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arXiv:1001.1677 · Physical Review Letters

Excitations of Strongly Correlated Lattice Polaritons

Sebastian Schmidt, G. Blatter

Published May 24, 2010• 46 citations
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Abstract

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.

DOI
10.1103/physrevlett.104.216402

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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.
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.
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.
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 Bose Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. In the strong coupling Mott insulating regime, we propose a mean field theory based on a constraint SU (3) pseudo-boson representation on the effective model and discuss the excitation spectra and the phase transition to the superfluid state. Further to the superfluid phase, we use the coherent-state approach to derive the collective excitation modes. It is found that the Mott phase has two degenerate gapped quadratic excitation spectra which graduate into two degenerate gapless linear ones at the transition point, and one gapless linear mode with one gapped quadratic mode in the superfluid phase.
We calculate the single-particle spectral function for the one-band Bose-Hubbard model within the random-phase approximation (RPA). In the strongly correlated superfluid, in addition to the gapless phonon excitations, we find extra gapped modes, which become particularly relevant near the superfluid-Mott quantum phase transition (QPT). The strength in one of the gapped modes, a precursor of the Mott phase, grows as the QPT is approached and evolves into a hole (particle) excitation in the Mott insulator depending on whether the chemical potential $\ensuremath{\mu}$ is above (below) the tip of the lobe. The sound velocity ccc of the Goldstone modes remains finite when the transition is approached at constant density; otherwise, it vanishes at the transition. It agrees well with Bogoliubov theory except close to the transition. We also calculate the spatial correlations for bosons in an inhomogeneous trapping potential creating alternating shells of Mott insulator and superfluid. Finally, we discuss the capability of the RPA to correctly account for quantum fluctuations in the vicinity of the QPT.
We study the excitation spectrum of strongly correlated lattice bosons for the Mott-insulating phase and for the superfluid phase close to localization. Within a Schwinger-boson mean-field approach we find two gapped modes in the Mott insulator and the combination of a sound mode (Goldstone) and a gapped (Higgs) mode in the superfluid. To make our findings comparable with experimental results, we calculate the dynamic structure factor as well as the linear response to the optical lattice modulation introduced by St\"oferle et al. [Phys. Rev. Lett. 92, 130403 (2004)]. We find that the puzzling finite frequency absorption observed in the superfluid phase could be explained via the excitation of the gapped (Higgs) mode. We check the consistency of our results with an adapted fff-sum rule and propose an extension of the experimental technique by St\"oferle et al. to further verify our findings.