Damping Of Bloch Oscillations Research Articles

Damping of Bloch oscillations: Variational solutions of the Boltzmann equation beyond linear response

Variational solutions of the Boltzmann equation usually rely on the concept of linear response. We extend the variational approach for tight-binding models at high entropies to a regime far beyond linear response. We analyze both weakly interacting fermions and incoherent bosons on a lattice. We consider a case where the particles are driven by a constant force, leading to the well-known Bloch oscillations, and we consider interactions that are weak enough not to overdamp these oscillations. This regime is computationally demanding and relevant for ultracold atoms in optical lattices. We derive a simple theory in terms of coupled dynamic equations for the particle density, energy density, current, and heat current, allowing for analytic solutions. As an application, we identify damping coefficients for Bloch oscillations in the Hubbard model at weak interactions and compute them for a one-dimensional toy model. We also approximately solve the long-time dynamics of a weakly interacting, strongly Bloch-oscillating cloud of fermionic particles in a tilted lattice, leading to a subdiffusive scaling exponent.

Superfluid Bloch dynamics in an incommensurate optical lattice

We investigate the interplay of disorder and interactions in the accelerated transport of a Bose–Einstein condensate through an incommensurate optical lattice. We show that interactions can effectively cancel the damping of Bloch oscillations (BOs) due to the disordered potential and we provide a simple model to qualitatively capture this screening effect. We find that the characteristic interaction energy, above which interactions and disorder cooperate to enhance, rather than reduce, the damping of BOs, coincides with the average disorder depth. This is consistent with results of a mean-field simulation.

Real-Time Current of a Charge Carrier in a Strongly Correlated System Coupled to Phonons, Driven by a Uniform Electric Field

We perform a quantum time evolution of a single charge carrier doped into strongly correlated system and coupled to phonons, driven by a uniform electric field. We study a two-dimensional t–J-Holstein model and calculate the real-time current. At large values of electric field, the response of the system exhibits damped Bloch oscillations, and the values of the steady current decrease with increasing electric field. On the other hand, the maximal amplitude of the real-time current increase with increasing field. We discuss the appearance of the negative differential resistivity regime, observed recently in various nonequilibrium studies of interacting many-body systems.

Damping of Bloch Oscillations in the Hubbard Model

Using nonequilibrium dynamical mean-field theory, we study the isolated Hubbard model in a static electric field in the limit of weak interactions. Linear response behavior is established at long times, but only if the interaction exceeds a critical value, below which the system exhibits an ac-type response with Bloch oscillations. The transition from ac to dc response is defined in terms of the universal long-time behavior of the system, which does not depend on the initial condition.

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.

Nonequilibrium dynamics of the Holstein polaron driven by an external electric field

This work represents a fundamental study of a Holstein polaron in one dimension driven away from the ground state by a constant electric field. Taking fully into account quantum effects we follow the time-evolution of the system from its ground state as the constant electric field is switched on at t = 0, until it reaches a steady state. At weak electron phonon coupling (EP) the system experiences damped Bloch oscillations (BO) characteristic for noninteracting electron band. An analytic expression of the steady state current is proposed in terms of weak EP coupling and large electric field. For moderate values of EP coupling the oscillations are almost critically damped and the system reaches the steady state after a short time. In the strong coupling limit weakly damped BO, consistent with nearly adiabatic evolution within the polaron band, persist up to extremely large electric fields. A traveling polaron under the influence of the electric field leaves behind a trail of phonon excitations absorbing the excess energy gained from the electric field. The shape of the traveling polaron is investigated in details.

Bloch oscillations in lattice potentials with controlled aperiodicity

We numerically investigate the damping of Bloch oscillations in a one-dimensional lattice potential whose translational symmetry is broken in a systematic manner, either by making the potential bichromatic or by introducing scatterers at distinct lattice sites. We find that the damping strongly depends on the ratio of lattice constants in the bichromatic potential and that even a small concentration of scatterers can lead to strong damping. Moreover, collisional interparticle interactions are able to counteract aperiodicity-induced damping of Bloch oscillations. The discussed effects should readily be observable for ultracold atoms in optical lattices.

Bloch oscillation, dynamical localization, and optical probing of electron gases in quantum-dot superlattices in high electric fields

In this paper, we present numerical results for steady-state and time-dependent currents as well as for a long-time average current in strong nonlinear dc and ac electric fields for an electron gas in a one-dimensional (1D) quantum-dot superlattice. A microscopic model is employed for the scattering of electrons by phonons and static impurities by means of the Boltzmann equation method. The dc results are favorably compared with recent exact analytic results based on a relaxation-time model for electron-phonon scattering. Our results demonstrate the different roles played by elastic and inelastic scattering on the damped Bloch oscillations as well as the nonlinear steady-state current and their opposite roles on the damped dynamical localization. We also find a suppression of dynamical localization by strong Bloch oscillations and features in the Esaki-Tsu peaks in the presence of an ac electric field when electron scattering is included. On the basis of a nonequilibrium electron distribution obtained from the Boltzmann equation, a self-consistent-field approach is employed to establish a general formalism for the optical response of current-driven electrons in both the linear and nonlinear regimes to a 1D quantum-dot superlattice. The dc-field dependences of both the peak energy and peak strength in the absorption spectrum for a 1D quantum-dot superlattice are calculated, from which we find: (1) both the peak energy and its strength are significantly reduced with increasing dc electric field; and (2) the peak energy and peak strength are anomalously enhanced by raising the temperature for the nonlinear transport of electrons when a strong dc electric field is applied.

Damped Bloch oscillations of Bose–Einstein condensates in disordered potential gradients

We investigate both experimentally and theoretically disorder- induced damping of Bloch oscillations of Bose–Einstein condensates in optical lattices. The spatially inhomogeneous force responsible for the damping is realized by a combination of a disordered optical and a magnetic gradient potential. We show that the inhomogeneity of this force results in a broadening of the quasimomentum spectrum, which in turn causes damping of the centre-of-mass oscillation. We quantitatively compare the obtained damping rates to the simulations using the Gross–Pitaevskii equation. Our results are relevant for high precision experiments on very small forces, which require the observation of a large number of oscillation cycles.

Damping of bloch oscillations in quantum dot superlattices: A general approach

A quantum kinetic equation describing damping of the Bloch oscillations in ideal quantum-dot (QD) superlattices of various dimensionalities (1D, 2D, 3D) has been derived using the density matrix formalism. The possibility of suppressing completely single-phonon scattering by optical phonons and considerably suppressing the acoustic-phonon scattering in the QD superlattice by effectively controlling the spectrum by varying the DC electric field magnitude and orientation is demonstrated. Conditions ensuring that the only photon-scattering mechanism responsible for damping of the Bloch oscillations is scattering by acoustic phonons within transverse minibands of the Stark carrier-state ladder are obtained.

Damping of bloch oscillations in one-, two-, and three-dimensional quantum-dot superlattices

In the preceding paper by the same authors, the density-matrix formalism was used to derive a quantum kinetic equation describing the damping of Bloch oscillations (BOs) in perfect one-, two-, and three-dimensional quantum-dot superlattices (QDSLs) and the conditions were determined under which the only process of the charge-carrier scattering by phonons in 2D and 3D QDSLs that contributes to the BO damping is the acoustic-phonon scattering within the transverse minibands of the Stark ladder of the carrier states. In this paper, the possibilities of suppressing this remaining scattering channel are analyzed. It is shown that the BO damping time in 2D and 3D QDSLs at room temperature may exceed the oscillation period by a factor of several hundreds and the conditions necessary for such strong suppression of the scattering are revealed. This makes a considerable difference between the QDSLs and the quantum-well superlattices, where, in reality, the BOs damping over a single oscillation period at room temperature.

Damped Bloch oscillations of cold atoms in optical lattices

The paper studies Bloch oscillations of cold neutral atoms in the optical lattice. The effect of spontaneous emission on the dynamics of the system is analyzed both analytically and numerically. The spontaneous emission is shown to cause (i) the decay of Bloch oscillations with the decrement given by the rate of spontaneous emission and (ii) the diffusive spreading of the atoms with a diffusion coefficient depending on {\em both} the rate of spontaneous emission and the Bloch frequency.

Detection of THz radiation with semiconductor superlattices at polar-optic phonon frequencies

The nonlinear response of GaAs/AlAs superlattices to THz radiation has been analyzed over a wide frequency range (0.1 THz–15 THz), including the range of polar-optic phonon frequencies. Assuming that free electrons in a superlattice subjected to both a static and a THz field perform frequency-modulated damped Bloch oscillations, we have calculated a superlattice current responsivity, i.e., the ratio of the direct current change to the power of the incident radiation. The responsivity of superlattices has been measured in several recent experiments. An equivalent circuit taking into account the resonant properties associated with polar-optic phonons was used in a self-consistent treatment of the problem. It is shown that the responsivity is suppressed at frequencies of infrared-active, transverse polar-optic phonons due to dynamic screening of the THz field by the lattice. In contrast, the responsivity strongly increases at longitudinal polar-optic phonon frequencies due to a large enhancement of the THz field in the superlattice indicated by a longitudinal polar-optic phonon resonance, i.e., by an “anti- screening” effect. The described phenomenon can strongly influence the design and optimization of superlattice-based ultra-fast detectors for THz radiation.

Nonlinear transport in superlattices: Bloch oscillations and Zener breakdown

Semiconductor superlattices have been intensively used as a model system for the investigation of high field transport in solids. Here, we discuss ultrafast optical experiments which allow us to monitor the electron wave packet motion in detail. First, we discuss a novel technique which directly traces the center of mass spatial motion. We use this method for the detection of a linear motion of the wave packets, which is superimposed on the harmonic Bloch oscillations. A comparison with theory shows that this coherent analog to the Shapiro effect in superconductors is associated with gain at THz frequencies. In a second part, we discuss recent results which address the Zener breakdown due to tunneling to higher bands by linear spectroscopy, which directly shows the wave function delocalization. We also trace the dynamics of the Zener tunneling by time-resolved spectroscopy and show the damping of Bloch oscillations due to Zener tunneling.

Frequency doubling and tripling of terahertz radiation in a GaAs/AlAs superlattice due to frequency modulation of Bloch oscillations

We report on frequency doubling and tripling of THz radiation in a voltage-biased GaAs/AlAs superlattice. By use of a corner cube antenna system, radiation from the Santa Barbara free-electron laser (frequency 0.7 THz) was guided into a superlattice mesa element and the second and third harmonic were coupled out of the mesa. Without bias only radiation of the third harmonic was generated, while the biased superlattice emitted radiation of both the second and third harmonic. We attribute the harmonic generation to frequency modulation of damped Bloch oscillations of the miniband electrons in the superlattice.

Transient and steady-state analysis of electron transport in one-dimensional coupled quantum-box structures.

We investigate electron transport in one-dimensional coupled quantum-box (1D-CQB) structures at room temperature by using an iterative technique for solving the time-dependent Boltzmann equation. The scattering rates in the mini-Brillouin zone are characterized by several large peaks reflecting the singularities of the 1D density of states and the features of the miniband structure. As a result of Bragg reflection, the momentum distribution function deviates significantly from a displaced Maxwellian, with carrier accumulation at the miniband edges. Under the condition of suppression of optic-phonon scattering, the time evolution of the distribution function, and the electron velocity under high electric field undergo damped Bloch oscillations with a period of a few picoseconds. In the steady-state analysis, we found that the carrier mobility is a strong function of the structure confinement and periodicity parameters.