We report new oscillations of wavepackets in quantum walks subjected to electric fields, that decorate the usual Bloch-Zener oscillations of insulators. The number of turning points (or sub-oscillations) within one Bloch period of these oscillations is found to be governed by the winding of the quasienergy spectrum. Thus, this provides a new physical manifestation of a topological property of periodically driven systems that can be probed experimentally. Our model, based on an oriented scattering network, is readily implementable in photonic and cold atomic setups.
Bloch oscillations are exotic phenomena describing the periodic motion of a wave packet subjected to the external force in a lattice, where the system possessing single- or multipleparticles could exhibit distinct oscillation behaviors. In particular, it has been pointed out that quantum statistics could dramatically affected the Bloch oscillation even in the absence of particle interactions, where the oscillation frequency of two pseudofermions with the anyonic statistical angle being pi becomes half of that for two bosons. However, these statisticdependent Bloch oscillations have never been …
We have developed a formalism suitable for calculation of the output spectrum of a detector continuously measuring quantum coherent oscillations in a solid-state qubit, starting from microscopic Bloch equations. The results coincide with that obtained using Bayesian and master equation approaches. The previous results are generalized to the cases of arbitrary detector response and finite detector temperature.
We study the coherent dynamics of a qubit excited by an amplitude-modulated electromagnetic field under the Rabi resonance when the frequency of the low-frequency modulation field matches the Rabi frequency in the high-frequency field. Due to destructive interference of multiple photon processes at the ultrastrong coupling between the qubit and the low-frequency driving field, Rabi oscillations result exclusively from the Bloch-Siegert effect. It is directly observed in the time-resolved coherent dynamics as the Bloch-Siegert oscillation. In this case, triplets in Fourier spectra of the cohere…
We consider dynamics of a charged particle in a finite along the $x$ direction square lattice in the presence of normal to the lattice plane magnetic field and in-plane electric field aligned with the $y$ axis. For vanishing magnetic field this dynamics would be common Bloch oscillations where the particle oscillates in the $y$ direction with amplitude inverse proportional to the electric field. We show that a non-zero magnetic field crucially modifies this dynamics. Namely, the new Bloch oscillations consist of time intervals where the particle moves with constant velocity in the $x$ directio…
The possibility of Bloch oscillations for a degenerate and superfluid Fermi gas of atoms in an optical lattice is considered. For a one-component degenerate gas the oscillations are suppressed for high temperatures and band fillings. For a two-component gas the Landau criterion is used for specifying the regime where Bloch oscillations of the superfluid may be observed. We show how the amplitude of Bloch oscillations varies along the BCS-BEC crossover.
We investigate optical Bloch oscillation, Zener tunneling and breathing modes in arrays of optical waveguides. We perform a new method of calculation based on the multiple scattering formalism. To demonstrate Bloch oscillation and breathing modes, we consider a planar array of parallel cylindrical waveguides with the refractive index gradually varying across the array. We demonstrate that the form of Bloch oscillation may be predicted by means of dispersion law analysis. To demonstrate Zener tunneling, we consider a planar array of cylindrical waveguides of two types situated by turn. The band…
In a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that convective nonlinearities may compensate it and Bloch oscillations persist even in the hydrodynamic regime. In this case, numerical solutions show that there are stable Bloch oscillations confined to a region near the collector with inhomogeneous field, charge, current density and energy density profiles. These Bloch oscillations disappear when damping due to inelastic collisions becomes sufficiently strong.
Electrons in periodic potentials exhibit oscillatory motion in presence of an electric field. Such oscillations are known as Bloch oscillations. In this article we theoretically investigate the emergence of Bloch oscillations for systems where the electric field is confined to a finite region, like in typical electronic devices. We use a one-dimensional tight-binding model within the single-band approximation to numerically study the dynamics of electrons after a sudden switching-on of the electric field. We find a transition from a regime with direct current to Bloch oscillations when increas…
We show that superlattices based on zero-gap semiconductors such as graphene and mercury telluride exhibit characteristic Bloch--Zener oscillations that emerge from the coherent superposition of Bloch oscillations and multiple Zener tunneling between the electron and hole branch. We demonstrate this mechanism by means of wave packet dynamics in various spatially periodically modulated nanoribbons subject to an external bias field. The associated Bloch frequencies exhibit a peculiar periodic bias dependence which we explain within a two-band model. Supported by extensive numerical transport cal…
We investigate the dephasing dynamics of Bloch oscillations in semiconductor superlattices by means of a very simple model including disorder and applied electric fields. A thorough numerical study of our model allows us to claim that small, unintentional well width fluctuations can be responsible for fast dephasing of Bloch oscillations at low temperatures. We show that the lifetime of Bloch oscillations is controlled by a characteristic time which depends on the degree of disorder and is independent of the electric field. This result is further supported by the excellent agreement between ou…
We investigate the electronic Bloch oscillation in bilayer graphene gradient superlattices using transfer matrix method. By introducing two kinds of gradient potentials of square barriers along electrons propagation direction, we find that Bloch oscillations up to terahertz can occur. Wannier-Stark ladders, as the counterpart of Bloch oscillation, are obtained as a series of equidistant transmission peaks, and the localization of the electronic wave function is also signature of Bloch oscillation. Forthermore, the period of Bloch oscillation decreases linearly with increasing gradient of barri…
In a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that nonlinearities may compensate it and Bloch oscillations persist even in the hydrodynamic regime. To demonstrate this, a Boltzmann-Poisson transport model of miniband superlattices with inelastic collisions is proposed and hydrodynamic equations for electron density, electric field and the complex amplitude of the Bloch oscillations are derived by singular perturbation methods. For appropriate parameter ranges, numerical solutions of these equations show stable Bloch osci…
We identify a mapping between two-dimensional (2D) electron transport in a minimally twisted graphene bilayer and a 1D quantum walk, where one spatial dimension plays the role of time. In this mapping a magnetic field B perpendicular to the bilayer maps onto an electric field. Bloch oscillations due to the periodic motion in a 1D Bloch band can then be observed in purely DC transport as magnetoconductance oscillations with periodicity set by the Bloch frequency.
This work provides a convenient and powerful means towards the engineering of Floquet bands via Bloch oscillations, by adding a tilted linear potential to periodically driven lattice systems. The added linear field not only restricts the spreading of a time-evolving wavepacket but also, depending on the ratio between the Bloch oscillation frequency and the modulation frequency of the periodic driving, dramatically modifies the band profile and topology. Specifically, we consider a driven Aubry-André-Harper model as a working example, in the presence of a linear field. Almost flat Floquet bands…
We report the numerical and experimental study of elastic Wannier-Stark Ladders and Bloch Oscillations in a tunable one-dimensional granular chain consisting of cylindrical particles. The Wannier-Stark Ladders are obtained by tuning the contact angles to introduce a gradient in the contact stiffness along the granular chain. These ladders manifest as resonant modes localized in the space. When excited at the corresponding resonant frequencies, we demonstrate the existence of time-resolved Bloch Oscillations. The direct velocity measurements using Laser Doppler Vibrometry agree well with the nu…
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 fr…
We propose to measure band topology via quantized drift of Bloch oscillations in a two-dimensional Harper-Hofstadter lattice subjected to tilted fields in both directions. When the difference between the two tilted fields is large, Bloch oscillations uniformly sample all momenta, and hence the displacement in each direction tends to be quantized at multiples of the overall period, regardless of any momentum of initial state. The quantized displacement is related to a reduced Chern number defined as a line integral of Berry curvature in each direction, providing an almost perfect measurement of…
The multiple scattering formalism is proposed describing the guided modes in the optical waveguide array within the framework of macroscopic electrodynamics. It is shown that, under sufficiently general assumptions, our approach justifies the phenomenological model used widely to treat various physical phenomena in the optical micro- and nano-structures. It is found that the theory developed in this paper describes the real experiments in which the the Bloch oscillations are observed. Surprisingly, not only qualitative but also reasonably quantitative agreement is found.
We study a nonadiabatic effect on the conductances in the quantum Hall effect of two-dimensional electrons with a periodic potential. We found that the Hall and longitudinal conductances oscillate in time with a very large frequencies due to quantum fluctuation.
We study the quantum dynamics of soliton-like domain walls in anisotropic spin-1/2 chains in the presence of magnetic fields. In the absence of fields, domain walls form a Bloch band of delocalized quantum states while a static field applied along the easy axis localizes them into Wannier wave packets and causes them to execute Bloch oscillations, i.e. the domain walls oscillate along the chain with a finite Bloch frequency and amplitude. In the presence of the field, the Bloch band, with a continuum of extended states, breaks up into the Wannier-Zeeman ladder -- a discrete set of equally spac…
The Bloch-oscillating transistor (BOT) is an amplifier that utilizes semiclassical dynamics of states in energy bands under traveling quasimomentum. In a BOT, a single quasiparticle tunneling across a base tunnel junction switches the state of a superconducting tunnel junction to a lower Bloch band, triggering a series of resonant Cooper-pair tunnelings through an emitter Josephson junction (Bloch oscillations). Here, we investigate experimentally and theoretically an alternative realization of this device, based only on superconducting tunnel junctions. We discover new amplification schemes, …
We study the effect of charge discreteness in a quantum mesoscopic ring wih inductance L. The ring is pierced by a time depending external magnetic field. When the external magnetic flux varies uniformly, the current induced in the ring oscillates with a frequency proportional to the charge discreteness and the flux variation. This phenomenon is very similar to the well known Bloch's oscillation in crystals. The similitude is related to the charge discreteness in the charge-current representation, which plays the same role as the constant lattice in crystals.
We consider the quantum Hall effect of two-dimensional electrons with a periodic potential and study the time dependence of the Hall and longitudinal currents when the electric field is applied abruptly. We find that the currents oscillate in time with very large frequencies because of quantum fluctuation and the oscillations eventually vanish, for their amplitudes decay as 1/t.
Sinusoidal Bloch oscillations appear in band structures exposed to external fields. Landau-Zener (LZ) tunneling between different bands is usually a counteracting effect limiting Bloch oscillations. Here we consider a flat band network with two dispersive and one flat bands, e.g. for ultracold atoms and optical waveguide networks. Using external synthetic gauge and gravitational fields we obtain a perturbed yet gapless band structure with almost flat parts. The resulting Bloch oscillations consist of two parts - a fast scan through the nonflat part of the dispersion structure, and an almost co…
Subjecting a nanohelix to a transverse electric field gives rise to superlattice behavior with tunable electronic properties. We theoretically investigate such a system and find Bloch oscillations and negative differential conductance when a longitudinal electric field (along the nanohelix axis) is also applied. Furthermore, we study dipole transitions across the transverse-electric-field-induced energy gap, which can be tuned to the eulogized terahertz frequency range by experimentally attainable external fields. We also reveal a photogalvanic effect by shining circularly polarized light onto…
Bloch oscillations predicted to occur in current-biased single Josephson junctions have eluded direct observation up to now. Here, we demonstrate similar Bloch oscillations in a slightly richer Josephson circuit, the quantronium. The quantronium is a Bloch transistor with two small junctions in series, defining an island, in parallel with a larger junction. In the ground state, the microwave impedance of the device is modulated periodically with the charge on the gate capacitor coupled to the transistor island. When a current flows across this capacitor, the impedance modulation occurs at the …
In a pristine monolayer graphene subjected to a constant electric field along the layer, the Bloch oscillation of an electron is studied in a simple and efficient way. By using the electronic dispersion relation, the formula of a semi-classical velocity is derived analytically, and then many aspects of Bloch oscillation, such as its frequency, amplitude, as well as the direction of the oscillation, are investigated. It is interesting to find that the electric field affects the component of motion, which is non-collinear with electric field, and leads the particle to be accelerated or oscillate…
The anharmonic Bloch oscillations of a light beam in the array of optical waveguides are considered. The coupling modes model (CMM) with the second order interaction is used to describe the effect analytically. The formula obtained predicts explicitly the path of the optical beam, in particular, the positions of the turning points are found. A total agreement of this formula with the numerical simulation is confirmed.
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 equati…
Bloch oscillations are a powerful tool to investigate spectra with Dirac points. By varying band parameters, Dirac points can be manipulated and merged at a topological transition towards a gapped phase. Under a constant force, a Fermi sea initially in the lower band performs Bloch oscillations and may Zener tunnel to the upper band mostly at the location of the Dirac points. The tunneling probability is computed from the low energy universal Hamiltonian describing the vicinity of the merging. The agreement with a recent experiment on cold atoms in an optical lattice is very good.
The Lieb Lattice exhibits intriguing properties that are of general interest in both the fundamental physics and practical applications. Here, we investigate the topological Landau-Zener Bloch oscillation in a photonic Floquet Lieb lattice, where the dimerized helical waveguides is constructed to realize the synthetic spin-orbital interaction through the Floquet mechanism, rendering us to study the impacts of topological transition from trivial gaps to non-trivial ones. The compact localized states of flat bands supported by the local symmetry of Lieb lattice will be associated with other band…
We consider a Bose-Einstein condensate of ultracold atoms loaded into a square optical lattice and subject to a static force. For vanishing atom-atom interactions the atoms perform periodic Bloch oscillations for arbitrary direction of the force. We study the stability of these oscillations for non-vanishing interactions, which is shown to depend on an alignment of the force vector with respect to the lattice crystallographic axes. If the force is aligned along any of the axes, the mean field approach can be used to identify the stability conditions. On the contrary, for a misaligned force one…
In two recent Letters [Phys. Rev. Lett. 90, 046806; Phys. Rev. Lett. 94, 057408], Hirakawa et al. investigate the emission of coherent terahertz (THz) radiation from optically excited superlattices. The authors interpret the spectra of the THz transients in terms of a semiclassical transport model and conclude that the data provide evidence for the existence of the so-called Bloch gain. We show that the interpretation of the data in terms of a conductivity is, however, not performed correctly, thus making the conclusions of cited authors void.
Under a perfect periodic potential, the electric current density induced by a constant electric field may exhibit nontrivial oscillations, so-called Bloch oscillations, with an amplitude that remains nonzero in the large system size limit. Such oscillations have been well studied for nearly noninteracting particles and observed in experiments. In this work, we revisit Bloch oscillations in strongly interacting systems. By analyzing the spin-1/2 XXZ chain, which can be mapped to a model of spinless electrons, we demonstrate that the current density at special values of the anisotropy parameter …
We develop an artificial neural network (ANN) approach to classify simulated signals corrsponding to the semi-classical description of Bloch oscillations in pristine graphene. After the ANN is properly trained, we consider the inverse problem of Bloch oscillations (BO),namely, a new signal is classified according to the external electric field strength oriented along either the zig-zag or arm-chair edges of the graphene membrane, with a correct classification that ranges from 82.6% to 99.3% depending on the accuracy of the predicted electric field. This approach can be improved depending on th…
The paper presents results of numerical experiments simulating Bloch oscillations of solitons in a deformable molecular chain in a constant electric field. By the example of a homogeneous polynucleotide chain it is shown that the system under consideration can demonstrate complicated dynamical regimes when at the field intensities less than a certain critical value, a soliton as a whole exhibits oscillations, while at the field intensities exceeding the threshold, a soliton turns to a breather which oscillates. It is shown that the motion of a charge in a deformable chain is infinite as contra…
Bloch oscillations in nanoscale Josephson junctions with a Coulomb charging energy comparable to the Josephson coupling energy are explored within the context of a model previously considered by Geigenmüller and Schön that includes Zener tunneling and treats quasiparticle tunneling as an explicit shot-noise process. The dynamics of the junction quasicharge are investigated numerically using both Monte Carlo and ensemble approaches to calculate voltage--current characteristics in the presence of microwaves. We examine in detail the origin of harmonic and subharmonic Bloch steps at dc biases $I=…
The dynamics in a nonlinear Schrodinger chain in an homogeneous electric field is studied. We show that discrete translational invariant integrability-breaking terms can freeze the Bloch nonlinear oscillations and introduce new faster frequencies in their dynamics. These phenomena are studied by direct numerical integration and through an adiabatic approximation. The adiabatic approximation allows a description in terms of an effective potential that greatly clarifies the phenomenon.
The Bloch oscillations in the zigzag array of the optical waveguides are considered. The multiple scattering formalism (MSF) is used for the numerical simulation of the optical beam which propagates within the array. The effect of the second-order coupling which depends on the geometrical parameters of the array is investigated. The results obtained within the MSF are compared with the calculation based on the phenomenological coupling modes model. The calculations are performed for the waveguides fabricated in alkaline earth boro-aluminosilicate glass sample, which are the most promising for …
