Emergence of superfluid transport in a dynamical system of ultra-cold atoms

The dynamics of a Bose-Einstein condensate is studied theoretically in a combined periodic plus harmonic external potential. Different dynamical regimes of stable and unstable collective dipole and Bloch oscillations are analysed in terms of a quantum mechanical pendulum model. Nonlinear interactions are shown to counteract quantum-mechanical dephasing and lead to phase-coherent, superfluid transport.     

Umklapp collisions and center-of-mass oscillations of a trapped Fermi gas

Starting from the Boltzmann equation, we study the center-of-mass oscillation of a harmonically trapped normal Fermi gas in the presence of a one-dimensional periodic potential. We show that for values of the Fermi energy above the first Bloch band the center of mass motion is overdamped in the collisional regime due to umklapp processes. This should be contrasted with the behavior of a superfluid where one instead expects the occurrence of persistent Josephson-like oscillations.     

Supercurrent survival under a Rosen-Zener quench of hard-core bosons

We study the survival of supercurrents in a system of impenetrable bosons on a lattice, subject to a quantum quench from its critical superfluid phase to an insulating phase. We show that the evolution of the current when the quench follows a Rosen-Zener profile is exactly solvable. This allows us to analyze a quench of arbitrary rate, from a sudden destruction of the superfluid to a slow opening of a gap. The decay and oscillations of the current are analytically derived and studied numerically along with the momentum distribution after the quench. In the case of small supercurrent boosts nu, we find that the current surviving at long times is proportional to nu3.     

Theoretical analysis of a large momentum beamsplitter using Bloch oscillations

In this paper, we present the implementation of Bloch oscillations in an atomic interferometer to increase the separation of the two interfering paths. A numerical model, in very good agreement with the experiment, is developed. The contrast of the interferometer and its sensitivity to phase fluctuations and to intensity fluctuations are also calculated. We demonstrate that the sensitivity to phase fluctuations can be significantly reduced by using a suitable arrangement of Bloch oscillations pulses.     

Quasiparticle scattering by quantum phase slips in one-dimensional superfluids

Quantum phase slips (QPS) in narrow superfluid channels generate momentum by unwinding the supercurrent. In a uniform Bose gas, this momentum needs to be absorbed by quasiparticles (phonons). We show that this requirement results in an additional exponential suppression of the QPS rate (compared to the rate of QPS induced by a sharply localized perturbation). In BCS-paired fluids, momentum can be transferred to fermionic quasiparticles, and we find an interesting interplay between quasiparticle scattering on QPS and on disorder.     

Thermally driven josephson oscillations in superfluid 4He

We find that a temperature differential can drive superfluid oscillations in 4He. The oscillations are excited by a heater which causes a time dependent temperature differential across an array of 70 nm apertures. By measuring the oscillation frequency and simultaneously determining both temperature and pressure differentials we prove the validity of the most general form of the Josephson frequency relation. These observations were made near saturated vapor pressure, within a few mK of the superfluid transition temperature.     

Optomechanical effects in superfluid properties of BEC in an optical lattice

We investigate the effects of a movable mirror (cantilever) of an optical cavity on the superfluid properties and the Mott phase boundary of a Bose-Einstein condensate (BEC) in an optical lattice. The Bloch energy, effective mass, Bogoliubov energy and the superfluid fraction are modified due to the mirror motion. The mirror motion is also found to modify the Mott-superfluid phase boundaries. This study reveals that the mirror emerges as a new handle to coherently control the superfluid properties of the BEC.     

Super Bloch oscillations in the Peyrard-Bishop-Holstein model

Recently, polarons in the Peyrard-Bishop-Holstein model under DC electric fields were established to perform Bloch oscillations, provided the charge-lattice coupling is not large. In this work, we study this model when the charge is subjected to an applied field with both DC and AC components. Similarly to what happens in the rigid lattice, we find that the carrier undergoes a directed motion or coherent oscillations when the AC field is resonant or detuned with respect to the Bloch frequency, respectively. The electric density current and its Fourier spectrum are also studied to reveal the frequencies involved in the polaron dynamics.     

Transient Dynamics of Super Bloch Oscillations of a 1D Holstein Polaron under the Influence of an External AC Electric Field

Theoretical formalism for DC‐field polaron dynamics is extended to the dynamics of a 1D Holstein polaron in an external AC electric field using multiple Davydov trial states. Effects of carrier–phonon coupling on detuned and resonant scenarios are investigated for both phase and nonzero phase. For slightly off‐resonant or detuned cases, a beat between the usual Bloch oscillations and an AC driving force results in super Bloch oscillations, that is, rescaled Bloch oscillations in both the spatial and the temporal dimension. Super Bloch oscillations are damped by carrier–phonon coupling. For resonant cases, if the carrier is created on two nearest‐neighboring sites, the carrier wave packet spreads with small‐amplitude oscillations. Adding carrier–phonon coupling localizes the carrier wave packet. If an initial broad Gaussian wave packet is adopted, the centroid of the carrier wave packet moves with a certain velocity and with its shape unchanged. Adding carrier–phonon coupling broadens the carrier wave packet and slows down the carrier movement. Our findings may help provide guiding principles on how to manipulate the dynamics of the super Bloch oscillations of carriers in semiconductor superlattice and optical lattices by modifying DC and AC field strengths, AC phases, and detuning parameters.     

Dynamics of Bose–Einstein condensate in driven tilted optical lattices

We study the dynamics of Bose–Einstein condensate in one-dimensional driven tilted periodic optical lattices by using variational approximation and numerical simulation. Rich phenomena are revealed, including diffusion, self-trapping, breather and soliton, which strongly depend on the atomic interaction, the amplitude of the modulation, the constant force and the phase difference between the Bloch oscillations and the drive. The critical conditions for the dynamical transition from diffusion to self-trapping and for the formation of the soliton are derived analytically. In addition, the phase diagrams of dynamical transitions are presented in full parameters space. We find that the dynamics of the system can be completely controlled by adjusting the constant force, the amplitude of the modulation and the phase difference between the Bloch oscillations and the drive. The results are confirmed by the direct numerical simulation of the full Gross–Pitaevskii equation.     

Probing two Higgs oscillations in a one-dimensional Fermi superfluid with Raman-type spin–orbit coupling

We theoretically investigate the Higgs oscillation in a one-dimensional Raman-type spin–orbit-coupled Fermi superfluid with the time-dependent Bogoliubov–de Gennes equations. By linearly ramping or abruptly changing the effective Zeeman field in both the Bardeen–Cooper–Schrieffer state and the topological superfluid state, we find the amplitude of the order parameter exhibits an oscillating behaviour over time with two different frequencies (i.e., two Higgs oscillations) in contrast to the single one in a conventional Fermi superfluid. The observed period of oscillations has a great agreement with the one calculated using the previous prediction [Volkov and Kogan, J. Exp. Theor. Phys. 38, 1018 (1974)], where the oscillating periods are now determined by the minimums of two quasi-particle spectrum in this system. We further verify the existence of two Higgs oscillations using a periodic ramp strategy with theoretically calculated driving frequency. Our predictions would be useful for further theoretical and experimental studies of these Higgs oscillations in spin–orbit-coupled systems.     

Exact Bloch States of a Spin-orbit Coupled Bose-Einstein Condensate in an Optical Lattice

We study the exact Bloch states of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) held in an optical lattice. Under a natural condition of the symmetry between the two species, we obtain two different forms of exact solutions corresponding to different existing conditions. Then, we analytically demonstrate that (a) the average atomic number per well can enlarge the region area (consisting of instability and stability parameter regions) existing exact solutions; (b) the sizes of the instability and stability parameter regions exhibit opposite variation trend with the increase in Rabi coupling strength, and the results of different solutions are just opposite. Besides, we find that spin-orbit coupling (SOC) results in the generation of spin-motion entanglement for the Bloch states, the SOC strength and lattice depth can influence the population transfer between two BEC components, and varying the SOC strength and lattice depth can also reveal the dynamical superfluid-insulator transition from the superfluid state to the critical insulating state. These results present a feasible scheme to manipulate the stable superfluid currents, which will be useful to control quantum transport of BEC.

     

Rabi oscillations between dissipative Bloch bands

Within a two-band tight-binding model driven by DC–AC electric fields, we investigate the dynamics of electrons with Markoffian dephasing. We find that Rabi oscillations between the Bloch bands under the resonant condition may be destroyed by scattering from lattice imperfections. Through a perturbative calculation, we also obtain the effective decay time for the approach to equal Bloch band populations under conditions of small interband coupling and in the long-time limit. The decay rate shows characteristic sharp peaks at values of the parameters that give a signature of Rabi oscillations, and quasienergy spectra display avoided crossings at the same time.     

Topologically induced avoided band crossing in an optical checkerboard lattice

We report on the condensation of bosons in the 4th band of an optical checkerboard lattice providing a topologically induced avoided band crossing involving the 2nd, 3rd, and 4th Bloch bands. When the condensate is slowly tuned through the avoided crossing, accelerated band relaxation arises and the zero momentum approximately C4-invariant condensate wave function acquires finite momentum order and reduced C2 symmetry. For faster tuning Landau-Zener oscillations between different superfluid orders arise, which are used to characterize the avoided crossing.     

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.     

Collective Rabi oscillations and solitons in a time-dependent BCS pairing problem

Motivated by recent efforts to achieve cold fermions pairing, we study the nonadiabatic regime of the Bardeen-Cooper-Schrieffer state formation. After the interaction is turned on, at times shorter than the quasiparticle energy relaxation time, the system oscillates between the superfluid and normal state. The collective nonlinear evolution of the BCS-Bogoliubov amplitudes u(p), v(p), along with the pairing function Delta, is shown to be an integrable dynamical problem which admits single soliton and soliton train solitons. We interpret the collective oscillations as Bloch precession of Anderson pseudospins, where each soliton causes a pseudospin 2pi Rabi rotation.     

Numerical method for hydrodynamic modulation equations describing Bloch oscillations in semiconductor superlattices

We present a finite difference method to solve a new type of nonlocal hydrodynamic equations that arise in the theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices. The hydrodynamic equations describe the evolution of the electron density, electric field and the complex amplitude of the Bloch oscillations for the electron current density and the mean energy density. These equations contain averages over the Bloch phase which are integrals of the unknown electric field and are derived by singular perturbation methods. Among the solutions of the hydrodynamic equations, at a 70 K lattice temperature, there are spatially inhomogeneous Bloch oscillations coexisting with moving electric field domains and Gunn-type oscillations of the current. At higher temperature (300 K) only Bloch oscillations remain. These novel solutions are found for restitution coefficients in a narrow interval below their critical values and disappear for larger values. We use an efficient numerical method based on an implicit second-order finite difference scheme for both the electric field equation (of drift-diffusion type) and the parabolic equation for the complex amplitude. Double integrals appearing in the nonlocal hydrodynamic equations are calculated by means of expansions in modified Bessel functions. We use numerical simulations to ascertain the convergence of the method. If the complex amplitude equation is solved using a first order scheme for restitution coefficients near their critical values, a spurious convection arises that annihilates the complex amplitude in the part of the superlattice that is closer to the cathode. This numerical artifact disappears if the space step is appropriately reduced or we use the second-order numerical scheme.     

Self-trapping of bosons and fermions in optical lattices

We theoretically investigate the enhanced localization of bosonic atoms by fermionic atoms in three-dimensional optical lattices and find a self-trapping of the bosons for attractive boson-fermion interaction. Because of this mutual interaction, the fermion orbitals are substantially squeezed, which results in a strong deformation of the effective potential for bosons. This effect is enhanced by an increasing bosonic filling factor leading to a large shift of the transition between the superfluid and the Mott-insulator phase. We find a nonlinear dependency of the critical potential depth on the boson-fermion interaction strength. The results, in general, demonstrate the important role of higher Bloch bands for the physics of attractively interacting quantum gas mixtures in optical lattices and are of direct relevance to recent experiments with 87Rb-40K mixtures, where a large shift of the critical point has been found.     

Bose-Einstein Condensates in Optical Lattices with Higher-Order Interactions

The higher-order interactions of Bose-Einstein condensate in multi-dimensional optical lattices are discussed both analytically and numerically.It is demonstrated that the effects of the higher-order atomic interactions on the sound speed and the stabilities of Bloch waves strongly depend on the lattice strength.In the presence of higher-order effects,tighter and high-dimensional lattices are confirmed to be two positive factors for maintaining the system's energetic stability,and the dynamical instability of Bloch waves can take place simultaneously with the energetic instability.In addition,we find that the higher-order interactions exhibit a long-range behavior and the long-lived coherent Bloch oscillations in a tilted optical lattice exist.Our results provide an effective way to probe the higher-order interactions in optical lattices.     

Surface optical Bloch oscillations in semi-infinite waveguide arrays

We predict that surface optical Bloch oscillations can exist in semi-infinite waveguide arrays with a linear index variation, if the array parameters close to the boundary are appropriately perturbed. The perturbation is such that the surface states obtain the Wannier-Stark ladder eigenvalues of the unperturbed infinite array. The number of waveguides, whose parameters need to be controlled, decreases with increasing ratio of index gradient over coupling. The configuration can find applications as a "matched" termination of waveguide arrays to eliminate the distortion of Bloch oscillations due to reflection on the boundaries.