Geometrical frustration and long-range couplings are key contributors to create quantum phases with different properties throughout physics. We propose a scheme where both ingredients naturally emerge in a Raman induced subwavelength lattice. We first demonstrate that Raman-coupled multicomponent quantum gases can realize a highly versatile frustrated Hubbard Hamiltonian with long-range interactions. The deeply subwavelength lattice period leads to strong long-range interparticle repulsion with tunable range and decay. We numerically demonstrate that the combination of frustration and long-range couplings generates many-body phases of bosons, including a range of density-wave and superfluid phases with broken translational and time reversal symmetries, respectively. Our results thus represent a powerful approach for efficiently combining long-range interactions and frustration in quantum simulations.
Geometrical frustration and long-range couplings are key contributors to create quantum phases with different properties throughout physics. We propose a scheme where both ingredients naturally emerge in a Raman induced subwavelength lattice. We first demonstrate that Raman-coupled multicomponent quantum gases can realize a highly versatile frustrated Hubbard Hamiltonian with long-range interactions. The deeply subwavelength lattice period leads to strong long-range interparticle repulsion with tunable range and decay. We numerically demonstrate that the combination of frustration and long-range couplings generates many-body phases of bosons, including a range of density-wave and superfluid phases with broken translational and time reversal symmetries, respectively. Our results thus represent a powerful approach for efficiently combining long-range interactions and frustration in quantum simulations.
The study of geometrically frustrated many-body quantum systems is of central importance to uncover novel quantum mechanical effects. We design a scheme where ultracold bosons trapped in a one-dimensional state-dependent optical lattice are modeled by a frustrated Bose-Hubbard Hamiltonian. A derivation of the Hamiltonian parameters based on Cesium atoms, further show large tunability of contact and nearest-neighbor interactions. For pure contact repulsion, we discover the presence of two phases peculiar to frustrated quantum magnets: the bond-order-wave insulator with broken inversion symmetry and a chiral superfluid. When the nearest-neighbor repulsion becomes sizable, a further density-wave insulator with broken translational symmetry can appear. We show that the phase transition between the two spontaneously symmetry-broken phases is continuous, thus representing a one-dimensional deconfined quantum critical point not captured by the Landau-Ginzburg-Wilson symmetry-breaking paradigm. Our results provide a solid ground to unveil the novel quantum physics induced by the interplay of nonlocal interactions, geometrical frustration, and quantum fluctuations.
We study the many-body phases of bosonic atoms with N internal states confined to a one-dimensional (1D) optical lattice under the influence of a synthetic magnetic field and strong repulsive interactions. The N internal states of the atoms are coupled via Raman transitions creating the synthetic magnetic field in the space of internal spin states corresponding to recent experimental realizations. We focus on the case of strong SU(N) invariant local density-density interactions in which each site of the 1D lattice is at most singly occupied, and strong Raman coupling, in distinction to previous work which has focused on the weak Raman coupling case. This allows us to keep only a single state per site and derive a low-energy effective spin-1/2 model. The effective model contains first-order nearest-neighbor tunneling terms, second-order nearest-neighbor interactions, and correlated next-nearest-neighbor tunneling terms. By adjusting the flux $\ensuremath{\phi}$, one can tune the relative importance of first-order and second-order terms in the effective Hamiltonian. In particular, first-order terms can be set to zero, realizing a model with dominant second-order terms. We show that the resulting competition between density-dependent tunneling and repulsive density-density interaction leads to an interesting phase diagram including a phase with long-range pair-superfluid correlations. The method can be straightforwardly extended to higher dimensions and lattices of arbitrary geometry, including geometrically frustrated lattices where the interplay of frustration, interactions, and kinetic terms is expected to lead to even richer physics.
This thesis contains theoretical research on ultracold quantum gases in spatially periodic potentials, featuring high-frequency periodic driving, long-range interactions, or both. The largest part features deep potentials where the behaviour of the gas is well-described by quantum lattice models. The periodic driving is then integrated out to obtain effective time-independent descriptions. One project investigates emergent long-range interactions in a stationary, weak, spatially periodic potential, where a lattice theory is not appropriate.In two short introductory chapters, the topics of ultracold atoms, optical lattice potentials, periodic driving, and long-range interactions, are sketched, without attempting to give a complete overview. Some experimentally relevant length and energy scales are given, but the main focus is on deriving and constructing theoretical descriptions of ultracold gases in various spatially and/or temporally periodic potentials.The first project presented, is focused on how the single-particle spectrum of a Bose gas in a non-separable two-dimensional square lattice is affected by high-frequency periodic driving; the most striking conclusion is that under suitable circumstances, it develops two inequivalent minima, leading to finite-momentum Bose-Einstein condensation. Perturbative calculations indicate that local interactions induce spontaneous time-reversal symmetry breaking (TRSB) in such a system.The second project investigates the interplay between kinetic frustration and long-range interactions in fermionic gases. Both a mean-field approximation and exact diagonalisations predict that such a system, studied in the more specific realisation of a weakly interacting dipolar fermionic gas in a 2D triangular lattice, also leads to spontaneous TRSB. Furthermore, a density wave could form at quarter filling, where the Fermi surface is perfectly nested. Perhaps more interesting yet, a spatially inhomogeneous TRSB pattern is predicted, confined to the low-density sublattice that emerges in the density wave.The third project revolves around the question of supersolidity in the presence of a gauge field. Applying the Bogolyubov approximation to a variation of the extended Bose-Hubbard model, indicates that combining an artificial staggered magnetic field in a 2D square lattice with nearest-neighbour density-density interactions, not only leads to a supersolid with staggered vortices, but also induces an inhomogeneous distribution of the associated currents around the elementary plaquette.In the fourth project, a one-dimensional Bose gas with strong local interactions in a weak lattice at incommensurate densities is shown to feature excitations corresponding to excess or deficit particles. The excitations interact repulsively at long distances, in spite of the fact that the underlying atoms themselves do not. As a consequence, the incommensurability of the density with the lattice can drive a transition to a density wave and even a supersolid.The four above-mentioned research projects combine bosonic and fermionic gases, weak and strong interactions, perturbative and mean-field approximations, effective field theories and exact diagonalisations. The main overall conclusion is that long-range interactions and high-frequency periodic driving lead to a very diverse range of fascinating phenomena in ultracold lattice gases.
Understanding how frustration and symmetry breaking shape collective behavior is a central problem in quantum many-body systems. In this work, we investigate this problem in large one- and two-dimensional arrays of coupled Dicke models on a periodic lattice, where strong light-matter coupling gives rise to a superradiant phase and competition between neighboring order parameters induces spontaneous translational symmetry breaking. Such Dicke lattice models constitute a fundamentally new class of quantum many-body systems, as they simultaneously realize the thermodynamic limit associated with the lattice size and an intrinsic thermodynamic limit arising from collective on-site interactions with quantum emitters. We show that frustration drives photonic density-wave ordering, and that the resulting broken periodicity can be predicted from the excitation spectrum of the symmetric phase, without requiring computationally prohibitive thermodynamic energy minimization. Furthermore, we demonstrate that an emergent Nambu-Goldstone mode arises near the critical point in a one-dimensional chain despite the presence of only discrete symmetry, and uncover the mechanism that enables this otherwise forbidden gapless excitation. We also find quasi-periodic ordering in the superradiant phase, reminiscent of quasicrystals, and demonstrate that synthetic magnetic flux provides a powerful knob to control the nature of translational symmetry breaking. Our results establish a new direction in quantum many-body physics where the coexistence of local and global thermodynamic limits gives rise to unconventional symmetry breaking and emergent collective behavior.
We show that coupling ultracold atoms in optical lattices to quantized modes of an optical cavity leads to quantum phases of matter, which at the same time possess properties of systems with both short- and long-range interactions. This opens perspectives for novel quantum simulators of finite-range interacting systems, even though the light-induced interaction is global (i.e., infinitely long range). This is achieved by spatial structuring of the global light-matter coupling at a microscopic scale. Such simulators can directly benefit from the collective enhancement of the global light-matter interaction and constitute an alternative to standard approaches using Rydberg atoms or polar molecules. The system in the steady state of light induces effective many-body interactions that change the landscape of the phase diagram of the typical Bose-Hubbard model. Therefore, the system can support nontrivial superfluid states, bosonic dimer, trimer, etc., states, and supersolid phases depending on the choice of the wavelength and pattern of the light with respect to the classical optical lattice potential. We find that by carefully choosing the system parameters one can investigate diverse strongly correlated physics with the same setup, i.e., modifying the geometry of light beams. In particular, we present the interplay between the density and bond (or matter-wave coherence) interactions. We show how to tune the effective interaction length in such a hybrid system with both short-range and global interactions.
A density-dependent gauge field may induce density-induced geometric frustration, leading to a non-trivial interplay between density modulation and frustration, which we illustrate for the particular case of ultra-cold bosons in zig-zag optical lattices with a density-dependent hopping amplitude. We show that the density-induced frustration leads to a rich landscape of quantum phases, including Mott insulator, bond-order insulator, two-component superfluids, chiral superfluids, and partially paired superfluids. We show as well that the density-dependent hopping results in an effective repulsive or attractive interaction, and that for the latter case the vacuum may be destabilized leading to a strong compressibility. Finally, we discuss the characteristic momentum distribution of the predicted phases, which can be used to detect the phases in time-of-flight measurements.