We investigate the ground-state phase diagram of the one-dimensional attractive Fermi-Hubbard model with spin-dependent hoppings and an on-site Rabi coupling using the density matrix renormalization group method. In particular, we show that even in the limit of one component being immobile the pair superfluidity can be resonantly enhanced when the Rabi coupling is on the order of the interaction strength just before the system starts to strongly polarize. We derive an effective spin-1/2 XXZ model in order to understand the ground-state properties in the strong attraction limit.
We demarcate the unstable regimes of superfluids in a Rabi-coupled two-component Bose-Einstein condensate in the presence of optical lattices. We find that the Rabi coupling can stabilize superfluids. A significant separation between Landau and dynamical instabilities is presented in a Rabi-coupled Zeeman lattice.
We study superfluidity in the 1D Bose-Hubbard model using a variational matrix product state technique. We determine the superfluid density as a function of the Hubbard parameters by calculating the energy cost of phase twists in the thermodynamic limit. As the system is critical, correlation functions decay as power laws and the entanglement entropy grows with the bond dimension of our variational state. We relate the resulting scaling laws to the superfluid density. We compare two different algorithms for optimizing the infinite matrix product state and develop a physical explanation why one…
We investigate the attractive Hubbard model in infinite spatial dimensions by means of dynamical mean-field theory. Using a continuous-time Monte Carlo algorithm in the Nambu formalism as an impurity solver, we directly deal with the superfluid phase in the population imbalanced system. By calculating the superfluid order parameter, the magnetization, and the density of states, we discuss how the polarized superfluid state is realized in the attractive Hubbard model at quarter filling. We find that a drastic change in the density of states is induced by spin imbalanced populations in the super…
We use cluster dynamical mean field theory to study the phase diagram of the square lattice bilayer Hubbard model with an interlayer interaction. The layers are populated by two-component fermions, and the densities in both layers and the strength of the interactions are varied. We find that an attractive interlayer interaction can induce a checkerboard density ordered phase and superfluid phases, with either interlayer or intralayer pairing. Remarkably, the latter phase does not require an intralayer interaction to be present: it can be attributed to an induced attractive interaction caused b…
Motivated by the experimental realization of synthetic spin-orbit coupling for ultracold atoms, we investigate the phase diagram of the Bose Hubbard model in a non-abelian gauge field in two dimensions. Using a strong coupling expansion in the combined presence of spin-orbit coupling and tunable interactions, we find a variety of interesting magnetic Hamiltonians in the Mott insulator (MI), which support magnetic textures such as spin spirals and vortex and Skyrmion crystals. An inhomogeneous mean field treatment shows that the superfluid (SF) phases inherit these exotic magnetic orders from t…
With use of the U(1) quantum rotor method in the path integral effective action formulation, we have confirmed the mathematical similarity of the phase Hamiltonian and of the extended Bose-Hubbard model with density-induced tunneling (DIT). Moreover, we have shown that the latter model can be mapped to a pseudospin Hamiltonian that exhibits two coexisting (single-particle and pair) superfluid phases. Phase separation of the two has also been confirmed, determining that there exists a range of coefficients in which only pair condensation, and not single-particle superfluidity, is present. The D…
In this paper, we study a system of two-component Bose gas in an artificial magnetic field trapped by concentric harmonic and annular potentials, respectively. The system is realized by gases with two-internal states like the hyperfine states of $^{87}$Rb. We are interested in effects of a Rabi oscillation between them. Two-component Bose Hubbard model is introduced to describe the system, and Gross-Pitaevskii equations are used to study the system. We first study the Bose gas system in the annular trap by varying the width of the annulus and strength of the magnetic field, in particular, we f…
We show that photon number measurement can be used to detect superfluidity for a two-band Bose-Hubbard model coupled to a cavity field. The atom-photon coupling induces transitions between the two internal atomic levels and results in entangled polaritonic states. In the presence of a cavity field, we find different photon numbers in the Mott-insulating versus superfluid phases, providing a method of distinguishing the atomic phases by photon counting. Furthermore, we examine the dynamics of the photon field after a rapid quench to zero atomic hopping by increasing the well depth. We find a ro…
We study fermionic superfluidity in strongly anisotropic optical lattices with attractive interactions utilizing the cluster DMFT method, and focusing in particular on the role of non-local quantum fluctuations. We show that non-local quantum fluctuations impact the BCS superfluid transition dramatically. Moreover, we show that exotic superfluid states with delicate order parameter structure, such as the Fulde-Ferrell-Larkin-Ovchinnikov phase driven by spin population imbalance, can emerge even in the presence of such strong fluctuations.
A semiclassical theory is provided for the metastability regime-diagram of atomtronic superfluid circuits. Such circuits typically exhibit high-dimensional chaos; and non-linear resonances that couple the Bogoliubov excitations manifest themselves. Contrary to the expectation these resonances do not originate from the familiar Beliaev and Landau damping terms. Rather, they are described by a variant of the Cherry Hamiltonian of celestial mechanics. Consequently we study the induced decay process, and its dependence on the number of sites and of condensed particles.
Despite the multi-band spectrum of the widely-known Hofstadter butterfly, it turns out that the pairing correlations of the time-reversal-symmetric Hofstadter-Hubbard model are well-described by a single order parameter that is uniform in real space. By exploiting a BCS mean-field theory for the nearly-flat butterfly-bands regime of low magnetic-flux limit, here we reveal a number of unusual superfluid properties both in the ground state and at finite temperatures. Our thorough analysis includes but is not limited to the order parameter, condensate and superfluid fractions, and the critical BC…
We obtain a phase diagram of the spin imbalanced Hubbard model on the Lieb lattice, which is known to feature a flat band in its single-particle spectrum. Using the BCS mean-field theory for multiband systems, we find a variety of superfluid phases with imbalance. In particular, we find four different types FFLO phases, i.e. superfluid phases with periodic spatial modulation. They differ by the magnitude and direction of the centre-of-mass momentum of Cooper pairs. We also see a large region of stable Sarma phase, where the density imbalance is associated with zero Cooper pair momentum. In the…
The hallmark of superfluidity is the appearance of metastable flow-states that carry a persistent circulating current. Considering Bose-Hubbard superfluid rings, we clarify the role of "quantum chaos" in this context. We show that the standard Landau and Bogoliubov superfluidity criteria fail for such low-dimensional circuits. We also discuss the feasibility for a coherent operation of a SQUID-like setup. Finally, we address the manifestation of the strong many-body dynamical localization effect.
The ground state and transport properties of the Lieb lattice flat band in the presence of an attractive Hubbard interaction are considered. It is shown that the superfluid weight can be large even for an isolated and strictly flat band. Moreover the superfluid weight is proportional to the interaction strength and to the quantum metric, a band structure invariant obtained from the flat-band Bloch functions. These predictions are amenable to verification with ultracold gases and may explain the anomalous behaviour of the superfluid weight of high-Tc superconductors.
Fermi-Hubbard system with a periodically-modulated interaction has been recently shown to resonantly absorb energy at series of drive frequencies. In the present work, with the help of static perturbation theory we argue that driving couples to Hubbard bands in a similar fashion as classical field couples to the two-level atom. The later, significantly simpler set-up described by the Rabi model is known to support resonant energy absorption at virtually the same series of driving frequencies. Our interpretation is also supported by showing that dynamics of the two-site periodically-driven Hubb…
We analyze the finite-temperature phase diagram of the boson-fermion-Hubbard model with Feshbach converting interaction, using the coherent-state path-integral method. We show that depending on the position of the bosonic band, this type of interaction, even if weak, can drive the system into the resonant superfluid phase in the strong bosonic interaction limit. It turns out that this phase can exist for an arbitrary number of fermions (i.e., fermionic concentration between 0 and 2) but with the bosonic particle number very close to an integer value. We point out that the standard time-of-flig…
We study the ground state phase diagram of a nonlinear two-photon Rabi-Hubbard (RH) model in one dimension using quantum Monte Carlo (QMC) simulations and density matrix renormalization group (DMRG) calculations. Our model includes a nonlinear photon-photon interaction term. Absent this term, the RH model has only one phase, the normal disordered phase, and suffers from spectral collapse at larger values of the photon-qubit interaction or inter-cavity photon hopping. The photon-photon interaction, no matter how small, stabilizes the system which now exhibits {\it two} quantum phase transitions…
We investigate the spin-polarized chain of ultracold fermionic atoms with spin-3/2 described by the fermionic Hubbard model with SU(4) symmetric attractive interaction. The competition of bound pairs, trions, quartets and unbound atoms is studied analytically and by density matrix renormalization group simulations. We find several distinct states where bound particles coexist with the ferromagnetic state of unpaired fermions. In particular, an exotic inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-type superfluid of quartets in a magnetic background of uncorrelated atoms is found for wea…
We use unbiased computational methods to elucidate the onset and properties of pair superfluidity in two-species fermionic and bosonic systems with onsite interspecies attraction loaded in one-dimensional optical lattice. We compare results from quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG), emphasizing the one-to-one correspondence between the Drude weight tensor, calculated with DMRG, and the various winding numbers extracted from the QMC. Our results show that, for any nonvanishing attractive interaction, pairs form and are the sole contributors to superfluidity,…
We study fermion pairing in a population-imbalanced mixture of $^{6}$Li atomic gas loaded in a three-dimensional lattice at very low temperatures. Using the number equation for each population, the gap equation and the equation for the Helmholtz free energy, we determine the gap, chemical potentials and pair-momentum as functions of polarization. These parameters define the stability regions for: a Fulde-Ferrell-Larkin-Ovchinnikov phase; a phase separation region where BCS and normal phases coexist; a Sarma phase when the pair-momentum vanishes, and the transition to the normal phase when the …
Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly-correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi-Hubbard model with ultracold atoms. After introducing the Fermi-Hubbard model in the context of condensed matter, its implementat…
The Bose-Hubbard Hamiltonian describes the competition between superfluidity and Mott insulating behavior at zero temperature and commensurate filling as the strength of the on-site repulsion is varied. Gapped insulating phases also occur at non-integer densities as a consequence of longer ranged repulsive interactions. In this paper we explore the formation of gapped phases in coupled chains due instead to anisotropies $t_x \neq t_y$ in the bosonic hopping, extending the work of Crepin {\it et al.} [Phys. Rev. B 84, 054517 (2011)] on two coupled chains, where a gap was shown to occur at half …
We study a system of ultracold fermionic Potassium (40K) atoms in a three-dimensional optical lattice in the vicinity of an s-wave Feshbach resonance. Close to resonance, the system is described by a multi-band Bose-Fermi Hubbard Hamiltonian. We derive an effective lowest-band Hamiltonian in which the effect of the higher bands is incorporated by a self-consistent mean-field approximation. The resulting model is solved by means of Generalized Dynamical Mean-Field Theory. In addition to the BEC/BCS crossover we find a phase transition to a fermionic Mott insulator at half filling, induced by th…
Motivated by recent experiments on atomic Dirac fermions in a tunable honeycomb optical lattice, we study the attractive Hubbard model of superfluidity in the anisotropic honeycomb lattice. At weak-coupling, we find that the maximum mean field pairing transition temperature, as a function of density and interaction strength, occurs for the case with isotropic hopping amplitudes. In this isotropic case, we go beyond mean field theory and study collective fluctuations, treating both pairing and density fluctuations for interaction strengths ranging from weak to strong coupling. We find evidence …
Extended Hubbard models have proven to bear novel quantum states, but their experimental realization remains challenging. In this work we propose to use bosonic quantum gases dressed with molecular bound states in Rydberg interaction potentials for the observation of these quantum states. We study the molecular Rabi coupling with respect to principal quantum number and trapping frequency of the ground state atoms for various molecular potentials of Rubidium and Potassium, and the hereby resulting dressed interaction strength. Additionally, we propose a two-color excitation scheme which signifi…
We report our findings on quantum phase transitions in cold bosonic atoms in a one dimensional optical lattice using the finite size density matrix renormalization group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest neighbor interactions. At commensurate fillings, we obtain two different types of charge density wave phases and a Mott insulator phase. However, departure from commensurate fillings yield the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we o…
The successful emulation of the Hubbard model in optical lattices has stimulated world wide efforts to extend their scope to also capture more complex, incompletely understood scenarios of many-body physics. Unfortunately, for bosons, Feynmans fundamental "no-node" theorem under very general circumstances predicts a positive definite ground state wave function with limited relevance for many-body systems of interest. A promising way around Feynmans statement is to consider higher bands in optical lattices with more than one dimension, where the orbital degree of freedom with its intrinsic anis…
We investigate the superfluid properties of d-wave pairing symmetry within the Extended Hubbard Model (EHM) in a magnetic field. We analyze the temperature and magnetic field dependencies of the order parameter. We find that in the two-dimensional case, the spatially homogeneous spin polarized superfluidity ($SC(P\neq0)$) is stable in the weak coupling limit, at T=0, as opposed to the s-wave pairing symmetry case in 2D. We construct the ground state phase diagrams both for fixed chemical potential ($μ$) and electron concentration ($n$). Furthermore, we obtain the temperature vs. magnetic field…
To analyze the ground-state phase diagram of Bose-Bose mixtures loaded into $d$-dimensional hypercubic optical lattices, we perform a strong-coupling power-series expansion in the kinetic energy term (plus a scaling analysis) for the two-species Bose-Hubbard model with onsite boson-boson interactions. We consider both repulsive and attractive interspecies interaction, and obtain an analytical expression for the phase boundary between the incompressible Mott insulator and the compressible superfluid phase up to third order in the hoppings. In particular, we find a re-entrant quantum phase trans…
Angle-resolved photoemission spectroscopy (ARPES) measures the single-particle excitations of a many-body quantum system with both energy and momentum resolution, providing detailed information about strongly interacting materials. ARPES is a direct probe of fermion pairing, and hence a natural technique to study the development of superconductivity in a variety of experimental systems ranging from high temperature superconductors to unitary Fermi gases. In these systems a remnant gap-like feature persists in the normal state, which is referred to as a pseudogap. A quantitative understanding o…
Supersolidity - a coexistence of superfluidity and crystalline or amorphous density variations - has been vividly debated ever since its conjecture. While the initial focus was on helium-4, recent experiments uncovered supersolidity in ultra-cold dipolar quantum gases. Here, we propose a new self-bound supersolid phase in a binary mixture of Bose gases with short-range interactions, making use of the non-trivial properties of spin-orbit coupling. We find that a first-order phase transition from a self-bound supersolid stripe phase to a zero-minimum droplet state of the Bose gas occurs as a fun…
We investigate the quantum phase transitions of a two-dimensional Bose-Hubbard model in the presence of a Rashba spin-orbit coupling with and without thermal fluctuations. The interplay of single-particle hopping, strength of spin-orbit coupling, and interspin interaction leads to superfluid phases with distinct properties. With interspin interactions weaker than intraspin interactions, the spin-orbit coupling induces two finite-momentum superfluid phases. One of them is a phase-twisted superfluid that exists at low hopping strengths and reduces the domain of insulating phases. At comparativel…
The effect of disorder in the intensity of the driving laser on a coupled array of cavities described by a Bose-Hubbard Hamiltonian for dark-state polaritons is investigated. A canonically-transformed Gutzwiller wave function is used to investigate the phase diagram and dynamics of a one-dimensional system with uniformly distributed disorder in the Rabi frequency. In the phase diagram, we find the emergence of a Bose glass phase that increases in extent as the strength of the disorder increases. We study the dynamics of the system when subject to a ramp in the Rabi frequency which, starting fr…
We describe the treatment of Rashba spin-orbit coupling (SOC) in interacting many-fermion systems within the auxiliary-field quantum Monte Carlo framework, and present a set of illustrative results. These include numerically exact calculations on the ground-state properties of the spin-balanced, attractive two-dimensional Fermi gas, as well as a study of a tight-binding Hamiltonian with repulsive interaction. These systems are formally connected via the Hubbard Hamiltonian with SOC, but cover different physics ranging from superfluidity and triplet pairing to SOC in real materials in the prese…
We study the attractive Hubbard model with spin imbalance on two lattices featuring a flat band: the Lieb and kagome lattices. We present mean-field phase diagrams featuring exotic superfluid phases, similar to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, whose stability is confirmed by dynamical mean-field theory (DMFT). The nature of the pairing is found to be richer than just the Fermi surface shift responsible for the usual FFLO state. The presence of a flat band allows for changes in the particle momentum distributions at null energy cost. This facilitates formation of nontrivial su…
We study the interplay between large-spin, spin-orbit coupling, and superfluidity for bosons in a two dimensional optical lattice, focusing on the spin-1 spin-orbit coupled system recently realized at the Joint Quantum Institute [Campbell et. al., arXiv:1501.05984]. We find a rich quantum phase diagram, where, in addition to the conventional phases ---superfluid and insulator--- contained in the spin-$1$ Bose-Hubbard model, there are new lattice symmetry breaking phases. For weak interactions, the interplay between two length scales, the lattice momentum and the spin-orbit wave-vector induce a…
