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arXiv:1005.1501 · Physical Review B

Quantum phase transition and excitations of the Tavis-Cummings lattice model

Michael Knap, Enrico Arrigoni, Wolfgang von der Linden

Published Jul 29, 2010• 18 citations
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Abstract

The enormous progress in controlling quantum optical and atomic systems has prompted ideas for new experimental realizations of strongly correlated many-body systems operating with light. These systems consist of photons confined in optical cavities, which interact strongly with atoms or atomiclike structures. Due to the interaction between the two particle species optical nonlinearities appear, leading to a quantum phase transition from Mott to superfluid phase. Here, we address the Tavis-Cummings lattice model, which describes light-matter systems containing multiple atomiclike structures in each cavity. In particular, we investigate the phase boundary delimiting Mott from superfluid phase and the elementary excitations of the two-dimensional Tavis-Cummings lattice model in dependence of the number of atomiclike structures per cavity. In order to obtain the results we employ the variational cluster approach. We evaluate spectral functions and densities of states of both particle species, which allows us to characterize the fundamental excitations of light-matter systems. These excitations are termed polaritons and are superpositions of photons and atomic excitations. We introduce polariton quasiparticles as appropriate linear combinations of both particle species and analyze the weights of their constituents. Our results demonstrate the dependence of the quantum phase transition and the elementary excitations on the number of atomiclike structures per cavity and provide thus valuable insight into the physics of light-matter systems.

DOI
10.1103/physrevb.82.045126

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The enormous progress in controlling quantum optical and atomic systems has prompted ideas for new experimental realizations of strongly correlated many-body systems operating with light. These systems consist of photons confined in optical cavities, which interact strongly with atoms or atomiclike structures. Due to the interaction between the two particle species optical nonlinearities appear, leading to a quantum phase transition from Mott to superfluid phase. Here, we address the Tavis-Cummings lattice model, which describes light-matter systems containing multiple atomiclike structures in each cavity. In particular, we investigate the phase boundary delimiting Mott from superfluid phase and the elementary excitations of the two-dimensional Tavis-Cummings lattice model in dependence of the number of atomiclike structures per cavity. In order to obtain the results we employ the variational cluster approach. We evaluate spectral functions and densities of states of both particle species, which allows us to characterize the fundamental excitations of light-matter systems. These excitations are termed polaritons and are superpositions of photons and atomic excitations. We introduce polariton quasiparticles as appropriate linear combinations of both particle species and analyze the weights of their constituents. Our results demonstrate the dependence of the quantum phase transition and the elementary excitations on the number of atomiclike structures per cavity and provide thus valuable insight into the physics of light-matter systems.
The experimental observation of quantum phenomena in strongly correlated many particle systems is difficult because of the short length- and timescales involved. Obtaining at the same time detailed control of individual constituents appears even more challenging and thus to date inhibits employing such systems as quantum information processing devices. Substantial progress to overcome these problems has been achieved with cold atoms in optical lattices, where a detailed control of collective properties is feasible. However it is very difficult to address and hence control or measure individual sites [1, 2]. In this work, we demonstrate that polaritons, combined atom and photon excitations, in an array of cavities can form a strongly interacting many body system [3]. This scheme has several advantages: First of all, individual particles can, by construction, be controlled and measured. In contrast to optical lattices, it therefore allows to create inhomogeneous systems where different phases may coexists in adjacent spatial regions. Finally not only an effective Bose- Hubbard Hamiltonian might be created but several different many body systems including spin chains.
The rapid progress in quantum technology enables the implementation of artificial many-body systems with correlated photons and polaritons. A multiconnected Jaynes-Cummings (MCJC) lattice can be constructed by connecting qubits and cavities alternately. Such models can be realized with superconducting qubits coupled to superconducting microwave resonators or with quantum dots coupled to optical nanocavities. We study the physical properties of a one-dimensional MCJC lattice using the density-matrix renormalization-group method. This model has an intrinsic symmetry between the left and right qubit-cavity couplings. The competition between these couplings may drive the ground state either to a Mott-insulating phase or to a superfluid phase at integer fillings. We calculate the single-particle and density-density correlation functions, the correlation lengths in the Mott-insulating phase, and the Luttinger parameters in the superfluid phase and determine accurately the critical points that separate these two phases.
We use the mean field approximation method to study the quantum phase transitions of the Jaynes-Cummings lattice model and the Rabi lattice model. The effective Hamiltonians are obtained for the JC and Rabi model including the Kerr nonlinear term. Numerically we diagonalized the Hamiltonian matrix and calculated the superfluidity order parameter and the two-photon correlation function by solving the iteration equations. We have explored the Mott insulating-superfluid quantum phase transition, the bunching-antibunching behavior of light, and the effect of Kerr nonlinear term on the quantum phase transition and photon statistical characteristics. Our results show that in the JC lattice model, by increasing J, a quantum phase transition takes place and the system is driven to a superfluid phase. The phase boundaries of the Mott lobes are N-dependent. However the photon will always be in a bunching statistical behavior irrelevant of the coupling strength between the two-level atom and the phonton and the nonlinear Kerr effect. In the Rabi lattice model, the anti-rotating wave term breaks Mott-lobe structure of the phase diagram and the increase of the two-level atom and photon interaction strength g and the photon transition strength J between the lattices drive the system from the Mott insulating phase to the superfluid phase. The photon statistical behavior changes from the bunching to the antibunching one when considering the anti-rotating wave term, which is important in the strongly coupled systems. Most interestingly, the increase of the Kerr nonlinear coefficient will inhibit the Mott insulating phase-superfluid phase transition, but favor the superfluid phase and the transition from the bunching to anti-bunching statistics.
Systems of strongly interacting atoms and photons, which can be realized wiring up individual cavity QED systems into lattices, are perceived as a new platform for quantum simulation. While sharing important properties with other systems of interacting quantum particles, here we argue that the nature of light-matter interaction gives rise to unique features with no analogs in condensed matter or atomic physics setups. By discussing the physics of a lattice model of delocalized photons coupled locally with two-level systems through the elementary light-matter interaction described by the Rabi model, we argue that the inclusion of counterrotating terms, so far neglected, is crucial to stabilize finite-density quantum phases of correlated photons out of the vacuum, with no need for an artificially engineered chemical potential. We show that the competition between photon delocalization and Rabi nonlinearity drives the system across a novel Z(2) parity symmetry-breaking quantum criticality between two gapped phases that share similarities with the Dicke transition of quantum optics and the Ising critical point of quantum magnetism. We discuss the phase diagram as well as the low-energy excitation spectrum and present analytic estimates for critical quantities.
We present an analytic slave-boson approach to calculate the elementary excitations of the Jaynes-Cummings-Hubbard model (JCHM) describing strongly correlated polaritons on a lattice in various quantum optical systems. In the superfluid phase near the Mott transition we find a gapless, linear Goldstone mode and a gapped amplitude mode corresponding to phase and density fluctuations, respectively. The sound velocity of the Goldstone mode develops a peculiar anomaly as a function of detuning at low densities, which persists into the weakly interacting regime of a polariton BEC.
Spectral properties of the Bose-Hubbard model and a recently proposed coupled-cavity model are studied by means of quantum Monte Carlo simulations in one dimension. Both models exhibit a quantum phase transition from a Mott insulator to a superfluid phase. The dynamic structure factor $S(k,\ensuremath{\omega})$ and the single-particle spectrum $A(k,\ensuremath{\omega})$ are calculated, focusing on the parameter region around the phase transition from the Mott insulator with density one to the superfluid phase, where correlations are important. The strongly interacting nature of the superfluid phase manifests itself in terms of additional gapped modes in the spectra. Comparison is made to recent analytical work on the Bose-Hubbard model. Despite some subtle differences due to the polaritonic particles in the cavity model, the gross features are found to be very similar to the Bose-Hubbard case. For the polariton model, emergent particle-hole symmetry near the Mott lobe tip is demonstrated and temperature and detuning effects are analyzed. A scaling analysis for the generic transition suggests mean-field exponents, in accordance with field-theory results.