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arXiv:1309.7777 · Advances in Theoretical and Mathematical Physics

Quantum phase transition of light in coupled optical cavity arrays: A renormalization group study

Sujit Sarkar

Published Jan 1, 2014• 2 citations
arXivHTMLPDF

Abstract

We study the quantum phase transition of light of a system when atom trapped in microcavities and interacting through the exchange of virtual photons.We predict the quantum phase transition between the photonic Coulomb blocked induce insulating phase and anisotropic exchange induced photonic superfluid phase in the system due to the existence of two Rabi frequency oscillations.The renormalization group equation shows explicitly that for this system there is no self-duality.The system also shows two Berezinskii-Kosterlitz-Thouless (BKT) transitions for the different physical situation of the system.The presence of single Rabi frequency oscillation in the system leads to the BKT transition where system shows the quantum phase transition from photonic metallic state to the Coulomb blocked induced insulating phase.For the other BKT transition when the z-component of exchange interaction is absent, the system shows the transition from the photonic metallic state to the photonic superfluid phase.We also predict the commensurate to incommensurate transition under the laser field detuning.

DOI
10.4310/atmp.2014.v18.n3.a6

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We study the quantum phase transition of light of a system when atom trapped in microcavities and interacting through the exchange of virtual photons.We predict the quantum phase transition between the photonic Coulomb blocked induce insulating phase and anisotropic exchange induced photonic superfluid phase in the system due to the existence of two Rabi frequency oscillations.The renormalization group equation shows explicitly that for this system there is no self-duality.The system also shows two Berezinskii-Kosterlitz-Thouless (BKT) transitions for the different physical situation of the system.The presence of single Rabi frequency oscillation in the system leads to the BKT transition where system shows the quantum phase transition from photonic metallic state to the Coulomb blocked induced insulating phase.For the other BKT transition when the z-component of exchange interaction is absent, the system shows the transition from the photonic metallic state to the photonic superfluid phase.We also predict the commensurate to incommensurate transition under the laser field detuning.
An attempt is made to understand the quantum simulation of quantum Berezinskii–Kosterlitz–Thouless (QBKT) transition for interacting light-matter system. We derive the QBKT equation for our system along with the exact results. We present emergence of different quantum phases in the different regimes of parameter space for this quantum simulated system. We interpret the collective excitations of the system in terms of bosonic excitations (Bose metal phase) as well as the photon blocked state (photonic insulator state) in our study. We present the behavior of renormalization group (RG) flow lines from the numerical studies of RG flow equations and also from the exact solution. We study the quantum critical surface of the simulated model Hamiltonian and also present the exact results for Majumdar–Ghosh point as well as for refermionization point from the perspective of quantum simulation.
Summary form only given. The studies of insulator to superfluid transitions in many body systems and their realization in optical lattices have opened great possibilities for simulating many body systems. It is thus interesting to explore which other systems permit such phases and simulations, especially if the problem of accessibility of the individual sites is not present. Particularly arresting will be to find such phases in a system of photons which, by being non-interacting, are unlikely candidates for the studies of many-body phenomena. Here we show that a Mott phase can arise in an array of coupled high Q electromagnetic cavities between which photons can hop, when each cavity is coupled to a single two level system (atom/quantum dot/Cooper pair). In this phase each atom-cavity system has the same integral number of polaritonic (atomic plus photonic) excitations. It occurs for resonant photonic and atomic frequencies when photon blockade provides an effective repulsion between the excitations in each atom-cavity system. Detuning the atomic and photonic frequencies suppresses this repulsion and induces a transition from the Mott phase to a photonic superfluid. We also show that for zero detuning, the system can simulate the dynamics of a spin chain with arbitrary number of excitations and can be used to implement quantum information processing tasks.
We consider the interacting helical liquid system at the one-dimensional edge of a two-dimensional topological insulator, coupled to an external magnetic field and s-wave superconductor and map it to an XYZ spin chain system. This model undergoes quantum Berezinskii–Kosterlitz–Thouless (BKT) transition with two limiting conditions. We derive the renormalization group (RG) equations explicitly and also present the flow lines behavior. We also present the behavior of RG flow lines based on the exact solution. We observe that the physics of Majorana fermion zero modes and the gaped Ising-ferromagnetic phase, which appears in a different context. We observe that the evidence of gapless helical Luttinger liquid phase as a common non-topological quantum phase for both quantum BKT transitions. We explain analytically and physically that there is no Majorana-Ising transition. In the presence of chemical potential, the system shows the commensurate to incommensurate transition.
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In this manuscript, we analyze the mechanism of the superradiant phase transition in the anisotropic Rabi model under the classical oscillator limit using the pattern picture. By expanding the anisotropic Rabi model Hamiltonian in operator space, we obtained three patterns, and we find that the phase transition arises from the competition between patterns. The difficulty in achieving the classical oscillator limit motivates our investigation into the quantum phase transition within a parametrically-driven Jaynes-Cummings model. This parametrically-driven Jaynes-Cummings model can reproduce the dynamics of an ultrastrong-coupling anisotropic Rabi model in a squeezed-light frame. According to the eigenenergies and eigenstates of the normal and superradiant phases of this equivalent anisotropic Rabi model, we find that the excitation energy of the normal phase and the superradiant phase vanishes at the critical point. The photon number becomes infinite beyond the critical point. These results indicate that the system undergoes a superradiant phase transition at the critical point.
We present extensive calculation and the results of quantum Berezinskii-Kosterlitz-Thouless (BKT) transition for interacting helical liquid system. This system shows the quantum BKT transition for the different physical situation which we present by two model Hamiltonians. We derive the renormalization group (RG) equations explicitly and present the flow lines behavior. We also present RG flow lines based on the exact solution. We observe that the Majorana fermion zero modes physics and the gapped Ising phase of the system. We also observe that the evidence of gapless Luttinger liquid phase as a common phase for both quantum BKT transitions.