The quantum dynamics of population-balanced fractional vortices and population-imbalanced vortices in an effective two-state bosonic system, made of two coupled discrete circuits with few sites, is addressed within the Bose-Hubbard model. % We show that for low on-site interaction, the tunneling of quantized vortices between the rings performs a coherent, oscillating dynamics connecting current states with chiral symmetry. The vortex-flux transfer dually follows the usual sinusoidal particle current of the Josephson effect, in good agreement with a mean-field approximation. Within such regime, the switch of persistent currents in the rings resembles flux-qubit features, and is feasible to experimental realization. On the contrary, strong interatomic interactions suppress the chiral current and lead the system into fragmented condensation.
We study the Mott phase of the Bose-Hubbard model on a tilted lattice. On the (Gutzwiller) mean-field level, the tilt has no effect -- but quantum fluctuations entail particle-hole pair creation via tunneling. For small potential gradients (long-wavelength limit), we derive a quantitative analogy to the Sauter-Schwinger effect, i.e., electron-positron pair creation out of the vacuum by an electric field. For large tilts, we obtain resonant tunneling related to Bloch oscillations.
We investigate cold bosonic impurity atoms trapped in a vortex lattice formed by condensed bosons of another species. We describe the dynamics of the impurities by a bosonic Hubbard model containing occupation-dependent parameters to capture the effects of strong impurity-impurity interactions. These include both a repulsive direct interaction and an attractive effective interaction mediated by the BEC. The occupation dependence of these two competing interactions drastically affects the Hubbard model phase diagram, including causing the disappearance of some Mott lobes
In this article we show that a Dirac Hamiltonian in a curved background spacetime can be interpreted, when discretized, as a tight binding Fermi-Hubbard model with non unitary tunnelings. We find the form of the nonunitary tunneling matrices in terms of the metric tensor. The main motivation behind this exercise is the feasibility of such Hamiltonians by means of laser assisted tunnelings in cold atomic experiments. The mapping thus provide a physical interpretation of such Hamiltonians. We demonstrate the use of the mapping on the example of time dependent metric in 2+1 dimensions. Studying t…
We show that multi-orbital and density-induced tunneling have a significant impact on the phase diagram of bosonic atoms in optical lattices. Off-site interactions lead to density-induced hopping, the so-called bond-charge interactions, which can be identified with an effective tunneling potential and can reach the same order of magnitude as conventional tunneling. In addition, interaction-induced higher-band processes also give rise to strongly modified tunneling, on-site and bond-charge interactions. We derive an extended occupation-dependent Hubbard model with multi-orbitally renormalized p…
We report on the experimental implementation of tunable occupation-dependent tunneling in a Bose-Hubbard system of ultracold atoms via time-periodic modulation of the on-site interaction energy. The tunneling rate is inferred from a time-resolved measurement of the lattice site occupation after a quantum quench. We demonstrate coherent control of the tunneling dynamics in the correlated many-body system, including full suppression of tunneling as predicted within the framework of Floquet theory. We find that the tunneling rate explicitly depends on the atom number difference in neighboring lat…
We consider a theoretical model of a four-mode Bose-Hubbard model consisting of two pairs of wells coupled via two processes with two different rates. The model is naturally divided into two subsystems with strong intra-system coupling and much weaker coupling between the two subsystems and has previously been introduced as a model for Josephson heat oscillations by Strzys and Anglin [\pra {\bf 81}, 043616 (2010) ]. We examine the quantum dynamics of this model for a range of different initial conditions, in terms of both the number distribution among the wells and the quantum statistics. We f…
A vortex can tunnel between two pinning potentials in an atomic Bose-Einstein condensate on a time scale of the order of 1s under typical experimental conditions. This makes it possible to detect the tunneling experimentally. We calculate the tunneling rate by phenomenologically treating vortices as point-like charged particles moving in an inhomogeneous magnetic field. The obtained results are in close agreement with numerical simulations based on the stochastic c-field theory.
We study an experimentally realizable paradigm of complex many-body quantum systems, a two-band Wannier-Stark model, for which diffusion in Hilbert space as well as many-body Landau-Zener processes can be engineered. A cross-over between regular to quantum chaotic spectra is found within the many-body avoided crossings at resonant tunneling conditions. The spectral properties are shown to determine the evolution of states across a cascade of Landau-Zener events. We apply the obtained spectral information to study the non-equilibrium dynamics of our many-body system in different parameter regim…
Recently, it has become apparent that, when the interactions between polar molecules in optical lattices becomes strong, the conventional description using the extended Hubbard model has to be modified by additional terms, in particular a density-dependent tunneling term. We investigate here the influence of this term on the ground-state phase diagrams of the two dimensional extended Bose-Hubbard model. Using Quantum Monte Carlo simulations, we investigate the changes of the superfluid, supersolid, and phase-separated parameter regions in the phase diagram of the system. By studying the interp…
In this work, we study the out-of-equilibrium many-body tunneling dynamics of a Bose-Einstein condensate in a two-dimensional radial double well. We investigate the impact of interparticle repulsion and compare the influence of angular momentum on the many-body tunneling dynamics. Accurate many-body dynamics are obtained by solving the full many-body Schrödinger equation. We demonstrate that macroscopic vortex states of definite total angular momentum indeed tunnel and that, even in the regime of weak repulsions, a many-body treatment is necessary to capture the correct tunneling dynamics. As …
Recently, it has been shown that the momentum distribution of a metallic state of fermionic atoms in a lattice Fermi-Bose mixture exhibits coherent oscillations after a global quench that suppresses tunneling. The oscillation period is determined by the Fermi-Bose interaction strength. Here we show that similar dynamics occurs in the fermionic Hubbard model when we quench a noninteracting metallic state by introducing a Hubbard interaction and suppressing tunneling. The period is determined primarily by the interaction strength. Conversely, we show that one can accurately determine the Hubbard…
We construct the effective lowest-band Bose-Hubbard model incorporating interaction-induced on-site correlations. The model is based on ladder operators for local correlated states, which deviate from the usual Wannier creation and annihilation, allowing for a systematic construction of the most appropriate single-band low-energy description in the form of the extended Bose-Hubbard model. A formulation of this model in terms of ladder operators not only naturally contains the previously found effective multibody interactions, but also contains multibody-induced single-particle tunneling, pair …
The emergence of vortex-bright soliton dipoles in two-component Bose-Einstein condensates through bifurcations from suitable eigenstates of the underlying linear system is examined. These dipoles can have their bright solitary structures be in phase (symmetric) or out of phase (anti-symmetric). The dynamical robustness of each of these two possibilities is considered and the out-of-phase case is found to exhibit an intriguing symmetry-breaking instability that can in turn lead to tunneling of the bright wavefunction between the two vortex "wells". We interpret this phenomenon by virtue of a vo…
We apply the Bose-Hubbard Hamiltonian to a three-well system and show analytically that coherent transport via adiabatic passage (CTAP) of $N$ non-interacting particles across the chain is possible. We investigate the effect of detuning the middle well to recover CTAP when on-site interparticle interactions would otherwise disrupt the transport. The case of small interactions is restated using first-order perturbation theory to develop criteria for adibaticity that define the regime where CTAP is possible. Within this regime we investigate restricting the Hilbert space to the minimum necessary…
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…
We analyze the tunneling of vortex states from elliptically shaped traps. Using the hydrodynamic representation of the Gross-Pitaevskii (Nonlinear Schrödinger) equation, we derive analytically and demonstrate numerically a novel type of quantum fluid flow: a jet-like singularity formed by the interaction between the vortex and the nonhomogenous field. For strongly elongated traps, the ellipticity overwhelms the circular rotation, resulting in the ejection of field in narrow, well-defined directions. These jets can also be understood as a formation of caustics since they correspond to a converg…
We introduce a scheme that combines photon-assisted tunneling by a moving optical lattice with strong Hubbard interactions, and allows for the quantum simulation of paradigmatic quantum many-body models. We show that, in a certain regime, this quantum simulator yields an effective Hubbard Hamiltonian with tunable bond-charge interactions, a model studied in the context of strongly-correlated electrons. In a different regime, we show how to exploit a correlated destruction of tunneling to explore Nagaoka ferromagnetism at finite Hubbard repulsion. By changing the photon-assisted tunneling param…
We present the quantum and classical study of a four-well trapped Bose-Einstein condensate (BEC) modeled by the Bose-Hubbard Hamiltonian. The model used is fashioned as a minimal bipartite system consisting of a trimer coupled weakly to a monomer. Semiclassical insights into the fragmentation dynamics of the condensate is obtained by mapping out the Arnold web of the high dimensional classical phase space. A remarkable one-to-one correspondence between the quantum state space in occupation number representation and the classical Arnold web in action space is observed. The relevance of dynamica…
We study the dynamical properties of a few bosons confined in an one-dimensional split hard wall trap with the interaction strength varying from the weakly to strongly repulsive regime. The system is initially prepared in one side of the double well by setting the barrier strength of the split trap to be infinity and then the barrier strength is suddenly changed to a finite value. Both exact diagonalization method and Bose-Hubbard model (BHM) approximation are used to study the dynamical evolution of the initial system. The exact results based on exact diagonaliztion verify the enhancement of …
The effect of the next-nearest-neighbor (nnn) tunneling on the hard-core extended Bose-Hubbard model on square lattices is investigated. By means of the cluster mean-field theory, the ground-state phase diagrams are determined. When a modest nnn tunneling is introduced, depending on its sign, two distinct supersolid states with checkerboard crystal structures are found away from half-filing. The characters of various phase transitions out of these two supersolid states are discussed. In particular, for the case with kinetic frustration, the existence of a half supersolid phase possessing both …
We study the tunneling dynamics in a time-periodically modulated two-mode Bose-Hubbard model using Floquet theory. We consider situations where the system is in the self-trapping regime and either the tunneling amplitude, the interaction strength, or the energy difference between the modes is modulated. In the former two cases, the tunneling is enhanced in a wide range of modulation frequencies, while in the latter case the resonance is narrow. We explain this difference with the help of Floquet analysis. If the modulation amplitude is weak, the locations of the resonances can be found using t…
We study macroscopic superpositions in the orbital rather than the spatial degrees of freedom, in a three-dimensional double-well system. We show that the ensuing dynamics of $N$ interacting excited ultracold bosons, which in general requires at least eight single-particle modes and ${N+7 \choose N}$ Fock vectors, is described by a surprisingly small set of many-body states. An initial state with half the atoms in each well, and purposely excited in one of them, gives rise to the tunneling of axisymmetric and transverse vortex structures. We show that transverse vortices tunnel orders of magni…
Recent realization of well-controlled quantum simulators of the triangular-lattice Fermi-Hubbard model, including the triangular optical lattices loaded with ultracold Fermions and the heterostructures of the transition-metal dichalcogenides, as well as the more advanced techniques to probe them, pave the way for studying frustrated Fermi-Hubbard physics. Here, we theoretically predict asymmetric photoemission and tunneling spectroscopies for a lightly hole-doped and electron-doped triangular Mott antiferromagnet, and reveal two distinct types of magnetic polarons: a \emph{lightly} renormalize…
The extended Bose-Hubbard model for a double-well potential with pair tunneling is studied through both exact diagonalization and mean field theory (MFT). When pair tunneling is strong enough, the ground state wavefunction predicted by the MFT is complex and doubly degenerate while the quantum ground state wavefunction is always real and unique. The time reversal symmetry is spontaneously broken when the system transfers from the quantum ground state into one of the mean field ground states upon a small perturbation. As the gap between the lowest two levels decreases exponentially with particl…
We study quantum vortex states of strongly interacting bosons in a two-dimensional rotating optical lattice. The system is modeled by Bose-Hubbard Hamiltonian with rotation. We consider lattices of different geometries, such as square, rectangular and triangular. Using numerical exact diagonalization method we show how the rotation introduces vortex states of different ground-state symmetries and the transition between these states at discrete rotation frequencies. We show how the geometry of the lattice plays crucial role in determining the maximum number of vortex states as well as the gener…
We study a Bose-Hubbard model having on-site repulsion, nearest-neighbor tunneling, and ferromagneticlike coupling between occupation parities of nearest-neighbor sites. For a uniform system in any dimension at zero tunneling, we obtain an exact phase diagram characterized by Mott-insulator (MI) and pair liquid phases and regions of phase separation of two MIs. For a general trapped system in one and two dimensions with finite tunneling, we perform quantum Monte Carlo and Gutzwiller mean-field calculations, both of which show the evolution of the system, as the parity coupling increases, from …
We investigate the quantum phases of ultracold atoms trapped in a vortex lattice using a mixture of two bosonic species (A and B), in the presence of an artificial gauge field. Heavy atoms of species B are confined in the array of vortices generated in species A, and they are described through a Bose-Hubbard model. In contrast to the optical-lattice setups, the vortex lattice has an intrinsic dynamics, given by its Tkachenko modes. Including these quantum fluctuations in the effective model for B atoms yields an extended Bose-Hubbard model, with an additional "phonon"-mediated long-range attra…
The extended Bose-Hubbard model with pure three-body local interactions is studied using the Density Matrix Renormalization Group approach. The shapes of the first two insulating lobes are discussed, and the values of the critical tunneling for which the system undergoes the quantum phase transition from insulating to superfluid phase are predicted. It is shown that stability of insulating phases, in contrast to the standard Bose-Hubbard model, is enhanced for larger fillings. It is also shown that, on the tip of the boundary of the insulating phase, the model under consideration belongs to th…
We study the 3D Hubbard model with anisotropic nearest neighbor tunneling amplitudes using the dynamical cluster approximation and compare the results with a quantum simulation experiment using ultracold fermions in an optical lattice, focussing on magnetic correlations. We find that the short-range spin correlations are significantly enhanced in the direction with stronger tunneling amplitudes. Our results agree with the experimental observations and show that the experimental temperature is lower than the strong tunneling amplitude. We characterize the system by examining the spin correlatio…
We study the quantum phase transition between the superfluid and the Mott insulator in the one-dimensional (1D) Bose-Hubbard model. Using the time-evolving block decimation method, we numerically calculate the tunneling splitting of two macroscopically distinct states with different winding numbers. From the scaling of the tunneling splitting with respect to the system size, we determine the critical point of the superfluid to Mott insulator transition for arbitrary integer filling factors. We find that the critical values versus the filling factor in 1D, 2D, and 3D are well approximated by a …
We have prepared two ultracold fermionic atoms in an isolated double-well potential and obtained full control over the quantum state of this system. In particular, we can independently control the interaction strength between the particles, their tunneling rate between the wells and the tilt of the potential. By introducing repulsive (attractive) interparticle interactions we have realized the two-particle analog of a Mott-insulating (charge-density-wave) state. We have also spectroscopically observed how second-order tunneling affects the energy of the system. This work realizes the first ste…
We investigate the ground state properties of ultracold atoms trapped in a two-leg ladder potential in the presence of an artificial magnetic field in a staggered configuration. We focus on the strongly interacting regime and use the Landau theory of phase transitions and a mean field Gutzwiller variational method to identify the stable superfluid phases and their boundaries with the Mott-insulator regime as a function of magnetic flux. In addition, we calculate the local and chiral currents of these superfluid phases, which show a staggered vortex anti-vortex configuration. The analytical res…
The Bose-Hubbard model is well-defined description of a Bose solid which may be realistic for cold atoms in a periodic optical lattice. We show that contrary to accepted theories it can never have as a ground state a perfect Mott insulator solid and that it has a low-energy spectrum of vortex-like phase fluctuations. Whether the ground state is necessarily commensurate remains an open question.
The realization of antiferromagnetic (AF) correlations in ultracold fermionic atoms on an optical lattice is a significant achievement. Experiments have been carried out in one, two, and three dimensions, and have also studied anisotropic configurations with stronger tunneling in some lattice directions. Such anisotropy is relevant to the physics of cuprate superconductors and other strongly correlated materials. Moreover, this anisotropy might be harnessed to enhance AF order. Here we numerically investigate, using Determinant Quantum Monte Carlo, a simple realization of anisotropy in the 3D …
We use lithium-6 atoms in an optical tweezer array to realize an eight-site Fermi-Hubbard chain near half filling. We achieve single site detection by combining the tweezer array with a quantum gas microscope. By reducing disorder in the energy offsets to less than the tunneling energy, we observe Mott insulators with strong antiferromagnetic correlations. The measured spin correlations allow us to put an upper bound on the entropy of 0.26(4)$k_\mathrm{B}$ per atom, comparable to the lowest entropies achieved with optical lattices. Additionally, we establish the flexibility of the tweezer plat…
We consider theoretically ultracold interacting bosonic atoms confined to quasi-one-dimensional ladder structures formed by optical lattices and coupled to the field of an optical cavity. The atoms can collect a spatial phase imprint during a cavity-assisted tunneling along a rung via Raman transitions employing a cavity mode and a transverse running wave pump beam. By adiabatic elimination of the cavity field we obtain an effective Hamiltonian for the bosonic atoms, with a self-consistency condition. Using the numerical density matrix renormalization group method, we obtain a rich steady stat…
The Fermi-Hubbard model describes ultracold fermions in an optical lattice and exhibits antiferromagnetic long-ranged order below the Néel temperature. However, reaching this temperature in the lab has remained an elusive goal. In other atomic systems, such as trapped ions, low temperatures have been successfully obtained by adiabatic demagnetization, in which a strong effective magnetic field is applied to a spin-polarized system, and the magnetic field is adiabatically reduced to zero. Unfortunately, applying this approach to the Fermi-Hubbard model encounters a fundamental obstacle: the $SU…
In this paper, we study the dynamics of the Bose-Hubbard model by using time-dependent Gutzwiller methods. In particular, we vary the parameters in the Hamiltonian as a function of time, and investigate the temporal behavior of the system from the Mott insulator to the superfluid (SF) crossing a second-order phase transition. We first solve a time-dependent Schrödinger equation for the experimental setup recently done by Braun et.al. [Proc. Nat. Acad. Sci. 112, 3641 (2015)] and show that the numerical and experimental results are in fairly good agreement. However, these results disagree with t…
Recent quantum-gas microscopy of ultracold atoms and scanning tunneling microscopy of the cuprates reveal new detailed information about doped Mott antiferromagnets, which can be compared with calculations. Using cellular dynamical mean-field theory, we map out the antiferromagnetic (AF) phase of the two-dimensional Hubbard model as a function of interaction strength $U$, hole doping $δ$ and temperature $T$. The Néel phase boundary is non-monotonic as a function of $U$ and $δ$. Frustration induced by second-neighbor hopping reduces Néel order more effectively at small $U$. The doped AF is stab…
We study the dynamics of bosonic atoms in a tilted one-dimensional optical lattice and report on the first direct observation of density-induced tunneling. We show that the interaction affects the time evolution of the doublon oscillation via density-induced tunneling and pinpoint its density- and interaction-dependence. The experimental data for different lattice depths are in good agreement with our theoretical model. Furthermore, resonances caused by second-order tunneling processes are studied, where the density-induced tunneling breaks the symmetric behavior for attractive and repulsive i…
We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose-Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling the system features a phase-transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background -- instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of pa…
We present a two-band Bose-Hubbard model which is shown to be minimal in the necessary coupling terms at resonant tunneling conditions. The dynamics of the many-body problem is studied by sweeping the system across an avoided level crossing. The linear sweep generalizes Landau-Zener transitions from single-particle to many-body realizations. The temporal evolution of single- and two-body observables along the sweeps is investigated in order to characterize the non-equilibrium dynamics in our complex quantum system.
The high-barrier quantum tunneling regime of a Bose-Einstein condensate confined in a ring-shaped optical lattice is investigated. By means of a change of basis transformation, connecting the set of `vortex' Bloch states and a Wannier-like set of localized wave functions, we derive a generalized Bose-Hubbard Hamiltonian. In addition to the usual hopping rate terms, such a Hamiltonian takes into account interaction-driven tunneling processes, which are shown to play a principal role at high filling factors, when the standard hopping rate parameter turns out to be negative. By calculating the en…
