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Acta Physica Sinica

The influences of detuning on the duperfluid-nsulator phase transition in coupled dissipative cavity arrays

Bao Jia, Lei Tan

Published Jan 1, 2014• 2 citations
Publisher

Abstract

In this paper, based on the effective Jaynes-Cummings-Hubbard model Hamiltonian in the presence of detuning, we use the mean-field and the perturbation theory to figure out the superfluid order parameter of the system. By which we find that detuning from resonance allows one to drive the system from the superfluid into the insulator state of the polaritons and the reverse. In addition, combining with the properties of transportation of coupled dissipative cavity arrays with detuning, we discuss the influence of detuning on the number of superfluid polaritons and the lifetime of superfluid states. It suggests that the number of the superfluid polaritons will increase to its maximum and then reduce again along the negative part of detuning, which is similar to the spectrum of the transmission.

DOI
10.7498/aps.63.084201

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In this paper, based on the effective Jaynes-Cummings-Hubbard model Hamiltonian in the presence of detuning, we use the mean-field and the perturbation theory to figure out the superfluid order parameter of the system. By which we find that detuning from resonance allows one to drive the system from the superfluid into the insulator state of the polaritons and the reverse. In addition, combining with the properties of transportation of coupled dissipative cavity arrays with detuning, we discuss the influence of detuning on the number of superfluid polaritons and the lifetime of superfluid states. It suggests that the number of the superfluid polaritons will increase to its maximum and then reduce again along the negative part of detuning, which is similar to the spectrum of the transmission.
The nature of the ground states for a system composed of two coupled cavities with each containing a pair of dipole-coupled two-level atoms are studied over a wide range of detunings and dipole coupling strengths. The cases for three limits of exact resonance, large positive and negative detunings are discussed, and four types of the ground states are revealed. Then the phase diagrams of the ground state are plotted by choosing three different "order parameters". We find that the phase space, determined by the combinative action of detuning and the dipole coupling strength, is divided into four regions. This is different from the general Bose-Hubbard model and more richer physics are presented in the two-site coupled cavities system. That is, the insulator region may be polaritonic or atomic and the superfluid region may be polaritonic or photonic in nature.
We discuss the Jaynes–Cummings–Hubbard model describing the superfluid–Mott insulator transition of polaritons (i.e., dressed photon–qubit states) in coupled qubit–cavity arrays in the crossover from strong to weak correlations. In the strongly correlated regime the phase diagram and the elementary excitations of lattice polaritons near the Mott lobes are calculated analytically using a slave-boson theory (SBT). The opposite regime of weakly interacting polariton superfluids is described by a weak-coupling mean-field theory for a generalized multi-mode Dicke model. We show that a remarkable relation between the two theories exists in the limit of large photon bandwidth and large negative detuning, i.e., when the nature of polariton quasiparticles becomes qubit-like. In this regime, the weak-coupling theory predicts the existence of a single Mott lobe with a change of the universality class of the phase transition at the tip of the lobe, in perfect agreement with the SBT. Moreover, the spectra of low energy excitations, i.e., the sound velocity of the Goldstone mode and the gap of the amplitude mode match exactly as calculated from both theories.
Regular arrays of electromagnetic resonators, in turn coupled coherently to individual quantum two-level systems, exhibit a quantum phase transition of polaritons from a superfluid phase to a Mott-insulating phase. The critical behavior of such a Jaynes-Cummings lattice thus resembles the physics of the Bose-Hubbard model. We explore this analogy by elaborating on the mean-field theory of the phase transition and by presenting several useful mappings which pinpoint both similarities and differences of the two models. We show that a field-theory approach can be applied to prove the existence of multicritical curves analogous to the multicritical points of the Bose-Hubbard model, and we provide analytical expressions for the position of these curves.
Abstract We investigated the superfluid Mott-insulator phase transition within an open coupled cavity optomagnonic array system. Based on the quasibosonic approach and employing perturbation approximation and mean-field theory, we obtain the time-dependent analytical superfluid order parameter. Our analysis revealed that dissipation induces decoherence within the system, while a strong magnon-cavity coupling enhances coherence significantly. Moreover, we explored the mechanisms by which increasing the magnon-cavity coupling strength drives the system towards the superfluid phase. The work holds significant guidance for the study of superfluidMott insulator phase transition under dissipative conditions, and providing a reliable reference for experimental implementation in open quantum systems.
A generalisation of the Jaynes-Cummings-Hubbard model for coupled-cavity arrays is introduced, where the embedded two-level system in each cavity is replaced by a Ξ-type three-level system. We demonstrate that the resulting effective polariton-polariton interactions at each site are both two-body and three-body. By tuning the ratio of the two transition dipole matrix elements, we show that the strength and sign of the two-body interaction can be controlled whilst maintaining a three-body repulsion. We then proceed to demonstrate how different two-body and three-body interactions alter the mean field superfluid-Mott insulator phase diagram, with the possible emergence of a pair superfluid phase in the two-body attractive regime.
A generalisation of the Jaynes-Cummings-Hubbard model for coupled-cavity arrays is introduced, where the embedded two-level system in each cavity is replaced by a Ξ-type three-level system. We demonstrate that the resulting effective polariton-polariton interactions at each site are both two-body and three-body. By tuning the ratio of the two transition dipole matrix elements, we show that the strength and sign of the two-body interaction can be controlled whilst maintaining a three-body repulsion. We then proceed to demonstrate how different two-body and three-body interactions alter the mean field superfluid-Mott insulator phase diagram, with the possible emergence of a pair superfluid phase in the two-body attractive regime.