One-dimensional Periodic Potential Research Articles

Modulation of Magneto-Intersubband Oscillations in a One-Dimensional Lateral Superlattice

Low-temperature magnetotransport in a quasi-two-dimensional electron system based on a selectively doped GaAs quantum well with two occupied quantum-confinement subbands with one-dimensional periodic modulation of a potential is investigated. It is shown that commensurability oscillations of the resistance in this electron system coexist with magneto-intersubband oscillations. It is found that, in addition to commen-surability oscillations, the one-dimensional periodic potential in the two-subband electron system leads to the modulation of the magneto-intersubband oscillation amplitude. The experimental results are explained by the formation of Landau bands in the quasi-two-dimensional electron system with one-dimensional periodic modulation of the potential.

Quantum Rings Engineered by Atom Manipulation.

We created hexagonal rings on a semiconductor surface by atom manipulation in a scanning tunneling microscope (STM). Our measurements reveal the generic level structure of a quantum ring, including its single ground state and doubly degenerate excited states. The ring shape leads to a periodic potential modulation and thereby a perturbation of the level structure that can be understood in analogy to band gap formation in a one-dimensional periodic potential. The modulation can be enhanced or inverted by further adding or removing atoms with the STM tip. Our results demonstrate the possibility of designing and controlling electron dynamics in a tunable periodic potential, holding promise for the construction of two-dimensional artificial lattices on a semiconductor surface.

Coexistence of absolute negative mobility and anomalous diffusion

Using extensive numerical studies we demonstrate that absolute negative mobility of a Brownian particle (i.e. the net motion into the direction opposite to a constant biasing force acting around zero bias) does coexist with anomalous diffusion (AD). The latter is characterised in terms of a nonlinear scaling with time of the mean-square deviation of the particle position. Such AD covers ‘coherent’ motion (i.e. the position dynamics x(t) approaches in evolving time a constant dispersion), ballistic diffusion, subdiffusion, superdiffusion and hyperdiffusion. In providing evidence for this coexistence we consider a paradigmatic model of an inertial Brownian particle moving in a one-dimensional symmetric periodic potential being driven by both an unbiased time-periodic force and a constant bias. This very setup allows for various sorts of different physical realisations.

Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit

In this work we focus on fluctuations of time-integrated observables for a particle diffusing in a one-dimensional periodic potential in the weak-noise asymptotics. Our interest goes to rare trajectories presenting an atypical value of the observable, that we study through a biased dynamics in a large-deviation framework. We determine explicitly the effective probability-conserving dynamics which makes rare trajectories of the original dynamics become typical trajectories of the effective one. Our approach makes use of a weak-noise path-integral description in which the action is minimised by the rare trajectories of interest. For ‘current-type’ additive observables, we find criteria for the emergence of a propagative trajectory minimising the action for large enough deviations, revealing the existence of a dynamical phase transition at a fluctuating level, whose singular behaviour is between first and second order. In addition, we provide a new method to determine the scaled cumulant generating function of the observable without having to optimise the action. It allows one to show that the weak-noise and the large-time limits commute in this problem. Finally, we show how the biased dynamics can be mapped in practice to an explicit effective driven dynamics, which takes the form of a driven Langevin dynamics in an effective potential. The non-trivial shape of this effective potential is key to understand the link between the dynamical phase transition in the large deviations of current and the standard depinning transition of a particle in a tilted potential.

A study of periodic potentials based on quadratic splines

In this paper, we discuss a method based on a segmentary approximation of solutions of the Schrödinger equation by quadratic splines, for which the coefficients are determined by a variational method that does not require the resolution of complicated algebraic equations. The idea is the application of the method to one-dimensional periodic potentials. We include the determination of the eigenvalues up to a given level, and therefore an approximation to the lowest energy bands. We apply the method to concrete examples with interest in physics and discussed the numerical errors.

Dark gap solitons in exciton-polariton condensates in a periodic potential.

We show that dark spatial gap solitons can occur inside the band gap of an exciton-polariton condensate (EPC) in a one-dimensional periodic potential. The energy dispersions of an EPC loaded into a periodic potential show a band-gap structure. Using the effective-mass model of the complex Gross-Pitaevskii equation with pump and dissipation in an EPC in a periodic potential, dark gap solitons are demonstrated near the minimum energy points of the band center and band edge of the first and second bands, respectively. The excitation energies of dark gap solitons are below these minimum points and fall into the band gap. The spatial width of a dark gap soliton becomes smaller as the pump power is increased.

Experimental Observation of a Generalized Thouless Pump with a Single Spin.

Adiabatic cyclic modulation of a one-dimensional periodic potential will result in quantized charge transport, which is termed the Thouless pump. In contrast to the original Thouless pump restricted by the topology of the energy band, here we experimentally observe a generalized Thouless pump that can be extensively and continuously controlled. The extraordinary features of the new pump originate from interband coherence in nonequilibrium initial states, and this fact indicates that a quantum superposition of different eigenstates individually undergoing quantum adiabatic following can also be an important ingredient unavailable in classical physics. The quantum simulation of this generalized Thouless pump in a two-band insulator is achieved by applying delicate control fields to a single spin in diamond. The experimental results demonstrate all principal characteristics of the generalized Thouless pump. Because the pumping in our system is most pronounced around a band-touching point, this work also suggests an alternative means to detect quantum or topological phase transitions.

Phase diagrams for quantum Brownian motion on two-dimensional Bravais lattices

We study quantum Brownian motion (QBM) models for a particle in a dissipative environment coupled to a periodic potential. We review QBM for a particle in a one-dimensional periodic potential and extend the study to that for a particle in two-dimensional (2D) periodic potentials of four Bravais lattice types: square, rectangular, triangular (hexagonal), and centered rectangular. We perform perturbative renormalization group analyses to derive the zero temperature flow diagrams and phase boundaries for a particle in these potentials, and observe localization behavior dependent on the anisotropy of the lattice parameters.

Negative mobility of a Brownian particle: Strong damping regime

We study impact of inertia on directed transport of a Brownian particle under non-equilibrium conditions: the particle moves in a one-dimensional periodic and symmetric potential, is driven by both an unbiased time-periodic force and a constant force, and is coupled to a thermostat of temperature T. Within selected parameter regimes this system exhibits negative mobility, which means that the particle moves in the direction opposite to the direction of the constant force. It is known that in such a setup the inertial term is essential for the emergence of negative mobility and it cannot be detected in the limiting case of overdamped dynamics. We analyse inertial effects and show that negative mobility can be observed even in the strong damping regime. We determine the optimal dimensionless mass for the presence of negative mobility and reveal three mechanisms standing behind this anomaly: deterministic chaotic, thermal noise induced and deterministic non-chaotic. The last origin has never been reported. It may provide guidance to the possibility of observation of negative mobility for strongly damped dynamics which is of fundamental importance from the point of view of biological systems, all of which in situ operate in fluctuating environments.

Collective transport of Lennard–Jones particles through one-dimensional periodic potentials**Project supported by the Natural Science Foundation of Guangdong Province, China (Grant No. 2014A030313367) and the Fundamental Research Fund for the Central Universities, China (Grant No. 11614341).

The surrounding media in which transport occurs contains various kinds of fields, such as particle potentials and external potentials. One of the important questions is how elements work and how position and momentum are redistributed in the diffusion under these conditions. For enriching Fick’s law, ordinary non-equilibrium statistical physics can be used to understand the complex process. This study attempts to discuss particle transport in the one-dimensional channel under external potential fields. Two kinds of potentials—the potential well and barrier—which do not change the potential in total, are built during the diffusion process. There are quite distinct phenomena because of the different one-dimensional periodic potentials. By the combination of a Monte Carlo method and molecular dynamics, we meticulously explore why an external potential field impacts transport by the subsection and statistical method. Besides, one piece of evidence of the Maxwell velocity distribution is confirmed under the assumption of local equilibrium. The simple model is based on the key concept that relates the flux to sectional statistics of position and momentum and could be referenced in similar transport problems.

Information and Self-Organization

The process of “self-organization” takes place in open and complex systems that acquire spatio-temporal or functional structures without specific ordering instructions from the outside. [...]

Modal characterization of nanophotonic waveguides for atom trapping

Nanophotonic waveguides are a promising platform to trap cold atoms using red-and blue-detuned evanescent-field optical dipole forces. The asymmetric structure of integrated waveguides leads to a large birefringence that is not encountered in cylindrically symmetric optical nanofibers. We have studied both theoretically and experimentally the modal properties and suitability of silicon nitride rib waveguides for cold-atom trapping. The dependence of the modal effective index on the rib width is explored experimentally by measuring beat lengths between propagating modes. These measurements are made using a novel spatial Fourier analysis technique based on conventional far-field imaging of elastic scattering from the waveguide. We find that the beat length between the lowest order TE00 and TM00 modes is approximately 5µm, in excellent agreement with numerical calculations. We propose to take advantage of this birefringence and mode structure to create novel, one-dimensional periodic trapping potentials for atoms within the evanescent field of the waveguide.

Nonlinear Dynamics of Exciton-Polariton Condensates in a One-Dimensional Lattice

We consider the problem of exciton-polariton-condensate formation in a semiconductor microcavity in the strong coupling regime. The condensate is confined in a one-dimensional periodic potential and coupled to an exciton reservoir that is formed by the external cw pumping. The condensate dynamics is studied in the center and in the edges of the Brillouin zone (BZ). Modeling the formation of the condensate from weak initial noise shows that besides steady states the macroscopic oscillations of polariton density can also occur. Within the framework of the mean field approach, we obtain important analytic relations for the condensate eigenstates using the developed simplified model for three coupled spatial harmonics. A numerical analysis verifies the correctness of the analytic results.

Nonlinear dynamics of nonequilibrium exciton-polaritons in a periodic potential

An exciton-polariton condensate formed in a semiconductor microcavity coupled to an exciton reservoir in the strong coupling regime is studied. The condensate is trapped in onedimensional periodic potential, and we work in the centre of Brillouin zone. We develop a model for coupled three spatial harmonics of mean field. Using the simplified model we get important analytical relations for polaritonic eigenstates and band-structure. The analytical results are supported by numerical analysis. The strong influence of external potential and nonlinearity is discussed and the feedback induced by the inhomogeneity of the incoherent reservoir on the dynamics of coherent polaritons.

Zero differential resistance of a two-dimensional electron gas in a one-dimensional periodic potential at high filling factors

The nonlinear magnetotransport of a two-dimensional (2D) electron gas in one-dimensional lateral superlattices based on a selectively doped GaAs/AlAs heterostructure is studied. The one-dimensional potential modulation of the 2D electron gas is performed by means of a series of metallic strips formed on the surface of a heterostructure with the use of electron beam lithography and a lift-off process. The dependence of the differential resistance r xx on the magnetic field B < 1.5T in superlattices with the period a = 400 nm at a temperature of T = 4.2 K is investigated. It is found that electronic states with r xx ≈ 0 appear in one-dimensional lateral superlattices in crossed electric and magnetic fields. It is shown that states with r xx ≈ 0 in 2D electronic systems with one-dimensional periodic modulation arise at the minima of commensurability oscillations of the magnetoresistance.

Indirect interband transition induced by optical near fields with large wave numbers

Optical near fields (ONFs) have Fourier components with large wave numbers that are two or three orders of magnitude larger than those of far-field propagating light owing to their nonuniformity in space. By utilizing these large wave numbers, the ONF is expected to induce an indirect interband transition between Bloch states having different wave numbers and directly generate an electron-hole pair without electron-phonon coupling. We perform time-dependent dynamics calculations of a one-dimensional periodic potential with an indirect band-gap structure and demonstrate that the ONF definitely induces an indirect interband transition. Instead of using the general Bloch boundary condition, which is usually imposed in conventional band structure calculations, we adopt an alternative boundary condition, the Born--von K\'arm\'an boundary condition, to appropriately treat indirect interband transitions. The calculated absorption spectra for the far-field and ONF excitations show different absorption edges and spectral patterns. We argue that this difference can be experimentally measured as evidence of the effects of the large wave numbers of the ONF.

Collective state transitions of exciton-polaritons loaded into a periodic potential

We study the loading of a nonequilibrium, dissipative system of composite bosons---exciton polaritons---into a one-dimensional periodic lattice potential. Utilizing momentum resolved photoluminescence spectroscopy, we observe a transition between an incoherent Bose gas and a polariton condensate, which undergoes further transitions between different energy states in the band-gap spectrum of the periodic potential with increasing pumping power. We demonstrate controlled loading into distinct energy bands by modifying the size and shape of the excitation beam. The observed effects are comprehensively described in the framework of a nonequilibrium model of polariton condensation. In particular, we implement a stochastic treatment of quantum and thermal fluctuations in the system and conclude that polariton-phonon scattering is a plausible energy relaxation mechanism enabling transitions from the highly nonequilibrium polariton condensate in the gap to the ground band condensation for large pump powers.

The electronic structure and intervalley coupling of artificial and genuine graphene superlattices

A so-called artificial graphene is an artificial material whose low-energy carriers are described by the massless Dirac equation. Applying a periodic potential with triangular symmetry to a two-dimensional electron gas is one way to make such a material. According to recent experimental results, it is now possible to realize an artificial graphene in the lab and to even apply an additional lateral, one-dimensional periodic potential to it. We name the latter system an artificial graphene superlattice in order to distinguish it from a genuine graphene superlattice made from graphene. In this study, we investigate the electronic structure of artificial graphene superlattices, which exhibit the emergence of energy band gaps, merging and splitting of the Dirac points, etc. Then, from a similar investigation on genuine graphene superlattices, we show that many of these features originate from the coupling between Dirac fermions residing in two different valleys, the intervalley coupling. Furthermore, contrary to previous studies, we find that the effects of intervalley coupling on the electronic structure cannot be ignored no matter how long the spatial period of the superlattice is.

Topological Thouless pumping of ultracold fermions

A gas of electrons in a one-dimensional periodic potential can be transported even in the absence of a voltage bias if the potential is modulated slowly and periodically in time. Remarkably, the transferred charge per cycle is only sensitive to the topology of the path in parameter space. Although this so-called Thouless charge pump has first been proposed more than thirty years ago, it has not yet been realized. Here we report the first demonstration of topological Thouless pumping using ultracold atoms in a dynamically controlled optical superlattice. We observe a shift of the atomic cloud as a result of pumping and extract the topological invariance of the pumping process from this shift. We demonstrate the topological nature of the Thouless pump by varying the topology of the pumping path and verify that the topological pump indeed works in the quantum region by varying speed and temperature.

Observation of sub-GeV electrons mirrored by ultrathin crystalline Si

Detailed experimental studies are performed on the mirroring effect for 255-MeV electrons channeled through a 0.74-μm-thick Si crystal at the injector linac of the SAGA-LS facility. For the planar channeling alignment, deflection of the beam by 0.45 mrad is observed with 29% efficiency. The effect is explained by computer simulations as a sequence of trajectories of planar-channeled relativistic electrons in an attractive one-dimensional periodic potential of crystallographic planes. Possible applications as a beam splitter are proposed.