International audienceWe propose a semiclassical description of the low-energy properties of quantum spin ice in the strong Ising limit. Within the framework of a semiclassical, perturbative Villain expansion, that can be truncated at arbitrary order, we give an analytic and quantitative treatment of the deconfining phase. We find that photon-photon interactions significantly renormalize the speed of light and split the two transverse photon polarizations at intermediate wave vectors. We calculate the photon velocity and the ground-state energy to first and second order in perturbation theory, respectively. Both are in good agreement with recent numerical simulations. We further compute the classical energy of the vison excitation

We discuss the effects of quantum fluctuations on the properties of vortex lattices in rapidly rotating ultracold atomic gases. We develop a variational method that goes beyond the Bogoliubov theory by including the effects of interactions between the quasiparticle excitations. These interactions are found to have significant quantitative effects on physical properties even at relatively large filling factors. We use our theory to predict the expected experimental signatures of quantum fluctuations of vortices and to assess the competition of the triangular vortex lattice phase with other phases in finite-sized systems.

We study theoretically the collective dynamics of rotational excitations of polar molecules loaded into an optical lattice in two dimensions. These excitations behave as hard-core bosons with a relativistic energy dispersion arising from the dipolar coupling between molecules. This has interesting consequences for the collective many-body phases. The rotational excitations can form a Bose-Einstein condensate at non-zero temperature, manifesting itself as a divergent T2 coherence time of the rotational transition even in the presence of inhomogeneous broadening. The dynamical evolution of a dense gas of rotational excitations shows regimes of non-ergodicity, characteristic of many-body localization and localization protected quantum order. 72.15.Rn The ability to create and control gases of cold polar molecules has sparked great interest in the quantum manybody physics associated with long-range and anisotropic dipolar interactions [1][2][3][4][5][6][7][8]. These systems open up possibilities to create and to probe interesting many-body phases involving the positional and/or rotational degrees of freedom of the molecules [9]. For polar molecules loaded into deep optical lattices -with positional motion frozen out -the rotational excitations can be used to emulate interesting forms of quantum magnet [10][11][12][13][14][15][16][17][18][19][20][21][22]. Recent experiments [23] have shown evidence of the dipole-dipole interactions between molecules in different lattice sites, which appear as an additional source of decoherence of rotational excitations [23,24].In this paper, we study the many-body physics of the rotational excitations of polar molecules in a two-dimensional (2D) system. We show that in regimes of weak disorder, rather than causing decoherence [23,24], the dipole-dipole interactions can in fact stabilize the coherence up to arbitrarily long times. This stability of coherence arises from the formation of a collective many-body phase with true long-range order. The essential physics arises from the power-law (1/r 3 ) form of dipolar interactions between molecules. This coupling causes the rotational excitations to behave as a gas of (hardcore) bosons with a relativistic dispersion δ k ∝ |k| at small wavevector k. In contrast to massive particles (δ k ∝ |k| 2 ) this relativistic dispersion allows a Bose-Einstein Condensate (BEC) to exist in 2D at non-zero temperature. We show that the formation of this BEC phase leads to a resistance to decoherence of the rotational excitations formed by a microwave pulse, even in the presence of inhomogeneities that would broaden the rotational transition for uncoupled molecules. For very strong inhomogeneous broadening there is a phase transition into an uncondensed phase for which the initial coherence decays exponentially in time.An important feature of the rotational excitations of polar molecules is that they are effectively isolated from any external heat bath. In the presence of disorder such systems are natural candidates to show many-body localization and ...

We study the decoherence dynamics of dipole-coupled two-level quantum systems in Ramsey-type experiments. We focus on large networks of two-level systems, confined to two spatial dimensions and with positional disorder giving rise to disordered dipolar couplings. This setting is relevant for modeling the decoherence dynamics of the rotational excitations of polar molecules confined to deep optical lattices, where disorder arises from the random filling of lattice sites with occupation probability p. We show that the decoherence dynamics exhibits a phase transition at a critical filling pc 0.15. For p < pc the dynamics is disorder-dominated and the Ramsey interference signal decays on a timescale T2 ∝ p −3/2 . For p > pc the dipolar interactions dominate the disorder, and the system behaves as a collective spin-ordered phase, representing synchronization of the two-level systems and persistent Ramsey oscillations with divergent T2 for large systems. For a finite number of two-level systems, N , the spin-ordered phase at p > pc undergoes a crossover to a collective spin-squeezed state on a timescale τsq ∝ √ N . We develop a self-consistent mean-field theory that is capable of capturing the synchronization transition at pc, and provide an intuitive theoretical picture that describes the phase transition in the long-time dynamics. We also show that the decoherence dynamics appear to be ergodic in the vicinity of pc, the long-time behaviour being well described by the predictions of equilibrium thermodynamics. The results are supported by the results of exact diagonalization studies of small systems.

Describing the experimental signatures of quantum spin ice has been the focus of many theoretical efforts, as definitive experimental verification of this candidate quantum spin liquid is yet to be achieved. Gapped excitations known as visons have largely eluded those efforts. We provide a theoretical framework, which captures their dynamics and predicts new signatures in the magnetic response. We achieve this by studying the ring-exchange Hamiltonian of quantum spin ice in the large-s approximation, taking into account the compact nature of the emergent U(1) gauge theory. We find the stationary solutions of the action-the instantons-which correspond to visons tunneling between lattice sites. By integrating out the instantons, we calculate the effective vison Hamiltonian, including their mass. We show that in the ground state virtual vison pairs simply renormalize the speed of light and give rise to an inelastic continuum of excitations. At low temperatures, however, thermally activated visons form a Debye plasma and introduce a mass gap in the photon spectrum, equal to the plasma frequency, which we calculate as a function of temperature. We demonstrate that this dynamical mass gap should be visible in energy-resolved neutron scattering spectra but not in the energy-integrated ones. We also show that it leads to the vanishing of the susceptibility of an isolated system, through a mechanism analogous to the Meissner effect, but that it does not lead to confinement of static spinons.