One-dimensional Optical Superlattice Research Articles

Study of finite fermionic chains with edge modes using an appropriate momentum representation

This work is based on the Su-Schrieffer-Heeger model, which describes a system of non-interacting polarized fermions, i.e. without spin, moving in a one-dimensional optical superlattice with fixed boundary conditions. Starting from the Hamiltonian of the system in second quantization, in which the optical lattice has discretized the space, and taking into account that the basis that diagonalizes the kinetic energy is the one of momentum, we perform the discrete sine transform type-I, which respects the hard-wall boundary conditions of the system and allows us to expressour Hamiltonian in the momentum basis, in such a way that we can think that it is possible to extend the study to an arbitrary number of sites. Finally we apply the Bogoliubov-de Gennes formalism getting the dispersion relation and the bare vertex function where together they form the couplings matrix. By diagonalizing this matrix, we visualize the parameter set where the system hosts zero energy modes.

Simulating bosonic Chern insulators in one-dimensional optical superlattices

We study the topological properties of an extended Bose-Hubbard model with cyclically modulated hopping and on-site potential parameters, which can be realized with ultracold bosonic atoms in a one-dimensional optical superlattice. We show that the interacting bosonic chain at half filling and in the deep Mott insulating regime can simulate bosonic Chern insulators with a topological phase diagram similar to that of the Haldane model of noninteracting fermions. Furthermore, we explore the topological properties of the ground state by calculating the many-body Chern number, the quasiparticle energy spectrum with gapless edge modes, the topological pumping of the interacting bosons, and the topological phase transition from normal (trivial) to topological Mott insulators. We also present the global phase diagram of the many-body ground state, which contains a superfluid phase and two Mott insulating phases with trivial (a zero Chern number) and nontrivial topologies (a nonzero Chern number), respectively.

Spinor bosons in optical superlattices: A numerical study

The ground state of spin-1 ultracold bosons trapped in a periodic one-dimensional optical superlattice is studied. The two sites of the unit cell have an energy shift between them, whose competition with the spin-dependent strength is the main focus of this paper. Charge density wave (CDW) phases appear for semi-integer and integer densities, leading to rich phase diagrams with Mott insulator, superfluid and CDW phases. The spin-dependent interaction favors insulator phases for integer densities and disfavors CDW phases for semi-integer densities, which tend to disappear. Also, quantum phase transitions at finite values of the spin-dependent strength were observed. For integer densities, Mott insulator-superfluid-CDW insulator transitions appear for an energy shift lower (higher) than the local repulsion for the global density $\rho=1$ ($\rho=2$).

Topological Mott insulator with bosonic edge modes in one-dimensional fermionic superlattices

We investigate topological phase transitions driven by interaction and identify a novel topological Mott insulator state in one-dimensional fermionic optical superlattices through numerical density matrix renormalization group (DMRG) method. Remarkably, the low-energy edge excitations change from spin-1/2 fermionic single-particle modes to spin-1 bosonic collective modes across the phase transition. Due to spin-charge separation, the low-energy theory is governed by an effective spin superexchange model, whereas the charge degree of freedom is fully gapped out. Such topological Mott state can be characterized by a spin Chern number and gapless magnon modes protected by a finite spin gap. The proposed experimental setup is simple and may pave the way for the experimental observation of exotic topological Mott states.

Topology, edge states, and zero-energy states of ultracold atoms in one-dimensional optical superlattices with alternating on-site potentials or hopping coefficients

One-dimensional superlattices with periodic spatial modulations of onsite potentials or tunneling coefficients can exhibit a variety of properties associated with topology or symmetry. Recent developments of ring-shaped optical lattices allow a systematic study of those properties in superlattices with or without boundaries. While superlattices with additional modulating parameters are shown to have quantized topological invariants in the augmented parameter space, we also found localized or zero-energy states associated with symmetries of the Hamiltonians. Probing those states in ultracold-atoms is possible by utilizing recently proposed methods analyzing particle depletion or the local density of states. Moreover, we summarize feasible realizations of configurable optical superlattices using currently available techniques.

Quantum anomalous Hall-quantum spin Hall effect in optical superlattices.

We consider the topological characteristics of the spin-orbital coupling particles loaded in one-dimensional (1D) optical superlattices subject to the Zeeman field. The phase shift of the superlattice provides a virtual dimension which allows us to simulate two-dimensional topological phases with a physically 1D system. The system possesses a variety of quantum phase transitions over a large parametric space and two important topological phases, namely, quantum anomalous Hall (QAH) and quantum spin Hall (QSH) phases are found to coexist in the system, but they reside in different bandgaps. This new category of gap-dependent QAH--QSH insulator paves the way for the possible observation of the coexistence of QSH and QAH effects at one platform.

Engineering Weyl Superfluid in Ultracold Fermionic Gases by One-Dimensional Optical Superlattices

In this paper, we theoretically demonstrate by using one-dimensional superlattices to couple two-dimensional time-reversal-breaking gapped topological superfluid models, an anomalous Weyl superfluid (WS) can be obtained. This new phase features its unique Fermi arc states (FAS) on the surfaces. In the conventional WS, FAS exist only for a part of the line connecting the projections of Weyl points and extending to the border and/or center of surface Brillouin zone. But for the anomalous WS, FAS exist for the whole line. As a proof of principle, we self-consistently at the mean-field level claim the achievement of the anomalous WS in the model with a dichromatic superlattice. In addition, inversion symmetry and band inversion in this model are analyzed to provide the unique features of identifying the anomalous WS experimentally by the momentum-resolved radio-frequency spectroscopy.

Manipulating matter waves in an optical superlattice

We investigate the potential for controlling a non-interacting Bose-Einstein condensate loaded into a one-dimensional optical superlattice. Our control strategy combines Bloch oscillations originating from accelerating the lattice and from time-dependent control of the superlattice parameters. We investigate two experimentally viable scenarios, very low and very high potential depths. We are able to exhibit a wide range of control over energy band populations using the superlattice control parameters. With this analysis we consider several examples of quantum state preparation in the superlattice structure that may be difficult to achieve in a regular lattice.

Effect of disorders on topological phases in one-dimensional optical superlattices**Project supported by the National Natural Science Foundation of China (Grant No. 41174116), the Graduate Student Education Teaching Reform Project, China (Grant No. JG201512), and the Young Teachers’ Research Project of Yanshan University, China (Grant No. 13LGB028).

In a recent paper, Lang et al. proposed that edge states and topological phases can be observed in one-dimensional optical superlattices. They showed that the topological phases can be revealed by observing the density profile of a trapped fermion system, which displays plateaus with their positions. However, disorders are not considered in their model. To study the effect of disorders on the topological phases, we introduce random potentials to the model for optical superlattcies. Our calculations show that edge states are robust against the disorders. We find the edge states are very sensitive to the number of the sites in the optical superlattice and we propose a simple rule to describe the relationship between the edge states and the number of sites. The density plateaus are also robust against weak disorders provided that the average density is calculated over a long interval. The widths of the plateaus are proportional to the widths of the bulk energy gaps when there are disorders. The disorders can diminish the bulk energy gaps. So the widths of the plateaus decrease with the increase of disorders and the density plateaus disappear when disorders are too strong. The results in our paper can be used to guide the experimental detection of topological phases in one-dimensional systems.

Direct-substitution method for studying second harmonic generation in arbitrary optical superlattices

In this paper, we present the direct-substitution (DS) method to study the second-harmonic generation (SHG) in arbitrary one-dimensional optical superlattices (OS). Applying this method to Fibonacci and generalized Fibonacci systems, we obtain the relative intensity of SHG and compare them with previous works. We confirmed the validity of the proposed DS method by comparing our results of SHG in quasiperiodic Fibonacci OS with previous works using analytical Fourier transform method. Furthermore, the three-dimension SHG spectra obtained by DS method present the properties of SHG in Fibonacci OS more distinctly. What’s more important, the DS method demands very few limits and can be used to compute directly and conveniently the intensity of SHG in arbitrary OS where the quasi-phase-matching (QPM) can be achieved. It shows that the DS method is powerful for the calculation of electric field and intensity of SHG and can help experimentalists conveniently to estimate the distributions of SHG in any designed polarized systems.

πBerry phase and topological excitation in interacting boson-fermion mixtures

The topological property of boson-fermion mixture in a one-dimensional optical superlattice is studied and the topological insulating phase of interacting boson-fermion mixture characterized by a nontrivial Berry phase is identified. The single-particle and boson-fermion exchanging excitation spectrums are calculated and we identify the boson-fermion exchanging excitation as the gapless topological excitation in the topological phase of the mixture. The different kinds of excitations are explained explicitly from the competition among the bulk gap, the on-site boson-boson and boson-fermion interactions. The Hamiltonian studied has been partly realized in the state-of-art cold atom experiments, and the results are very relevant to the experiments.

Quasiadiabatic dynamics of ultracold bosonic atoms in a one-dimensional optical superlattice

We study the quasiadiabatic dynamics of a one-dimensional system of ultracold bosonic atoms loaded in an optical superlattice. Focusing on a slow linear variation in time of the superlattice potential, the system is driven from a conventional Mott insulator phase to a superlattice-induced Mott insulator, crossing in between a gapless critical superfluid region. Due to the presence of a gapless region, a number of defects depending on the velocity of the quench appear. Our findings suggest a power-law dependence similar to the Kibble-Zurek mechanism for intermediate values of the quench rate. For the temporal ranges of the quench dynamics that we considered, the scaling of defects depends nontrivially on the width of the superfluid region.

Anomalous charge pumping in a one-dimensional optical superlattice

We model atomic motion in a sliding superlattice potential to explore topological "charge pumping" and to find optimal parameters for experimental observation of this phenomenon. We analytically study the band-structure, finding how the Wannier states evolve as two sinusoidal lattices are moved relative to one-another, and relate this evolution to the center of mass motion of an atomic cloud. We pay particular attention to counterintuitive or anomalous regimes, such as when the atomic motion is opposite to that of the lattice.

Ultracompact Superlattices for Multi-frequency Optical Bloch Oscillations Simultaneously

In this paper, we investigate the photonic transmission properties of a kind of one-dimensional optical superlattices composed of alternately stacked metal and dielectric films. A geometric thickness gradient of the dielectric layers, which is analog to an external electric field applied to the electronic crystals for observing electron Bloch oscillations, is introduced in the superlattices along the photonic propagation direction. Analytical results from the transfer matrix method reveal that three sets of photonic Wannier-Stark ladder with different frequency-space in terahertz level exist simultaneously from visible to near infrared frequency domain as the gradient is varied from 0.5 to 0.8, which indicates that the optical superlattices can support three different terahertz Bloch oscillations simultaneously. In particular, at a certain gradient, the Zener tunneling effect between two adjacent Wannier-Stark ladders is achieved. Finite-difference time-domain simulations on the dynamic evolution of photons propagation in the superlattices confirm the analytical predictions. The largest total thickness of the superlattices is around 8 μm, which is a quarter of that of superlattices composed of alternately stacked Bragg reflectors and dielectric microcavities.

Loading and detecting a three-dimensional Fermi gas in a one-dimensional optical superlattice

We investigate the procedures of loading and detecting three-dimensional fermionic quantum gases in a one-dimensional optical superlattice potential subjected to a trapping potential. Additionally, we consider the relaxation dynamics after a sudden change of the superlattice potential. We numerically simulate the time-dependent evolution of the continuous system using exact diagonalization of non-interacting fermions. During the loading procedure we analyze the occupation of the instantaneous energy levels and compare the situation in a homogeneous system with the trapped one. Strong differences are found in particular in the evolution of excitations which we trace back to the distinct global density distribution. Starting from an imbalanced state in the superlattice potential, we consider the relaxation dynamics of fermions after a slow change of the superlattice potential and find a bimodule distribution of excitations. To be able to compare with the experimental results we also simulate the measurement sequence of the even and odd local density and find a strong dependence of the outcome on the actual ramp procedure. We suggest how the loading and detecting procedure can be optimized.

Magnetic kink states emulated with dipolar superlattice gases

We propose an effective Ising spin chain constructed with dipolar quantum gases confined in a one-dimensional optical superlattice. Mapping the motional degree of freedom of a single particle in the lattice onto a pseudo-spin results in an effective Ising type chain dressed with transverse and longitudinal magnetic fields. The ground state of this effective Ising chain changes from a paramagnetic to a single-kink state as the dipolar interaction increases. Particularly in the single-kink state this effective chain permits emulations of magnetic kink effects. Being realizable with current experimental techniques, this effective Ising chain presents a unique platform for emulations of Ising physics and enriches the toolbox for quantum emulation of spin models by ultracold quantum gases.

Defect solitons in parity-time symmetric superlattices with focusing saturable nonlinearity

In this paper, we find that defect superlattice solitons (DSSs) exist at the defect site in one-dimensional optical superlattices with a parity-time (PT) symmetric potential and focusing saturable nonlinearity. We discuss the existence and stability of DSSs numerically and find that both the saturation parameter s and the defect strength ε can affect the power, the existence and stable regions of solitons significantly. For given saturation parameter s and defect strength ε (propagation constant μ), the power of DSSs increases with the increase (decrease) of μ (ε). For positive and zero defects, DSSs only exist in the semi-infinite band gap, whereas for negative defects, DSSs exist not only in the semi-infinite band gap but also in the first finite band gap. Besides, our numerical calculations show that when the saturation nonlinearity increases up to some level, the increasing rate of soliton power with μ is very fast and the stable regions of DSSs will become obviously narrow and eventually disappear with a decrease of ε for negative defects.

Some topological states in one-dimensional cold atomic systems

Ultracold atoms trapped in optical lattices nowadays have been widely used to mimic various models from condensed-matter physics. Recently, many great experimental progresses have been achieved for producing artificial magnetic field and spin–orbit coupling in cold atomic systems, which turn these systems into a new platform for simulating topological states. In this paper, we give a review focusing on quantum simulation of topologically protected soliton modes and topological insulators in one-dimensional cold atomic system. Firstly, the recent achievements towards quantum simulation of one-dimensional models with topological non-trivial states are reviewed, including the celebrated Jackiw–Rebbi model and Su–Schrieffer–Heeger model. Then, we will introduce a dimensional reduction method for systematically constructing high dimensional topological states in lower dimensional models and review its applications on simulating two-dimensional topological insulators in one-dimensional optical superlattices.

Unusual behavior of sound velocity of a Bose gas in an optical superlattice at quasi-one-dimension

A Bose gas trapped in a one-dimensional optical superlattice has emerged as a novel superfluid characterized by tunable lattice topologies and tailored band structures. In this work, we focus on the propagation of sound in such a novel system and have found new features on sound velocity, which arises from the interplay between the two lattices with different periodicity and is not present in the case of a condensate in a monochromatic optical lattice. Particularly, this is the first time that the sound velocity is found to first increase and then decrease as the superlattice strength increases even at one dimension. Such unusual behavior can be analytically understood in terms of the competition between the decreasing compressibility and the increasing effective mass due to the increasing superlattice strength. This result suggests a new route to engineer the sound velocity by manipulating the superlattice's parameters. All the calculations based on the mean-field theory are justified by checking the exponent $\gamma$ of the off-diagonal one-body density matrix that is much smaller than 1. Finally, the conditions for possible experimental realization of our scenario are also discussed.

Relaxation dynamics of a Fermi gas in an optical superlattice.

This Letter comprises an experimental and theoretical investigation of the time evolution of a Fermi gas following fast and slow quenches of a one-dimensional optical double-well superlattice potential. We investigate both the local tunneling in the connected double wells and the global dynamics towards a steady state, i.e., a time-independent state. The local observables in the steady state resemble those of a thermal equilibrium state, whereas the global properties indicate a strong nonequilibrium situation.