Dimensional Optical Lattice Research Articles

Bose-Einstein condensation in an optical lattice: A perturbation approach

We derive closed analytical expressions for the order parameter $\Phi (x)$ and for the chemical potential $\mu $ of a Bose-Einstein Condensate loaded into a harmonically confined, one dimensional optical lattice, for sufficiently weak, repulsive or attractive interaction, and not too strong laser intensities. Our results are compared with exact numerical calculations in order to map out the range of validity of the perturbative analytical approach. We identify parameter values where the optical lattice compensates the interaction-induced nonlinearity, such that the condensate ground state coincides with a simple, single particle harmonic oscillator wave function.

Quantum correlations of spin-1 atoms in an optical lattice

In this work, we investigate the system of cold spin-1 atoms in a one dimensional optical lattice in relation with squeezing and entanglement. By using the corresponding Bose-Hubbard Hamiltonian, both superfluid and Mott-insulator phases are studied by using numerical methods in the mean-field approximation. To observe the presence of entanglement, we used a squeezing measure as a criterion for quantum correlations. We further investigate the two interaction regimes, namely ferromagnetic and antiferromagnetic in the case of zero and nonzero but very small angle between the counterpropagating laser beams that form the optical lattice. States in the superfluid phase are calculated analytically by using the perturbation theory.

How the effective boson-boson interaction works in Bose-Fermi mixtures in periodic geometries

We study mixtures of spinless bosons and not spin-polarized fermions loaded in two dimensional optical lattices. We approach the problem of the ground state stability within the framework of the linear response theory; by the mean of an iterative procedure, we are able to obtain a relation for the dependence of boson-boson effective interaction on the absolute temperature of the sample. Proceeding from such a formula, we write down analytical expressions for supersolid (SS) and phase separation (PS) transition temperatures, and plot the phase diagrams.

Superfluid properties of a Bose–Einstein condensate in an optical lattice confined in a cavity

We study the effect of a one dimensional optical lattice in a cavity field with quantum properties on the superfluid dynamics of a Bose–Einstein condensate (BEC). In the cavity the influence of atomic backaction and the external driving pump become important and modify the optical potential. Due to the coupling between the condensate wavefunction and the cavity modes, the cavity light field develops a band structure. This study reveals that the pump and the cavity emerges as a new handle to control the superfluid properties of the BEC.

Density-Matrix Renormalization Group studies of mixture of two different ultracold bosonic atoms

We investigate the ground state phase diagram for a two species Bose mixture in a one dimensional optical lattice using the finite size density matrix renormalization group (FSDMRG) method. We present our result for different combinations of inter and intra-species repulsion strengths with a commensurate filling factor. We obtain a superfluid (SF) to Mott insulator (MI) transition when the inter species interaction term is less than the intra-species interaction term. However, when the former is slightly greater than the latter we find that the two different species reside in spatially separate regions.

Flat Bands and Wigner Crystallization in the Honeycomb Optical Lattice

We study the ground states of cold atoms in the tight-binding bands built from p orbitals on a two dimensional honeycomb optical lattice. The band structure includes two completely flat bands. Exact many-body ground states with on-site repulsion can be found at low particle densities, for both fermions and bosons. We find crystalline order at n=1/6 with a sqrt[3] x sqrt[3] structure breaking a number of discrete lattice symmetries. In fermionic systems, if the repulsion is strong enough, we find the bonding strength becomes dimerized at n=1/2. Experimental signatures of crystalline order can be detected through the noise correlations in time of flight experiments.

Metastable States of a Gas of Dipolar Bosons in a 2D Optical Lattice

We investigate the physics of dipolar bosons in a two-dimensional optical lattice. It is known that due to the long-range character of dipole-dipole interaction, the ground state phase diagram of a gas of dipolar bosons in an optical lattice presents novel quantum phases, like checkerboard and supersolid phases. In this Letter, we consider the properties of the system beyond its ground state, finding that it is characterized by a multitude of almost degenerate metastable states, often competing with the ground state. This makes dipolar bosons in a lattice similar to a disordered system and opens possibilities of using them as quantum memories.

COLLAPSE OF K-Rb FERMI-BOSE MIXTURES IN OPTICAL LATTICES

We study a confined mixture of Rb and K atoms in a one dimensional optical lattice, at low temperature, in the quanta1 degeneracy regime. This mixture exhibits an attractive boson-fermion interaction, and thus above certain values of the number of particles the mixture collapses. We investigate, in the mean-field approximation, the curve for which this phenomenon occurs, in the space of number of particles of both species. This is done for different types of optical lattices.

Nonequilibrium coherence dynamics of a soft boson lattice

We study the non-equilibrium evolution of the phase coherence of a Bose-Einstein condensate (BEC) in a one dimensional optical lattice, as the lattice is suddenly quenched from an insulating to a superfluid state. We observe slowly damped phase coherence oscillations in the regime of large filling factor (~100 bosons per site) at a frequency proportional to the generalized Josephson frequency. The truncated Wigner approximation (TWA) predicts the frequency of the observed oscillations.

Finite-temperature treatment of ultracold atoms in a one-dimensional optical lattice

We consider the effects of temperature upon the superfluid phase of ultracold, weakly interacting bosons in a one dimensional optical lattice. We use a finite temperature treatment of the Bose-Hubbard model based upon the Hartree-Fock-Bogoliubov formalism, considering both a translationally invariant lattice and one with additional harmonic confinement. In both cases we observe an upward shift in the critical temperature for Bose condensation. For the case with additional harmonic confinement, this is in contrast with results for the uniform gas.

Stabilization of a (D+1)-dimensional dispersion-managed solitons in Kerr media by an alternating dispersion structure

We study the propagation of chirped (D+1)-dimensional optical pulses in bulk media with periodic dispersion, analytically by using the variational approach and numerically by using a new, to our knowledge, numerical technique relying on the adaptive fast Hankel split-step method using cylindrical and spherical symmetries for two and three dimensions, respectively. Stability criteria for (2+1)- and (3+1)-dimensional solitons are identified, and the long-term dynamics of the solitons are studied with the averaged equations obtained using the Kapitza approach. Also, the slow dynamics of the solitons around the fixed points for the width and the chirp are studied. The importance of this research is in generating dispersion-managed optical solitons in optical communication. Also, this research is applied to the stabilization of the Bose-Einstein condensate in (2+1)- and (3+1)-dimensional optical lattices. We compare results of the new numerical technique with those obtained using the fast Fourier split-step technique.

Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures

We study the Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures, extending our recent work on one-dimensional (1D) optical lattices. We use a Bose-Hubbard tight-binding model and the Popov approximation to calculate the temperature dependence of the number of condensate atoms ${n}^{\mathrm{c}0}(T)$ in each lattice well. As with 1D optical lattices, damping only occurs if the Bogoliubov excitations exhibit anomalous dispersion (i.e., the excitation energy bends upward at low momentum), analogous to the case of phonons in superfluid $^{4}\mathrm{He}$. This leads to the disappearance of all damping processes in a $D$-dimensional simple cubic optical lattice when $U{n}^{\mathrm{c}0}\ensuremath{\geqslant}6DJ$, where $U$ is the on-site interaction, and $J$ is the hopping matrix element.

Sodium Bose-Einstein condensates in an optical lattice

The phase transition from a superfluid to a Mott insulator has been observed in a $^{23}$Na Bose-Einstein condensate. A dye laser detuned $\approx 5$nm red of the Na $3^2$S$ \to 3^2$P$_{1/2}$ transition was used to form the three dimensional optical lattice. The heating effects of the small detuning as well as the three-body decay processes constrained the timescale of the experiment. Certain lattice detunings were found to induce a large loss of atoms. These loss features were shown to be due to photoassociation of atoms to vibrational levels in the Na$_2$ $(1) ^3\Sigma_g^+$ state.

Decay of superfluid currents in a moving system of strongly interacting bosons

We analyze the stability and decay of supercurrents of strongly interacting bosons on optical lattices. At the mean field level, the system undergoes an irreversible dynamic phase transition, whereby the current decays beyond a critical phase gradient that depends on the interaction strength. At commensurate filling the transition line smoothly interpolates between the classical modulational instability of weakly interacting bosons and the equilibrium Mott transition at zero current. Below the mean field instability, the current can decay due to quantum and thermal phase slips. We derive asymptotic expressions of the decay rate near the critical current. In a three dimensional optical lattice this leads to very weak broadening of the transition. In one and two dimensions the broadening leads to significant current decay well below the mean field critical current. We show that the temperature scale below which quantum phase slips dominate the decay of supercurrents, is easily within experimental reach.

Solitons in trapped Bose-Einstein condensates in one-dimensional optical lattices

We use Quantum Monte Carlo simulations to show the presence and study the properties of solitons in the one dimensional soft-core bosonic Hubbard model with near neighbor interaction in traps. We show that when the half-filled Charge Density Wave (CDW) phase is doped, solitons are produced and quasi long range order established. We discuss the implications of these results for the presence and robustness of this solitonic phase in Bose-Einstein Condensates (BEC) on one dimensional optical lattices in traps and study the associated excitation spectrum. The density profile exhibits the coexistence of Mott insulator, CDW, and superfluid regions.

Fermionic Atoms in a Three Dimensional Optical Lattice: Observing Fermi Surfaces, Dynamics, and Interactions

We have studied interacting and noninteracting quantum degenerate Fermi gases in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Because of the confining potential, gradual filling of the lattice transforms the system from a normal state into a band insulator. The dynamics of the transition from a band insulator to a normal state is studied, and the time scale is measured to be an order of magnitude larger than the tunneling time in the lattice. Using a Feshbach resonance, we increase the interaction between atoms in two different spin states and dynamically induce a coupling between the lowest energy bands. We observe a shift of this coupling with respect to the Feshbach resonance in free space which is anticipated for strongly confined atoms.

Strong correlation effects and quantum information theory of low dimensional atomic gases

These lecture notes present an introduction to the strongly correlated regime of low dimensional atomic gases. The discussion is concentrated on situations in which the strongly correlated limit is achieved by creating degeneracies in the one-particle motional states. Three different schemes of experimental relevance are analyzed: bosonic atoms in a two dimensional rapidly rotating trap, bosonic atoms in a one dimensional optical lattice, and bosonic atoms with frozen motional degrees of freedom and two internal states. The corresponding entangled multiparticle states (Laughlin liquids, Mott phases, squeezed states), and the different strongly correlated phenomena that appear (fermionization, fractional statistics) are studied. Emphasis is given to the possibility of observing novel strongly correlated phenomena as well as to the possible implementations for quantum computation and quantum information.

Quasi-2D Bose-Fermi mixtures in an optical lattice

We give an overview on our current experiments with Bose-Fermi degenerate mixtures in a one dimensional (ID) optical lattice. Our system consists of a Fermi gas of 40 K atoms and a Bose-Einstein condensate of 87 Rb. The two species are simultaneously trapped in a combined magnetic and optical lattice potential. We have investigated the thermodynamical properties of the mixture in a tight lattice and observed a change in the density of states. This is a signature of a quasi two dimensional confinement of the atoms in the lattice sites. We also discuss the mechanical stability of the mixture in presence of the 1D lattice.

Oscillations of atomic fermions in a one-dimensional optical lattice

A semiclassical model is used to investigate oscillations of atomic fermions in a combined magnetic trap and one dimensional optical lattice potential following axial displacement of the trap. The oscillations are shown to have a characteristic small amplitude, damped behavior in the collisionless regime. The presence of a separatrix in the semiclassical Brillouin zone phase space is predicted and shown to produce a strongly asymmetric phase space distribution function.

Mixtures of bosonic and fermionic atoms in optical lattices

We discuss the theory of mixtures of Bosonic and Fermionic atoms in periodic potentials at zero temperature. We derive a general Bose--Fermi Hubbard Hamiltonian in a one--dimensional optical lattice with a superimposed harmonic trapping potential. We study the conditions for linear stability of the mixture and derive a mean field criterion for the onset of a Bosonic superfluid transition. We investigate the ground state properties of the mixture in the Gutzwiller formulation of mean field theory, and present numerical studies of finite systems. The Bosonic and Fermionic density distributions and the onset of quantum phase transitions to demixing and to a Bosonic Mott--insulator are studied as a function of the lattice potential strength. The existence is predicted of a disordered phase for mixtures loaded in very deep lattices. Such a disordered phase possessing many degenerate or quasi--degenerate ground states is related to a breaking of the mirror symmetry in the lattice.