We investigate Bloch-Zener oscillations and mean-field Bloch bands of a Bose-Einstein condensate (BEC) in a Lieb optical lattice. We find that the atomic interaction will break the point group symmetry of the system, leading to the destruction of the Dirac cone structure, while the flat band is preserved on the highly symmetric lines. Due to the nonlinear effect, a tubular band structure with a flat band will appear in the system. Furthermore, comparing with that the tight-binding (TB) model fails to describe the interacting bosonic systems in the honeycomb lattice, we show that the TB model is applicable to study the nonlinear energy band structures for the Lieb lattice. In addition, we show that the loop structure can be determined by the observation of the chaos of the state in the Bloch-Zener oscillations.
We report on experiments investigating quantum transport and band interferometry of an atomic Bose-Einstein condensate in an optical lattice with a two-band miniband structure, realized with a Fourier-synthesized optical lattice potential. Bloch-Zener oscillations, the coherent superposition of Bloch oscillations and Landau-Zener tunneling between the two bands are observed. When the relative phase between paths in different bands is varied, an interference signal is observed, demonstrating the coherence of the dynamics in the miniband system. Measured fringe patterns of this Stückelberg inter…
Stimulated by the experimental realization of spin-dependent tunneling via gradient magnetic field [Phys. Rev. Lett. 111, 225301 (2013); Phys. Rev. Lett. 111, 185301 (2013)], we investigate dynamics of Bloch oscillations and Landau-Zener tunneling of single spin-half particles in a periodic potential under the influence of a spin-dependent constant force. In analogy to the Wannier-Stark system, we call our system as the Wannier-Zeeman system. If there is no coupling between the two spin states, the system can be described by two crossing Wannier-Stark ladders with opposite tilts. The spatial c…
Bloch oscillations are a powerful tool to investigate spectra with Dirac points. By varying band parameters, Dirac points can be manipulated and merged at a topological transition towards a gapped phase. Under a constant force, a Fermi sea initially in the lower band performs Bloch oscillations and may Zener tunnel to the upper band mostly at the location of the Dirac points. The tunneling probability is computed from the low energy universal Hamiltonian describing the vicinity of the merging. The agreement with a recent experiment on cold atoms in an optical lattice is very good.
Cold atoms in an optical lattice execute Bloch-Zener oscillations when they are accelerated. We have performed a theoretical investigation into the case when the optical lattice is the intra-cavity field of a driven Fabry-Perot resonator. When the atoms oscillate inside the resonator, we find that their back-action modulates the phase and intensity of the light transmitted through the cavity. We solve the coupled atom-light equations self-consistently and show that, remarkably, the Bloch period is unaffected by this back-action. The transmitted light provides a way to observe the oscillation c…
Suppression of Bloch Oscillations and Nonreciprocal Landau-Zener Tunneling in Bose-Einstein Quantum Droplets
Chinese Culture University（中国文化大学）；National Taiwan University（台湾大学）；University of Taipei（台北大学）；National Yang Ming Chiao Tung University（国立阳明交通大学）；University of Iceland（冰岛大学）
Quantum walks are processes that model dynamics in coherent systems. Their experimental implementations proved key to unveil novel phenomena in Floquet topological insulators. Here we realize a photonic quantum walk in the presence of a synthetic gauge field, which mimics the action of an electric field on a charged particle. By tuning the energy gaps between the two quasi-energy bands, we investigate intriguing system dynamics characterized by the interplay between Bloch oscillations and Landau-Zener transitions. When both gaps at quasi-energy values 0 and $π$ are vanishingly small, the Floqu…
The interference between a sequence of Landau-Zener (LZ) transitions can produce Rabi oscillations(LZROs). This phenomenon is a kind of time-domain Landau-Zener-Stuckelberg-Majorana (LZSM) interference. However, experimental demonstrations of this LZSM interference induced Rabi oscillation are extremely hard due to the short coherence time of the driven quantum system. Here, we study theoretically the time-domain LZSM interference between the clock transition in one-dimensional (1D) Sr-87 optical lattice clock (OLC) system. With the help of both the adiabatic-impulse model and Floquet numerica…
The ground state and transport properties of the Lieb lattice flat band in the presence of an attractive Hubbard interaction are considered. It is shown that the superfluid weight can be large even for an isolated and strictly flat band. Moreover the superfluid weight is proportional to the interaction strength and to the quantum metric, a band structure invariant obtained from the flat-band Bloch functions. These predictions are amenable to verification with ultracold gases and may explain the anomalous behaviour of the superfluid weight of high-Tc superconductors.
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 tu…
The topological properties of non-Hermitian Hamiltonian is a hot topic, and the theoretical studies along this research line are usually based on the two-level non-Hermitian Hamiltonian (or, equivalently, a spin-$1/2$ non-Hermitian Hamiltonian). We are motivated to study the geometrical phases of a three-level Lieb lattice model (or, equivalently, a spin-$1$ non-Hermitian Hamiltonian) with the complex hopping and flat band in the context of a polariton condensate, with the emphasis on the higher spin degree of freedom on topological properties of non-Hermitian Hamiltonian. The topological inva…
We identify a new type of periodic evolution that appears in driven quantum systems. Provided that the instantaneous (adiabatic) energies are equidistant we show how such systems can be mapped to (time-dependent) tilted single-band lattice models. Having established this mapping, the dynamics can be understood in terms of Bloch oscillations in the instantaneous energy basis. In our lattice model the site-localized states are the adiabatic ones, and the Bloch oscillations manifest as a periodic repopulation among these states, or equivalently a periodic change in the system's instantaneous ener…
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 sta…
We report on Bloch-Zener oscillations of an ultracold Fermi gas in a tunable honeycomb lattice. The quasi-momentum distribution of the atoms is measured after sequentially passing through two Dirac points. We observe a double-peak feature in the transferred fraction to the second band, both as a function of the band gap at the Dirac points and the quasi-momentum of the trajectory. Our results are in good agreement with a simple analytical model based on two successive Landau-Zener transitions. Owing to the variation of the potential gradient over the cloud size, coherent Stückelberg oscillatio…
We report on the condensation of bosons in the 4th band of an optical chequerboard lattice providing a topologically induced avoided band crossing involving the 2nd, 3rd, and 4th Bloch bands. When the condensate is slowly tuned through the avoided crossing, accelerated band relaxation arises and the zero momentum approximately $C4$-invariant condensate wave function acquires finite momentum order and reduced $C2$ symmetry. For faster tuning Landau-Zener oscillations between different superfluid orders arise, which are used to characterize the avoided crossing.
The dynamic engineering of band structures for ultracold atoms in optical lattices represents an innovative approach to understand and explore the fundamental principles of topological matter. In particular, the folded Floquet spectrum determines the associated band topology via band inversion. We experimentally and theoretically study two-frequency phase modulation to asymmetrically hybridize the lowest two bands of a one-dimensional lattice. Using quasi-degenerate perturbation theory in the extended Floquet space we derive an effective two-band model that quantitatively describes our setting…
Time evolution of spin-orbit-coupled cold atoms in an optical lattice is studied, with a two-band energy spectrum having two avoided crossings. A force is applied such that the atoms experience two consecutive Landau-Zener tunnelings while transversing the avoided crossings. Stückelberg interference arises from the phase accumulated during the adiabatic evolution between the two tunnelings. This phase is gauge field-dependent and thus provides new opportunities to measure the synthetic gauge field, which is verified via calculation of spin transition probabilities after a double passage proces…
We experimentally study the scattering of guided matter waves on an amplitude-modulated optical lattice. We observe different types of frequency-dependent dips in the asymptotic output density distribution. Their positions are compared quantitatively with numerical simulations. A semiclassical model that combines \emph{local} Floquet-Bloch bands analysis and Landau-Zener transitions provides a simple picture of the observed phenomena in terms of elementary \emph{Floquet photon} absorption-emission processes and envelope-induced reflections. Finally, we propose and demonstrate the use of this t…
We describe the theory of the dynamics of atoms in two-dimensional quasicrystalline optical lattices. We focus on a regime of shallow lattice depths under which the applied force can cause Landau-Zener tunneling past a dense hierarchy of gaps in the quasiperiodic energy spectrum. We derive conditions on the external force that allow for a "semiadiabatic" regime in which semiclassical equations of motion can apply, leading to Bloch oscillations between the edges of a pseudo-Brillouin-zone. We verify this semiclassical theory by comparing to the results of an exact numerical solution. Interestin…
We investigate the ground state properties of a lattice trapped bosonic system coupled to a Lieb-Liniger type gas. Our main goal is the description and in depth exploration and analysis of the two-species many-body quantum system including all relevant correlations beyond the standard mean-field approach. To achieve this, we use the Multi-Configuration Time-Dependent Hartree method for Mixtures (ML-MCTDHX). Increasing the lattice depth and the interspecies interaction strength, the wave function undergoes a transition from an uncorrelated to a highly correlated state, which manifests itself in…
We propose a scheme to simulate and explore Weyl semimetal physics with ultracold fermionic atoms in a two-dimensional square optical lattice subjected to experimentally realizable spin-orbit coupling and an artificial dimension from an external parameter space, which may increase experimental feasibility compared with the cases in three dimensional optical lattices. It is shown that this system with a tight-binding model is able to describe essentially three-dimensional Weyl semimetals with tunable Weyl points. The relevant topological properties are also addressed by means of the Chern numbe…
We report on ground state properties of a one-dimensional, weakly-interacting Bose gas constrained by an infinite multi-rods periodic structure at zero temperature. We solve the stationary Gross-Pitaevskii equation (GPE) to obtain the Bloch wave functions from which we give a semi-analytical solution for the density profile, as well as for the phase of the wave function in terms of the Jacobi elliptic functions, and the incomplete elliptic integrals of the first, second and third kind. Then, we determine numerically the energy of the ground state, the chemical potential and the compressibility…
Phase frustration in periodic lattices is responsible for the formation of dispersionless flat bands. The absence of any kinetic energy scale makes flat band physics critically sensitive to perturbations and interactions. We report here on the experimental investigation of the nonlinear dynamics of cavity polaritons in the gapped flat band of a one-dimensional Lieb lattice. We observe the formation of gap solitons with quantized size and very abrupt edges, signature of the frozen propagation of switching fronts. This type of gap solitons belongs to the class of truncated Bloch waves, and had o…
Since the well-known PT symmetry has its fundamental significance and implication in physics, where PT denotes the combined operation of space-inversion P and time-reversal T, it is extremely important and intriguing to completely classify exotic PT-invariant topological metals and to physically realize them. Here we, for the first time, establish a rigorous classification of topological metals that are protected by the PT symmetry using KO-theory. As a physically realistic example, a PT-invariant nodal loop (NL) model in a 3D Brillouin zone is constructed, whose topological stability is revea…
