Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1D optical lattices

Hexagonal warping effects on Bloch oscillations in proximitized Rashba systems

Bloch oscillations (BOs) in Rashba systems, taking into account the effects of hexagonal warping and proximity-induced band gap, are reported. We find that in addition to real-space trajectories, the group and Berry velocities of Bloch electrons exhibit novel BOs which strongly depend on the crystal momentum. This oscillatory motion is affected significantly by variations in the strength of hexagonal warping and the proximity-induced band gap, originating from the substantial changes in the energy spectrum induced by these factors. In addition, it is shown that the Bloch oscillations are modified considerably under the influence of applied uniform in-plane electric and transverse magnetic fields, which allow for a geometric visualization of the Bloch dynamics. Interestingly, when the system is subjected to these fields simultaneously, it undergoes a dynamic phase transition between confined and de-confined states. This phase transition is tuned by the relative strength of the applied fields and is further influenced by variations in the strength of hexagonal warping and proximity-induced band gap. The appearance of such a transition is attributed to the interplay between the external fields and the intrinsic properties of the crystal lattice. Moreover, we find that the direct-current drift velocity shows negative differential conductivity, which is a characteristic feature of the BO regime.

Visual observation of photonic Floquet-Bloch oscillations

Bloch oscillations (BOs), an important transport phenomenon, have been studied extensively in static systems but remain mysterious in Floquet systems. Here, by harnessing notions from photonic analogy, we propose a generalization of the existing BOs in photonic Floquet lattices, namely the "photonic Floquet-Bloch oscillations", which refer to rescaled photonic Bloch oscillations with a period of extended least common multiple of the modulation period and the Bloch oscillation period. Next, we report the first visual observation of such photonic Floquet-Bloch oscillations (FBOs) by employing waveguide fluorescence microscopy. Most significantly, the FBOs surpass the existing BOs in Floquet systems and exhibit exotic properties on their own, including fractal spectrum and fractional Floquet tunneling. This new transport mechanism offers an intriguing method of wave manipulation that may contribute to rapidly developing fields in photonics, condensed matter physics, and quantum physics.

Observation of Period-Doubling Bloch Oscillations

Bloch oscillations refer to the periodic oscillation of a wave packet in a lattice under a constant force. Typically, the oscillation has a fundamental period that corresponds to the wave packet traversing the first Brillouin zone once. Here, we demonstrate, both theoretically and experimentally, the optical Bloch oscillations where the wave packet must traverse the first Brillouin zone twice to complete a full cycle, resulting in a period of oscillation that is 2 times longer than that of usual Bloch oscillations. The unusual Bloch oscillations arise due to the band crossing of valley-Hall topological edge states at the Brillouin boundary for zigzag domain walls between two staggered honeycomb lattices with inverted on-site energy detuning, which are protected by the glide-reflection symmetry of the underlying structures. Our work sheds light on the direct detection of band crossings resulting from intrinsic symmetries that extend beyond the fundamental translational symmetry in topological systems.

Spectral Analysis of Bloch-Like Oscillations in Conjugated Polymers

We present a spectrum investigation of the behavior of dissociated polarons under high electric fields in conjugated polymers. The study employs the Su-Schrieffer-Heeger model along with nonadiabatic molecular dynamics and frequency-domain analysis methods to analyze the Bloch-like oscillations. It is found that the fundamental frequencies of the current density agree well with the theoretical Bloch frequencies of the perfect crystals. The electron-phonon coupling is a key factor in inducing the deviation between the Bloch-like oscillation behavior in conjugated polymers and that in perfect superlattices. Moreover, the increase in lattice thermal fluctuation is not conducive to the maintenance of Bloch-like oscillation behavior in conjugated polymers.

Observation of Bloch oscillations dominated by effective anyonic particle statistics

Bloch oscillations are exotic phenomena describing the periodic motion of a wave packet subjected to an external force in a lattice, where a system possessing single or multiple particles could exhibit distinct oscillation behaviors. In particular, it has been pointed out that quantum statistics could dramatically affect the Bloch oscillation even in the absence of particle interactions, where the oscillation frequency of two pseudofermions with an anyonic statistical angle of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{\boldsymbol{\pi }}}}$$\end{document}π becomes half of that for two bosons. However, these statistically dependent Bloch oscillations have never been observed in experiments until now. Here, we report the experimental simulation of anyonic Bloch oscillations using electric circuits. By mapping the eigenstates of two anyons to the modes of the designed circuit simulators, the Bloch oscillations of two bosons and two pseudofermions are verified by measuring the voltage dynamics. The oscillation period in the two-boson simulator is almost twice of that in the two-pseudofermion simulator, that is consistent with the theoretical prediction. Our proposal provides a flexible platform to investigate and visualize many interesting phenomena related to particle statistics and could have potential applications in the field of the signal control.

Electric circuits represent a versatile platform for simulations of exotic phenomena that are difficult to realize is condensed matter systems. Here the authors simulate particle statistics-dependent Bloch oscillations with electric circuits and observe features predicted for a model of anyons on a 1D lattice.

Polarization-dependent Bloch oscillations in optical waveguides

Optical systems provide a new and practical platform for studying Bloch oscillations. This study investigates the fundamental-mode propagation of polarization-dependent Bloch oscillations. By using the three-dimensional properties of femtosecond laser direct writing, we fabricate a polymer-based gradient waveguide array and determine the Bloch oscillations under different polarization inputs by using the birefringence gradient and the equivalent refractive index, thus exhibiting a polarization-dependent Bloch period. Our results provide a new, to the best of our knowledge, paradigm for two-dimensional optical Bloch modes and highlight the influence of optical polarization in the same system, which provides a possibility to observe richer physics related to Bloch oscillations in one structure.

Longitudinal and transversal resonant tunneling of interacting bosons in a two-dimensional Josephson junction

We unravel the out-of-equilibrium quantum dynamics of a few interacting bosonic clouds in a two-dimensional asymmetric double-well potential at the resonant tunneling scenario. At the single-particle level of resonant tunneling, particles tunnel under the barrier from, typically, the ground-state in the left well to an excited state in the right well, i.e., states of different shapes and properties are coupled when their one-particle energies coincide. In two spatial dimensions, two types of resonant tunneling processes are possible, to which we refer to as longitudinal and transversal resonant tunneling. Longitudinal resonant tunneling implies that the state in the right well is longitudinally-excited with respect to the state in the left well, whereas transversal resonant tunneling implies that the former is transversely-excited with respect to the latter. We show that interaction between bosons makes resonant tunneling phenomena in two spatial dimensions profoundly rich, and analyze these phenomena in terms of the loss of coherence of the junction and development of fragmentation, and coupling between transverse and longitudinal degrees-of-freedom and excitations. To this end, a detailed analysis of the tunneling dynamics is performed by exploring the time evolution of a few physical quantities, namely, the survival probability, occupation numbers of the reduced one-particle density matrix, and the many-particle position, momentum, and angular-momentum variances. To accurately calculate these physical quantities from the time-dependent many-boson wavefunction, we apply a well-established many-body method, the multiconfigurational time-dependent Hartree for bosons (MCTDHB), which incorporates quantum correlations exhaustively. By comparing the survival probabilities and variances at the mean-field and many-body levels of theory and investigating the development of fragmentation, we identify the detailed mechanisms of many-body longitudinal and transversal resonant tunneling in two dimensional asymmetric double-wells. In particular, we find that the position and momentum variances along the transversal direction are almost negligible at the longitudinal resonant tunneling, whereas they are substantial at the transversal resonant tunneling which is caused by the combination of the density and breathing mode oscillations. We show that the width of the interparticle interaction potential does not affect the qualitative physics of resonant tunneling dynamics, both at the mean-field and many-body levels. In general, we characterize the impact of the transversal and longitudinal degrees-of-freedom in the many-boson tunneling dynamics at the resonant tunneling scenarios.

Synchronizing Bloch-Oscillating Free Carriers in Moiré Flat Bands

Achieving Bloch oscillations of free carriers under a direct current, a long-sought-after collective many-body behavior, has been challenging due to stringent constraints on the band properties. We argue that the flat bands in moiré graphene fulfill the basic requirements for observing Bloch oscillations, offering an appealing alternative to the stacked quantum wells used in previous work aiming to access this regime. Bloch-oscillating moiré superlattices emit a comblike spectrum of incommensurate frequencies, a property of interest for converting direct currents into high-frequency currents and developing broadband amplifiers in terahertz domain. The oscillations can be synchronized through coupling to an oscillator mode in a photonic or plasmonic resonator. Phase-coherent collective oscillations in the resonant regime provide a realization of current-pumped terahertz lasing.

Nonexponential Tunneling due to Mean-Field-Induced Swallowtails

Typically, energy levels change without bifurcating in response to a change of a control parameter. Bifurcations can lead to loops or swallowtails in the energy spectrum. The simplest quantum Hamiltonian that supports swallowtails is a nonlinear 2×2 Hamiltonian with nonzero off-diagonal elements and diagonal elements that depend on the population difference of the two states. This work implements such a Hamiltonian experimentally using ultracold atoms in a moving one-dimensional optical lattice. Self-trapping and nonexponential tunneling probabilities, a hallmark signature of band structures that support swallowtails, are observed. The good agreement between theory and experiment validates the optical lattice system as a powerful platform to study, e.g., Josephson junction physics and superfluidity in ring-shaped geometries.

Noise cancellation system for shaking optical lattice by controlling optical path

We present a simple way to control the phase of an optical lattice by detecting the interference signal of two beams. The optical lattice is intentionally shaken by varying the relative phase of the beams. However, the lattice may also be shaken by unwanted variations of the relative optical path length, e.g., due to mirror vibrations. The purpose of the servo is to attenuate these unwanted variations while the intended shaking remains. We demonstrate that the servo changes the relative phase between beams and follows the intended shaking function with 99% accuracy. The bandwidth for the acceptable attenuation of unwanted shaking, -13 dB, is measured to 1.2 kHz to control the atomic Bloch state. The servo will be implemented to attenuate the unknown system vibrations for a shaken lattice and engineer the momentum state of atoms trapped in the lattice. This idea can also be applied to any time varying experiment.

Many-Body Quantum Dynamics of Initially Trapped Systems due to a Stark Potential: Thermalization versus Bloch Oscillations

We analyze the dynamics of an initially trapped cloud of interacting quantum particles on a lattice under a linear (Stark) potential. We reveal a dichotomy: initially trapped interacting systems possess features typical of both many-body-localized and thermalizing systems. We consider both fermions (t-V model) and bosons (Bose-Hubbard model). For the zero and infinite interaction limits, both systems are integrable: we provide analytic solutions in terms of the moments of the initial cloud shape and clarify how the recurrent dynamics (many-body Bloch oscillations) depends on the initial state. Away from the integrable points, we identify and explain the timescale at which Bloch oscillations decohere.

Non-Bloch-Band Collapse and Chiral Zener Tunneling

Non-Bloch-band theory describes bulk energy spectra and topological invariants in non-Hermitian crystals with open boundaries, where the bulk eigenstates are squeezed toward the edges (skin effect). However, the interplay of non-Bloch-band theory, skin effect, and coherent Bloch dynamics is so far unexplored. In two-band non-Hermitian lattices, it is shown here that collapse of non-Bloch bands and skin modes deeply changes the Bloch dynamics under an external force. In particular, for resonance forcing non-Bloch-band collapse results in Wannier-Stark ladder coalescence and chiral Zener tunneling between the two dispersive Bloch bands.

Engineering Quantum States of Matter for Atomic Clocks in Shallow Optical Lattices

We investigate the effects of stimulated scattering of optical lattice photons on atomic coherence times in a state-of-the art ^{87}Sr optical lattice clock. Such scattering processes are found to limit the achievable coherence times to less than 12 s (corresponding to a quality factor of 1×10^{16}), significantly shorter than the predicted 145(40) s lifetime of ^{87}Sr's excited clock state. We suggest that shallow, state-independent optical lattices with increased lattice constants can give rise to sufficiently small lattice photon scattering and motional dephasing rates as to enable coherence times on the order of the clock transition's natural lifetime. Not only should this scheme be compatible with the relatively high atomic density associated with Fermi-degenerate gases in three-dimensional optical lattices, but we anticipate that certain properties of various quantum states of matter-such as the localization of atoms in a Mott insulator-can be used to suppress dephasing due to tunneling.

Observation of Valley Landau-Zener-Bloch Oscillations and Pseudospin Imbalance in Photonic Graphene

We demonstrate intervalley Bloch oscillation (BO) and Landau-Zener tunneling (LZT) in an optically induced honeycomb lattice with a refractive-index gradient. Unlike previously observed BO in a gapped square lattice, we show nonadiabatic beam dynamics that are highly sensitive to the direction of the index gradient and the choice of the Dirac cones. In particular, a symmetry-preserving potential leads to nearly perfect LZT and coherent BO between the inequivalent valleys, whereas a symmetry-breaking potential generates asymmetric scattering, imperfect LZT, and valley-sensitive generation of vortices mediated by a pseudospin imbalance. This clearly indicates that, near the Dirac points, the transverse gradient does not always act as a simple scalar force, as commonly assumed, and the LZT probability is strongly affected by the sublattice symmetry as analyzed from an effective Landau-Zener Hamiltonian. Our results illustrate the anisotropic response of an otherwise isotropic Dirac platform to real-space potentials acting as strong driving fields, which may be useful for manipulation of pseudospin and valley degrees of freedom in graphenelike systems.

Observation and Uses of Position-Space Bloch Oscillations in an Ultracold Gas

We report the observation and characterization of position-space Bloch oscillations using cold atoms in a tilted optical lattice. While momentum-space Bloch oscillations are a common feature of optical lattice experiments, the real-space center-of-mass dynamics are typically unresolvable. In a regime of rapid tunneling and low force, we observe real-space Bloch oscillation amplitudes of hundreds of lattice sites, in both ground and excited bands. We demonstrate two unique capabilities enabled by tracking of Bloch dynamics in position space: measurement of the full position-momentum phase-space evolution during a Bloch cycle, and direct imaging of the lattice band structure. These techniques, along with the ability to exert long-distance coherent control of quantum gases without modulation, may open up new possibilities for quantum control and metrology.

Tunable band-gap structure and gap solitons in the generalized Gross-Pitaevskii equation with a periodic potential

The tunable band-gap structure is fundamentally important in the dynamics of both linear and nonlinear modes trapped in a lattice because Bloch modes can only exist in the bands of the periodic system and nonlinear modes associating with them are usually confined to the gaps. We reveal that when a momentum operator is introduced into the Gross-Pitaevskii equation (GPE), the bandgap spectra of the periodic system can be shifted upward parabolically by the growth of the constant momentum coefficient. During this process, the band edges become asymmetric, in sharp contrast to the standard GPE with an external periodic potential. Extended complex Bloch modes with asymmetric profiles can be derived by applying a phase transformation to the symmetric profiles. We find that the inherent parity-time symmetry of the complex system is never broken with increasing momentum coefficient. Under repulsive interactions, solitons with different numbers of peaks bifurcating from the band edges are found in finite gaps. We also address the existence of embedded solitons in the generalized two-dimensional GPE. Linear stability analysis corroborated by direct evolution simulations demonstrates that multi-peaked solitons are almost completely stable in their entire existence domains.

Two-terminal transport measurements with cold atoms

In recent years, the ability of cold atom experiments to explore condensed-matter-related questions has dramatically progressed. Transport experiments, in particular, have expanded to the point in which conductance and other transport coefficients can now be measured in a way that is directly analogous to solid-state physics, extending cold-atom-based quantum simulations into the domain of quantum electronic devices. In this topical review, we describe the transport experiments performed with cold gases in the two-terminal configuration, with an emphasis on the specific features of cold atomic gases compared to solid-state physics. We present the experimental techniques and the main experimental findings, focusing on-but not restricted to-the recent experiments performed by our group. We finally discuss the perspectives opened up by this approach, the main technical and conceptual challenges for future developments, and potential applications in quantum simulation for transport phenomena and mesoscopic physics problems.

The New Concept of Nano-Device Spectroscopy Based on Rabi–Bloch Oscillations for THz-Frequency Range

We considered one-dimensional quantum chains of two-level Fermi particles coupled via the tunneling driven both by ac and dc fields in the regimes of strong and ultrastrong coupling. The frequency of ac field is matched with the frequency of the quantum transition. Based on the fundamental principles of electrodynamics and quantum theory, we developed a general model of quantum dynamics for such interactions. We showed that the joint action of ac and dc fields leads to the strong mutual influence of Rabi- and Bloch oscillations, one to another. We focused on the regime of ultrastrong coupling, for which Bloch- and Rabi-frequencies are significant values of the frequency of interband transition. The Hamiltonian was solved numerically, with account of anti-resonant terms. It manifests by the appearance of a great number of narrow high-amplitude resonant lines in the spectra of tunneling current and dipole moment. We proposed the new concept of terahertz (THz) spectroscopy, which is promising for different applications in future nanoelectronics and nano-photonics.

Bloch oscillations sustained by nonlinearity

We demonstrate that nonlinearity may play a constructive role in supporting Bloch oscillations in a model which is discrete, in one dimension and continuous in the orthogonal one. The model can be experimentally realized in several fields of physics such as optics and Bose-Einstein condensates. We demonstrate that designing an optimal relation between the nonlinearity and the linear gradient strength provides extremely long-lived Bloch oscillations with little degradation. Such robust oscillations can be observed for a broad range of parameters and even for moderate nonlinearities and large enough values of linear potential. We also present an approximate analytical description of the wave packet’s evolution featuring a hybrid Bloch oscillating wave-soliton behavior that excellently corresponds to the direct numerical simulations.

Bloch oscillations in organic and inorganic polymers

The transport of polarons above the mobility threshold in organic and inorganic polymers is theoretically investigated in the framework of a one-dimensional tight-binding model that includes lattice relaxation. The computational approach is based on parameters for which the model Hamiltonian suitably describes different polymer lattices in the presence of external electric fields. Our findings show that, above critical field strengths, a dissociated polaron moves through the polymer lattice as a free electron performing Bloch oscillations. These critical electric fields are considerably smaller for inorganic lattices in comparison to organic polymers. Interestingly, for inorganic lattices, the free electron propagates preserving charge and spin densities' localization which is a characteristic of a static polaron. Moreover, in the turning points of the spatial Bloch oscillations, transient polaron levels are formed inside the band gap, thus generating a fully characterized polaron structure. For the organic case, on the other hand, no polaron signature is observed: neither in the shape of the distortion-those polaron profile signatures are absent-nor in the energy levels-as no such polaron levels are formed during the simulation. These results solve controversial aspects concerning Bloch oscillations recently reported in the literature and may enlighten the understanding about the charge transport mechanism in polymers above their mobility edge.

Interaction-Assisted Quantum Tunneling of a Bose-Einstein Condensate Out of a Single Trapping Well

We experimentally study tunneling of Bose-condensed ^{87}Rb atoms prepared in a quasibound state and observe a nonexponential decay caused by interatomic interactions. A combination of a magnetic quadrupole trap and a thin 1.3  μm barrier created using a blue-detuned sheet of light is used to tailor traps with controllable depth and tunneling rate. The escape dynamics strongly depend on the mean-field energy, which gives rise to three distinct regimes-classical spilling over the barrier, quantum tunneling, and decay dominated by background losses. We show that the tunneling rate depends exponentially on the chemical potential. Our results show good agreement with numerical solutions of the 3D Gross-Pitaevskii equation.

Ground states of a Bose-Einstein Condensate in a one-dimensional laser-assisted optical lattice

We study the ground-state behavior of a Bose-Einstein Condensate (BEC) in a Raman-laser-assisted one-dimensional (1D) optical lattice potential forming a multilayer system. We find that, such system can be described by an effective model with spin-orbit coupling (SOC) of pseudospin (N-1)/2, where N is the number of layers. Due to the intricate interplay between atomic interactions, SOC and laser-assisted tunnelings, the ground-state phase diagrams generally consist of three phases-a stripe, a plane wave and a normal phase with zero-momentum, touching at a quantum tricritical point. More important, even though the single-particle states only minimize at zero-momentum for odd N, the many-body ground states may still develop finite momenta. The underlying mechanisms are elucidated. Our results provide an alternative way to realize an effective spin-orbit coupling of Bose gas with the Raman-laser-assisted optical lattice, and would also be beneficial to the studies on SOC effects in spinor Bose systems with large spin.

Bloch Oscillations in Optical and Zeeman Lattices in the Presence of Spin-Orbit Coupling

We address Bloch oscillations of a spin-orbit coupled atom in periodic potentials of two types: optical and Zeeman lattices. We show that in optical lattices the spin-orbit coupling allows controlling the direction of atomic motion and may lead to complete suppression of the oscillations at specific values of the coupling strength. In Zeeman lattices the energy bands are found to cross each other at the boundaries of the Brillouin zone, resulting in period doubling of the oscillations. In all cases, the oscillations are accompanied by rotation of the pseudospin, with a dynamics that is determined by the strength of the spin-orbit coupling. The predicted effects are discussed also in terms of a Wannier-Stark ladder, which in optical lattices consist of two mutually shifted equidistant subladders.

Plasmonic Zener tunneling in binary graphene sheet arrays

We investigate the plasmonic Zener tunneling (ZT) in arrays of weakly coupled graphene sheet waveguides. By alternatively arranging the graphene waveguides with two different chemical potentials, the single surface plasmon polariton (SPP) band splits into two minibands, and tunneling between them occurs at the edge of the Brillouin zone. With a linear gradient of the propagation constant introduced by appropriately tuning the chemical potential distribution over the graphene sheet, the SPPs exhibit a sequence of Bloch oscillations and ZT transitions in the arrays. The simulated tunneling rate coincides with the theoretical analysis based on the coupled-mode theory, which can be tuned by varying the chemical potential difference between adjacent graphene.

Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice

As an important electron transportation phenomenon, Bloch oscillations have been extensively studied in condensed matter. Due to the similarity in wave properties between electrons and other quantum particles, Bloch oscillations have been observed in atom lattices, photonic lattices, and so on. One of the many distinct advantages for choosing these systems over the regular electronic systems is the versatility in engineering artificial potentials. Here by utilizing dissipative elements in a CMOS-compatible photonic platform to create a periodic complex potential and by exploiting the emerging concept of parity-time synthetic photonics, we experimentally realize spatial Bloch oscillations in a non-Hermitian photonic system on a chip level. Our demonstration may have significant impact in the field of quantum simulation by following the recent trend of moving complicated table-top quantum optics experiments onto the fully integrated CMOS-compatible silicon platform.

Dynamical phase diagram of Gaussian wave packets in optical lattices

We study the dynamics of self-trapping in Bose-Einstein condensates (BECs) loaded in deep optical lattices with Gaussian initial conditions, when the dynamics is well described by the discrete nonlinear Schrödinger equation (DNLSE). In the literature an approximate dynamical phase diagram based on a variational approach was introduced to distinguish different dynamical regimes: diffusion, self-trapping, and moving breathers. However, we find that the actual DNLSE dynamics shows a completely different diagram than the variational prediction. We calculate numerically a detailed dynamical phase diagram accurately describing the different dynamical regimes. It exhibits a complex structure that can readily be tested in current experiments in BECs in optical lattices and in optical waveguide arrays. Moreover, we derive an explicit theoretical estimate for the transition to self-trapping in excellent agreement with our numerical findings, which may be a valuable guide as well for future studies on a quantum dynamical phase diagram based on the Bose-Hubbard Hamiltonian.

Excitation of atoms in an optical lattice driven by polychromatic amplitude modulation

We investigate the mutiphoton process between different Bloch states in an amplitude modulated optical lattice. In the experiment, we perform the modulation with more than one frequency components, which includes a high degree of freedom and provides a flexible way to coherently control quantum states. Based on the study of single frequency modulation, we investigate the collaborative effect of different frequency components in two aspects. Through double frequency modulations, the spectrums of excitation rates for different lattice depths are measured. Moreover, interference between two separated excitation paths is shown, emphasizing the influence of modulation phases when two modulation frequencies are commensurate. Finally, we demonstrate the application of the double frequency modulation to design a large-momentum-transfer beam splitter. The beam splitter is easy in practice and would not introduce phase shift between two arms.

Quasi-periodic Wannier–Stark ladders from driven atomic Bloch oscillations

Periodic Wannier–Stark ladder structures of the energy resonances associated with Bloch oscillations can be readily modified into quasi-periodic ones that exhibit peculiar self-similar effects. A compact theoretical description of the dynamics of driven Bloch oscillations is developed here within the quasi-momentum representation. We identify a rather viable scheme based on ultracold atomic wavepackets subject to gravity in a driven optical lattice potential where a self-similar scaling could be observed. Its feasibility in terms of realistic experimental parameters is also discussed.

Interaction-induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1D atomic Bloch oscillations

We study atomic Bloch oscillations in an ensemble of one-dimensional tilted superfluids in the Bose-Hubbard regime. For large values of the tilt, we observe interaction-induced coherent decay and matter-wave quantum phase revivals of the Bloch oscillating ensemble. We analyze the revival period dependence on interactions by means of a Feshbach resonance. When reducing the value of the tilt, we observe the disappearance of the quasiperiodic phase revival signature towards an irreversible decay of Bloch oscillations, indicating the transition from regular to quantum chaotic dynamics.

Observing the onset of effective mass

The response of a particle in a periodic potential to an applied force is commonly described by an effective mass, which accounts for the detailed interaction between the particle and the surrounding potential. Using a Bose-Einstein condensate of (87)Rb atoms initially in the ground band of an optical lattice, we experimentally show that the initial response of a particle to an applied force is in fact characterized by the bare mass. Subsequently, the particle response undergoes rapid oscillations and only over time scales that are long compared to those of the interband dynamics is the effective mass observed to be an appropriate description. Our results elucidate the role of the effective mass on short time scales, which is relevant for example in the interaction of few-cycle laser pulses with dielectric and semiconductor materials.

Dynamical instability of a Bose-Einstein condensate with higher-order interactions in an optical potential through a variational approach

We investigate the dynamical instability of Bose-Einstein condensates (BECs) with higher-order interactions immersed in an optical lattice with weak driving harmonic potential. For this, we compute both analytically and numerically a modified Gross-Pitaevskii equation with higher-order nonlinearity and external potentials generated by magnetic and optical fields. Using the time-dependent variational approach, we derive the ordinary differential equations for the time evolution of the amplitude and phase of modulational perturbation. Through an effective potential, we obtain the modulational instability condition of BECs and discuss the effect of the higher-order interaction in the dynamics of the condensates in presence of optical potential. We perform direct numerical simulations to support our analytical results, and good agreement is found.

Engineering novel optical lattices

Optical lattices have developed into a widely used and highly recognized tool to study many-body quantum physics with special relevance for solid state type systems. One of the most prominent reasons for this success is the high degree of tunability in the experimental setups. While at the beginning quasi-static, cubic geometries were mainly explored, the focus of the field has now shifted toward new lattice topologies and the dynamical control of lattice structures. In this review we intend to give an overview of the progress recently achieved in this field on the experimental side. In addition, we discuss theoretical proposals exploiting specifically these novel lattice geometries.

Interacting fermionic atoms in optical lattices diffuse symmetrically upwards and downwards in a gravitational potential

We consider a cloud of fermionic atoms in an optical lattice described by a Hubbard model with an additional linear potential. While homogeneous interacting systems mainly show damped Bloch oscillations and heating, a finite cloud behaves differently: It expands symmetrically such that gains of potential energy at the top are compensated by losses at the bottom. Interactions stabilize the necessary heat currents by inducing gradients of the inverse temperature 1/T, with T<0 at the bottom of the cloud. An analytic solution of hydrodynamic equations shows that the width of the cloud increases with t^{1/3} for long times consistent with results from our Boltzmann simulations.

Cyclotron-Bloch dynamics of a quantum particle in a two-dimensional lattice

This paper studies the quantum dynamics of a charged particle in a two-dimensional square lattice, under the influence of electric and magnetic fields, the former being aligned with one of the lattice axes and the latter perpendicular to the lattice plane. While in free space these dynamics consist of uniform motions in the direction orthogonal to the electric field vector, we find that, in a lattice, this directed drift takes place only for specific initial conditions and for electric field magnitudes smaller than a critical value. Otherwise, the quantum wave packet spreads ballistically in both directions orthogonal to the electric field. We quantify this ballistic spreading and identify the subspace of initial conditions ensuring directed transport with the drift velocity. We also describe the effect of disorder in the system.

Inducing transport in a dissipation-free lattice with super Bloch oscillations

Particles in a perfect lattice potential perform Bloch oscillations when subject to a constant force, leading to localization and preventing conductivity. For a weakly interacting Bose-Einstein condensate of Cs atoms, we observe giant center-of-mass oscillations in position space with a displacement across hundreds of lattice sites when we add a periodic modulation to the force near the Bloch frequency. We study the dependence of these "super" Bloch oscillations on lattice depth, modulation amplitude, and modulation frequency and show that they provide a means to induce linear transport in a dissipation-free lattice.

Bloch oscillations of THz acoustic phonons in coupled nanocavity structures

Nanophononic Bloch oscillations and Wannier-Stark ladders have been recently predicted to exist in specifically tailored structures formed by coupled nanocavities. Using pump-probe coherent phonon generation techniques we demonstrate that Bloch oscillations of terahertz acoustic phonons can be directly generated and probed in these complex nanostructures. In addition, by Fourier transforming the time traces we had access to the proper eigenmodes in the frequency domain, thus evidencing the related Wannier-Stark ladder. The observed Bloch oscillation dynamics are compared with simulations based on a model description of the coherent phonon generation and photoelastic detection processes.

Surface acoustic BLOCH oscillations, the Wannier-Stark ladder, and Landau-Zener tunneling in a solid

We present the experimental observation of Bloch oscillations, the Wannier-Stark ladder, and Landau-Zener tunneling of surface acoustic waves in perturbed grating structures on a solid substrate. A model providing a quantitative description of our experimental observations, including multiple Landau-Zener transitions of the anticrossed surface acoustic Wannier-Stark states, is developed. The use of a planar geometry for the realization of the Bloch oscillations and Landau-Zener tunneling allows a direct access to the elastic field distribution. The vertical surface displacement has been measured by interferometry.

Delocalization and spreading in a nonlinear Stark ladder

We study the evolution of a wave packet in a nonlinear Stark ladder. In the absence of nonlinearity all normal modes are spatially localized giving rise to an equidistant eigenvalue spectrum and Bloch oscillations. Nonlinearity induces frequency shifts and mode-mode interactions and destroys localization. For large strength of nonlinearity we observe single-site trapping as a transient, with subsequent explosive spreading, followed by subdiffusion. For moderate nonlinearities an immediate subdiffusion takes place. Finally, for small nonlinearities we find linear Stark localization as a transient, with subsequent subdiffusion. For single-mode excitations and weak nonlinearities, stability intervals are predicted and observed upon variation in the dc bias strength, which affects the short- and the long-time dynamics.

Time-resolved measurement of Landau-Zener tunneling in periodic potentials

We report time-resolved measurements of Landau-Zener tunneling of Bose-Einstein condensates in accelerated optical lattices, clearly resolving the steplike time dependence of the band populations. Using different experimental protocols we were able to measure the tunneling probability both in the adiabatic and in the diabatic bases of the system. We also experimentally determine the contribution of the momentum width of the Bose condensates to the temporal width of the tunneling steps and discuss the implications for measuring the jump time in the Landau-Zener problem.

Bloch oscillations in a one-dimensional spinor gas

A force applied to a spin-flipped particle in a one-dimensional spinor gas may lead to Bloch oscillations of the particle's position and velocity. The existence of Bloch oscillations crucially depends on the viscous friction force exerted by the rest of the gas on the spin excitation. We evaluate the friction in terms of the quantum fluid parameters. In particular, we show that the friction is absent for integrable cases, such as an SU(2) symmetric gas of bosons or fermions. For small deviations from the exact integrability the friction is very weak, opening the possibility to observe Bloch oscillations.

Bloch-Zener oscillations in binary superlattices

Bloch-Zener oscillations, i.e., the coherent superposition of Bloch oscillations and Zener tunneling between minibands of a binary lattice, are experimentally demonstrated for light waves in curved femtosecond laser-written waveguide arrays. Visualization of double-periodicity breathing and oscillation modes is reported, and synchronous tunneling leading to wave reconstruction is demonstrated.

Long-living BLOCH oscillations of matter waves in periodic potentials

The dynamics of matter waves in linear and nonlinear optical lattices subject to a spatially uniform linear force is studied both analytically and numerically. It is shown that by properly designing the spatial dependence of the scattering length it is possible to induce long-living Bloch oscillations of gap-soliton matter waves in optical lattices. This occurs when the effective nonlinearity and the effective mass of the soliton have opposite signs for all values of the crystal momentum in the Brillouin zone. The results apply to all systems modeled by the periodic nonlinear Schrödinger equation, including propagation of light in photonic and photorefractive crystals with tilted band structures.

Controlled generation of coherent matter currents using a periodic driving field

We study the effect of a strong, oscillating driving field on the dynamics of ultracold bosons held in an optical lattice. Modeling the system as a Bose-Hubbard model, we show how the driving field can be used to produce and maintain a coherent atomic current by controlling the phase of the intersite tunneling processes. We investigate both the stroboscopic and time-averaged behavior using Floquet theory, and demonstrate that this procedure provides a stable and precise method of controlling coherent quantum systems.

Control of interaction-induced dephasing of Bloch oscillations

We report on the control of interaction-induced dephasing of Bloch oscillations for an atomic Bose-Einstein condensate in an optical lattice. We quantify the dephasing in terms of the width of the quasimomentum distribution and measure its dependence on time for different interaction strengths which we control by means of a Feshbach resonance. For minimal interaction, the dephasing time is increased from a few to more than 20 thousand Bloch oscillation periods, allowing us to realize a BEC-based atom interferometer in the noninteracting limit.

Observation of photon-assisted tunneling in optical lattices

We have observed tunneling suppression and photon-assisted tunneling of Bose-Einstein condensates in an optical lattice subjected to a constant force plus a sinusoidal shaking. For a sufficiently large constant force, the ground energy levels of the lattice are shifted out of resonance and tunneling is suppressed; when the shaking is switched on, the levels are coupled by low-frequency photons and tunneling resumes. Our results agree well with theoretical predictions and demonstrate the usefulness of optical lattices for studying solid-state phenomena.

Time-averaged adiabatic potentials: versatile matter-wave guides and atom traps

We demonstrate a novel class of trapping potentials, time-averaged adiabatic potentials (TAAP), which allows the generation of a large variety of traps for quantum gases and matter-wave guides for atom interferometers. Examples include stacks of pancakes, rows of cigars, and multiple rings or sickles. The traps can be coupled through controllable tunneling barriers or merged altogether. We present analytical expressions for pancake-, cigar-, and ring-shaped traps. The ring geometry is of particular interest for guided matter-wave interferometry as it provides a perfectly smooth waveguide of widely tunable diameter and thus adjustable sensitivity of the interferometer. The flexibility of the TAAP would make possible the use of Bose-Einstein condensates as coherent matter waves in large-area atom interferometers.

Many-body interband tunneling as a witness of complex dynamics in the Bose-Hubbard model

A perturbative model is studied for the tunneling of many-particle states from the ground band to the first excited energy band, mimicking Landau-Zener decay for ultracold, spinless atoms in quasi-one-dimensional optical lattices subjected to a tunable tilting force. The distributions of the computed tunneling rates provide an independent and experimentally accessible signature of the regular-chaotic transition in the strongly correlated many-body dynamics of the ground band.

Acoustic analogue of electronic BLOCH oscillations and resonant Zener tunneling in ultrasonic superlattices

We demonstrate the existence of Bloch oscillations of acoustic fields in sound propagation through a superlattice of water cavities and layers of methyl methacrylate. To obtain the acoustic equivalent of a Wannier-Stark ladder, we employ a set of cavities with different thicknesses. Bloch oscillations are observed as time-resolved oscillations of transmission in a direct analogy to electronic Bloch oscillations in biased semiconductor superlattices. Moreover, for a particular gradient of cavity thicknesses, an overlap of two acoustic minibands occurs, which results in resonant Zener-like transmission enhancement.