superfluid-Mott Insulator Research Articles

Magnetothermoelectric response near quantum critical points

Following on from our previous work [M. J. Bhaseen , Phys. Rev. Lett. 98, 166801 (2007)] we examine the finite temperature magnetothermoelectric response in the vicinity of a quantum critical point (QCP). We begin with general scaling considerations relevant to an arbitrary QCP, either with or without Lorentz invariance, and in arbitrary dimension. In view of the broad connections to high-temperature superconductivity and cold atomic gases, we focus on the quantum critical fluctuations of the relativistic Landau-Ginzburg theory. This paradigmatic model arises in many contexts and describes the (particle-hole symmetric) superfluid-Mott insulator quantum phase transition in the Bose-Hubbard model. The application of a magnetic field opens up a wide range of physical observables, and we present a detailed overview of the charge and thermal transport and thermodynamic response. We combine several different approaches including the epsilon expansion and associated quantum Boltzmann equation, entropy drift, and arguments based on Lorentz invariance. The results differ markedly from the zero-field case, and we include an extended discussion of the finite thermal conductivity which emerges in the presence of a magnetic field. We derive an integral equation that governs its response and explore the crossover upon changing the magnetic field. This equation may be interpreted as a projection equation in the low-field limit, and clearly highlights the important role of collision invariants (or zero modes) in the hydrodynamic regime. Using an epsilon expansion around three dimensions, our analytic and numerical results interpolate between our previously published value and the exact limit of two-dimensional relativistic magnetohydrodynamics.

Quantum phase diagram of bosons in optical lattices

We work out two different analytical methods for calculating the boundary of the Mott-insulator--superfluid (MI-SF) quantum phase transition for scalar bosons in cubic optical lattices of arbitrary dimension at zero temperature which improve upon the seminal mean-field result. The first one is a variational method, which is inspired by variational perturbation theory, whereas the second one is based on the field-theoretic concept of effective potential. Within both analytical approaches we achieve a considerable improvement of the location of the MI-SF quantum phase transition for the first Mott lobe in excellent agreement with recent numerical results from quantum Monte Carlo simulations in two and three dimensions. Thus, our analytical results for the whole quantum phase diagram can be regarded as being essentially exact for all practical purposes.

Effective action approach for quantum phase transitions in bosonic lattices

Based on standard field-theoretic considerations, we develop an effective action approach for investigating quantum phase transitions in lattice Bose systems at arbitrary temperature. We begin by adding to the Hamiltonian of interest a symmetry breaking source term. Using time-dependent perturbation theory, we then expand the grand-canonical free energy as a double power series in both the tunneling and the source term. From here, an order parameter field is introduced in the standard way and the underlying effective action is derived via a Legendre transformation. Determining the Ginzburg-Landau expansion to first order in the tunneling term, expressions for the Mott insulator-superfluid phase boundary, condensate density, average particle number, and compressibility are derived and analyzed in detail. Additionally, excitation spectra in the ordered phase are found by considering both longitudinal and transverse variations of the order parameter. Finally, these results are applied to the concrete case of the Bose-Hubbard Hamiltonian on a three-dimensional cubic lattice, and compared with the corresponding results from mean-field theory. Although both approaches yield the same Mott insulator–superfluid phase boundary to first order in the tunneling, the predictions of our effective action theory turn out to be superior to the mean-field results deeper into the superfluid phase.

Superfluid to Mott-insulator transition in an anisotropic two-dimensional optical lattice

We study the superfluid to Mott-insulator transition of bosons in an optical anisotropic lattice by employing the Bose-Hubbard model living on a two-dimensional lattice with anisotropy parameter κ. The compressible superfluid state and incompressible Mott-insulator (MI) lobes are efficiently described analytically, using the quantum U(1) rotor approach. The ground state phase diagram showing the evolution of the MI lobes is quantified for arbitrary values of κ, corresponding to various kind of lattices: from square, through rectangular to almost one-dimensional.

SU(2)-Invariant Continuum Theory for an Unconventional Phase Transition in a Three-Dimensional Classical Dimer Model

We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid-Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.

Influence of the trap shape on the detection of the superfluid—Mott-insulator transition

The coexistence of superfluid and Mott insulator, due to the quadratic confinement potential in current optical lattice experiments, makes the accurate detection of the superfluid-Mott transition difficult. Studying alternative trapping potentials which are experimentally realizable and have a flatter center, we find that the transition can be better resolved, but at the cost of a more difficult tuning of the particle filling. When mapping out the phase diagram using local probes and the local density approximation we find that the smoother gradient of the parabolic trap is advantageous.

Phases and transitions in the spin-1 Bose-Hubbard model: Systematics of a mean-field theory

We generalize the mean-field theory for the spinless Bose-Hubbard model to account for the different types of superfluid phases that can arise in the spin-1 case. In particular, our mean-field theory can distinguish polar and ferromagnetic superfluids, Mott insulator, that arise at integer fillings at zero temperature, and normal Bose liquids into which the Mott insulators evolve at finite temperatures. We find, in contrast to the spinless case, that several of the superfluid-Mott insulator transitions are of first order at finite temperatures. Our systematic study yields rich phase diagrams that include first-order and second-order transitions and a variety of tricritical points. We discuss the possibility of realizing such phase diagrams in experimental systems.

Signatures of the superfluid to Mott-insulator transition in the excitation spectrum of ultracold atoms

We present a detailed analysis of the dynamical response of ultracold bosonic atoms in a one-dimensional optical lattice subjected to a periodic modulation of the lattice depth. Following the experimental realization by Stöferle et al (2004 Phys. Rev. Lett.92 130403), we study the excitation spectrum of the system as revealed by the response of the total energy as a function of the modulation frequency Ω. By using the Time Evolving Block Decimation algorithm, we are able to simulate one-dimensional systems comparable in size to those in the experiment, with harmonic trapping and across many lattice depths ranging from the Mott-insulator (MI) to the superfluid (SF) regime. Our results produce many of the features seen in the experiment, namely a broad response in the SF regime, and narrow discrete resonances in the MI regime. We identify several signatures of the SF–MI transition that are manifested in the spectrum as it evolves from one limit to the other.

Superfluid–Mott Insulator Transition of Spin-1 Bosons in Optical Lattice under Magnetic Field

We study the first- and second-order superfluid–Mott insulator transitions of spin-1 bosons in an optical lattice under a magnetic field by the Gutzwiller approximation. We find that, in contrast to previous perturbative studies, the phase boundary curve continuously changes as a function of magnetic field. We also find a sharp cusp structure on the phase boundary curve under some circumstances. When the phase boundary curve deviates from that obtained with the perturbative studies, the phase transition is a first-order one. We further clarify the specific features of the phase transition in the present system. The order parameters exactly at the boundary point, where the transition changes from first to second order, remain finite under a finite magnetic field and continuously vanish as the magnetic field approaches zero.

Imaging the Mott Insulator Shells by Using Atomic Clock Shifts

Microwave spectroscopy was used to probe the superfluid-Mott insulator transition of a Bose-Einstein condensate in a three-dimensional optical lattice. By using density-dependent transition frequency shifts, we were able to spectroscopically distinguish sites with different occupation numbers and to directly image sites with occupation numbers from one to five, revealing the shell structure of the Mott insulator phase. We used this spectroscopy to determine the onsite interaction and lifetime for individual shells.

Simulations of ultracold bosonic atoms in optical lattices with anharmonic traps

We report results of quantum Monte Carlo simulations in the canonical and the grand-canonical ensemble of the two- and three-dimensional Bose-Hubbard model with quadratic and quartic confining potentials. The quantum criticality of the superfluid-Mott insulator transition is investigated both on the boundary layer separating the two coexisting phases and at the center of the traps where the Mott-insulating phase is first established. Recent simulations of systems in quadratic traps have shown that the transition is not in the critical regime due to the finite gradient of the confining potential and that critical fluctuations are suppressed. In addition, it has been shown that quantum critical behavior is recovered in flat confining potentials as they approach the uniform regime. Our results show that quartic traps display a behavior similar to quadratic ones, yet locally at the center of the traps the bulk transition has enhanced critical fluctuations in comparison to the quadratic case. Therefore quartic traps provide a better prerequisite for the experimental observation of true quantum criticality of ultracold bosonic atoms in optical lattices.

Phonon Superfluids in Sets of Trapped Ions

We show that transverse phonons in a set of trapped ions under the action of lasers are described by an interacting boson model whose parameters can be externally adjusted. If the radial trapping frequency is large enough, the system is described by a Bose–Hubbard model, in which hopping of the phonons between different ions is provided by the Coulomb interaction. On the other hand, the non-linear terms in the interaction of the ions with a standing-wave provide us with the phonon–phonon interaction. We investigate the possibility of observing several quantum many—body phenomena, including (quasi)Bose–Einstein Condensation as well as a superfluid-Mott insulator quantum phase transition.

Probing Number Squeezing of Ultracold Atoms across the Superfluid-Mott Insulator Transition

The evolution of on-site number fluctuations of ultracold atoms in optical lattices is experimentally investigated by monitoring the suppression of spin-changing collisions across the superfluid-Mott insulator transition. For low atom numbers, corresponding to an average filling factor close to unity, large on-site number fluctuations are necessary for spin-changing collisions to occur. The continuous suppression of spin-changing collisions is thus direct evidence for the emergence of number-squeezed states. In the Mott insulator regime, we find that spin-changing collisions are suppressed until a threshold atom number, consistent with the number where a Mott plateau with doubly occupied sites is expected to form.

Nonlinear Quantum Critical Transport and the Schwinger Mechanism for a Superfluid-Mott-Insulator Transition of Bosons

Scaling arguments imply that quantum-critical points exhibit universal nonlinear responses to external probes. We investigate the origins of such nonlinearities in transport, which is especially problematic since the system is necessarily driven far from equilibrium. We argue that for a wide class of systems the new ingredient that enters is the Schwinger mechanism--the production of carriers from the vacuum by the applied field--which is then balanced against a scattering rate that is itself set by the field. We show by explicit computation how this works for the case of the symmetric superfluid-Mott insulator transition of bosons.

Localized Excitations at the Mott Insulator-Superfluid Interfaces for Confined Bose-Einstein Condensates

In this Letter, we derive the dispersion relation of the surface waves at the interfaces between Mott-insulating and superfluid domains for a two-dimensional Bose-Einstein condensate in an optical lattice subjected to a confining potential. We then calculate their contribution to the heat capacity of the system and show how its low-temperature scaling allows an experimental test of the existence and properties of Mott insulator-superfluid domains.

Phase Coherence, Visibility, and the Superfluid–Mott-Insulator Transition on One-Dimensional Optical Lattices

We study the phase coherence and visibility of trapped atomic condensates on one-dimensional optical lattices, by means of quantum Monte Carlo simulations. We obtain structures in the visibility similar to the kinks recently observed experimentally by Gerbier et al. [Phys. Rev. Lett. 95, 050404 (2005); 10.1103/PhysRevLett.95.050404cond-mat/0507087]. We examine these features in detail and offer a connection to the evolution of the density profiles as the depth of the lattice is increased. Our simulations reveal that, as the interaction strength U is increased, the evolution of superfluid and Mott-insulating domains stall for finite intervals of U. The density profiles do not change with increasing U. We show here that in one dimension the visibility provides unequivocal signatures of the melting of Mott domains with densities larger than 1.

Ultracold atoms confined in an optical lattice plus parabolic potential: A closed-form approach

We discuss interacting and non-interacting one dimensional atomic systems trapped in an optical lattice plus a parabolic potential. We show that, in the tight-binding approximation, the non-interacting problem is exactly solvable in terms of Mathieu functions. We use the analytic solutions to study the collective oscillations of ideal bosonic and fermionic ensembles induced by small displacements of the parabolic potential. We treat the interacting boson problem by numerical diagonalization of the Bose-Hubbard Hamiltonian. From analysis of the dependence upon lattice depth of the low-energy excitation spectrum of the interacting system, we consider the problems of "fermionization" of a Bose gas, and the superfluid-Mott insulator transition. The spectrum of the noninteracting system turns out to provide a useful guide to understanding the collective oscillations of the interacting system, throughout a large and experimentally relevant parameter regime.

Equilibrium and Dynamical Properties of the Boson Hubbard Model in One Dimension

We describe quantum monte carlo simulations of the static and dynamic properties of the one dimensional boson Hubbard model, emphasizing the extent to which an external confining potential modifies the behavior. While the superfluid-Mott insulator quantum phase transition no longer exists when the system is confined, Mott and superfluid regions persist locally in the system. We construct a ‘state diagram’ based on the local density and compressibility profiles. Solitons present in the dynamics of the unconfined system survive the addition of a trapping potential.

Energy spectra of ultracold Bose–Fermi mixtures in optical lattices

We show the energy band structure of ultracold atomic Bose–Fermi mixtures in optical lattices: two energy bands for bosonic atoms and a single band for fermionic atoms. The energy band structure can determine the superfluid Mott-insulator phase transition. We find the phase diagram of the mixture by means of path integral, and the phase transition depending on the experimental parameters. The possibility of observing these new phases and their transitions in future experiments is discussed.

Long-range order in gapped magnetic systems induced by Bose-Einstein condensation

We study the Heisenberg antiferromagnet with single-ion anisotropy in two and three dimensions and present self-consistent intuitive theory to show the Bose-Einstein condensation-induced long-range order in the gapped magnetic systems, when the energy gap is tuned to zero by changing the physical parameters or by applying an external magnetic field. The recent experimental results on ${\mathrm{NiCl}}_{2}∙4\mathrm{SC}{({\mathrm{NH}}_{2})}_{2}$ are interpreted by the theory. Many other gapped magnetic systems share the same physical picture. The theory is also helpful in understanding the superfluid-Mott insulator transition observed in the system of ultracold atoms in the optical lattice.