Coexistence of Bloch and Parametric Mechanisms of High-Frequency Gain in Doped Superlattices.

The detailed theoretical study of high-frequency signal gain, when a probe microwave signal is comparable to the AC pump electric field in a semiconductor superlattice, is presented. We identified conditions under which a doped superlattice biased by both DC and AC fields can generate or amplify high-frequency radiation composed of harmonics, half-harmonics, and fractional harmonics. Physical mechanisms behind the effects are discussed. It is revealed that in a general case, the amplification mechanism in superlattices is determined by the coexistence of both the phase-independent Bloch and phase-dependent parametric gain mechanisms. The interplay and contribution of these gain mechanisms can be adjusted by the sweeping AC pump strength and leveraging a proper phase between the pump and strong probe electric fields. Notably, a transition from the Bloch gain to the parametric gain, often naturally occurring as the amplitude of the amplified signal field grows, can facilitate an effective method of fractional harmonic generation in DC-AC-driven superlattices. The study also uncovers that the pure parametric generation of the fractional harmonics can be initiated via their ignition by switching the DC pump electric field. The findings open a promising avenue for the advancement of new miniature GHz-THz frequency generators, amplifiers, and dividers operating at room temperature.

Dissipative Parametric Gain in a GaAs/AlGaAs Superlattice.

Parametric generation of oscillations and waves is a paradigm, which is known to be realized in various physical systems. Unique properties of quantum semiconductor superlattices allow us to investigate high-frequency phenomena induced by the Bragg reflections and negative differential velocity of the miniband electrons. Effects of parametric gain in the superlattices at different strengths of dissipation have been earlier discussed in a number of theoretical works, but their experimental demonstrations are so far absent. Here, we report on the first observation of the dissipative parametric generation in a subcritically doped GaAs/AlGaAs superlattice subjected to a dc bias and a microwave pump. We argue that the dissipative parametric mechanism originates from a periodic variation of the negative differential velocity. It enforces excitation of slow electrostatic waves in the superlattice that provide a significant enhancement of the gain coefficient. This work paves the way for a development of a miniature solid-state parametric generator of GHz-THz frequencies operating at room temperature.

Stability properties of periodically driven overdamped pendula and their implications to physics of semiconductor superlattices and Josephson junctions.

We consider the first order differential equation with a sinusoidal nonlinearity and periodic time dependence, that is, the periodically driven overdamped pendulum. The problem is studied in the case that the explicit time dependence has symmetries common to pure ac-driven systems. The only bifurcation that exists in the system is a degenerate pitchfork bifurcation, which describes an exchange of stability between two symmetric nonlinear modes. Using a type of Prüfer transform to a pair of linear differential equations, we derive an approximate condition of the bifurcation. This approximation is in very good agreement with our numerical data. In particular, it works well in the limit of large drive amplitudes and low external frequencies. We demonstrate the usefulness of the theory applying it to the models of pure ac-driven semiconductor superlattices and Josephson junctions. We show how the knowledge of bifurcations in the overdamped pendulum model can be utilized to describe the effects of rectification and amplification of electric fields in these microstructures.

Model of the influence of an external magnetic field on the gain of terahertz radiation from semiconductor superlattices.

We theoretically analyze the influence of magnetic field on small-signal absorption and gain in a superlattice. We predict a very large and tunable THz gain due to nonlinear cyclotron oscillations in crossed electric and magnetic fields. In contrast to Bloch gain, here the superlattice is in an electrically stable state. We also find that THz Bloch gain can be significantly enhanced with a perpendicular magnetic field. If the magnetic field is tilted with respect to the superlattice axis, the usually unstable Bloch gain profile becomes stable in the vicinity of Stark-cyclotron resonances.

Terahertz Bloch oscillator with a modulated bias.

Electrons performing Bloch oscillations in an energy band of a dc-biased superlattice in the presence of weak dissipation can potentially generate THz fields at room temperature. The realization of such a Bloch oscillator is a long-standing problem due to the instability of a homogeneous electric field in conditions of negative differential conductivity. We establish the theoretical feasibility of stable THz gain in a long superlattice device in which the bias is quasistatically modulated by microwave fields. The modulation waveforms must have at least two harmonics in their spectra.

Theory of parametric amplification in superlattices.

We consider a high-frequency response of electrons in a single miniband of superlattice subject to dc and ac electric fields. We show that Bragg reflections in miniband result in a parametric resonance which is detectable using ac probe field. We establish theoretical feasibility of phase-sensitive THz amplification at the resonance. The parametric amplification does not require operation in conditions of negative differential conductance. This prevents a formation of destructive domains of high electric field inside the superlattice.

Symmetry breaking in a driven and strongly damped pendulum.

We examine the conditions for appearance of a symmetry breaking bifurcation in damped and periodically driven pendulums in the case of strong damping. We show that symmetry breaking, unlike other nonlinear phenomena, can exist at high dissipation. We prove that symmetry breaking phases exist between phases of symmetric normal and symmetric inverted oscillations. We find that symmetry broken solutions occupy a smaller region of the pendulum's parameter space in comparison to the statements made in earlier considerations [McDonald and Plischke, Phys. Rev. B 27, 201 (1983)]. Our research on symmetry breaking in a strongly damped pendulum is relevant to an understanding of the phenomena of dynamic symmetry breaking and rectification in pure ac driven semiconductor superlattices.