We study the dynamical stability of Bose-Einstein condensates in an optical lattice with a time-periodic modulation potential and a constant acceleration force simultaneously. We derive the explicit expressions of quasienergies and obtain the stability diagrams in the parameter space of the interaction strength and the modulation amplitude. The ratio of the acceleration force to the modulation frequency characterizes two cases: integer and non-integer resonances. For integer resonances, the critical interaction strength $g_{\mathrm{c}}$ shows an alternate behavior where the completely unstable regions correspond to the negative effective tunneling strength. Among non-integer resonances, we observe that $g_{\mathrm{c}}$ peaks are centered around half-integer resonances for which the completely unstable regions disappear, accompanied with a whole displacement of $g_{\mathrm{c}}$. Compared with integer and half-integer resonances, the crossovers between them show no explicit dependence of $g_{\mathrm{c}}$ on the modulation amplitude.
Bloch oscillations of Bose-Einstein condensates realize sensitive matter-wave interferometers. We investigate the dynamics and stability of bright-soliton wave packets in one-dimensional tilted optical lattices with a modulated mean-field interaction $g(t)$. By means of a time-reversal argument, we prove the stability of Bloch oscillations of breathing solitons that would be quasistatically unstable. Floquet theory shows that these breathing solitons can be more stable against certain experimental perturbations than rigid solitons or even non-interacting wave packets.
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 consider a $^{168}$Er-$^{164}$Dy dipolar mixture, trapped by a cigar shaped harmonic potential. We derive the quasi-1D inter-species effective potential exhibiting the tilting angles and show that it is a quite natural generalization of the situation of a single dipolar gas. By solving the coupled Gross-Pitaevskii equations, we observe a transition from miscible to immiscible mixture as the orientations of the magnetic moments are varied. The atom numbers are also shown to lead to noticeable effects on the mixture.
We theoretically investigate a Bose-Einstein condensate confined by a rotating harmonic trap whose rotation axis is not aligned with any of its principal axes. The principal axes of the Thomas-Fermi density profiles of the resulting stationary solutions are found to be tilted with respect to those of the rotating trap, representing an extra degree of freedom that is associated with the existence of additional branches of stationary solutions for any given rotation axis alignment. By linearizing the time-dependent theory about the stationary states, we obtain a semi-analytical prediction of the…
An integrable model subjected to a periodic driving gives rise generally to a non-integrable Floquet Hamiltonian. Here we show that the Floquet Hamiltonian of the integrable Lieb--Liniger model in presence of a linear potential with a periodic time--dependent strength is instead integrable and its quasi-energies can be determined using the Bethe ansatz approach. We discuss various aspects of the dynamics of the system at stroboscopic times and we also propose a possible experimental realisation of the periodically driven tilting in terms of a shaken rotated ring potential.
We present calculations of the ground state and excitations of an anisotropic dipolar Bose gas in two dimensions, realized by a non-perpendicular polarization with respect to the system plane. For sufficiently high density an increase of the polarization angle leads to a density instability of the gas phase in the direction where the anisotropic interaction is strongest. Using a dynamic many-body theory, we calculate the dynamic structure function in the gas phase which shows the anisotropic dispersion of the excitations. We find that the energy of roton excitations in the strongly interacting…
The momentum distribution and dynamical structure factor in a weakly interacting Bose gas with a time-dependent periodic modulation in terms of the Bogoliubov treatment are investigated. The evolution equation related to the Bogoliubov weights happens to be a solvable Mathieu equation when the coupling strength is periodically modulated. An exact relation between the time derivatives of momentum distribution and dynamical structure factor is derived, which indicates that the single-particle property strongly related to the two-body property in the evolutions of Bose-Einstein condensates. It is…
We study the Mott phase of the Bose-Hubbard model on a tilted lattice. On the (Gutzwiller) mean-field level, the tilt has no effect -- but quantum fluctuations entail particle-hole pair creation via tunneling. For small potential gradients (long-wavelength limit), we derive a quantitative analogy to the Sauter-Schwinger effect, i.e., electron-positron pair creation out of the vacuum by an electric field. For large tilts, we obtain resonant tunneling related to Bloch oscillations.
Based on a unified theoretical treatment of the 1D Bogoliubov-de Genes equations, the superfluidity phenomenon of the Bose-Einstein condensates (BEC) loaded into trapped optical lattice is studied. Within the perturbation regime, an all-analytical framework is presented enabling a straightforward phenomenological mapping of the collective excitation and oscillation character of a trapped BEC where the available experimental configurations also fit.
This paper investigates the synchronization of chaotic behavior in a model of Bose-Einstein condensate (BEC) held in a 1D tilted bichromatical optical lattice potential by using the active control technique. The synchronization is presented in the master-slave configuration which implies that the master system evolves freely and drives the dynamics of the slave system. Also the numerical simulations are given to indicate the practicability and the effectiveness of the used controllers.
We study the tunneling decay of a Bose-Einstein condensate out of tilted optical lattices within the mean-field approximation. We introduce a novel method to calculate also excited resonance eigenstates of the Gross-Pitaevskii equation, based on a grid relaxation procedure with complex absorbing potentials. This algorithm works efficiently in a wide range of parameters where established methods fail. It allows us to study the effects of the nonlinearity in detail in the regime of resonant tunneling, where the decay rate is enhanced by resonant coupling to excited unstable states.
Bloch oscillations appear for a particle in a weakly tilted periodic potential. The intrinsic spin Hall effect is an outcome of a spin-orbit coupling. We demonstrate that both these phenomena can be realized simultaneously in a gas of weakly interacting ultracold atoms exposed to a tilted optical lattice and to a set of spatially dependent light fields inducing an effective spin-orbit coupling. It is found that both the spin Hall as well as the Bloch oscillation effects may coexist, showing, however, a strong correlation between the two. These correlations are manifested as a transverse spin c…
The dynamics of a (quasi)one-dimensional interacting atomic Bose-Einstein condensate in a tilted optical lattice is studied in a discrete mean-field approximation, i.e., in terms of the discrete nonlinear Schrödinger equation. If the static field is varied the system shows a plethora of dynamical phenomena. In the strong field limit we demonstrate the existence of (almost) non-spreading states which remain localized on the lattice region populated initially and show coherent Bloch oscillations with fractional revivals in the momentum space (so called quantum carpets). With decreasing field, th…
We study the instability of a ring Bose-Einstein condensate under a periodic modulation of inter-atomic interactions. The condensate exhibits temporal and spatial patterns induced by the parametric resonance, which can be characterized by Bogoliubov quasi-particle excitations in the Floquet basis. As the ring geometry significantly limits the number of excitable Bogoliubov modes, we are able to capture the non-linear dynamics of the condensate using a three-mode model. We further demonstrate the robustness of the temporal and spatial patterns against disorder, which are attributed to the mode-…
We predict the effect of the roton instability for a two-dimensional weakly interacting gas of tilted dipoles in a single homogeneous quantum layer. Being typical for strongly correlated systems, the roton phenomena appear to occur in a weakly interacting gas. It is important that in contrast to a system of normal to wide layer dipoles, breaking of the rotational symmetry for a system of tilted dipoles leads to the convergence of the condensate depletion even up to the threshold of the roton instability, with mean-field approach being valid. Predicted effects can be observed in a wide class of…
We report on the out-of-equilibrium dynamics of a Bose-Einstein condensate (BEC) placed in an optical lattice whose phase is suddenly modulated. The frequency and the amplitude of modulation are chosen to ensure a negative renormalized tunneling rate. Under these conditions, staggered states are nucleated by a spontaneous four wave mixing mechanism. The nucleation time is experimentally studied as a function of the renormalized tunnel rate, the atomic density and the modulation frequency. Our results are quantitatively well accounted for by a Truncated Wigner approach and reveal the nucleation…
We study the quantum dynamics of Bose-Einstein condensates when the scattering length is modulated periodically or quasi-periodically in time within the Bogoliubov framework. For the periodically driven case, we consider two protocols where the modulation is a square-wave or a sine-wave. In both protocols for each fixed momentum, there are heating and non-heating phases, and a phase boundary between them. The two phases are distinguished by whether the number of excited particles grows exponentially or not. For the quasi-periodically driven case, we again consider two protocols: the square-wav…
We numerically examine slow and hierarchical relaxation dynamics of interacting bosons described by a tilted two-band Bose-Hubbard model. The system is found to exhibit signatures of quantum chaos within the spectrum and the validity of the eigenstate thermalization hypothesis for relevant physical observables is demonstrated for certain parameter regimes. Using the truncated Wigner representation in the semiclassical limit of the system, dynamics of relevant observables reveal hierarchical relaxation and the appearance of prethermalized states is studied from the perspective of statistics of …
The effect of dipolar orientation with respect to the soliton plane on the physics of two-dimensional bright solitons in dipolar Bose-Einstein condensates is discussed. Previous studies on such a soliton involved dipoles either perpendicular or parallel to the condensate-plane. The tilting angle constitutes an additional tuning parameter, which help us to control the in-plane anisotropy of the soliton as well as provides access to previously disregarded regimes of interaction parameters for soliton stability. In addition, it can be used to drive the condensate into phonon instability without c…
We study theoretically the superfluidity and stability of a Bose-Einstein condensate (BEC) whose interatomic scattering length is periodically modulated with optical Feshbach resonance. Our numerical study finds that the properties of this periodic BEC are strongly influenced by the modulation strength. When the modulation strength is small, only the Bloch waves close to the Brillouin zone edge suffer both Landau and dynamical instabilities. When the modulation strength is strong enough, all Bloch waves become dynamically unstable. In other words, the periodic BEC loses its superfluidity compl…
We study the single-particle dispersion of a spin-orbit coupled (SOC) Bose-Einstein condensate (BEC) under the periodical modulation of the Raman coupling. This modulation introduces a further coupling of the SOC dressed eigenlevels, thus creating a second generation of modulation-dressed eigenlevels. Theoretical calculations show that these modulation-dressed eigenlevels feature a pair of avoided crossings and a richer spin-momentum locking, which we observe using BEC transport measurements. Furthermore, we use the pair of avoided crossings to engineer a tunable Stueckelberg interferometer th…
Krylov complexity of a tilted extended Bose-Hubbard chain with Rydberg-dressed interactions
School of Physics and Astronomy, University of Nottingham（诺丁汉大学物理与天文学学院）；Taishan College, Shandong University（山东大学泰山学堂）；Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham（诺丁汉大学量子非平衡系统数学与理论物理中心）；School of Physics, Henan Normal University（河南师范大学物理学院）
We consider a coupled nonlinear Schrödinger equations describing an atomic Bose-Einstein condensates coupled to a molecular condensates through the stimulated Raman adiabatic passage loaded in an external potential. The existence of dark state are investigated within the full parameter space accounts for all the nonlinear collisions, together with the atom-molecule conversion coupling and external potential. The results show that there are a class of external potentials such as double-well, periodical and double periodical, and harmonic potentials, where the exact dark solutions can be formed.…
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…
Motivated by recent experiments, we analyse the stability of a three-dimensional Bose-Einstein condensate (BEC) loaded in a periodically driven one-dimensional optical lattice. Such periodically driven systems do not have a thermodynamic ground state, but may have a long-lived steady state which is an eigenstate of a "Floquet Hamiltonian". We explore collisional instabilities of the Floquet ground state which transfer energy into the transverse modes. We calculate decay rates, finding that the lifetime scales as the inverse square of the scattering length and inverse of the peak three- dimensi…
Dynamical Signatures and Kibble-Zurek Scaling of Localization in Tilted Bose-Einstein Condensates
Harish-Chandra Research Institute（哈里希-钱德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Faculty of Physics, Adam Mickiewicz University（亚当·密茨凯维奇大学物理学院）；Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）
A PT-symmetric Bose-Einstein condensate can theoretically be described using a complex optical potential, however, the experimental realization of such an optical potential describing the coherent in- and outcoupling of particles is a nontrivial task. We propose an experiment for a quantum mechanical realization of a PT-symmetric system, where the PT-symmetric currents are implemented by an accelerating Bose-Einstein condensate in a titled optical lattice. A defect consisting of two wells at the same energy level then acts as a PT-symmetric double-well if the tilt in the energy offsets of all …
We report measurements of dynamical tunneling rates of a Bose-Einstein condensate across a barrier in classical phase space. The atoms are initially prepared in quantum states that extend over a classically regular island region. We focus on the specific system of quantum accelerator modes of the kicked rotor in the presence of gravity. Our experimental data is supported by numerical simulations taking into account imperfections mainly from spontaneous emission. Furthermore, we predict experimentally accessible parameter ranges over which direct tunneling could be readily observed if spontaneo…
We explore prethermal Floquet steady states and instabilities of the weakly interacting two-dimensional Bose-Hubbard model subject to periodic driving. We develop a description of the nonequilibrium dynamics, at arbitrary drive strength and frequency, using a weak-coupling conserving approximation. We establish the regimes in which conventional (zero-momentum) and unconventional [$(π,π)$-momentum] condensates are stable on intermediate time scales. We find that condensate stability is \emph{enhanced} by increasing the drive strength, because this decreases the bandwidth of quasiparticle excita…
The expansion of an initially confined Bose-Einstein condensate into either free space or a tilted optical lattice is investigated in a mean-field approach. The effect of the interactions is to enhance or suppress the transport depending on the sign and strength of the interactions. These effects are discusses in detail in view of recent experiments probing non-equilibrium transport of ultracold quantum gases.
We investigate a Bose Einstein condensate held in a 1D optical lattice whose phase undergoes a fast oscillation using a statistical analysis. The averaged potential experienced by the atoms boils down to a periodic potential having the same spatial period but with a renormalized depth. However, the atomic dynamics also contains a \emph{micromotion} whose main features are revealed by a Kolmorogov-Smirnov analysis of the experimental momentum distributions. We furthermore discuss the impact of the micromotion on a quench process corresponding to a proper sudden change of the driving amplitude w…
We suggest that nonequilibrium Bose-Einstein condensates may occur in time-periodically driven interacting Bose gases. Employing the model of a periodically forced bosonic Josephson junction, we demonstrate that resonance-induced ground state-like many-particle Floquet states possess an almost perfect degree of coherence, as corresponding to a mesoscopically occupied, explicitly time-dependent single-particle orbital. In marked contrast to the customary time-independent Bose-Einstein condensates, the order parameter of such systems is destroyed by violent fluctuations when the particle number …
We discuss the dynamical response of strongly interacting Bose atoms in an adiabatically tilted optical lattice. The analysis is performed in terms of the multi-level Landau-Zenner tunneling. Different regimes of tunneling are identified and analytical expressions for the doublon number, which is the quantity measured in laboratory experiments, are derived.
We consider a Bose-Einstein bicondensate (BEC) of $^{87}Rb$, trapped in two different internal levels, in a situation where the density undergoes a symmetry breaking in momentum space. This occurs for a suitable number of condensed atoms within a double well dispersion curve, obtained by Raman coupling two internal states with two tilted and detuned light fields. Evidence of bistability results from the Gross-Pitaevskii equation. By second quantization, we evaluate the tunneling rate between the two asymmetric states; the effects of losses on coherence are also considered.
We investigate the ground-state phases of a mixture of spin-1 and spin-2 Bose-Einstein condensates at zero magnetic field. In addition to the intra-spin interactions, two spin-dependent interaction coefficients are introduced to describe the inter-spin interaction. We systematically explore the wide parameter space, and obtain phase diagrams containing a rich variety of phases. For example, there exists a phase in which the spin-1 and spin-2 vectors are tilted relative to each other breaking the axial symmetry.
An unit filling Bose-Hubbard Hamilonian embedded in strong Stark field is studied in the off-resonant regime inhibiting single and many-particle first order tunneling resonances. We investigate the occurrence of coherent dipole wave-like propagation along of an optical lattice by means of an effective Hamiltonian accounting for second order tunneling processes. It is shown that dipole wavefunction evolution in the short-time limit is ballistic and that finite size effects induce dynamical self-interference patterns known as quantum carperts. We also present the effects of the border right afte…
The dynamics of cold Bose atoms in driven tilted optical lattices is analyzed focusing on destruction of Wannier-Stark localization and the phenomenon of band collapse. It is argued that an understanding of the experimental results requires thorough account for interaction effects. These are suppression of the ballistic spreading of atoms for resonant driving (a multiple of the driving frequency coincides with the Bloch frequency) and unbounded sub-diffusive spreading of atoms for off-resonant driving.
We have employed the theory of harmonically trapped dipolar Bose-Einstein condensates to examine the influence of a uniform magnetic field that rotates at an arbitrary angle to its own orientation. This is achieved by semi-analytically solving the dipolar superfluid hydrodynamics of this system within the Thomas-Fermi approximation and by allowing the body frame of the condensate's density profile to be tilted with respect to the symmetry axes of the nonrotating harmonic trap. This additional degree of freedom manifests itself in the presence of previously unknown stationary solution branches …
We investigate spatiotemporal vortex rings with phase dislocation both in space and time. It is demonstrated that these structures naturally appear as a periodical in time edge phase dislocation at the low-density region of a perturbed atomic Bose-Einstein condensate. The condition of formation, dynamics and stability of the spatiotemporal vortex rings are investigated for repulsive and attractive interatomic interactions. These theoretical findings open up a perspective for experimental observation of novel type of topological coherent structures in ultracold gases.
We consider interacting bosons in a 2D square and a 3D cubic optical lattice with a periodic modulation of the s-wave scattering length. At first we map the underlying periodically driven Bose-Hubbard model for large enough driving frequencies approximately to an effective time-independent Hamiltonian with a conditional hopping. Combining different analytical approaches with quantum Monte Carlo simulations then reveals that the superfluid-Mott insulator quantum phase transition still exists despite the periodic driving and that the location of the quantum phase boundary turns out to depend qui…
We analytically calculate phase boundaries of tunable spin-orbit coupled BECs with effective two-body interactions by using variational method. Phase diagrams for periodically driving $^{87}\rm{Rb}$ and $^{23}\rm{Na}$ systems are presented, respectively, which display several characteristic features contrast with those of undriven systems. In the $^{87}\rm{Rb}$ BECs, the critical density $n_{c}$ (density at quantum tricritical point) can be dramatically reduced in some parameter regions, thus the prospect of observing this intriguing quantum tricritical point is greatly enlarged. Moreover, a s…
Spin exchange interaction between atoms in a spin-1 Bose-Einstein condensate causes atomic spin evolving periodically under the single spatial mode approximation in the mean field theory. By applying fast magnetic pulses according to a two-step or a four-step control protocol, we find analytically that the spin dynamics is significantly suppressed for an arbitrary initial state. Numerical calculations under single mode approximation are carried out to confirm the validity and robustness of these protocols. This localization method can be readily utilized to improve the sensitivity of a magneto…
We examine the stability of quasi-two-dimensional dipolar Bose-Einstein condensates in the presence of weak optical lattices of various geometries. We find that when the condensate possesses a roton-maxon quasiparticle dispersion, the conditions for stability exhibit a strong dependence both on the lattice geometry and the polarization tilt. This results in rich structures in the system's stability diagram akin to spectroscopic signatures. We show how these structures originate from the mode matching of rotons to the perturbing lattice. In the case of a one-dimensional lattice, some of the fea…
We discuss the quantum phase transition from the Mott-insulator state to the density-wave state for cold Bose atoms in a 2D square lattice as the lattice is adiabatically tilted along one of its primary axes. It is shown that a small misalignment of the tilt drastically changes the result of the adiabatic passage and, instead of the density-wave state, one obtains a disordered state. Intrinsic relation of the problem to Bloch oscillations of hard-core bosons in a 2D lattice is illuminated.
Phase transitions from Heating to non-heating in SU(1, 1) quantum dynamics: applications to Bose-Einstein condensates and periodically driven coupled oscillators
We investigate the Stückelberg oscillations of a spin-1 Bose-Einstein condensate subject to a spatially inhomogeneous transverse magnetic field and a periodic longitudinal field. We show that the time-domain Stückelberg oscillations result in interference fringes in the density profiles of all spin components due to the spatial inhomogeneity of the transverse field. This phenomenon represents the Landau-Zener-Stückelberg interference in the space-domain. Since the magnetic dipole-dipole interaction between spin-1 atoms induces an inhomogeneous effective magnetic field, interference fringes als…
Tilt-Induced Localization in Interacting Bose-Einstein Condensates for Quantum Sensing
Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute（哈里什-昌德拉研究所，霍米·巴巴国立学院下属机构）；Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）
