Photon correlations in a two-site nonlinear cavity system under coherent drive and dissipation

Abstract

We calculate the normalized second-order correlation function for a system of two tunnel-coupled photonic resonators, each one exhibiting a single-photon nonlinearity of the Kerr type. We employ a full quantum formulation: the master equation for the model, which takes into account both a coherent continuous drive and radiative as well as non-radiative dissipation channels, is solved analytically in steady state through a perturbative approach, and the results are compared to exact numerical simulations. The degree of second-order coherence displays values between 0 and 1, and divides the diagram identified by the two energy scales of the system -the tunneling and the nonlinear Kerr interaction -into two distinct regions separated by a crossover. When the tunneling term dominates over the nonlinear one, the system state is delocalized over both cavities and the emitted light is coherent. In the opposite limit, photon blockade sets in and the system shows an insulator-like state with photons locked on each cavity, identified by antibunching of emitted light.

Two coupled nonlinear cavities in a driven-dissipative environment

“…For the closed system, the physics of double well has been studied in great detail [21][22][23][24][25][26], giving rise to phenomena such as the Josephson effect, matter wave interference and self-trapped and symmetry breaking states, among others. For open systems, studies of two coupled cavities have appeared in several contexts in both theory [27][28][29][30][31][32][33][34][35] and experiment [17,18,36,37]. For an enddriven cavity, studies focused on the topics of unconventional photon blockade [31][32][33] and multi-stability [17], among others.…”

“…For an enddriven cavity, studies focused on the topics of unconventional photon blockade [31][32][33] and multi-stability [17], among others. For symmetrically driven cavities, studies appeared on quantum correlations [29], classical to quantum phase transitions for a Jaynes-Cummings dimer [18], and symmetry breaking for incoherent drives [36], among others.…”

Multiphoton blockades in pulsed regimes beyond stationary limits

“…In this respect, strong nonlinearities on the few-photon level can be produced by interaction between photons and an atom in a cavity [6][7][8][9], in systems with interacting photons or polaritons in arrays of cavities coupled to atoms or qubits [10][11][12][13], in optomechanical systems and Kerr type nonlinear cavities [14][15][16].…”

Ab initiodescription of nonlinear dynamics of coupled microdisk resonators with application to self-trapping dynamics

“…At the same time, the nonlinear optics of coupled microresonators is still in its infancy. While lately there was a significant uptick in theoretical attention to this field [15][16][17][18], no experiments in this area have yet been reported. This rise of interest to optically coupled resonators is fueled by expectations that these systems would allow for a convenient experimental studies by optical means of some important nonlinear effects of generic nature.…”

“…This system is significantly simpler for experimental realization than those considered in Ref. [15,17,18], and we expect, therefore, that this work will motivate experimental studies of nonlinear optical properties of microdisks and other coupled WGM resonators.…”