We review the superfluid to Mott-insulator transition of cold atoms in optical lattices. The experimental signatures of the transition are discussed and the RPA theory of the Bose-Hubbard model briefly described. We point out that the critical behavior at the transition, as well as the prediction by the RPA theory of a gapped mode (besides the Bogoliubov sound mode) in the superfluid phase, are difficult to understand from the Bogoliubov theory. On the other hand, these findings appear to be intimately connected to the non-trivial infrared behavior of the superfluid phase as recently studied within the non-perturbative renormalization group.
Weakly interacting atomic or molecular bosons in quantum degenerate regime and trapped in harmonically confined optical lattices, exhibit a wedding cake structure consisting of insulating (Mott) shells. It is shown that superfluid regions emerge between Mott shells as a result of fluctuations due to finite hopping. It is found that the order parameter equation in the superfluid regions is not of the Gross-Pitaeviskii type except near the insulator to superfluid boundaries. The excitation spectra in the Mott and superfluid regions are obtained, and it is shown that the superfluid shells posses …
In this paper we derive the dispersion relation of the surface waves at the interfaces between Mott insulating and Superfluid phases for confined Bose-Einstein Condensates. 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.
We study the effect of parametric excitations on systems of confined ultracold Bose atoms in periodically modulated optical lattices. In the regime where Mott insulating and Superfluid domains coexist, we show that the dependence of the energy absorbed by the system on the frequency of the modulation serves as an experimental probe for the existence and properties of Mott insulating-Superfluid domains.
We study the superfluid to Mott-insulator transition of bosons in an optical anizotropic lattice by employing the Bose-Hubbard model living on a two-dimensional lattice with anizotropy 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.
We report on the direct observation of the transition from a compressible superfluid to an incompressible Mott insulator by recording the in-trap density distribution of a Bosonic quantum gas in an optical lattice. Using spatially selective microwave transitions and spin changing collisions, we are able to locally modify the spin state of the trapped quantum gas and record the spatial distribution of lattice sites with different filling factors. As the system evolves from a superfluid to a Mott insulator, we observe the formation of a distinct shell structure, in good agreement with theory.
A two-dimensional system of atoms in an anisotropic optical lattice is studied theoretically. If the system is finite in one direction, it is shown to exhibit a transition between a two-dimensional superfluid and a one-dimensional Mott insulating chain of superfluid tubes. Monte Carlo simulations are consistent with the expectation that the phase transition is of Kosterlitz-Thouless type. The effect of the transition on experimental time-of-flight images is discussed.
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 a direct evidence for the emergence of number-squeezed states. In the Mott insulator regime, we find that spin-changing collisions are suppressed u…
We have studied the superfluid - Mott insulator transition in a BEC confined in an optical lattice and driven by an additional external electromagnetic field, which excites another internal state. It is shown that due to resonant strong driving the critical values of the transition parameter depend on external field parameters (the Rabi frequency and the detuning from resonance) and can be tuned to a given value. It is also shown that for driven system there are two optical potential depths at a phase transition which are always more than without driving.
We present in this paper an analytical model for a cold bosonic gas on an optical lattice (with densities of the order of 1 particle per site) targeting the critical regime of the Bose - Einstein Condensate superfluid - Mott insulator transition. We focus on the computation of the one - body density matrix and its Fourier transform, the momentum distribution which is directly obtainable from `time of flight'' measurements. The expected number of particles with zero momentum may be identified with the condensate population, if it is close to the total number of particles. Our main result is an …
We report the Bragg spectroscopy of interacting one-dimensional Bose gases loaded in optical lattices across the superfluid to Mott-insulator phase transition. Elementary excitations are created with a non-zero momentum and the response of the correlated 1D gases is in the linear regime. The complexity of the strongly correlated quantum phases is directly displayed in the spectra which exhibit novel features. This work paves the way for a precise characterization of the state of correlated atomic phases in optical lattices.
We analyze the correspondence of many-particle and mean-field dynamics for a Bose-Einstein condensate in an optical lattice. Representing many-particle quantum states by a classical phase space ensemble instead of one single mean-field trajectory and taking into account the quantization of the density by a modified integer Gross-Pitaevskii equation, it is possible to simulate the superfluid to Mott insulator transition and other phenomena purely classically. This approach can be easily extended to higher particle numbers and multidimensional lattices. Moreover it provides an excellent tool to …
We present a detailed analysis of the dynamical response of ultra-cold bosonic atoms in a one-dimensional optical lattice subjected to a periodic modulation of the lattice depth. Following the experimental realization by Stoferle et al [Phys. Rev. Lett. 92, 130403 (2004)] we study the excitation spectrum of the system as revealed by the response of the total energy as a function of the modulation frequency Omega. 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…
We investigate the superfluid--Mott-insulator quantum phase transition of spin-1 bosons in an optical lattice created by pairs of counterpropagating linearly polarized laser beams, driving an $F_g=1$ to $F_e=1$ internal atomic transition. The whole parameter space of the resulting two-component Bose-Hubbard model is studied. We find that the phase transition is not always second order as in the case of spinless bosons, but can be first order in certain regions of the parameter space. The calculations are done in the mean-field approximation by means of exact numerical diagonalization as well a…
Atomic or molecular bosons in harmonically confined optical lattices exhibit a wedding cake structure consisting of insulating (Mott) shells. It is shown that superfluid regions emerge between Mott shells as a result of fluctuations due to finite hopping. It is found that the order parameter equation in the superfluid region is not of the Gross-Pitaeviskii type except near the insulator to superfluid boundaries. The excitation spectra in the Mott and superfluid regions are obtained, and it is shown that the superfluid shells posses low energy sound modes with spatially dependent sound velocity…
We study the thermodynamics of ultracold Bose atoms in optical lattices by numerically diagonalizing the mean-field Hamiltonian of the Bose-Hubbard model. This method well describes the behavior of long-range correlations and therefore is valid deep in the superfluid phase. For the homogeneous Bose-Hubbard model, we draw the finite-temperature phase diagram and calculate the superfluid density at unity filling. We evaluate the finite-temperature effects in a recent experiment probing number fluctuation [Phys. Rev. Lett. \textbf{96}, 090401 (2006)], and find that our finite-temperature curves g…
Regular arrays of electromagnetic resonators, in turn coupled coherently to individual quantum two-level systems, exhibit a quantum phase transition of polaritons from a superfluid phase to a Mott-insulating phase. The critical behavior of such a Jaynes-Cummings lattice thus resembles the physics of the Bose-Hubbard model. We explore this analogy by elaborating on the mean-field theory of the phase transition, and by presenting several useful mappings which pinpoint both similarities and differences of the two models. We show that a field-theory approach can be applied to prove the existence o…
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.
We study the dynamics of the many-body state of ultracold bosons trapped in a bistable optical lattice in an optomechanical resonator controlled by a time-dependent input field. We focus on the dynamics of the many-body system following discontinuous jumps of the intracavity field. We identify experimentally realizable parameters for the bistable quantum phase transition between Mott insulator and superfluid.
We study the many-body state of ultracold bosons in a bistable optical lattice potential in an optomechanical resonator in the weak-coupling limit. New physics arises as a result of bistability and discontinuous jumps in the cavity field. Of particular interest is the situation where the optical cavity is engineered so that a single input beam can result in two radically different stable ground states for the intracavity gas: superfluid and Mott-insulator.
An ultracold gas of coupled two-component atoms in an optical field is studied. Due to the internal two-level structure of the atoms, three competing energy terms exist; atomic kinetic, atomic internal, and atom-atom interaction energies. A novel outcome of this interplay, not present in the regular Bose-Hubbard model, is that in the single band and tight binding approximations four different phases appear: two superfluid and two Mott phases. When passing through the critical point between the two superfluid or the two Mott phases, a swapping of the internal atomic populations takes place. By …
We prove the absence of a direct quantum phase transition between a superfluid and a Mott insulator in a bosonic system with generic, bounded disorder. We also prove compressibility of the system on the superfluid--insulator critical line and in its neighborhood. These conclusions follow from a general {\it theorem of inclusions} which states that for any transition in a disordered system one can always find rare regions of the competing phase on either side of the transition line. Quantum Monte Carlo simulations for the disordered Bose-Hubbard model show an even stronger result, important for…
We realize a single-band 2D Bose-Hubbard system with Rb atoms in an optical lattice and measure the condensate fraction as a function of lattice depth, crossing from the superfluid to the Mott-insulating phase. We quantitatively identify the location of the superfluid to normal transition by observing when the condensed fraction vanishes. Our measurement agrees with recent quantum Monte Carlo calculations for a finite-sized 2D system to within experimental uncertainty.
Recent experiments on strongly-interacting bosons in optical lattices have revealed the co-existence of spatially-separated Mott-insulating and number-fluctuating phases. The description of this inhomogeneous situation is the topic of this Letter. We establish that the number-fluctuating phase forms a superfluid trapped between the Mott-insulating regions and derive the associated collective mode structure. We discuss the interlayer's crossover between two- and three-dimensional behavior as a function of the lattice parameters and estimate the critical temperatures for the transition of the su…
We investigate the superfluid-Mott-insulator transition of a two-dimensional photon gas in a dye-filled optical microcavity and in the presence of a periodic potential. We show that in the random-phase approximation the effects of the dye molecules, which generally lead to dissipation in the photonic system, can be captured by two dimensionless parameters that only depend on dye-specific properties. Within the mean-field approximation, we demonstrate that one of these parameters decreases the size of the Mott lobes in the phase diagram. By considering also Gaussian fluctuations, we show that t…
We study transport dynamics of ultracold cesium atoms in a two-dimensional optical lattice across the superfluid-Mott insulator transition based on in situ imaging. Inducing the phase transition with a lattice ramping routine expected to be locally adiabatic, we observe a global mass redistribution which requires a very long time to equilibrate, more than 100 times longer than the microscopic time scales for on-site interaction and tunneling. When the sample enters the Mott insulator regime, mass transport significantly slows down. By employing fast recombination pulses to analyze the occupanc…
We study the Bose-Hubbard model using the finite size density matrix renormalization group method. We obtain for the first time a complete phase diagram for a system in the presence of a harmonic trap and compare it with that of the homogeneous system. To realize the transition from the superfluid to the Mott insulator phase we investigate different experimental signatures of these phases in quantities such as momentum distribution, visibility, condensate fraction and the total number of bosons at a particular density. The relationships between the various experimental signatures and the phase…
We investigate a strongly-correlated Bose gas in an optical lattice. Extending the standard-basis operator method developed by Haley and Erdos to a boson Hubbard model, we calculate excitation spectra in the superfluid phase, as well as in the Mott insulating phase, at T=0. In the Mott phase, the excitation spectrum has a finite energy gap, reflecting the localized character of atoms. In the superfluid phase, the excitation spectrum is shown to have an itinerant-localized dual structure, where the gapless Bogoliubov mode (which describes the itinerant character of superfluid atoms) and a band …
A large scale dynamical simulation of the superfluid to Mott insulator transition in the gas of ultra cold atoms placed in an optical lattice is performed using the time dependent Gutzwiller mean field approach. This approximate treatment allows us to take into account most of the details of the recent experiment [Nature 415, 39 (2002)] where by changing the depth of the lattice potential an adiabatic transition from a superfluid to a Mott insulator state has been reported. Our simulations reveal a significant excitation of the system with a transition to insulator in restricted regions of the…
We study the dynamics of phase transitions in the one dimensional Bose-Hubbard model. To drive the system from Mott insulator to superfluid phase, we change the tunneling frequency at a finite rate. We investigate the build up of correlations during fast and slow transitions using variational wave functions, dynamical Bogoliubov theory, Kibble-Zurek mechanism, and numerical simulations. We show that time-dependent correlations satisfy characteristic scaling relations that can be measured in optical lattices filled with cold atoms.
We have studied spin structures of fluctuation-driven fractionalized vortices and topological spin order in 2D nematic superfluids of cold sodium atoms. Our Monte Carlo simulations suggest a softened pi-spin disclination structure in a half-quantum vortex when spin correlations are short ranged; in addition, calculations indicate that a unique non-local topological spin order emerges simultaneously as cold atoms become a superfluid below a critical temperature. We have also estimated fluctuation-dependent critical frequencies for half-quantum vortex nucleation in rotating optical traps and dis…
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.[Phy. Rev. Lett. 95, 050404 (2005); Phys. Rev. A 72, 053606 (2005)]. 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 d…
We investigate the finite temperature momentum distribution of bosonic noncondensate particles inside a 3D optical lattice near the superfluid to Mott insulator transition point, treating the quantum fluctuation and thermal fluctuation effects on equal footing. We explicitly address the different momentum ($q$) dependence of quasi-particles excitations resulted from thermal and quantum origin: the former scales as $|\bfq|^{-2}$ and hence is dominant in the small momentum region, while the later scales as $|\bfq|^{-1}$ and hence dominant in the large momentum limit. Analytic and semi-analytic r…
We develop a Gutzwiller theory for the non-equilibrium steady states of a strongly-interacting photon fluid driven by a non-Markovian incoherent pump. In particular, we explore the collective excitation modes across the out-of-equilibrium Mott/superfluid transition, characterizing the diffusive Goldstone mode in the superfluid phase and the particle/hole excitations in the insulating one. Observable features in the pump-and-probe optical response of the system are highlighted. Our results appear as experimentally accessible to state-of-the-art circuit-QED devices and open the way for driven-di…
We study near-equilibrium thermodynamics of bosonic atoms in a two-dimensional optical lattice by ramping up the lattice depth to convert a superfluid into an inhomogeneous mixture of superfluid and Mott insulator. Detailed study of in situ density profiles shows that, first, locally adiabatic ramps do not guarantee global thermal equilibrium. Indeed, full thermalization for typical parameters only occurs for experiment times which exceed one second. Secondly, ramping non-adiabatically to the Mott insulator regime can result in strong localized cooling at short times and global cooling once eq…
We study two models realized by two-component Fermi gases loaded in optical lattices. We clarify that multi-band effects inevitably caused by the optical lattices generate a rich structure, when the systems crossover from the region of weakly bound molecular bosons to the region of strongly bound atomic bosons. Here the crossover can be controlled by attractive fermion interaction. One of the present models is a case with attractive fermion interaction, where an insulator-superfluid transition takes place. The transition is characterized as the transition between a band insulator and a Bose-Ei…
The superfluid-insulator transitions of the fermionic atoms in optical lattices are investigated by the two-site dynamical mean-field theory. It is shown that the Mott transition occurs as a result of the multiband effects. The quasiparticle weight in the superfluid state decreases significantly, as the system approaches the Mott transition point. By changing the interaction and the orbital splitting, we obtain the phase diagram at half filling. The numerical results are discussed in comparison with the effective boson model.
We calculate the superfluid transition temperature for a two-component 3D Fermi gas in a 1D tight optical lattice and discuss a dimensional crossover from the 3D to quasi-2D regime. For the geometry of finite size discs in the 1D lattice, we find that even for a large number of atoms per disc, the critical effective tunneling rate for a quantum transition to the Mott insulator state can be large compared to the loss rate caused by three-body recombination. This allows the observation of the Mott transition, in contrast to the case of Bose-condensed gases in the same geometry.
