Fully Quantum Scalable Description of Driven-Dissipative Lattice Models

Deuar, P.; Ferrier, A.; Matuszewski, Michał; Orso, Giuliano; Szymańska, M. H.

doi:10.1103/prxquantum.2.010319

Cited by 23 publications

(16 citation statements)

References 84 publications

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“…Importantly, as we shall see, the same applies for its differently ordered analogues like the doubled-Wigner and doubled-Q. While the positive-P is known to be limited to short times for closed systems due to a noise amplification instability [38,66], this abates in dissipative systems [45,66]. Recent work has shown that a very broad range of driven dissipative Bose-Hubbard models can be simulated with the positive-P into and beyond the stationary state [45].…”

Section: Introductionmentioning

confidence: 72%

“…These were derived in [45] for the positive-P. Here the matrix elements of the one-particle Hamiltonian are H sp jj = −∆, H sp 12 = H 21 = −J, the drives are F 1 = F , F 2 = 0, while ξ j and ξ j are delta-correlated independent white real noises with variance…”

Section: Non Normally-ordered Correlations In the Positive-p Representationmentioning

confidence: 99%

“…Consider first the strong antibunching parameters studied in [10] and [45]: U = 0.0856, J = 3, ∆ = −0.275, γ = 1, F = 0.01. We will study the correlations primarily in the stationary state.…”

Section: Two-time Photon-photon Correlationsmentioning

confidence: 99%

“…It has been used for solving and simulating a multitude of problems in various physical fields: e.g. quantum optics [21,28,30,32,52,54,84,91,110], ultracold atoms [22,39,40,49,74,82,94,95,101,102,108,125,131,134,144], fermionic systems [6,7,27,29], spin systems [11,106,107], nuclear physics [137], dissipative systems in condensed matter [26,45,143], or cosmology [111]. The vast majority of such calculations so far have considered only equal time correlations and observables.…”

Section: Introductionmentioning

confidence: 99%

“…While the positive-P is known to be limited to short times for closed systems due to a noise amplification instability [38,66], this abates in dissipative systems [45,66]. Recent work has shown that a very broad range of driven dissipative Bose-Hubbard models can be simulated with the positive-P into and beyond the stationary state [45]. This covers systems of current interest such as micropillars, transmon qubits, and includes strong quantum effects such two-photon interference in the unconventional photon blockade [10,96], making its extension quite timely.…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 72%

Section: Non Normally-ordered Correlations In the Positive-p Representationmentioning

confidence: 99%

Section: Two-time Photon-photon Correlationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

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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Decoherence limiting the cost to simulate an anharmonic oscillator

Propp,

Ray,

DeBrota

et al. 2023

Phys. Rev. A

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Coherent pair injection as a route towards the enhancement of supersolid order in many-body bosonic models

Grigoriou,

Ning,

et al. 2024

Phys. Rev. A

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Over the past couple of decades, quantum simulators have been probing quantum many-body physics with unprecedented levels of control. So far, the main focus has been on the access to novel observables and dynamical conditions related to condensed-matter models. However, the potential of quantum simulators goes beyond the traditional scope of condensed-matter physics: Being based on driven-dissipative quantum optical platforms, quantum simulators allow for processes that typically are not considered in condensed-matter physics. These processes can enrich in unexplored ways the phase diagram of well-established models. Taking the extended Bose-Hubbard model as the guiding example, in this work we examine the impact of coherent pair injection, a process readily available in, for example, superconducting circuit arrays. The interest behind this process is that, in contrast to the standard injection of single excitations, it can be configured to preserve the U(1) symmetry underlying the model. We prove that this process favors both superfluid and density-wave order, as opposed to insulation or homogeneous states, thereby providing a route towards the access of lattice supersolidity. Published by the American Physical Society 2024

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Fully Quantum Scalable Description of Driven-Dissipative Lattice Models

Cited by 23 publications

References 84 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

Decoherence limiting the cost to simulate an anharmonic oscillator

Coherent pair injection as a route towards the enhancement of supersolid order in many-body bosonic models

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