Incommensurate Optical Lattice Research Articles

Spectral and dynamical characters of 1D incommensurate optical lattices with [formula omitted]-symmetry

In this paper, we investigate the spectral and dynamical properties of a 1D incommensurate optical lattice, which displays a Parity-time (PT) symmetry described by the Non-Hermitian Aubry–André potential. We show through the spectral analysis of the eigenvalues and the associated eigenfunctions that, taking into account a non-Hermitian variant of the site energy modulated by a cosine form, leads the system to undergo a transition from the unbroken-PT phase to the broken-PT phase, which corresponds here to the delocalized-to-localized phase transition. Our findings also indicate that the critical point of transition can be selectively adjusted and consequently, the single-particle eigenstates taken in the metallic regime of the original Aubry–André model thus move from a conducting state to an insulating one upon an increase of the complex phase parameter. Furthermore, we also investigate the dynamical features of the system’s wave function according to different parameters.

Mobility edges and critical regions in a periodically kicked incommensurate optical Raman lattice

Conventionally the mobility edge (ME) separating extended states from localized ones is a central concept in understanding Anderson localization transition. The critical state, being delocalized and non-ergodic, is a third type of fundamental state that is different from both the extended and localized states. Here we study the localization phenomena in a one dimensional periodically kicked quasiperiodic optical Raman lattice by using fractal dimensions. We show a rich phase diagram including the pure extended, critical and localized phases in the high frequency regime, the MEs separating the critical regions from the extended (localized) regions, and the coexisting phase of extended, critical and localized regions with increasing the kicked period. We also find the fragility of phase boundaries, which are more susceptible to the dynamical kick, and the phenomenon of the reentrant localization transition. Finally, we demonstrate how the studied model can be realized based on current cold atom experiments and how to detect the rich physics by the expansion dynamics. Our results provide insight into studying and detecting the novel critical phases, MEs, coexisting quantum phases, and some other physics phenomena in the periodically kicked systems.

Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices

We investigate the wave packet dynamics for a one-dimensional incommensurate optical lattice with a special on-site potential which exhibits the mobility edge in a compactly analytic form. We calculate the density propagation, long-time survival probability and mean square displacement of the wave packet in the regime with the mobility edge and compare with the cases in extended, localized and multifractal regimes. Our numerical results indicate that the dynamics in the mobility-edge regime mix both extended and localized features which is quite different from that in the mulitfractal phase. We utilize the Loschmidt echo dynamics by choosing different eigenstates as initial states and sudden changing the parameters of the system to distinguish the phases in the presence of such system.

Quantum Adiabatic Doping with Incommensurate Optical Lattices.

Quantum simulations of Fermi-Hubbard models have been attracting considerable effort in the optical lattice research, with the ultracold antiferromagnetic atomic phase reached at half filling in recent years. An unresolved issue is to dope the system while maintaining the low thermal entropy. Here we propose to achieve the low temperature phase of the doped Fermi-Hubbard model using incommensurate optical lattices through adiabatic quantum evolution. In this theoretical proposal, we find that one major problem about the adiabatic doping is atomic localization in the incommensurate lattice, potentially causing an exponential slowing down of the adiabatic procedure. We study both one- and two-dimensional incommensurate optical lattices, and find that the localization prevents efficient adiabatic doping in the strong lattice regime for both cases. With density matrix renormalization group calculation, we further show that the slowing down problem in one dimension can be circumvented by considering interaction induced many-body delocalization, which is experimentally feasible using Feshbach resonance techniques. This protocol is expected to be efficient as well in two dimensions where the localization phenomenon is less stable.

Mobility edges in one-dimensional bichromatic incommensurate potentials

We theoretically study a one-dimensional (1D) mutually incommensurate bichromatic lattice system which has been implemented in ultracold atoms to study quantum localization. It has been universally believed that the tight-binding version of this bichromatic incommensurate system is represented by the well-known Aubry-Andre model. Here we establish that this belief is incorrect and that the Aubry-Andre model description, which applies only in the extreme tight-binding limit of very deep primary lattice potential, generically breaks down near the localization transition due to the unavoidable appearance of single-particle mobility edges (SPME). In fact, we show that the 1D bichromatic incommensurate potential system manifests generic mobility edges which disappear in the tight-binding limit, leading to the well-studied Aubry-Andre physics. We carry out an extensive study of the localization properties of the 1D incommensurate optical lattice without making any tight-binding approximation. We find that, for the full lattice system, an intermediate phase between completely localized and completely delocalized regions appears due to the existence of the SPME, making the system qualitatively distinct from the Aubry-Andre prediction. Using the Wegner flow approach, we show that the SPME in the real lattice system can be attributed to significant corrections of higher-order harmonics in the lattice potential which are absent in the strict tight-binding limit. We calculate the dynamical consequences of the intermediate phase in detail to guide future experimental investigations for the observation of 1D SPME and the associated intermediate phase. We consider effects of interaction numerically, and conjecture the stability of SPME to weak interaction effects, thus leading to the exciting possibility of an experimentally viable nonergodic extended phase in interacting 1D optical lattices.

Properties of bosons in a one-dimensional bichromatic optical lattice in the regime of the pinning transition: A worm-algorithm Monte Carlo study

The properties of interacting bosons in a weak, one-dimensional, and bichromatic optical with a rational ratio of the constituting wavelengths $\lambda_1$ and $\lambda_2$ are numerically examined along a broad range of the Lieb-Liniger interaction parameter $\gamma$ passing through the Sine-Gordon transition. It is argued that there should not be much difference in the results between those due to an irrational ratio $\lambda_1/\lambda_2$ and due to a rational approximation of the latter. For a weak bichromatic optical lattice, it is chiefly demonstrated that this transition is robust against the introduction of quasidisorder via a weaker, secondary, and incommensurate optical lattice superimposed on the primary one. The properties, such as the correlation function, Matsubara Green's function, and the single-particle density matrix, do not respond to changes in the depth of the secondary optical lattice $V_1$. For a stronger bichromatic optical lattice, however, a response is observed because of changes in $V_1$. It is found accordingly, that holes in the SG regime play an important role in the response of properties to changes in $\gamma$. The continuous-space worm algorithm Monte Carlo method [Boninsegni \ea, Phys. Rev. E $\mathbf{74}$, 036701 (2006)] is applied for the present examination. It is found that the worm algorithm is able to reproduce the Sine-Gordon transition that has been observed experimentally [Haller \ea, Nature $\mathbf{466}$, 597 (2010)].

Many-body ground state localization and coexistence of localized and extended states in an interacting quasiperiodic system

We study the localization problem of one-dimensional interacting spinless fermions in an incommensurate optical lattice, which changes from an extended phase to a nonergoic many-body localized phase by increasing the strength of the incommensurate potential. We identify that there exists an intermediate regime before the system enters the many-body localized phase, in which both the localized and extended many-body states coexist, thus the system is divided into three different phases, which can be characterized by normalized participation ratios of the many-body eigenstates and distributions of natural orbitals of the corresponding one-particle density matrix. This is very different from its noninterating limit, in which all eigenstaes undergo a delocaliztion-localization transtion when the strength of the incommensurate potential exceeds a critical value.

Superfluid Bloch dynamics in an incommensurate optical lattice

We investigate the interplay of disorder and interactions in the accelerated transport of a Bose–Einstein condensate through an incommensurate optical lattice. We show that interactions can effectively cancel the damping of Bloch oscillations (BOs) due to the disordered potential and we provide a simple model to qualitatively capture this screening effect. We find that the characteristic interaction energy, above which interactions and disorder cooperate to enhance, rather than reduce, the damping of BOs, coincides with the average disorder depth. This is consistent with results of a mean-field simulation.

Effects of Interactions and Temperature in Disordered Ultra-Cold Bose Gases

We simulate ultra-cold interacting bosons in quasi-one-dimensional, incommensurate optical lattices. In the tight-binding limit, these lattices have pseudo-random on-site energies and thus can potentially lead to Anderson localization. We use the Hartree-Fock-Bogoliubov formalism in the Bose-Hubbard model to explore the parameter regimes that lead to exponential localization of the ground state in a 3-colour optical lattice and investigate the role of repulsive interactions, harmonic confinement and finite temperature.

Quantum phases of incommensurate optical lattices due to cavity backaction

Ultracold bosonic atoms are confined by an optical lattice inside an optical resonator and interact with a cavity mode whose wavelength is incommensurate with the spatial periodicity of the confining potential. We predict that the intracavity photon number can be significantly different from zero when the atoms are driven by a transverse laser whose intensity exceeds a threshold value and whose frequency is suitably detuned from the cavity and the atomic transition frequency. In this parameter regime the atoms form clusters in which they emit in phase into the cavity. The clusters are phase locked, thereby maximizing the intracavity photon number. These predictions are based on a Bose-Hubbard model, whose derivation is reported here in detail. The Bose-Hubbard Hamiltonian has coefficients which are due to the cavity field and depend on the atomic density at all lattice sites. The corresponding phase diagram is evaluated using quantum Monte Carlo simulations in one dimension and mean-field calculations in two dimensions. Where the intracavity photon number is large, the ground state of the atomic gas lacks superfluidity and possesses finite compressibility, typical of a Bose glass.

Transport dynamics of an interacting binary Bose—Einstein condensate in an incommensurate optical lattice

We investigate the transport dynamics of an interacting binary Bose—Einstein condensate in an incommensurate optical lattice and predict a novel splitting of a matter wavepacket induced by disorder potential and inter-species interaction. The effect of atomic interaction on the dynamics of the mobile and localized atoms are also studied in detail. We also discuss the behavior of the balanced and inbalanced mixtures in the incommensurate optical lattice.

Visibility pattern of Bose–Fermi mixtures in one-dimensional incommensurate lattices

We performed numerical simulations to demonstrate localization phenomena of Bose–Fermi mixture systems on incommensurate optical lattices by changing Bose–Bose and Bose–Fermi interactions. Visibility patterns of the bosons were measured to observe bosonic coherence in various selections of the interaction parameters. We found that the coherence was enhanced with repulsive Bose–Fermi interactions. It was also enhanced with attractive Bose–Fermi interactions but only in certain conditions. The enhancement by repulsive interactions and that by attractive interactions occurred with different mechanisms.

Evidence for a Quantum-to-Classical Transition in a Pair of Coupled Quantum Rotors

The understanding of how classical dynamics can emerge in closed quantum systems is a problem of fundamental importance. Remarkably, while classical behavior usually arises from coupling to thermal fluctuations or random spectral noise, it may also be an innate property of certain isolated, periodically driven quantum systems. Here, we experimentally realize the simplest such system, consisting of two coupled, kicked quantum rotors, by subjecting a coherent atomic matter wave to two periodically pulsed, incommensurate optical lattices. Momentum transport in this system is found to be radically different from that in a single kicked rotor, with a breakdown of dynamical localization and the emergence of classical diffusion. Our observation, which confirms a long-standing prediction for many-dimensional quantum-chaotic systems, sheds new light on the quantum-classical correspondence.

Localization of Bose-Fermi Mixtures in One-Dimensional Incommensurate Lattices

We studied the localization property of Bose-Fermi mixture systems on incommensurate optical lattices by using quantum Monte-Carlo simulations. We found a characteristic behavior of the superfluid density when changing the Bose-Bose interactions and Bose-Fermi interactions over a wide range. The superfluidity of the bosons was enhanced in the presence of the fermions by the repulsive Bose-Fermi interactions which counteracted the localization of the bosons. With attractive Bose-Fermi interactions, on the other hand, the superfluidity is also enhanced by a different mechanism when the number of the bosons is much larger than that of the fermions.

Quantum criticality in disordered bosonic optical lattices

Using the exact Bose-Fermi mapping, we study universal properties of ground-state density distributions and finite-temperature quantum critical behavior of one-dimensional hard-core bosons in trapped incommensurate optical lattices. Through the analysis of universal scaling relations in the quantum critical regime, we demonstrate that the superfluid to Bose glass transition and the general phase diagram of disordered hard-core bosons can be uniquely determined from finite-temperature density distributions of the trapped disordered system.

Ground-state and dynamical properties of hard-core bosons in one-dimensional incommensurate optical lattices with a harmonic trap

We study properties of the strongly repulsive Bose gas on one-dimensional incommensurate optical lattices with a harmonic trap, which can be dealt with by use of an exact numerical method through Bose-Fermi mapping. We first exploit the phase transition of hard-core bosons in optical lattices from the superfluid to the Bose-glass phase as the strength of the incommensurate potential increases. Then we study the dynamical properties of the system after suddenly switching off the harmonic trap. We calculate the one-particle density matrices, the momentum distributions, and the natural orbitals and their occupations for both the static and dynamic systems. Our results indicate that the Bose-glass and superfluid phases display quite different properties and expansion dynamics.

Superfluid-to-Bose-glass transition of hard-core bosons in a one-dimensional incommensurate optical lattice

We study superfluid to Anderson insulator transition of strongly repulsive Bose gas in a one dimensional incommensurate optical lattice. In the hard core limit, the Bose-Fermi mapping allows us to deal with the system exactly by using the exact numerical method. Based on the Aubry-Andr\'{e} model, we exploit the phase transition of the hard core boson system from superfluid phase with all the single particle states being extended to the Bose glass phase with all the single particle states being Anderson localized as the strength of the incommensurate potential increasing relative to the amplitude of hopping. We evaluate the superfluid fraction, the one particle density matrices, momentum distributions, the natural orbitals and their occupations. All of these quantities show that there exists a phase transition from superfluid to insulator in the system.

Predicted Mobility Edges in One-Dimensional Incommensurate Optical Lattices: An Exactly Solvable Model of Anderson Localization

Localization properties of noninteracting quantum particles in one-dimensional incommensurate lattices are investigated with an exponential short-range hopping that is beyond the minimal nearest-neighbor tight-binding model. Energy dependent mobility edges are analytically predicted in this model and verified with numerical calculations. The results are then mapped to the continuum Schrödinger equation, and an approximate analytical expression for the localization phase diagram and the energy dependent mobility edges in the ground band is obtained.

Transition between extended and localized states in a one-dimensional incommensurate optical lattice

The quantum transport properties of a system are intimately related to the underlying symmetries of the Hamiltonian. In a perfectly periodic system all the eigenfunctions are extended Bloch waves @1#, while for a random potential in a quasi-one-dimensional system all the eigenfunctions are localized @2#. These properties can be experimentally studied through the dispersion of an initially localized wave packet; in the former case it grows ballistically, while in the latter the dispersion remains constant. In between these two extreme cases lie incommensurate and quasiperiodic systems. In these, the spectrum can range from having all extended states to all localized states or even to mixed behavior, as the parameters describing the system ~incommensurability, potential amplitude, etc.! are varied. For instance, in the Fibonacci lattice @3# all states are critical ~neither localized nor extended!, leading to anomalous dispersion. Another known example is the Harper model @4#, which models electrons in a two-dimensional lattice in the presence of a transverse magnetic field. The eigenfunctions for this model undergo a transition from localized to extended behavior as the amplitude of the potential of the lattice is decreased. These quantum properties could be related to the quite anomalous transport properties of quasicrystals @5#. These materials show large resistivity and a decreasing temperature dependence; this behavior is enhanced in cleaner samples, thus showing that impurities improve the transport instead of degrading it. A study of transport in a defect-free incommensurate system can then shed some light on the physics underlying quasicrystals.