Bichromatic Optical Lattice Research Articles

Localized states in an ultracold atomic gas trapped in a bichromatic potential: The effect of a time-varying phase

Localization phenomena observed in an ultracold atomic gas trapped in a bichromatic optical lattice were found to be sensitive to the degree of lattice disorder, and are affected by the extent of interatomic interaction. In this work, I shall discuss the dependence of localization on the phase difference between the two superimposed optical waves. The step and sinusoidal phase functions in region III identified in the work by Larcher et al. [1], are studied. A step varying phase mildly distorts localization, whereas a sinusoidally varying phase will take the system to a unique form of localization, which we call logarithmic localization.

An optical-lattice-based quantum simulator for relativistic field theories and topological insulators

We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from non-interacting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize a majority of phases in the periodic table of topological insulators.

Klein Tunneling of a Quasirelativistic Bose-Einstein Condensate in an Optical Lattice

A proof-of-principle experiment simulating effects predicted by relativistic wave equations with ultracold atoms in a bichromatic optical lattice that allows for a tailoring of the dispersion relation is reported. We observe the analog of Klein tunneling, the penetration of relativistic particles through a potential barrier without the exponential damping that is characteristic for nonrelativistic quantum tunneling. Both linear (relativistic) and quadratic (nonrelativistic) dispersion relations are investigated, and significant barrier transmission is observed only for the relativistic case.

Quantum simulator for the Schwinger effect with atoms in bichromatic optical lattices

Ultra-cold atoms in specifically designed optical lattices can be used to mimic the many-particle Hamiltonian describing electrons and positrons in an external electric field. This facilitates the experimental simulation of (so far unobserved) fundamental quantum phenomena such as the Schwinger effect, i.e., spontaneous electron-positron pair creation out of the vacuum by a strong electric field.

Quantum dynamics of hard-core bosons in tilted bichromatic optical lattices

We study the dynamics of strongly repulsive Bose gas in tilted or driven bichromatic optical lattices. Using the Bose-Fermi mapping and exact numerical method, we calculate the reduced single-particle density matrices, and study the dynamics of density profile, momentum distribution and condensate fraction. We show the oscillating and breathing mode of dynamics, and depletion of condensate for short time dynamics. For long time dynamics, we clearly show the reconstruction of system at integer multiples of Bloch-Zener time. We also show how to achieve clear Bloch oscillation and Landau-Zener tunnelling for many-particle systems.

Effective Dirac dynamics of ultracold atoms in bichromatic optical lattices

We study the dynamics of ultracold atoms in tailored bichromatic optical lattices. By tuning the lattice parameters, one can readily engineer the band structure and realize a Dirac point, i.e. a true crossing of two Bloch bands. The dynamics in the vicinity of such a crossing is described by the one-dimensional Dirac equation, which is rigorously shown beyond the tight-binding approximation. Within this framework we analyze the effects of an external potential and demonstrate numerically that it is possible to demonstrate Klein tunneling with current experimental setups.

Localization of a Bose-Fermi mixture in a bichromatic optical lattice

We study the localization of a cigar-shaped super-fluid Bose-Fermi mixture in a quasi-periodic bichromatic optical lattice (OL) for inter-species attraction and intra-species repulsion. The mixture is described by the Gross-Pitaevskii equation for the bosons, coupled to a hydrodynamic mean-field equation for fermions at unitarity. We confirm the existence of the symbiotic localized states in the Bose-Fermi mixture and Anderson localization of the Bose component in the interacting Bose-Fermi mixture on a bichromatic OL. The phase diagram in boson and fermion numbers showing the regions of the symbiotic and Anderson localization of the Bose component is presented. Finally, the stability of symbiotic and Anderson localized states is established under small perturbations.

Localization of collisionally inhomogeneous condensates in a bichromatic optical lattice

By direct numerical simulation and variational solution of the Gross-Pitaevskii equation, we studied the stationary and dynamic characteristics of a cigar-shaped, localized, collisionally inhomogeneous Bose-Einstein condensate trapped in a one-dimensional bichromatic quasiperiodic optical-lattice potential, as used in a recent experiment on the localization of a Bose-Einstein condensate [Roati et al., Nature (London) 453, 895 (2008)]. The effective potential characterizing the spatially modulated nonlinearity is obtained. It is found that the collisional inhomogeneity has influence not only on the central region but also on the tail of the Bose-Einstein condensate. The influence depends on the sign and value of the spatially modulated nonlinearity coefficient. We also demonstrate the stability of the stationary localized state by performing a standard linear stability analysis. Where possible, the numerical results are shown to be in good agreement with the variational results.

Anomalous Bloch oscillations in one-dimensional parity-breaking periodic potentials

We investigate the dynamics of a wave packet in a parity-breaking one-dimensional periodic potential slowly varied in time and perturbed by a linear potential. Parity is broken by considering an asymmetric double well per unit cell. By comparing the prediction of the semiclassical dynamics with the full Schr\"odinger solution, we show that Bloch oscillations are strongly affected by anomalous velocity corrections related to Berry's phase. We characterize how these effects depend on the degree of parity breaking of the potential and on the modulation parameters. We also discuss how to measure the effects of the anomalous velocity in current experiments with noninteracting Bose-Einstein condensates in bichromatic optical lattices, under the effect of gravity.

Quantum dynamics of Bose-Einstein condensates in tilted and driven bichromatic optical lattices

We study the dynamics of Bose-Einstein condensates in tilted and driven optical superlattices. For a bichromatic lattice, each Bloch band split up into two minibands such that the dynamics is governed by the interplay of Bloch oscillations and transitions between the bands. Thus, bichromatic potentials provide an excellent model system for the study of nonlinear Landau-Zener tunneling and allow for a variety of applications in matter wave interferometry and quantum metrology. In the present paper we investigate the coherent dynamics of an interacting Bose-Einstein condensate as well as its stability. Different mechanisms of instability are discussed, which lead to a rapid depletion of the condensate.

The Luttinger liquid in superlattice structures: atomic gases, quantum dots and the classical Ising chain

We study the physical properties of a Luttinger liquid in a superlattice that is characterized by alternating two tunneling parameters. Using the bosonization approach, we describe the corresponding Hubbard model by the equivalent Tomonaga–Luttinger model. We analyze the spin–charge separation and transport properties of the superlattice system. We suggest that cold Fermi gases trapped in a bichromatic optical lattice and coupled quantum dots offer the opportunity to measure these effects in a convenient manner. We also study the classical Ising chain with two tunneling parameters. We find that the classical two-point correlator decreases as the difference between the two tunneling parameters increases.

Localization of a dipolar Bose–Einstein condensate in a bichromatic optical lattice

By numerical simulation and variational analysis of the Gross–Pitaevskii equation we study the localization, with an exponential tail, of a dipolar Bose–Einstein condensate (DBEC) of 52Cr atoms in a three-dimensional bichromatic optical lattice (OL) generated by two monochromatic OLs of incommensurate wavelengths along three orthogonal directions. For a fixed dipole–dipole interaction, a localized state of a small number of atoms (∼1000) could be obtained when the short-range interaction is not too attractive or not too repulsive. A phase diagram showing the region of stability of a DBEC with a short-range interaction and dipole–dipole interaction is given.

Symmetry breaking in a localized interacting binary Bose-Einstein condensate in a bichromatic optical lattice

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation using the split-step Fourier spectral method we study different aspects of the localization of a cigar-shaped interacting binary (two-component) Bose-Einstein condensate (BEC) in a one-dimensional bi-chromatic quasi-periodic optical-lattice potential, as used in a recent experiment on the localization of a BEC [Roati et al., Nature 453, 895 (2008)]. We consider two types of localized states: (i) when both localized components have a maximum of density at the origin x=0, and (ii) when the first component has a maximum of density and the second a minimum of density at x=0. In the non-interacting case the density profiles are symmetric around x=0. We numerically study the breakdown of this symmetry due to inter-species and intra-species interaction acting on the two components. Where possible, we have compared the numerical results with a time-dependent variational analysis. We also demonstrate the stability of the localized symmetry-broken BEC states under small perturbation.

Exponential localization in one-dimensional quasi-periodic optical lattices

We investigate the localization properties of a one-dimensional bichromatic optical lattice in the tight-binding regime, by discussing how exponentially localized states emerge upon changing the degree of commensurability. We also review the mapping onto the discrete Aubry–André model, and provide evidence on how the momentum distribution gets modified in the crossover from extended to exponentially localized states. This analysis is relevant to the recent experiment on the Anderson localization of a noninteracting Bose–Einstein condensate in a quasi-periodic optical lattice (Roati et al 2008 Nature 453 895).

Ratchet-induced matter–wave transport and soliton collisions in Bose–Einstein condensates

We study the dynamics of bright matter–wave solitons in a Bose–Einstein condensate with negative scattering length under the influence of a time-periodic ratchet potential. The potential is formed by a one-dimensional bichromatic optical lattice which flashes on and off so that the time average of its amplitude vanishes. Due to the broken space and time-reversal symmetries of the potential, the soliton is transported with a nonzero average velocity. By employing the non-dissipative mean-field model for the matter waves, we study the dependence of the transport velocity on the initial state of the soliton and show how the properties of the individual localized states affect the outcome of their collisions. A useful insight into the transport properties is provided by Hamiltonian theory for the mean field, which treats the extended matter–wave excitation as an effective classical particle.

Dynamics of Matter-Wave Solitons in a Ratchet Potential

We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realizes a flashing ratchet for matter-wave solitons. We find that the average velocity of a soliton and the soliton current induced by the ratchet depend on the number of atoms in the soliton. As a consequence, soliton transport can be induced through scattering of different solitons. In the regime when matter-wave solitons are narrow compared to the lattice period the dynamics is well described by the effective Hamiltonian theory.

Mobility edges in bichromatic optical lattices

We investigate the localization properties of single-particle eigenstates in bichromatic one-dimensional optical lattices. Whereas such a lattice with a sufficiently deep primary component and a suitably adjusted incommensurate secondary component provides an approximate realization of the Harper model, the system's self-duality is broken when the lattice is comparatively shallow. As a consequence, the sharp metal-insulator transition exhibited by Harper's model is replaced by a sequence of mobility edges in realistic bichromatic optical lattices that do not reach the tight-binding regime.

Ultracold Atoms in a Disordered Crystal of Light: Towards a Bose Glass

We use a bichromatic optical lattice to experimentally realize a disordered system of ultracold strongly interacting 87Rb bosons. In the absence of disorder, the atoms are pinned by repulsive interactions in the sites of an ideal optical crystal, forming one-dimensional Mott-insulator states. We measure the excitation spectrum of the system as a function of disorder strength and characterize its phase-coherence properties with a time-of-flight technique. Increasing disorder, we observe a broadening of the Mott-insulator resonances and the transition to a state with vanishing long-range phase coherence and a flat density of excitations, which suggest the formation of a Bose-glass phase.

Near-resonant dark optical lattice with increased occupation

A bichromatic near-resonant dark optical lattice (DOL) with rubidium atoms is demonstrated, which provides confinement in the Lamb-Dicke regime in all spatial dimensions. We apply spatially phase-matched optical potentials for each hyperfine ground state in order to enable improved Sisyphus cooling, undisturbed by optical hyperfine pumping processes. We also explore a method to increase the occupation of the DOL. Initially $2\ifmmode\times\else\texttimes\fi{}{10}^{9}$ rubidium atoms with a temperature of $70\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{K}$ and a density of $5\ifmmode\times\else\texttimes\fi{}{10}^{10}\phantom{\rule{0.3em}{0ex}}\text{atoms}∕{\mathrm{cm}}^{3}$ are prepared in a magneto-optic trap (MOT) and a fraction of $5\ifmmode\times\else\texttimes\fi{}{10}^{7}$ atoms is loaded into a far detuned one-dimensional optical lattice (FOL). Subsequently, the MOT is replaced by the DOL, and the atoms become well localized within the microscopic light-shift potentials at a temperature of $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{K}$ with a typical density of $3\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.3em}{0ex}}\text{atoms}∕{\mathrm{cm}}^{3}$. We then apply alternating cycles of free evolution in the FOL and cooling and trapping in the DOL, obtaining a fourfold density increase to $1.2\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.3em}{0ex}}\text{atoms}∕{\mathrm{cm}}^{3}$---i.e., 7.5% occupation---while maintaining a temperature of $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{K}$. In a final adiabatic cooling step we reduce the well depth to 75 times the single-photon recoil energy, which leads to a temperature of $2.8\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{K}$ and a phase-space density of $1.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. Despite the increased density, no excess heating or collisional losses are observed.