Quasiperiodic Optical Lattice Research Articles

Bloch-Landau-Zener oscillations in a quasi-periodic potential

Bloch oscillations and Landau-Zener tunneling are ubiquitous phenomena which are sustained by a band-gap spectrum of a periodic Hamiltonian and can be observed in dynamics of a quantum particle or a wavepacket in a periodic potential under action of a linear force. Such physical setting remains meaningful for aperiodic potentials too, although band-gap structure does not exist anymore. Here we consider the dynamics of noninteracting atoms and Bose-Einstein condensates in a quasiperiodic one-dimensional optical lattice subjected to a weak linear force. Excited states with energies below the mobility edge, and thus localized in space, are considered. We show that the observed oscillatory behavior is enabled by tunneling between the initial state and a state (or several states) located nearby in the coordinate-energy space. The states involved in such Bloch-Landau-Zener oscillations are determined by the selection rule consisting of the condition of their spatial proximity and condition of quasiresonances occurring at avoided crossings of the energy levels. The latter condition is formulated mathematically using the Gershgorin circle theorem. The effect of the inter-atomic interactions on the dynamics can also be predicted on the bases of the developed theory. The reported results can be observed in any physical system allowing for observation of the Bloch oscillations, upon introducing incommensurablity in the governing Hamiltonian. Published by the American Physical Society 2024

Quench-induced chaotic dynamics of Anderson-localized interacting Bose-Einstein condensates in one dimension

We study the effect of atomic interaction on the localization and the associated dynamics of Bose-Einstein condensates in a one-dimensional quasiperiodic optical lattice and random disordered potentials. When the interactions are absent, the condensates exhibit localization, which weakens as we increase the interaction strength beyond a threshold value for both potential types. We inspect the localized and delocalized states by perturbing the system via quenching the interaction strength instantaneously to zero and studying the dynamics of the condensate, which we further corroborate using the out-of-time-order correlator. The temporal behavior of the time correlator displays regular dynamics for the localized state, while it shows temporal chaos for the delocalized state. We confirm this dynamical behavior by analyzing the power spectral density of the time correlator. We further identify that the condensate admits a quasiperiodic route to chaotic dynamics for both the potentials. Finally, we present the variation of the maximal Lyapunov exponents for different nonlinearity and disorder strengths that have a positive value in the regime where the time-correlator function shows chaotic behavior. Through this, we establish the strong connection between the spatially delocalized state of the condensate and its temporal chaos.

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.

Synergy between the negative absolute temperature and the external trap for a Bose-Einstein condensate under optical lattices

We provide a generic but exact analytical model for realizing negative absolute temperature in ultracold atoms under a quasi-periodic optical lattice (bi-chromatic) and an expulsive trap. We keep freedom for maximum tunability for both kinds of trap profile, where bi-chromatic lattice is quasi-periodic except two tunable limits, from a pure optical lattice to another doubly periodic optical lattice. The expulsive trap can be tuned from zero to a stronger one. All the required conditions for achieving negative temperature domain have been explored by identifying appropriate trap parameters. Condensate density in each lattice site is controlled and Anderson-like localization is emphasized. A thorough study of a quantitative estimate of the temperature is performed in the negative domain by controlling the trap, where the roles of all the trap parameters are precisely identified. A numerical stability analysis by Fourier split-step method makes the study more useful and the proposed family of solution are found quite stable. This is also connected to the merit of negative temperature through mean deviation data with varied trap parameters.

Exploring unconventional features of light dynamics in Aubrey–André–Harper model based quasi-periodic optical lattices

We report an Aubrey–André–Harper (AAH) model based quasi-periodic lossless evanescently coupled waveguide lattice to study the unconventional physics of light localization. We find an exclusively new way to establish localization phase transition in a 1D-AAH lattice by observing the slope variation of the band and accordingly study the modal characteristics to reveal the fact that a higher value of quasi-periodic modulation strength is imperative for observing a signature of fully localized light states having higher eigenenergy. This analytical concept has numerically been implemented in the proposed quasi-periodic lattice to achieve light localization, where we have shown that the supported states not only depend on localization phase transition parameter, but also on the specific location of excitation which is due to quasi-periodic nature of lattice. Furthermore, we have investigated a unique effect of the presence of disorder on light localization phenomenon, where it has been reported that the presence of off-diagonal disorder, which is otherwise detrimental, favours light localization in the proposed structure due to its quasi-periodic nature. The findings indeed have the potential to open up a fertile platform to manipulate light in passive photonic devices.

Learning single-particle mobility edges by a neural network based on data compression

The breaking of the well-known Aubry-Andr\'e model with a single-particle mobility edge (SPME) is a intriguing subject that has not yet been fully understood. In particular, how to accurately and efficiently recognize a SPME in an optical lattice is currently under active debate. In this work, we develop a data compression-based neural network (DCNN) approach to identify SPMEs in one-dimensional quasiperiodic optical lattice using eigenstates as the sole diagnostic. We find that such method can successfully identify SPMEs of a large system only using a small network trained by the small system data, without onerously and repetitively training a new and large-scale network by massive data of a large system. Furthermore, we show that this method is also applicable to recognize more complex phase transitions, such as many-body localization. Our DCNN approach first paves the way for the development of a generic tool for identifying unexplored phase transitions in large systems.

Bose–Einstein condensates in an eightfold symmetric optical lattice**Project supported by the National Natural Science Foundation of China (Grant Nos. 11434011, 11522436, and 11774425), the National Key R&D Program of China (Grants No. 2018YFA0306501), the Beijing Natural Science Foundation, China (Grant No. Z180013), and the Research Funds of Renmin University of China (Grants Nos. 16XNLQ03 and 18XNLQ15).

We investigate the properties of Bose–Einstein condensates (BECs) in a two-dimensional quasi-periodic optical lattice (OL) with eightfold rotational symmetry by numerically solving the Gross–Pitaevskii equation. In a stationary external harmonic trapping potential, we first analyze the evolution of matter-wave interference pattern from periodic to quasi-periodic as the OL is changed continuously from four-fold periodic to eight-fold quasi-periodic. We also investigate the transport properties during this evolution for different interatomic interaction and lattice depth, and find that the BEC crosses over from ballistic diffusion to localization. Finally, we focus on the case of eightfold symmetric lattice and consider a global rotation imposed by the external trapping potential. The BEC shows vortex pattern with eightfold symmetry for slow rotation, becomes unstable for intermediate rotation, and exhibits annular solitons with approximate axial symmetry for fast rotation. These results can be readily demonstrated in experiments using the same configuration as in Phys. Rev. Lett. 122 110404 (2019).

Localization Driven Superradiant Instability.

The prominent Dicke superradiant phase arises from coupling an ensemble of atoms to a cavity optical field when an external optical pumping exceeds a threshold strength. Here we report a prediction of the superradiant instability driven by Anderson localization, realized with a hybrid system of the Dicke and Aubry-André (DAA) model for bosons trapped in a one-dimensional (1D) quasiperiodic optical lattice and coupled to a cavity. Our central finding is that for bosons condensed in a localized phase given by the DAA model, the resonant superradiant scattering is induced, for which the critical optical pumping of the superradiant phase transition approaches zero, giving an instability driven by the Anderson localization. The superradiant phase for the DAA model with or without a mobility edge is investigated, showing that the localization driven superradiant instability is in sharp contrast to the superradiance as widely observed for a Bose-Einstein condensate in extended states, and should be insensitive to the temperature of the system. This study unveils a novel effect of localization on the Dicke superradiance, and is well accessible based on the current experiments.

Transport through degenerate tori and quantum-to-classical crossover in a driven Aubry-Andre model

Dynamics of ultracold atoms in a one-dimensional incommensurate quasiperiodic optical lattice is considered. The lattice is created as superposition of a large-amplitude primary lattice and a small-amplitude secondary lattice. In the tight-binding approximation motion of atoms is described by the Aubry-Andre model. Attention is focused on atom delocalization caused by amplitude modulation of the secondary lattice. We consider the semiclassical regime that is realized if the lattice spacing of the primary lattice is small compared to that of the secondary one. It is shown that efficient delocalization occurs if frequency of the modulation corresponds to resonant influence on degenerate tori in classical phase space. Inclusion of the next-to-nearest tunneling into the Aubry-Andre model leads to shift of the corresponding resonance to the lower frequency range. As ratio of primary and secondary lattice periods increases, effect of the resonance ceases.

Non-Abelian gauge potentials driven localization transition in quasiperiodic optical lattices

Derived from quantum waves immersed in an Abelian gauge potential, the quasiperiodic Aubry-André-Harper (AAH) model is a simple yet powerful Hamiltonian to study the Anderson localization of ultracold atoms. Here, we investigate the localization properties of ultracold atoms in quasiperiodic optical lattices subject to a non-Abelian gauge potential, which are depicted by non-Abelian AAH models. We identify that the non-Abelian AAH models can bear the self-duality. We analyze the localization of such non-Abelian self-dual optical lattices, revealing a rich phase diagram driven by the non-Abelian gauge potential involved: a transition from a pure delocalization phase, then to coexistence phases, and finally to a pure localization phase. This is in stark contrast to the Abelian counterpart that does not support the coexistence phases. Our results establish the connection between localization and gauge symmetry, and thus comprise a new insight on the fundamental aspects of localization in quasiperiodic systems, from the perspective of non-Abelian gauge potential.

Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice.

A single-particle mobility edge (SPME) marks a critical energy separating extended from localized states in a quantum system. In one-dimensional systems with uncorrelated disorder, a SPME cannot exist, since all single-particle states localize for arbitrarily weak disorder strengths. However, in a quasiperiodic system, the localization transition can occur at a finite detuning strength and SPMEs become possible. In this Letter, we find experimental evidence for the existence of such a SPME in a one-dimensional quasiperiodic optical lattice. Specifically, we find a regime where extended and localized single-particle states coexist, in good agreement with theoretical simulations, which predict a SPME in this regime.

Out-of-equilibrium dynamics of repulsive Fermi gases in quasiperiodic potentials: A density functional theory study

The dynamics of a one-dimensional two-component Fermi gas in the presence of a quasi-periodic optical lattice (OL) is investigated by means of a Density Functional Theory approach. Inspired by the protocol implemented in recent cold-atom experiments, designed to identify the many-body localization transition, we analyze the relaxation of an initially prepared imbalance between the occupation number of odd and of even sites. For quasi-disorder strength beyond the Anderson localization transition, the imbalance survives for long times, indicating the inability of the system to reach local equilibrium. The late time value diminishes for increasing interaction strength. Close to the critical quasi-disorder strength corresponding to the noninteracting (Anderson) transition, the interacting system displays an extremely slow relaxation dynamics, consistent with sub-diffusive behavior. The amplitude of the imbalance fluctuations around its running average is found to decrease with time, and such damping is more effective with increasing interaction strengths. While our study addresses the setup with two equally intense OLs, very similar effects due to interactions have been observed also in recent cold-atom experiments performed in the tight-binding regime, i.e. where one of the two OLs is very deep and the other is much weaker.

腔诱导的冷原子在一维准周期性光晶格中的布洛赫振荡

腔诱导的冷原子在一维准周期性光晶格中的布洛赫振荡

Influence of localization transition on dynamical properties for an extended Aubry–André–Harper model

We show the localization transition and its influence on two dynamical processes of an extended Aubry–André–Harper model with incommensurate on-site and hopping potentials. After specifying an extended Aubry–André–Harper model, we check the localization transition for all the eigenstates and eigenenergy band splitting behavior versus a system parameter. To check the influence of localization transition on dynamical processes, firstly, the slowly pumping of edge states are examined. The adiabatic pumping is suppressed in the localized region. Then by quantum Lyapunov control method in terms of different control Hamiltonians, we prepare an edge-localized state in the nonlocal region. The control effect is suppressed in the localized region compared to that in the nonlocal region. In the dynamical processes, the system acts as conductor for the excitation in the nonlocal region and insulator in the localized region. Then we adopt the occupation imbalance between even and odd sites and entropy to indicate the localization transition further. Finally, the experimental schemes based on cold atoms trapped in quasiperiodic optical lattice and coupled optical waveguide arrays are suggested.

Correlations of Pairs in Bichromatic Optical Lattices

Correlation functions of two interacting bosons in bound states confined in a quasi-periodic 1D optical lattice are investigated. This two-body problem is exactly solvable, and therefore, various correlation functions can be directly calculated. The first-order correlation and the resulting momentum distribution behave smoothly across the phase boundary and exhibit a strong dependence on the sign of on-site interactions. We demonstrate that this special signature of momentum distribution exists for both the extended phase and the localized phase. In addition to the dependence on the sign of on-site interactions, the second-order quantum coherence reveals complementary information about the quasi-periodic order of the system, the underling structure of the bound states and the characterization of the different phases of the bound states. We also study the second-order correlation in momentum space of the bound states in both the weak and strong coupling regimes and demonstrate different correlation patterns in these two regimes.

Phase controlled metal–insulator transition in multi-leg quasiperiodic optical lattices

A tight-binding model of a multi-leg ladder network with a continuous quasiperiodic modulation in both the site potential and the inter-arm hopping integral is considered. The model mimics optical lattices where ultra-cold fermionic or bosonic atoms are trapped in double well potentials. It is observed that, the relative phase difference between the on-site potential and the inter-arm hopping integral, which can be controlled by the tuning of the interfering laser beams trapping the cold atoms, can result in a mixed spectrum of one or more absolutely continuous subband(s) and point like spectral measures. This opens up the possibility of a re-entrant metal–insulator transition. The subtle role played by the relative phase difference mentioned above is revealed, and we corroborate it numerically by working out the multi-channel electronic transmission for finite two-, and three-leg ladder networks. The extension of the calculation beyond the two-leg case is trivial, and is discussed in the work.

Método variacional aplicado ao estudo de um gás de átomos de Fermi em um estado superfluido aprisionados por uma rede óptica quase periódica

Neste trabalho, nós consideramos um modelo derivado da densidade de um gás de Fermi em um estado superfluido BCS, aprisionado por uma rede óptica quase periódica unidimensional. Reduzindo a equação em 3D para 1D, construímos famílias de gaps sólitons estáveis (GSs) utilizando aproximações variacionais. No limite linear a aproximação variacional prediz exatamente a posição da banda de Bloch que separam os primeiros gaps. Através da aproximação variacional, mostramos a possibilidade de que a não linearidade efetiva atuando em combinação com o potencial de uma rede quase periódica em uma dimensão, permite o surgimento de gaps sólitons iluminados. Variando a amplitude da rede óptica, analisamos a existência e estabilidade dos gaps sólitons iluminados usando um ansatz gaussiano. Os gaps sólitons são estáveis diante de pequenas variações da rede óptica quase periódica. Este artigo pode ser utilizado como um guia de aprendizagem no estudo de átomos frios; estudantes são incentivados a realizarem os cálculos para outros valores de amplitude da rede óptica.

Fermi polaron in a one-dimensional quasiperiodic optical lattice: The simplest many-body localization challenge

We theoretically investigate the behavior of a moving impurity immersed in a sea of fermionic atoms that are confined in a quasi-periodic (bichromatic) optical lattice, within a standard variational approach. We consider both repulsive and attractive contact interactions for such a simplest many-body localization problem of Fermi polarons. The variational approach enables us to access relatively large systems and therefore may be used to understand many-body localization in the thermodynamic limit. The energy and wave-function of the polaron states are found to be strongly affected by the quasi-random lattice potential and their experimental measurements (i.e., via radio-frequency spectroscopy or quantum gas microscope) therefore provide a sensitive way to underpin the localization transition. We determine a phase diagram by calculating two critical quasi-random disorder strengths, which correspond to the onset of the localization of the ground-state polaron state and the many-body localization of all polaron states, respectively. Our predicted phase diagram could be straightforwardly examined in current cold-atom experiments.

Fibonacci optical lattices for tunable quantum quasicrystals

We describe a quasiperiodic optical lattice, created by a physical realization of the abstract cut-and-project construction underlying all quasicrystals. The resulting potential is a generalization of the Fibonacci tiling. Calculation of the energies and wavefunctions of ultracold atoms loaded into such a lattice demonstrate a multifractal energy spectrum, a singular continuous momentum-space structure, and the existence of controllable edge states. These results open the door to cold atom quantum simulation experiments in tunable or dynamic quasicrystalline potentials, including topological pumping of edge states and phasonic spectroscopy.

Localization of light in a parity-time-symmetric quasi-periodic lattice.

We address the propagation of light in a parity-time (PT) symmetric quasi-periodic optical lattice. We show that the PT-symmetry breaking threshold of the system depends on the relative strength of two simple lattices forming quasi-periodic structure. The increase of the imaginary part of such structure leads to a dynamical phase transition from delocalization to re-localization for all eigenmodes. The nontrivial interplay between PT-symmetry breaking and the delocalization-localization transition in the system opens new prospects for the manipulation of dynamical evolution of light beams.