arXiv subjects
Publications and source records attributed to Kirill N. Alekseev.
We examine a spatial evolution of lightwaves in a nonlinear photonic crystal with a quadratic nonlinearity when simultaneously a second harmonic and a sum-frequency generation are quasi-phase-matched. We find the conditions of a transition to Hamiltonian chaos for different amplitudes of lightwaves at the boundary of the crystal.
We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of quantum kicked rotator. This main model of quantum chaos, which allows for a transition from regular to to chaotic behavior in the classical limit, may be realized in experiments with cold atoms. We study the generation of squeezed states in the quasiclassical limit and in a time interval when quantum-classical correspondence is yet well-defined. We find that the degree of squeezing depends on the degree of local instability in the system and increases with the Chirikov parameter of stochasticity. We discuss the dependence of the degree of squeezing on the initial width of the packet, the problems of stability and observability of squeezed states at the transition to quantum chaos, as well as the dynamics of wave packet destruction.
We study the motion of electrons in a single miniband of a semiconductor superlattice driven by THz electric field polarized along the growth direction. We work in the semiclassical balance-equation model, including different elastic and inelastic scattering rates, and incorporating the self-consistent electric field generated by electron motion. We explore regions of complex dynamics, which can include chaotic behaviour and symmetry-breaking. We estimate the magnitudes of dc current and dc voltage that spontaneously appear in regions of broken-symmetry for parameters characteristic of modern semiconductor superlattices. This work complements PRL 80(1998)2669 [ cond-mat/9709026 ].
We discuss an effect of dc current and dc voltage (stopping bias) generation in a semiconductor superlattice subjected by an ac electric field and its phase-shifted n-th harmonic. In the low field limit, we find a simple dependence of dc voltage on a strength, frequency, and relative phase of mixing harmonics for an arbitrary even value of n. We show that the generated dc voltage has a maximum when a frequency of ac field is of the order of a scattering constant of electrons in a superlattice. This means that for typical semiconductor superlattices at room temperature operating in the THz frequency domain the effect is really observable. We also made a comparison of a recent paper describing an effect of a directed current generation in a semiconductor superlattice subjected by ac field and its second harmonic (n=2) [K.Seeger, Appl.Phys.Lett. 76(2000)82] with our earlier findings describing the same effect [K.Alekseev et al., Europhys. Lett. 47(1999)595; cond-mat/9903092 ]. For the mixing of an ac field and its n-th harmonic with n>=4, we found that additionally to the phase-shift controlling of the dc current, there is a frequency control. This frequency controlling of the dc current direction is absent in the case of n=2. The found effect is that, both the dc current suppression and the dc current reversals exist for some particular values of ac field frequency. For typical semiconductor superlattices such an interesting behavior of the dc current should be observable also in the THz domain. Finally, we briefly review the history of the problem of the dc current generation at mixing of harmonics in semiconductors and semiconductor microstructures.
We develop a method for the determination of thecdynamics of dissipative quantum systems in the limit of large number of quanta N, based on the 1/N-expansion of Heidmann et al. [ Opt. Commun. 54, 189 (1985) ] and the quantum-classical correspondence. Using this method, we find analytically the dynamics of nonclassical states generation in the higher-order anharmonic dissipative oscillators for an arbitrary temperature of a reservoir. We show that the quantum correction to the classical motion increases with time quadratically up to some maximal value, which is dependent on the degree of nonlinearity and a damping constant, and then it decreases. Similarities and differences with the corresponding behavior of the quantum corrections to the classical motion in the Hamiltonian chaotic systems are discussed. We also compare our results obtained for some limiting cases with the results obtained by using other semiclassical tools and discuss the conditions for validity of our approach.
Paper is withdrawn
We develop a semiclassical method for the determination of the nonlinear dynamics of dissipative quantum optical systems in the limit of large number of photons N, based on the 1/N-expansion and the quantum-classical correspondence. The method has been used to tackle two problems: to study the dynamics of nonclassical state generation in higher-order anharmonic dissipative oscillators and to establish the difference between the quantum and classical dynamics of the second-harmonic generation in a self-pulsing regime. In addressing the first problem, we have obtained an explicit time dependence of the squeezing and the Fano factor for an arbitrary degree of anharmonism in the short-time approximation. For the second problem, we have established analytically a characteristic time scale when the quantum dynamics differs insignificantly from the classical one.
We study electron transport through a semiconductor superlattice subject to an electric field parallel to and a magnetic field perpendicular to the growth axis. Using a single miniband, semiclassical balance equation model with both elastic and inelastic scattering, we find that (1) the current-voltage characteristic becomes multistable in a large magnetic field; and (2) ``hot'' electrons display novel features in their current-voltage characteristics, including absolute negative conductivity (ANC) and, for sufficiently strong magnetic fields, a spontaneous dc current at zero bias. We discuss possible experimental situations providing the necessary hot electrons to observe the predicted ANC and spontaneous dc current generation.
We describe a novel effect of the generation of direct current which may arise in semiconductors or semiconductor microstructures due to a mixing of coherent electromagnetic radiations of commensurate frequencies. The effect is, in essence, due to a nonparabolicity of the electron energy bands and is stronger in systems where this nonparabolicity is greater. We have made exact calculations in the framework of the Kane model, applicable to narrow gap semiconductors and the tight-binding model which we employ for a description of a semiconductor superlattice.
We investigate theoretically the dynamics of squeezed state generation in nonlinear systems possessing a transition from regular to chaotic dynamics in the limit of a large number of photons. As an example, the model of a kicked Kerr oscillator is considered. We show that at the transition to quantum chaos the maximum possible degree of squeezing increases exponentially in time, in contrast to the regular dynamics, where the degree of squeezing increases in time only power-wise. We demonstrate the one-to-one correspondence of the degree of squeezing and the value of the local Lyapunov instability rate in corresponding classical chaotic system.
The squeezing in a nonlinear system with chaotic dynamics is considered. The model describing interaction of collection of two-level atoms with a single-mode of self-consistent field and an external field is analyzed. It is shown that in the semiclassical limit, in contrast to the regular behaviour, the chaotic dynamics result in: (i) an increase in squeezing, (ii) unstable squeezing and contraction of time intervals of squeezing on large enough times. The possibility of the experimental observation of the described effects is discussed.
We investigate theoretically the dynamics of squeezed state generation in the nonlinear systems possessing the transition from regular to chaotic dynamics in the limit of a large number of photons. As an example, the model of kicked Kerr oscillator is considered. We show the direct correlation of the degree of squeezing and the value of local Lyapunov instability rate in corresponding classical chaotic system.
We consider the chaotic dynamics of the interaction between an ensemble of two-level atoms in a high-Q Fabry-Perot cavity with a single mode of self-consistent field and with an external amplitude-modulated field. It is shown that in the case of an exact atom-field resonance and at the initial population of the atomic ground state, the Hamiltonian chaos in the system is always transient. The differences in the chaotic dynamics for the Fabry-Perot and ring cavity geometries are considered. The conditions for the experimental observation of the transient Hamiltonian chaos are discussed.
We consider the motion of ballistic electrons within a superlattice miniband under the influence of an alternating electric field. We show that the interaction of electrons with the self-consistent electromagnetic field generated by the electron current may lead to the transition from regular to chaotic dynamics. We estimate the conditions for the experimental observation of this deterministic chaos and discuss the similarities of the superlattice system with the other condensed matter and quantum optical systems.
We study a resistively shunted semiconductor superlattice subject to a high-frequency electric field. Using a balance equation approach that incorporates the influence of the electric circuit, we determine numerically a range of amplitude and frequency of the ac field for which a dc bias and current are generated spontaneously and show that this region is likely accessible to current experiments. Our simulations reveal that the Bloch frequency corresponding to the spontaneous dc bias is approximately an integer multiple of the ac field frequency.
We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field. We use the semi-classical balance-equation approach which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free electron lasers, chaos may be observable in SSLs. We clarify the nature of this novel nonlinear dynamics in the superlattice-external field system by exploring analogies to the Dicke model of an ensemble of two-level atoms coupled with a resonant cavity field and to Josephson junctions.