which is far lower.…”

Section: E Correlation Dynamics In the Stationary Statementioning

confidence: 94%

Multi-time correlations in the positive-P, Q, and doubled phase-space representations

Deuar

2020

Preprint

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A number of physically intuitive results for the calculation of multi-time correlations in phasespace representations of quantum mechanics are obtained. They relate time-dependent stochastic samples to multi-time observables, and rely on the presence of derivative-free operator identities. In particular, expressions for time-and normal-ordered observables in the positive-P distribution are derived which replace Heisenberg operators with the bare time-dependent stochastic variables, confirming extension of earlier such results for the Glauber-Sudarshan P. Analogous expressions are found for the anti-normal-ordered case in the Q and doubled phase-space Q representations, along with conversion rules among doubled phase-space s-ordered representations. The latter are then shown to be readily exploited to further calculate anti-normal and mixed-ordered observables in the positive-P, Wigner, and doubled-Wigner representations. Which mixed-order observables are amenable and which not is indicated, and explicit tallies are given up to 4th order. Overall then, the theory of quantum multi-time observables in phase-space representations is extended, allowing non-perturbative treatment of many cases. The accuracy, usability, and scalability of the results to large systems is demonstrated using stochastic simulations of the unconventional photon blockade system, and a related Bose-Hubbard chain.

show abstract

Effects of quenching protocols based on parametric oscillators

Gianfreda

Landolfi

2021

Chinese Journal of Physics

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Correlation evolution in dilute Bose-Einstein condensates after quantum quenches

Cited by 8 publications

References 42 publications

Multi-time correlations in the positive-P, Q, and doubled phase-space representations

Multi-time correlations in the positive-P, Q, and doubled phase-space representations

Multi-time correlations in the positive-P, Q, and doubled phase-space representations

Effects of quenching protocols based on parametric oscillators

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