The inhomogeneous extended Bose-Hubbard model: A mean-field theory

We develop an inhomogeneous mean-field theory for the extended Bose-Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean-field theory yields the phase diagram of the homogeneous extended Bose-Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott-insulator (MI), density-wave (DW), and supersolid (SS) phases in the plane of the chemical potential mu and on-site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest-neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density-wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold-atom dipolar condensates in optical lattices in a confining potential.

GINZBURG-LANDAU LIKE THEORY OF HIGH TEMPERATURE SUPERCONDUCTIVITY IN THE CUPRATES: EMERGENT d-WAVE ORDER

High temperature superconductivity in the cuprates remains one of the most widely investigated, constantly surprising and poorly understood phenomena in physics. Here, we describe briefly a new phenomenological theory inspired by the celebrated description of superconductivity due to Ginzburg and Landau and believed to describe its essence. This posits a free energy functional for the superconductor in terms of a complex order parameter characterizing it. We propose that there is, for superconducting cuprates, a similar functional of the complex, in plane, nearest neighbor spin singlet bond (or Cooper) pair amplitude psi(ij). Further, we suggest that a crucial part of it is a (short range) positive interaction between nearest neighbor bond pairs, of strength J'. Such an interaction leads to nonzero long wavelength phase stiffness or superconductive long range order, with the observed d-wave symmetry, below a temperature T-c similar to zJ' where z is the number of nearest neighbors; d-wave superconductivity is thus an emergent, collective consequence. Using the functional, we calculate a large range of properties, e. g., the pseudogap transition temperature T* as a function of hole doping x, the transition curve T-c(x), the superfluid stiffness rho(s)(x, T), the specific heat (without and with a magnetic field) due to the fluctuating pair degrees of freedom and the zero temperature vortex structure. We find remarkable agreement with experiment. We also calculate the self-energy of electrons hopping on the square cuprate lattice and coupled to electrons of nearly opposite momenta via inevitable long wavelength Cooper pair fluctuations formed of these electrons. The ensuing results for electron spectral density are successfully compared with recent experimental results for angle resolved photo emission spectroscopy (ARPES), and comprehensively explain strange features such as temperature dependent Fermi arcs above T-c and the ``bending'' of the superconducting gap below T-c.

Bose-Hubbard models in confining potentials: Inhomogeneous mean-field theory

We present an extensive study of Mott insulator (MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with harmonic traps. For this we apply the inhomogeneous mean-field theory developed by Sheshadri et al. Phys. Rev. Lett. 75, 4075 (1995)]. Our results for the BH model with one type of spinless bosons agree quantitatively with quantum Monte Carlo simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculations on experimentally realistic, large three-dimensional systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also extend our inhomogeneous mean-field theory to study BH models with harmonic traps and (a) two species of bosons or (b) spin-1 bosons. With two species of bosons, we obtain rich phase diagrams with a variety of SF and MI phases and associated shells when we include a quadratic confining potential. For the spin-1 BH model, we show, in a representative case, that the system can display alternating shells of polar SF and MI phases, and we make interesting predictions for experiments in such systems.

Interacting fermions in synthetic non-Abelian gauge fields

Generation and study of synthetic gauge fields has enhanced the possibility of using cold atom systems as quantum emulators of condensed matter Hamiltonians. In this article we describe the physics of interacting spin -1/2 fermions in synthetic non-Abelian gauge fields which induce a Rashba spin-orbit interaction on the motion of the fermions. We show that the fermion system can evolve to a Bose-Einstein condensate of a novel boson which we call rashbon. The rashbon-rashbon interaction is shown to be independent of the interaction between the constituent fermions. We also show that spin-orbit coupling can help enhancing superfluid transition temperature of weak superfluids to the order of Fermi temperature. A non-Abelian gauge field, when used in conjunction with another potential, can generate interesting Hamiltonians such as that of a magnetic monopole.

Surface Instabilities and Generation of Multielectron Bubbles Under Pulsed Electric Fields

We studied the development of surface instabilities leading to the generation of multielectron bubbles (MEBs) in superfluid helium upon the application of a pulsed electric field. We found the statistical distribution of the charge of individual instabilities to be strongly dependent on the duration of the electric field pulse. The rate and probability of generation of these instabilities in relation to the temporal characteristics of the applied field was also investigated.

Chiral Mott insulator with staggered loop currents in the fully frustrated Bose-Hubbard model

Motivated by experiments on Josephson junction arrays in a magnetic field and ultracold interacting atoms in an optical lattice in the presence of a ``synthetic'' orbital magnetic field, we study the ``fully frustrated'' Bose-Hubbard model and quantum XY model with half a flux quantum per lattice plaquette. Using Monte Carlo simulations and the density matrix renormalization group method, we show that these kinetically frustrated boson models admit three phases at integer filling: a weakly interacting chiral superfluid phase with staggered loop currents which spontaneously break time-reversal symmetry, a conventional Mott insulator at strong coupling, and a remarkable ``chiral Mott insulator'' (CMI) with staggered loop currents sandwiched between them at intermediate correlation. We discuss how the CMI state may be viewed as an exciton condensate or a vortex supersolid, study a Jastrow variational wave function which captures its correlations, present results for the boson momentum distribution across the phase diagram, and consider various experimental implications of our phase diagram. Finally, we consider generalizations to a staggered flux Bose-Hubbard model and a two-dimensional (2D) version of the CMI in weakly coupled ladders.

Quantum phases and phase transitions of frustrated hard-core bosons on a triangular ladder

Kinetically frustrated bosons at half filling in the presence of a competing nearest-neighbor repulsion support a wide supersolid regime on the two-dimensional triangular lattice. We study this model on a two-leg ladder using the finite-size density-matrix renormalization-group method, obtaining a phase diagram which contains three phases: a uniform superfluid (SF), an insulating charge density wave (CDW) crystal, and a bond ordered insulator (BO). We show that the transitions from SF to CDW and SF to BO are continuous in nature, with critical exponents varying continuously along the phase boundaries, while the transition from CDW to BO is found to be first order. The phase diagram is also found to contain an exactly solvable Majumdar Ghosh point, and reentrant SF to CDW phase transitions.

Flow-enhanced pairing and other unusual effects in Fermi gases in synthetic gauge fields

Recent experiments on fermions in synthetic gauge fields result in systems with a spin-orbit coupling along one spatial axis, a detuning field, and a Zeeman field. We show theoretically that the presence of all three results in interesting and unusual phenomena in a system of interacting fermions (interactions described by a scattering length). For two fermions, bound states appear only over a certain range of the center-of-mass momenta. The deepest bound state appears at a nonzero center-of-mass momentum. For center-of-mass momenta without a bound state, the gauge field induces a resonance-like feature in the scattering continuum resulting in a large scattering phase shift. In the case of many particles, we demonstrate that the system, in a parameter range, shows flow-enhanced pairing, i.e., a Fulde-Farrell-Larkin-Ovchnnikov superfluid state made of robust pairs with a finite center-of-mass momentum. Yet another regime of parameters offers the opportunity to study strongly interacting normal states of spin-orbit-coupled fermionic systems utilizing the resonance-like feature induced by the synthetic gauge field.

Hard-core bosons in a zig-zag optical superlattice

We study a system of hard-core bosons at half-filling in a one-dimensional optical superlattice. The bosons are allowed to hop to nearest-and next-nearest-neighbor sites. We obtain the ground-state phase diagram as a function of microscopic parameters using the finite-size density-matrix renormalization-group method. Depending on the sign of the next-nearest-neighbor hopping and the strength of the superlattice potential the system exhibits three different phases, namely the bond-order (BO) solid, the superlattice induced Mott insulator (SLMI), and the superfluid (SF) phase. When the signs of both hopping amplitudes are the same (the unfrustratedase), the system undergoes a transition from the SF to the SLMI at a nonzero value of the superlattice potential. On the other hand, when the two amplitudes differ in sign (the frustrated case), the SF is unstable to switching on a superlattice potential and also exists only up to a finite value of the next-nearest-neighbor hopping. This part of the phase diagram is dominated by the BO phase which breaks translation symmetry spontaneously even in the absence of the superlattice potential and can thus be characterized by a bond-order parameter. The transition from BO to SLMI appears to be first order.

Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity

We develop a strong-coupling (t << U) expansion technique for calculating the density profile for bosonic atoms trapped in an optical lattice with an overall harmonic trap at finite temperature and finite on-site interaction in the presence of superfluid regions. Our results match well with quantum Monte Carlo simulations at finite temperature. We also show that the superfluid order parameter never vanishes in the trap due to the proximity effect. Our calculations for the scaled density in the vacuum-to-superfluid transition agree well with the experimental data for appropriate temperatures. We present calculations for the entropy per particle as a function of temperature which can be used to calibrate the temperature in experiments. We also discuss issues connected with the demonstration of universal quantum critical scaling in the experiments.

Hydrodynamics of compressible superfluids in confined geometries

We present a study of the hydrodynamics of compressible superfluids in confined geometries. We use a perturbative procedure in terms of the dimensionless expansion parameter (v/v(s))(2) where v is the typical speed of the flow and vs is the speed of sound. A zero value of this parameter corresponds to the incompressible limit. We apply the procedure to two specific problems: the case of a trapped superfluid with a Gaussian profile of the local density, and that of a superfluid confined in a rotating obstructed cylinder. We find that the corrections due to finite compressibility which are, as expected, negligible for liquid He, are important but amenable to the perturbative treatment for typical ultracold atomic systems.

Dynamical localization in a chain of hard core bosons under periodic driving

We study the dynamics of a one-dimensional lattice model of hard core bosons which is initially in a superfluid phase with a current being induced by applying a twist at the boundary. Subsequently, the twist is removed, and the system is subjected to periodic delta-function kicks in the staggered on-site potential. We present analytical expressions for the current and work done in the limit of an infinite number of kicks. Using these, we show that the current (work done) exhibits a number of dips (peaks) as a function of the driving frequency and eventually saturates to zero (a finite value) in the limit of large frequency. The vanishing of the current (and the saturation of the work done) can be attributed to a dynamic localization of the hard core bosons occurring as a consequence of the periodic driving. Remarkably, we show that for some specific values of the driving amplitude, the localization occurs for any value of the driving frequency. Moreover, starting from a half-filled lattice of hard core bosons with the particles localized in the central region, we show that the spreading of the particles occurs in a light-cone-like region with a group velocity that vanishes when the system is dynamically localized.

Fermions in Synthetic Non-Abelian Gauge Fields

Quantum emulation property of the cold atoms has generated a lot of interest in studying systems with synthetic gauge fields. In this article, we describe the physics of two component Fermi gas in the presence of synthetic non-Abelian SU(2) gauge fields. Even for the non-interacting system with the gauge fields, there is an interesting change in the topology of the Fermi surface by tuning only the gauge field strength. When a trapping potential is used in conjunction with the gauge fields, the non-interacting system has the ability to produce novel Hamiltonians and show characteristic change in the density profile of the cloud. Without trap, the gauge fields act as an attractive interaction amplifier and for special kinds of gauge field configurations, there are two-body bound states for any attraction even in three dimensions. For a many body system, the gauge fields can induce a crossover from a weak superfluid to a strong superfluid with transition temperature as high as the Fermi temperature. The superfluid state obtained for a very large gauge field strength is a superfluid of new kind of bosons, called ``rashbons'', the properties of which are independent of its constituent two component fermions and are solely determined by the gauge field strength. We also discuss the collective excitations over the superfluid ground states and the experimental relevance of the physics.

Fluctuation theory of Rashba Fermi gases: Gaussian and beyond

Fermi gases with generalized Rashba spin-orbit coupling induced by a synthetic gauge field have the potential of realizing many interesting states, such as rashbon condensates and topological phases. Here, we address the key open problem of the fluctuation theory of such systems and demonstrate that beyond-Gaussian effects are essential to capture the finite temperature physics of such systems. We obtain their phase diagram by constructing an approximate non-Gaussian theory. We conclusively establish that spin-orbit coupling can enhance the exponentially small transition temperature (T-c) of a weakly attracting superfluid to the order of the Fermi temperature, paving a pathway towards high T-c superfluids.

Doping dependence of fluctuation diamagnetism in high T-c superconductors

Using a recently proposed Ginzburg-Landau-like lattice free energy functional due to Banerjee et al. (2011) we calculate the fluctuation diamagnetism of high -T-c superconductors as a function of doping, magnetic field and temperature. We analyse the pairing fluctuations above the superconducting transition temperature in the cuprates, ranging from the strong phase fluctuation dominated underdoped limit to the more conventional amplitude fluctuation dominated overdoped regime. We show that a model where the pairing scale increases and the superfluid density decreases with underdoping produces features of the observed magnetization in the pseudogap region, in good qualitative and reasonable quantitative agreement with the experimental data. In particular, we explicitly show that even when the pseudogap has a pairing origin the magnetization actually tracks the superconducting dome instead of the pseudogap temperature, as seen in experiment. We discuss the doping dependence of the `onset' temperature for fluctuation diamagnetism and comment on the role of vortex core -energy jn our model. (C) 2015 Elsevier Inc. All rights reserved.