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arXiv:1410.5603 · Scientific Reports

Photon Devil’s staircase: photon long-range repulsive interaction in lattices of coupled resonators with Rydberg atoms

Yuanwei Zhang, Jingtao Fan, J.-Q. Liang, Jie Ma, Gang Chen, Suotang Jia, Franco Nori

Published Jun 25, 2015• 16 citations
arXivHTMLPDF

Abstract

The realization of strong coherent interactions between individual photons is a long-standing goal in science and engineering. In this report, based on recent experimental setups, we derive a strong photon long-range repulsive interaction, by controlling the van der Waals repulsive force between Cesium Rydberg atoms located inside different cavities in extended Jaynes-Cummings-Hubbard lattices. We also find novel quantum phases induced by this photon long-range repulsive interaction. For example, without photon hopping, a photon Devil's staircase, induced by the breaking of long-range translation symmetry, can emerge. If photon hopping occurs, we predict a photon-floating solid phase, due to the motion of particle- and hole-like defects. More importantly, for a large chemical potential in the resonant case, the photon hopping can be frozen even if the hopping term exists. We call this new phase the photon-frozen solid phase. In experiments, these predicted phases could be detected by measuring the number of polaritons via resonance fluorescence.

DOI
10.1038/srep11510

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The realization of strong coherent interactions between individual photons is a long-standing goal in science and engineering. In this report, based on recent experimental setups, we derive a strong photon long-range repulsive interaction, by controlling the van der Waals repulsive force between Cesium Rydberg atoms located inside different cavities in extended Jaynes-Cummings-Hubbard lattices. We also find novel quantum phases induced by this photon long-range repulsive interaction. For example, without photon hopping, a photon Devil's staircase, induced by the breaking of long-range translation symmetry, can emerge. If photon hopping occurs, we predict a photon-floating solid phase, due to the motion of particle- and hole-like defects. More importantly, for a large chemical potential in the resonant case, the photon hopping can be frozen even if the hopping term exists. We call this new phase the photon-frozen solid phase. In experiments, these predicted phases could be detected by measuring the number of polaritons via resonance fluorescence.
The devil's staircase is a fractal structure that characterizes the ground state of one-dimensional classical lattice gases with long-range repulsive convex interactions. Its plateaus mark regions of stability for specific filling fractions which are controlled by a chemical potential. Typically, such a staircase has an explicit particle-hole symmetry; i.e., the staircase at more than half filling can be trivially extracted from the one at less than half filling by exchanging the roles of holes and particles. Here, we introduce a quantum spin chain with competing short-range attractive and long-range repulsive interactions, i.e., a nonconvex potential. In the classical limit the ground state features generalized Wigner crystals that--depending on the filling fraction--are composed of either dimer particles or dimer holes, which results in an emergent complete devil's staircase without explicit particle-hole symmetry of the underlying microscopic model. In our system the particle-hole symmetry is lifted due to the fact that the staircase is controlled through a two-body interaction rather than a one-body chemical potential. The introduction of quantum fluctuations through a transverse field melts the staircase and ultimately makes the system enter a paramagnetic phase. For intermediate transverse field strengths, however, we identify a region where the density-density correlations suggest the emergence of quasi-long-range order. We discuss how this physics can be explored with Rydberg-dressed atoms held in a lattice.
We consider a single-component gas of dipolar bosons confined in a one-dimensional optical lattice, where the dipoles are aligned such that the long-ranged dipolar interactions are maximally repulsive. In the limit of zero inter-site hopping and sufficiently large on-site interaction, the phase diagram is a complete devil's staircase for filling fractions between 0 and 1: every commensurate state at a rational filling is stable over a finite interval in chemical potential, and for every chemical potential the system is in a gapped commensurate phase. We perturb away from this limit in two experimentally motivated directions involving the addition of hopping and a reduction of the onsite interaction. The addition of hopping alone yields a phase diagram, which we compute in perturbation theory in the hopping, where the commensurate Mott phases now compete with the superfluid. We capture the physics of the Mott-superfluid phase transitions via bosonization. In a finite trap, we argue using an LDA and simulated annealing that this results in regions of commensurate states separated by patches with dominant superfluid correlations. Further softening of the onsite interaction yields alternative commensurate states with double occupancies which can form a devil's staircase of their own; we describe these states and discuss the possible transitions between them. Adding a hopping term in this case produces one-dimensional "supersolids" which simultaneously exhibit discrete broken symmetries and superfluidity. The contents of this work was first published as a chapter in the doctoral thesis `On Exotic Orders in Strongly Correlated Systems' (Princeton University, 09/09, supervised by S. L. Sondhi), and constitutes a considerably more detailed version of [PRB 80: 174519 (2009)].
We analyse the ground-state quantum phase diagram of hardcore Bosons interacting with repulsive dipolar potentials. The bosons dynamics is described by the extended-Bose-Hubbard Hamiltonian on a two-dimensional lattice. The ground state results from the interplay between the lattice geometry and the long-range interactions, which we account for by means of a classical spin mean-field approach limited by the size of the considered unit cells. This extended classical spin mean-field theory accounts for the long-range density-density interaction without truncation. We consider three different lattice geometries: square, honeycomb, and triangular. In the limit of zero hopping the ground state is always a devil’s staircase of solid (gapped) phases. Such crystalline phases with broken translational symmetry are robust with respect to finite hopping amplitudes. At intermediate hopping amplitudes, these gapped phases melt, giving rise to various lattice supersolid phases, which can have exotic features with multiple sublattice densities. At sufficiently large hoppings the ground state is a superfluid. The stability of phases predicted by our approach is gauged by comparison to the known quantum phase diagrams of the Bose-Hubbard model with nearest-neighbour interactions as well as quantum Monte Carlo simulations for the dipolar case on the square and triangular lattice. Our results are of immediate relevance for experimental realisations of self-organised crystalline ordering patterns in analogue quantum simulators, e.g., with ultracold dipolar atoms in an optical lattice.
We present and analyze spin models with long-range interactions whose ground state features a so-called devil's staircase and where plateaus of the staircase are accessed by varying two-body interactions. This is in contrast to the canonical devil's staircase, for example, occurring in the one-dimensional Ising model with long-range interactions, where typically a single-body chemical potential is varied to scan through the plateaus. These systems, moreover, typically feature a particle-hole symmetry which trivially connects the hole part of the staircase (filling fraction $f\ensuremath{\ge}1/2$) to its particle part ($f\ensuremath{\le}1/2$). Such symmetry is absent in our models and hence the particle sector and the hole sector can be separately controlled, resulting in exotic hybrid staircases.
The fields of quantum simulation with cold atoms and quantum optics are currently being merged. In a set of recent pathbreaking experiments with atoms in optical cavities , lattice quantum many-body systems with both, a short-range interaction and a strong interaction potential of infinite range –mediated by a quantized optical light field– were realized. A theoretical modelling of these systems faces considerable complexity at the interface of: (i) spontaneous symmetry-breaking and emergent phases of interacting many-body systems with a large number of atoms N\rightarrow \infty N → ∞ , (ii) quantum optics and the dynamics of fluctuating light fields, and (iii) non-equilibrium physics of driven, open quantum systems. Here we propose what is possibly the simplest, quantum-optical magnet with competing short- and long-range interactions, in which all three elements can be analyzed comprehensively: a Rydberg-dressed spin lattice coherently coupled to a single photon mode. Solving a set of coupled even-odd sublattice master equations for atomic spin and photon mean-field amplitudes, we find three key results. (R1): Superradiance and a coherent photon field appears in combination with spontaneously broken magnetic translation symmetry. The latter is induced by the short-range nearest-neighbor interaction from weakly admixed Rydberg levels. (R2): This broken even-odd sublattice symmetry leaves its imprint in the light via a novel peak in the cavity spectrum beyond the conventional polariton modes. (R3): The combined effect of atomic spontaneous emission, drive, and interactions can lead to phases with anomalous photon number oscillations. Extensions of our work include nano-photonic crystals coupled to interacting atoms and multi-mode photon dynamics in Rydberg systems.
Jaynes-Cummings-Hubbard lattices provide unique properties for the study of correlated phases as they exhibit convenient state preparation and measurement, as well as in situ tuning of parameters. We show how to realize charge density and supersolid phases in Jaynes-Cummings-Hubbard lattices in the presence of long-range interactions. The long-range interactions are realized by the consideration of Rydberg states in coupled atom-cavity systems and the introduction of additional capacitive couplings in quantum-electrodynamics circuits. We demonstrate the emergence of supersolid and checkerboard solid phases, for calculations which take into account nearest-neighbor couplings, through a mean-field decoupling.