Controlling High-Frequency Collective Electron Dynamics via Single-Particle Complexity

Abstract

We demonstrate, through experiment and theory, enhanced high-frequency current oscillations due to magnetically-induced conduction resonances in superlattices. Strong increase in the ac power originates from complex single-electron dynamics, characterized by abrupt resonant transitions between unbound and localized trajectories, which trigger and shape propagating charge domains. Our data demonstrate that external fields can tune the collective behavior of quantum particles by imprinting configurable patterns in the single-particle classical phase space.PACS numbers: 05.45. Mt, 73.21.Cd Understanding the interplay between the properties of individual objects and their collective behavior is of fundamental interest in many fields [1][2][3][4]. It explains, for example, jamming and pattern formation in granular systems [1,[5][6][7], dynamical heterogeneity in phase transitions [3], tunneling dynamics and quantum phases in cold atoms [8,9], and the synchronization of networks and complex adaptive systems [2,10]. Moreover, interactions between particles play a key role in determining the structures formed when the particles come into contact [4]. Consequently, tailoring single-particle dynamics may provide a route to controlling the collective dynamics of many-body systems. This is a major challenge both in fundamental science [11][12][13] and for developing new technologies such as high-frequency electronic devices [14][15][16], whose performance can be greatly enhanced by applied quantizing magnetic fields [17,18].The phase space structure of individual particles, in particular the existence and relative location of regular and chaotic trajectories, critically affects thermalization and diffusion both in classical and quantum systems [19,20]. Therefore, manipulating the single-particle phase space, by generating new chaotic trajectories for example, is a promising strategy in the search for ways to control other collective phenomena.Usually, the transition to chaos in Hamiltonian systems occurs by the gradual destruction of stable orbits, in accordance with the Kolmogorov-Arnold-Moser (KAM) theorem [21]. In far rarer non-KAM chaos, the chaotic orbits become abruptly unbounded when the perturbation frequency attains critical values and map out intricate "stochastic webs" in phase space [19]. Experimental realization of non-KAM classical chaos was recently achieved using a quantum system [22]: a semiconductor superlattice (SL) with a magnetic field, B, tilted relative to an electric field, F, along the SL axis. When the frequency of single-electron Bloch oscillations along the SL axis is commensurate with that for cyclotron motion in the plane of the layers [14,22,23], the orbits map out stochastic webs in phase space, which delocalize the electrons in real space. This delocalization creates multiple resonant peaks in the single-electron drift velocity versus F characteristics, which enhance the measured dc conductivity [22].In this Letter, we show, via experiments and theoretical modeling, that non-KAM single-pa...

Lyapunov stability of charge transport in miniband semiconductor superlattices

“…which is used for evaluation of the Lyapunov exponents t : Equation (32) indicates that within the regimes outlined above, any perturbation is characterized by the same Lyapunov exponent. This means that all orthogonal perturbations of the steady state have the same growth rate (instability increment).…”

“…28 Therefore, until now Lyapunov stability of the charge transport in minband SLs has been limited by the estimation of the largest Lyapunov exponent from time series. 28 With this, recent experimental works [29][30][31][32] report on high-frequency mixing and highly nonlinear charge transport, which are apparently accompanied by complex spatially temporal dynamics of charge in miniband heavily doped SLs. Understanding of these dynamical regimes and instabilities associated with them in the appropriate models is important for further development and new design of the SL devices.…”

“…Thus, the models considered in this paper take into account application of various fields used in a range of experimental [29][30][31][32][33] and theoretical works. 6,34,35 We analytically and numerically show that when the electron transport in the SL is static, the method demonstrates good agreement with the nL criterion, conventionally used for the prediction of electric domain instability.…”

Effects of classical stochastic webs on the quantum dynamics of cold atomic gases in a moving optical lattice

“…Perturbing a simple harmonic oscillator by a plane wave whose frequency is commensurate with the oscillator frequency has been shown to rapidly excite the oscillator [17][18][19][20][21][22][23][24][25][26]. This resonant heating manifests itself experimentally in, for example, enhanced electron transport in semiconductor superlattices [20][21][22][23][24][25][26][27] and heating in Tokamak fusion reactors [17][18][19]28].…”

“…This resonant heating manifests itself experimentally in, for example, enhanced electron transport in semiconductor superlattices [20][21][22][23][24][25][26][27] and heating in Tokamak fusion reactors [17][18][19]28]. The excitation of the oscillator is due to the resonant creation of intricate phase-space structures known as "stochastic webs" [17][18][19][20][21][22][23][24][25][26]29], which enable the oscillator to diffuse through the web filaments away from the web center, thereby gaining energy and becoming delocalized in real space.…”