Universality of photon counting below a local bifurcation threshold

Arndt, Lisa; Hassler, Fabian

doi:10.1103/physreva.103.023506

Cited by 9 publications

(10 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So far, there have been several approaches to include the effect of higher-order correlation including exact diagonalization, diagrammatic expansions, functional renormalization group, numerical or density matrix renormalization group analysis, and phase space methods. [35][36][37][38][39][40][41][42][43][44].…”

Section: Gaussian Approximation and Beyond The Mf Resultsmentioning

confidence: 99%

Noise-Resilient Phase Transitions and Limit-Cycles in Coupled Kerr Oscillators

Alaeian¹,

Soriente²,

Najafi³

et al. 2021

Preprint

View full text Add to dashboard Cite

Driven-dissipative quantum many-body systems have been the subject of many studies in recent years. They possess unique, novel classes of dissipation-stabilized quantum many-body phases including the limit cycle. For a long time it has been speculated if such a behavior, a recurring phenomenon in non-linear classical and quantum many-body systems, can be classified as a time crystal. However, the robustness of these periodic dynamics, against quantum fluctuations is an open question. In this work we seek the answer to this question in a canonical yet important system, i.e., a multi-mode cavity with self and cross-Kerr non-linearity, including the fluctuation effects via higher order correlations. Employing the Keldysh path integral, we investigate the Green's function and correlation of the cavity modes in different regions. Furthermore, we extend our analysis beyond the mean-field by explicitly including the effect of two-body correlations via the 2 nd -cumulant expansion. Our results shed light on the emergence of dissipative phase transitions in open quantum systems and clearly indicate the robustness of limit-cycle oscillations in the presence of the quantum fluctuations.

show abstract

Section: Gaussian Approximation and Beyond The Mf Resultsmentioning

confidence: 99%

Noise-Resilient Phase Transitions and Limit-Cycles in Coupled Kerr Oscillators

Alaeian¹,

Soriente²,

Najafi³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Therefore, it is quite natural to examine the validity of MF-predicated phase boundaries and delineate the truncation artifacts from the true phase transitions. So far, there have been several approaches to include the effect of higher-order correlation including exact diagonalization, diagrammatic expansions, functional renormalization group, numerical or density matrix renormalization group analysis, and phase space methods [63][64][65][66][67][68][69][70][71][72].…”

Section: Beyond the Mf And The Phase Robustnessmentioning

confidence: 99%

Noise-resilient phase transitions and limit-cycles in coupled Kerr oscillators

Alaeian,

Soriente,

Najafi

et al. 2024

New J. Phys.

View full text Add to dashboard Cite

n recent years, there has been considerable focus on exploring driven-dissipative quantum systems, as they exhibit distinctive dissipation-stabilized phases. Among them, dissipative time crystal isa unique phase emerging as a shift from disorder or stationary states to periodic behaviors. However,understanding the resilience of these non-equilibrium phases against quantum fluctuations remainsunclear. This study addresses this query within a canonical parametric quantum optical system,specifically, a multi-mode cavity with self- and cross-Kerr non-linearity. Using mean-field theory weobtain the phase diagram and delimit the parameter ranges that stabilize a non-stationary limit-cycle phase. Leveraging the Keldysh formalism, we study the unique spectral features of each phase.Further, we extend our analyses beyond the mean-field theory by explicitly accounting for higher-order correlations through cumulant expansions. Our findings unveil insights into the modificationsof the open quantum systems phases, underscoring the significance of quantum correlations in non-equilibrium steady states. Importantly, our results conclusively demonstrate the resilience of thenon-stationary phase against quantum fluctuations, rendering it a dissipation-induced genuinequantum synchronous phase.

show abstract

“…Often, one is interested in the statistics of some observables O, such as the photon current. We can access the statistics by including a source term in the Liouvillian superoperator [18,19]…”

Section: Counting Statisticsmentioning

confidence: 99%

Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries

Kim,

Hassler

2023

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

Open quantum systems that interact with a Markovian environment can be described by a Lindblad master equation. The generator of time-translation is given by a Liouvillian superoperator L acting on the density matrix of the system. As the Fock space for a single bosonic mode is already infinite-dimensional, the diagonalization of the Liouvillian has to be done on the creation- and annihilation-superoperators, a process called `third quantization'. We propose a method to solve the Liouvillian for quadratic systems using a single symplectic transformation. We show that the non-Hermitian effective Hamiltonian of the system, next to incorporating the dynamics of the system, is a tool to analyze its symmetries. As an example, we use the effective Hamiltonian to formulate a PT-`symmetry' of an open system. We describe how the inclusion of source terms allows us to obtain the cumulant generating function for observablessuch as the photon current.

show abstract

Universality of photon counting below a local bifurcation threshold

Cited by 9 publications

References 45 publications

Noise-Resilient Phase Transitions and Limit-Cycles in Coupled Kerr Oscillators

Noise-Resilient Phase Transitions and Limit-Cycles in Coupled Kerr Oscillators

Noise-resilient phase transitions and limit-cycles in coupled Kerr oscillators

Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries

Contact Info

Product

Resources

About