Quasienergy Spectrum Research Articles

Quasienergy functions of electrons in a semiconductor affected by an external electromagnetic field

This paper is devoted to the study of the quasienergy spectrum and quasienergy functions of electrons in a semiconductor under the effect of a strong electromagnetic field whose frequency coincides with the forbidden band width. The case of a standing electromagnetic wave is analyzed. It is shown that in a standing wave the structure of the quasienergy spectrum is similar to that for quantum nonlinear resonance. An estimate of the frequency of electron nutation between valence and conduction bands is given.

Ac Stark effect and trapping of population on Rydberg levels in a strong ionizing field

Ac Stark splitting and ionization broadening of atomic Rydberg levels in a strong electromagnetic field are described. The quasi-energy atomic spectrum is shown to consist of a quasi-continuum plus two sets of narrow quasi-energy levels: weakly split and broadened almost field-free levels and strongly perturbed levels, whose width is a decreasing function of the field strength amplitude. The strong-field asymptotics of the photoelectron spectrum and of the time-dependent total photoionization probability are described. The photoelectron spectrum is shown to have a multipeak structure, and the shape of each peak is shown to be different from the Lorenz shape found earlier. This effect is explained by the contribution of the quasi-continuous quasi-energy spectrum. The same reason explains a partially nonexponential time dependence of the total photoionization probability.

Interference suppression of photoionization of Rydberg atoms in a strong electromagnetic field

Photoionization of highly excited atoms by a strong microwave field is considered. Secondary coherent population of some neighboring Rydberg levels in the process of ionization is shown to be a reason for interference of transitions from these levels to the continuum. Interference is shown to be a reason for some new effects: stabilization of the atom, suppression of its ionization, appearance of a multipeak structure in the photoelectron spectrum, field-induced narrowing of its peaks, narrowing and localization of quasi-energy atomic spectrum in a strong field, etc.

Intermediate statistics of the quasi-energy spectrum and quantum localisation of classical chaos

The statistical properties of the quasi-energy spectrum in a simple quantum model are investigated for the case when the corresponding classical system is fully chaotic while quantum chaos is restricted by the localisation effects. It is shown that the level spacing distribution depends effectively on some parameter which is the ratio of the dimension of the eigenfunctions (mean localisation length) to the total number of the quasi-energy levels. Numerical data for a wide range of parameters of the system are given.

The quantized Baker's transformation

A quantum analogue of the Baker's transformation is constructed using a specially developed quantization procedure. We obtain a unitary operator acting on an N-dimensional Hilbert space, with N finite (and even), that has similar properties to the classical baker's map, and reduces to it in the classical limit, which corresponds here to N → ∞. The operator can be described as a very simple, fully explicit N × N matrix. Generalized Baker's maps are also quantized and studied. Numerical investigations confirm that this model has nontrivial features which ought to represent quantal manifestations of classical chaoticity. The quasi-energy spectrum is given by irrational eigenangles, leading to no recurrences. Most eigenfunctions look irregular, but some exhibit puzzling regular features, such as peaks at coordinate values belonging to periodic orbits of the classical baker's map. We compare the quantal and classical time-evolutions, as applied to initially coherent quasi-classical states: the evolving states stay in close agreement for short times but seem to lose all relationship to each other beyond a critical time of the order of log2N ∼ −logh̷.

Quantum localization and statistics of quasienergy spectrum in a classically chaotic system

A new approach to describe the level spacing distribution is suggested for the case when the classical motion is fully chaotic while quantum chaos is restricted by the localization effects. Numerical data for a model with a finite number of states are compared with the analytical predictions.

On the response of a two-level quantum system to a class of time-dependent quasiperiodic perturbations

We study analytically the response of a two-level quantum system to a certain class of time-dependent quasiperiodic perturbations generated by a Fibonacci sequence. We show that the quasi-energy spectrum (Fourier transform of the evolution operator) generically is not a denumerable sum of delta functions. Hence the response is not quasiperiodic. Several numerical investigations (Poincare sections, polarization fluctuation, etc.) suggest an intermediate kind of behavior between quasiperiodic and chaotic.

Features of the quasienergy spectrum of the hydrogen atom in a microwave field

The nearest neighbour level spacing of the quasienergies of a hydrogen atom in a micro-wave field is studied. There is evidence of level repulsion among states corresponding to classically chaotic regions. In the regions of classical phase space where the motion is approximately regular, the corresponding quasienergy spectrum can be understood in terms of approximate dynamical constants. In particular, grouping the high lying quasienergy states into photons yields level spacing plots that are close to δ functions; there is little fluctuation about the average value predicted by the approximate constant. The grouping suggests a simple explanation of the “photon localization” recently observed by Casati et al. [1].

Spectral analysis of quantum-resonance zones, quantum Kolmogorov-Arnold-Moser theorem, and quantum-resonance overlap.

The quasienergy spectrum of a particle in an infinite square well perturbed by a monochromatic external field is analyzed in terms of single- and double-resonance Hamiltonians. At small-enough perturbations the quasienergies are accurately given by those obtained from a single-resonance, integrable Hamiltonian. This indicates the existence of a local constant of motion and is a quantum manifestation of the Kolmogorov-Arnold-Moser theorem. At larger perturbations, the quasienergy spacing distributions are Poissonian for the single-resonance Hamiltonian. But for the double-resonance Hamiltonian, the distributions undergo a transition from Poissonian toward Wigner-like behavior when the perturbation is increased from a regime without resonance overlap to a regime with resonance overlap. This indicates the destruction of the local constant of motion through quantum-resonance overlap and its associated quantum number. It is a quantum manifestation of classical-resonance overlap.

Quantum suppression of irregularity in the spectral properties of the kicked rotator.

The statistical properties of the quasienergy spectrum are used to measure the influence of quantum effects on the quantum kicked rotator which displays chaotic behavior in the classical limit. A transition from orthogonal-ensemble statistics in the semiclassical limit ($\ensuremath{\hbar}\ensuremath{\rightarrow}0$) to Poisson statistics in the quantum regime is observed. In view of previously obtained results for this system the dependence on the irrationality of $\ensuremath{\hbar}$ is discussed.

Renormalization method for the quantum system of interacting resonances

The procedure of constructing quasi-energy functions and a quasi-energy spectrum on the basis of renormalization of the hamiltonian is considered for a nonlinear quantum system in an external periodic field.

Statistical properties of the quasi-energy spectrum of a simple integrable system

We report numerical results about the statistical properties of a number sequence generated by a zero-entropy map on the two dimensional torus. The validity of Poisson statistics for this model, which is related to localization theory with a pseudorandom potential, is briefly discussed.

Quasienergy band structure of solids

The problem of the band structure of solids under the influence of intense laser fields is addressed via the concept of quasienergy bands. The difficulties in evaluation of the quasienergy spectrum in the general case are stated, and a simple effective mass nearly free electron model is treated qualitatively and quantitatively, yielding some useful results.

Study of a quantum fermi-acceleration model.

We consider the problem of a free particle in a rigid box with one wall fixed and the other oscillating periodically in time. The spectral properties of the evolution operator are calculated. We find that by a tuning of Planck's constant, the statistics of the quasienergy spectrum go continuously from showing Poisson to Gaussian-orthogonal-ensemble-like properties. This change is related to a transition from localized to extended states in energy space. We make the conjecture that recent results of microwave excitations on quasi one-dimensional highly excited hydrogen atoms may be related to this work.

Neutron scattering from forced and relaxing systems

Scattering from a forced harmonic oscillator is considered. A number of interesting features occur in the inelastic spectrum: enhancement of high-energy transfers and oscillations in the scattering intensity in any particular channel as resonance is approached, both of which may be useful in experimental situations. The behaviour on resonance is derived and is qualitatively different. The author discusses the relevance to general systems, and shows that neutron scattering directly measures the analogue of the energy levels of the forced system, its quasi-energy spectrum. Scattering from an oscillator out of equilibrium with its environment also considered. They find additional structure in the inelastic spectrum from which the relaxation time can be deduced.

The quasienergy spectrum of semiconductors with direct band gaps in the laser field

Explicit analytical expressions are derived for Floquet states and the quasienergy spectrum of semiconductors with zinc-blende structure and direct band gaps, taking into account the real symmetry properties of the degenerate valence bands.

Quasienergy spectra of quantum dynamical systems

We present a technique that yields in analytic fashion the quasienergy spectrum of bounded quantum systems in the presence of time-periodic perturbations. It also allows for the calculation of statistical averages using simple algebraic manipulations and provides tractable solutions even for systems with a large number of levels. We also report on numerical calculations for systems with few number of levels in and out of resonance, and which show the recurrences predicted by the Hogg-Huberman theorem [Phys. Rev. Lett. 48, 711 (1982); Phys. Rev. A 28, 22 (1983)].

Continuous versus discrete quasi-energy spectrum in the quantal description of a simple parametric resonator

We investigate the quasi-energy spectrum of a quantal parametric resonator, whose frequency is modulated by a periodic δ ( t) term. The system displays two distinct phases, depending on the nature (discrete or continuous) of the quasi-energy spectrum. We investigate the dynamics in the two phases and the transition between them which is induced by varying the coupling strength. Special attention is given to those observables which might be used as indicators of stochasticity in the quantum dynamics.

Non-recurrent behaviour in quantum dynamics

We study the motion of a quantum rotator under an external periodic perturbation. For the resonant case, i.e. when the frequency of driving pulses is rationally connected with the frequencies of the free rotator, the quasi-energy spectrum is known to be continuous. We prove that for a generic choice of the potential there is a non-empty set of non-resonant values of the external frequency such that the quasi-energy spectrum still has a continuous component.

The influence of intense electromagnetic field on the energy-gap between spin branches in ferromagnetic semiconductors

The influence of an intense laser field on the intraband motion of a charge carrier in the localized moment potential of a ferromagnetic semiconductor is discussed. The quasienergy spectrum of a free carrier is calculated and it is shown that for very large fields the energy-gap between the spin branches decreases with increasing laser amplitude.