One-dimensional Lattice Research Articles

Quantum engineering of a synthetic thermal bath for bosonic atoms in a one-dimensional optical lattice via Markovian feedback control

We propose and investigate a scheme for engineering a synthetic thermal bath for a bosonic quantum gas in a one-dimensional optical lattice based on Markovian feedback control. The performance of our scheme is quantified by the fidelity between the steady state of the system and the effective thermal state. For double-well and triple-well systems with non-interacting particles, the steady state is found to be an exact thermal state, which is attributed to the fact that the transfer rates between all pairs of coupled eigenstates satisfy detailed balance condition. The scenario changes when there are more lattice sites, where the detailed balance condition does not hold any more, but remains an accurate approximation. Remarkably, our scheme performs very well at low and high temperature regimes, with the fidelity close to one. The performance at intermediate temperatures~(where a crossover into a Bose condensed regime occurs) is slightly worse, and the fidelity shows a gentle decrease with increasing system size. We also discuss the interacting cases. In contrast to the non-interacting cases, the scheme is found to perform better at a higher temperature. Another difference is that the minimal temperature that can be engineered is nonzero and increases with the interaction strength.

Localization in a one-dimensional alloy with an arbitrary distribution of spacing between impurities: Application to Lévy glass.

We have studied the localization of waves in a one-dimensional lattice consisting of impurities where the spacing between consecutive impurities can take certain values with given probabilities. In general, such a distribution of impurities induces correlations in the disorder. In particular, with a power-law distribution of spacing, this system is used as a model for light propagation in Lévy glasses. We introduce a method of calculating the Lyapunov exponent which overcomes limitations in the previous studies and can be easily extended to higher orders of perturbation theory. We obtain the Lyapunov exponent up to fourth order of perturbation and discuss the range of validity of perturbation theory, transparent states, and anomalous energies which are characterized by divergences in different orders of the expansion. We also carry out numerical simulations which are in agreement with our analytical results.

Bose-Einstein condensates in quasiperiodic lattices: Bosonic Josephson junction, self-trapping, and multimode dynamics

A Bose-Einstein condensate loaded in a one-dimensional bichromatic optical lattice with constituent sublattices having incommensurate periods is considered. Using the rational approximations for the incommensurate periods, we show that below the mobility edge the localized states are distributed nearly homogeneously in the space and explore the versatility of such potentials. We show that superposition of symmetric and antisymmetric localized states can be used to simulate various physical dynamical regimes, known to occur in double-well and multiwell traps. As examples, we obtain an alternative realization of a bosonic Josephson junction, whose coherent oscillations display beatings or switching in the weakly nonlinear regime, and describe self-trapping and four-mode dynamics, mimicking coherent oscillations and self-trapping in four-well potentials. These phenomena can be observed for different pairs of modes, which are localized due to the interference rather than due to a confining trap. The results obtained using few-mode approximations are compared with the direct numerical simulations of the one-dimensional Gross-Pitaevskii equation. The localized states and the related dynamics are found to persist for long times even in the repulsive condensates. We also described bifurcations of the families of nonlinear modes, the symmetry breaking, and stable minigap solitons.

Bloch oscillations and matter-wave localization of a dipolar quantum gas in a one-dimensional lattice

Three-dimensional quantum gases of strongly dipolar atoms can undergo a crossover from a dilute gas to a dense macrodroplet, stabilized by quantum fluctuations. Adding a one-dimensional optical lattice creates a platform where quantum fluctuations are still unexplored, and a rich variety of phases may be observable. We employ Bloch oscillations as an interferometric tool to assess the role quantum fluctuations play in an array of quasi-two-dimensional Bose-Einstein condensates. Long-lived oscillations are observed when the chemical potential is balanced between sites, in a region where a macrodroplet is extended over several lattice sites. Further, we observe a transition to a state that is localized to a single lattice plane–driven purely by interactions–marked by the disappearance of the interference pattern in the momentum distribution. To describe our observations, we develop a discrete one-dimensional extended Gross-Pitaevskii theory, including quantum fluctuations and a variational approach for the on-site wavefunction. This model is in quantitative agreement with the experiment, revealing the existence of single and multisite macrodroplets, and signatures of a two-dimensional bright soliton.

Tensor-network approach to work statistics for one-dimensional quantum lattice systems

We introduce a tensor-network approach to calculate the statistics of work done on one-dimensional quantum lattice systems initially prepared in thermal equilibrium states. In this approach, the dynamics is simulated with time-evolving block decimation (TEBD), and the initial thermal equilibrium state is prepared either directly with TEBD or with minimally entangled typical thermal states, which generates a set of typical states representing the Gibbs canonical ensemble. As an illustrative example, we apply this approach to the Ising chain in mixed transverse and longitudinal fields. Under a prescribed protocol, the moment generating function for work distribution can be calculated, from which the quantum Jarzynski equality and the generalized quantum work relation involving a functional of an arbitrary observable are tested.

Emergent tracer dynamics in constrained quantum systems

We show how the tracer motion of tagged, distinguishable particles can effectively describe transport in various homogeneous quantum many-body systems with constraints. We consider systems of spinful particles on a one-dimensional lattice subjected to constrained spin interactions, such that some or even all multipole moments of the effective spin pattern formed by the particles are conserved. On the one hand, when all moments - and thus the entire spin pattern - are conserved, dynamical spin correlations reduce to tracer motion identically, generically yielding a subdiffusive dynamical exponent $z=4$. This provides a common framework to understand the dynamics of several constrained lattice models, including models with XNOR or $tJ_z$ - constraints. We consider random unitary circuit dynamics with such a conserved spin pattern and use the tracer picture to obtain exact expressions for their late-time dynamical correlations. Our results can also be extended to integrable quantum many-body systems that feature a conserved spin pattern but whose dynamics is insensitive to the pattern, which includes for example the folded XXZ spin chain. On the other hand, when only a finite number of moments of the pattern are conserved, the dynamics is described by a convolution of the internal hydrodynamics of the spin pattern with a tracer distribution function. As a consequence, we find that the tracer universality is robust in generic systems if at least the quadrupole moment of the pattern remains conserved. In cases where only total magnetization and dipole moment of the pattern are constant, we uncover an intriguing coexistence of two processes with equal dynamical exponent but different scaling functions, which we relate to phase coexistence at a first order transition.

Stabilized Dirac points in one-dimensional non-Hermitian optical lattices.

We demonstrate stable Dirac points (DPs) in low dimensions by taking advantage of non-Hermiticity in an optical lattice composed of two coupled Su-Schrieffer-Heeger chains. The occurrence of DPs stems from the constraints of pseudo-Hermiticity and charge-conjugation parity symmetry, which force the system to support both real bands and orthogonal eigenmodes despite its non-Hermitian nature. The two characteristics hold even at spectral degeneracies of zero energy, giving rise to non-Hermitian DPs. We show that DPs are stable with the variation of dissipation since they are topological charges and can develop into nodal rings in two dimensions. Moreover, we investigate the beam dynamics around DPs and observe beam splitting with stable power evolution. The study paves the way for controlling the flow of light to aid dissipation together with high stability of energy.

Thermal melting of a quantum electron solid in the presence of strong disorder: Anderson localization versus the Wigner crystal

We consider the temperature-induced melting of a Wigner solid in one-dimensional (1D) and two-dimensional (2D) lattices of electrons interacting via the long-range Coulomb interaction in the presence of strong disorder arising from charged impurities in the system. The system simulates semiconductor-based 2D electron layers where Wigner crystallization is often claimed to be observed experimentally. Using exact diagonalization and utilizing the inverse participation ratio as well as conductance to distinguish between the localized insulating solid phase and the extended metallic liquid phase, we find that the effective melting temperature may be strongly enhanced by disorder since the disordered crystal typically could be in a localized glassy state incorporating the combined nonperturbative physics of both Anderson localization and Wigner crystallization. This disorder-induced enhancement of the melting temperature may explain why experiments often manage to observe insulating disorder-pinned Wigner solids in spite of the experimental temperature being decisively far above the theoretical melting temperature of the pristine Wigner crystal phase in many cases.

Anomalous conduction in one-dimensional particle lattices: Wave-turbulence approach.

One-dimensional particle chains are fundamental models to explain anomalous thermal conduction in low-dimensional solids such as nanotubes and nanowires. In these systems the thermal energy is carried by phonons, i.e., propagating lattice oscillations that interact via nonlinear resonance. The average energy transfer between the phonons can be described by the wave kinetic equation, derived directly from the microscopic dynamics. Here we use the spatially nonhomogeneous wave kinetic equationof the prototypical β-Fermi-Pasta-Ulam-Tsingou model, to study thermal conduction in one-dimensional particle chains on a mesoscale description. By means of numerical simulations, we study two complementary aspects of thermal conduction: in the presence of thermostats setting different temperatures at the two ends and propagation of a temperature perturbation over an equilibrium background. Our main findings are as follows. (i) The anomalous scaling of the conductivity with the system size, in close agreement with the known results from the microscopic dynamics, is due to a nontrivial interplay between high and low wave numbers. (ii) The high-wave-number phonons relax to local thermodynamic equilibrium transporting energy diffusively, in the manner of Fourier. (iii) The low-wave-number phonons are nearly noninteracting and transfer energy ballistically. These results present perspectives for the applicability of the full nonhomogeneous wave kinetic equationto study thermal propagation.

Stability of (N+1) -body fermion clusters in a multiband Hubbard model

We start with a variational approach and derive a set of coupled integral equations for the bound states of $N$ identical spin-$\ensuremath{\uparrow}$ fermions and a single spin-$\ensuremath{\downarrow}$ fermion in a generic multiband Hubbard Hamiltonian with an attractive on-site interaction. As an illustration, we apply our integral equations to the one-dimensional sawtooth lattice up to $N\ensuremath{\le}3$, i.e., to the $(3+1)$-body problem, and we reveal not only the presence of tetramer states in this two-band model but also their quasiflat dispersion when formed in a flat band. Furthermore, for $N={4,5,\ensuremath{\cdots},10}$, our density-matrix renormalization-group simulations and exact diagonalization suggest the presence of larger and larger multimers with lower and lower binding energies, conceivably without an upper bound on $N$. These peculiar $(N+1)$-body clusters are in sharp contrast with the exact results on the single-band linear-chain model where none of the $N\ensuremath{\ge}2$ multimers appear. Hence their presence must be taken into account for a proper description of the many-body phenomena in flat-band systems, e.g., they may suppress superconductivity especially when there exists a large spin imbalance.

Resonant enhancement of particle emission from a parametrically driven condensate in a one-dimensional lattice

Motivated by recent experiments, we investigate particle emission from a Bose-Einstein condensate in a one-dimensional lattice, where the interaction strength is periodically modulated. The modulated interactions parametrically excite a collective mode, leading to density oscillations. These collective oscillations in turn drive particle emission. This multistep process amplifies the drive, producing larger particle jets. We find that the amplitude dependence of the emission rate has a characteristic threshold behavior, as seen in experiments.

Generating tensor-network states via combination of phonons and qubits in a trapped-ion platform

Tensor-network (TN) states supply one of the most powerful variational tools to simulate quantum many-body systems. Though classical simulation of TN states (with approximation) is efficient, the required computational (classical) resources are still beyond our current capability when the size of the system and bond dimension becomes large (which is necessary for studying complicated quantum many-body systems). The TN contraction, which is the dominant cost in TN algorithms, can be replaced by measuring the corresponding physical observables directly in the experimentally prepared TN states. The computational cost is thus dramatically reduced. Here, we propose a scheme to generate TN states by combining multiple phonon modes and qubits in the ion trap platform. With the full connectivity and parallelism of the phonon modes operation, we can generate TN states with rough but complex entanglement structures [such as the multiscale entanglement renormalization Ansatz on the one-dimensional (1D) lattice and the projected entangled pair states on the kagome lattice] by shallow generation circuits. With the abundant local free parameters of the qubits operation, we can refine the local details of the generated TN states. We further benchmark the expressive power of the generated TN states by optimizing the ground energy, which is very close to the exact results of the 1D transverse-field Ising model near the critical point and the 1D Heisenberg model. Our method supplies a quantum-classical hybrid way to simulate the ground states of many-body systems and paves a promising way to demonstrate the advantage of quantum simulation.

Observation of antiferromagnetic correlations in an ultracold SU(N) Hubbard model

Mott insulators are paradigms of strongly correlated physics, giving rise to phases of matter with novel and hard-to-explain properties. Extending the typical SU(2) symmetry of Mott insulators to SU($N$) is predicted to give exotic quantum magnetism at low temperatures, but understanding the effect of strong quantum fluctuations for large $N$ remains an open challenge. In this work, we experimentally observe nearest-neighbor spin correlations in the SU(6) Hubbard model realized by ytterbium atoms in optical lattices. We study one-dimensional, two-dimensional square, and three-dimensional cubic lattice geometries. The measured SU(6) spin correlations are dramatically enhanced compared to the SU(2) correlations, due to strong Pomeranchuk cooling. We also present numerical calculations based on exact diagonalization and determinantal quantum Monte Carlo. The experimental data for a one-dimensional lattice agree with theory, without any fitting parameters. The detailed comparison between theory and experiment allows us to infer from the measured correlations a lowest temperature of $\left[{0.096 \pm 0.054 \, \rm{(theory)} \pm 0.030 \, \rm{(experiment)}}\right]/k_{\rm B}$ times the tunneling amplitude. For two- and three-dimensional lattices, experiments reach entropies below where our calculations converge, highlighting the experiments as quantum simulations. These results open the door for the study of long-sought SU($N$) quantum magnetism.

Localization phenomena in a one-dimensional phononic lattice with finite mass modulation: Beyond nearest-neighbor interaction

One-dimensional phononic systems beyond conventional nearest-neighbor interaction have not been well explored, to the best of our knowledge. In this work, we critically investigate the localization properties of a 1D phononic lattice in presence of second-neighbor interaction along with the nearest-neighbor one. A finite modulation in masses is incorporated following the well known Aubry-Andre-Harper (AAH) form to make the system a correlated disordered one. Solving the motion equations we determine the phonon frequency spectrum, and characterize the localization properties of the individual phononic states by calculating inverse participation ratio (IPR). The key aspect of our analysis is that, in the presence of second-neighbor interaction, the phonon eigenstates exhibit frequency dependent transition from sliding to the pinned phase upon the variation of the modulation strength, exhibiting a mobility edge. This is completely in contrast to the nearest-neighbor interaction case, where all the states get localized beyond a particular modulation strength, and thus, no mobility edge appears. Our analysis can be utilized in many aspects to regulate phonon transmission through similar kind of aperiodic lattices that are described beyond the usual nearest-neighbor interaction.

Motion-selective coherent population trapping by Raman sideband cooling along two paths in a Λ configuration

We report our experiment on sideband cooling with two Raman transitions in a $\Lambda$ configuration that allows selective coherent population trapping (CPT) of the motional ground state. The cooling method is applied to $^{87}$Rb atoms in a circularly-polarized one-dimensional optical lattice. Owing to the vector polarizability, the vibration frequency of a trapped atom depends on its Zeeman quantum number, and CPT resonance for a pair of bound states in the $\Lambda$ configuration depends on their vibrational quantum numbers. We call this scheme motion-selective coherent population trapping (MSCPT) and it is a trapped-atom analogue to the velocity-selective CPT developed for free He atoms. We observe a pronounced dip in temperature near a detuning for the Raman beams to satisfy the CPT resonance condition for the motional ground state. Although the lowest temperature we obtain is ten times the recoil limit owing to the large Lamb-Dicke parameter of 2.3 in our apparatus, the experiment demonstrates that MSCPT enhances the effectiveness of Raman sideband cooling and enlarges the range of its application. Discussions on design parameters optimized for MSCPT on $^{87}$Rb atoms and opportunities provided by diatomic polar molecules, whose Stark shift shows strong dependence on the rotational quantum number, are included.

Motion-selective coherent population trapping for subrecoil cooling of optically trapped atoms outside the Lamb-Dicke regime

We propose a scheme that combines velocity-selective coherent population trapping (CPT) and Raman sideband cooling (RSC) for subrecoil cooling of optically trapped atoms outside the Lamb-Dicke regime. This scheme is based on an inverted $\mathsf{Y}$ configuration in an alkali-metal atom. It consists of a $\mathrm{\ensuremath{\Lambda}}$ formed by two Raman transitions between the ground hyperfine levels and the $D$ transition, allowing RSC along two paths and formation of a CPT dark state. Using the state-dependent difference in vibration frequency of the atom in a circularly polarized trap, we can tune the $\mathrm{\ensuremath{\Lambda}}$ to make only the motional ground state a CPT dark state. We call this scheme motion-selective coherent population trapping (MSCPT). We write the master equations for RSC and MSCPT and solve them numerically for a $^{87}\mathrm{Rb}$ atom in a one-dimensional optical lattice when the Lamb-Dicke parameter is 1. Although MSCPT reaches the steady state slowly compared with RSC, the former consistently produces colder atoms than the latter. The numerical results also show that subrecoil cooling by MSCPT outside the Lamb-Dicke regime is possible under a favorable, yet experimentally feasible, condition. We explain this performance quantitatively by calculating the relative darkness of each motional state. Finally, we discuss the application of the MSCPT scheme to an optically trapped diatomic polar molecule whose Stark shift and vibration frequency exhibit large variations depending on the rotational quantum number.

Sequential versus concurrent gradient-based optimal algorithms for the robust control of quantum systems

We investigate two different formulations of gradient-based algorithms for the robust control of quantum systems. We consider the simultaneous control of an ensemble of systems which differ by the value of a constant Hamiltonian parameter. The two versions of the iterative algorithm, called concurrent and sequential, correspond respectively to a joint update of the control at each iteration for all the elements of the ensemble or to a successive correction of the control in which the control law is different for each system. We analyze the relative efficiency of the two optimization procedures on two benchmark examples, namely the control of two-level quantum systems and Bose–Einstein condensates in a one-dimensional optical lattice. Intensive numerical simulations show the superiority of the sequential-update formulation with respect to the concurrent one for a similar numerical cost.

Spin nematic ordering in the spin-1 chain system

We predict the instability of the quantum spin-1 chain material with respect to the spin nematic ordering. For the spin subsystem the spin nematic order parameter is related to the onset of single-ion spin anisotropy. The ordering is caused by the coupling to the elastic subsystem of the crystal or, for spin-1 ultracold bosons in a one-dimensional optical lattice, by the interaction with a Bose-Einstein condensate. Our conclusions are based on the exact integrability of the spin model and on numerical simulations for the nonintegrable cases. Our exact results also describe the behavior of interacting gluons within the lattice toy Yang-Mills-like model, in which spontaneous and field-induced symmetry breaking can be realized.

Phonon dressing of a facilitated one-dimensional Rydberg lattice gas

We study the dynamics of a one-dimensional Rydberg lattice gas under facilitation (anti-blockade) conditions which implements a so-called kinetically constrained spin system. Here an atom can only be excited to a Rydberg state when one of its neighbors is already excited. Once two or more atoms are simultaneously excited mechanical forces emerge, which couple the internal electronic dynamics of this many-body system to external vibrational degrees of freedom in the lattice. This electron-phonon coupling results in a so-called phonon dressing of many-body states which in turn impacts on the facilitation dynamics. In our theoretical study we focus on a scenario in which all energy scales are sufficiently separated such that a perturbative treatment of the coupling between electronic and vibrational states is possible. This allows to analytically derive an effective Hamiltonian for the evolution of clusters of consecutive Rydberg excitations in the presence of phonon dressing. We analyze the spectrum of this Hamiltonian and show --- by employing Fano resonance theory --- that the interaction between Rydberg excitations and lattice vibrations leads to the emergence of slowly decaying bound states that inhibit fast relaxation of certain initial states.

First passage in discrete-time absorbing Markov chains under stochastic resetting

First passage of stochastic processes under resetting has recently been an active research topic in the field of statistical physics. However, most of previous studies mainly focused on the systems with continuous time and space. In this paper, we study the effect of stochastic resetting on first passage properties of discrete-time absorbing Markov chains, described by a transition matrix Q between transient states and a transition matrix R from transient states to absorbing states. Using a renewal approach, we exactly derive the unconditional mean first passage time (MFPT) to any absorbing state, the splitting probabilities and the conditional MFPT to a specific absorbing state without hitting any other absorbing state. All the quantities can be expressed in terms of a deformed fundamental matrix and R, where I is the identity matrix, and γ is the resetting probability at each time step. We further show a sufficient condition under which the unconditional MPFT can be optimized by stochastic resetting. Finally, we apply our results to two concrete examples: symmetric random walks on one-dimensional lattices with absorbing boundaries and voter model on complete graphs.