Degenerate Two-level System Research Articles

Evolution of twofold degenerate two-level system. Geometrical effects

Geometrical effects occurring in the cyclic evolution of twofold degenerate two-level system are considered. A projector representation for the objects involved (Hamiltonian, evolution operator) is constructed. The explicit expressions for connections and curvatures are quoted. Particular cases are considered and found to be in full correspondence with previously obtained results.

The degenerate two-level system and high-order harmonic generation

A previously considered two-level system interacting with an external electromagnetic wave is particularised to a degenerate system and utilized as a model for the process of high-order harmonic generation (HOHG). It is shown that this model can be reduced to a linear coupled map and that the plateau and cut-off which are characteristic signatures of HOHG can be obtained from this map. Exploring the dependence of the intensity of the generated harmonics on the amplitude of the external electromagnetic wave (parameterized in terms of the Rabi frequency), it is found that there are significant reductions in intensity for specific orders of the harmonics. It is conjectured that the experimentally observed absence of certain harmonics may not be due to the atomic structure and still may be a single-atom effect.

Laser Polarization Effect on Adiabatic Inversion of Degenerate Two-Level System

Coherent excitation dynamics of a degenerate two-level system by a frequency-swept laser were analyzed by solving the optical Bloch equations. Physical parameters (Rabi frequency, laser frequency sweep rate and laser frequency sweep width or pulse width) giving a high excitation efficiency were obtained. Laser polarization also affects the excitation efficiency because the variation of dipole matrix elements depends on the laser polarization and ΔJ, the difference between the J values of the upper and lower levels. It was found that circular polarization is preferable when ΔJ=0 and linear polarization is preferable when ΔJ=±1. This polarization effect was qualitatively analyzed.

Effect of polarization self-action in cubic crystals: peculiarities and applications

New concepts are developed to describe a wide area of nonlinear systems involving the phase relaxation peculiarities for the degenerate two-level system under the resonant optical excitation. Nonlinear susceptibility of the two-level system becomes anisotropic, and self-induced changes of polarization (SICP) are developed to the large (gigantic) magnitudes. The nonlinearities of two different natures are considered: the saturation of absorption and the resonant optical reorientation of anisotropic defects. For these particular cases, the SICP effects manifest themselves at a field much lower than that in traditional nonlinear optics. The larger magnitudes of the effects offer good possibilities for the development of optical devices based on the new physical principles. Various applications of SlOP effects are demonstrated, including the spectroscopic investigations of impure cubic crystals, optical diagnostics, optical storage, information processing, and the development of new optical devices.

Optically excited Zeeman coherences in atomic ground states: Nuclear-spin effects.

Optical experiments in alkali-metal atomic gases are usually interpreted in terms of the {ital J}=1/2 ground state, treating the electronic ground state as a degenerate two-level system. While this simplified level scheme has been quite successful in describing many experimental results, the nuclear spin can lead to significant modifications of the behavior. Apart from the obvious differences, such as the existence of hyperfine splitting, some more subtle effects are present that modify the dynamical as well as the equilibrium behavior of the system. An an example, the optical pumping process in the true atomic ground state is nonexponential and slower by at least an order of magnitude, compared to a hypothetical atom with nuclear spin zero. The limitations of the {ital J}=1/2 model are analyzed theoretically and experimentally for atomic sodium, and experimental methods are demonstrated that can help disentangle the contributions from different hyperfine components.

Degenerate spin-boson system.

The temporal evolution of a degenerate two-level system (spin) coupled to a dissipative bath (bosons) is studied in this Rapid Communication. Closed-form expressions for the occupancy probabilities and correlation functions are found by functional methods. The non-Markovian characteristics such as explicit dependence on the initial condition and a possible long-time tail behavior are shown to be present. We also suggest a reasonable procedure for the construction of the Green's function of the nondegenerate system.

A soluble random-matrix model for relaxation in quantum systems

We study the relaxation of a degenerate two-level system interacting with a heat bath, assuming a random-matrix model for the system-bath interaction. For times larger than the duration of a collision and smaller than the Poincare recurrence time, the survival probability of still finding the system at timet in the same state in which it was prepared att=0 is exactly calculated.

The effect of a resonance laser field on the level degeneracy

A simple proof is presented of a theorem, which makes clear the general property of the effect of a resonance field on an arbitrarily degenerate two-level system.

STUDY OF STIMULATED PHOTON ECHO IN DEGENERATE TWO-LEVEL SYSTEM GENERAL THEARY AND RELAXATION INDUCED STIMULATED PHOTON ECHO

The stimulated photon echo in degenerate two-level system has been studied. The stimulated photon echo signal for different polarization arrangement of incident lights was obtained basing on the third-order perturbation theory, where, the density matrix was expanded in an irreducible spherical-tensor operator. The characteristics of stimulated photon echo were discussed. Taking ja = jb = 1/2 system as example, we have also studied the relaxation induced stimulated photon echo, where, the polarization arrangement of the three incident pulses is σ+→σ+→σ-.

Polarization properties of phase-conjugate mirrors: Angular dependence and disorienting collision effects in resonant backward four-wave mixing for Doppler-broadened degenerate transitions

We present the theory of resonant backward degenerate four-wave mixing in gaseous media for Doppler-broadened degenerate two-level systems. The degeneracy of the atomic levels as well as the influence of the polarization of the incident fields are taken into account within the framework of a tensorial formalism. The amplitude, line shape, and polarization of the reemitted phase-conjugate field are calculated up to the third order in the incident fields. The velocity average is performed in the approximation of large Doppler linewidths. One considers in detail the influence of depolarizing relaxation processes and the effects of pump-probe angular separation. In particular, the importance of the residual Doppler effect (shortening of the lifetime of the optically induced gratings by the atomic motion) associated with the pump-probe angle is emphasized. We show that the polarization of the reemitted fields is governed by very simple laws as soon as the residual Doppler effect overcomes the lifetimes of the atomic levels. Phase-conjugate mirrors can be simply characterized by a linear dichroism (parallel pump polarizations) or a birefringence (cross-polarized pumps). Vectorial phase conjugation is also analyzed, in the case of counter-rotating circular polarizations of the pumps. Finally, the case of two-photon transition is studied and compared with the case of a resonant transition.

Coherent pulse propagation and self-induced transparency on degenerate transitions in atomic iodine

Coherent propagation of intense short laser pulses through degenerate absorbing media is investigated with the use of an atomic-iodine laser-absorber self-resonant combination. Four degenerate systems, the $^{2}P_{\frac{1}{2}}\ensuremath{-}^{2}P_{\frac{3}{2}}$, $F=3\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=4$, $\ensuremath{\Delta}{M}_{F}=0,\ifmmode\pm\else\textpm\fi{}1$ and $F=2\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=2$, $\ensuremath{\Delta}{M}_{F}=0,\ifmmode\pm\else\textpm\fi{}1$ transitions, are studied under various conditions. Theoretical analysis based on the pulse-area---pulse-energy approach shows different pulse propagation behaviors for three typical types of degeneracy. Experimental results give good agreement with theoretical predictions. It is concluded that self-induced transparency exists in any degenerate two-level system, provided that suitable polarization of radiation is used. The usefulness of self-induced-transparency phenomena for measurements of transitional dipole moment and homogeneous relaxation time is also demonstrated.

Reduction of degenerate two-level excitation to independent two-state systems

Examining the dynamics of a degenerate two-level system excited by coherent resonant light, we exhibit a transformation of basis states which reduces the problem to a set of independent nondegenerate one- and two-state systems. More generally, reduction of multilevel Hamiltonians requires only that the states can be collected into two sets; within each set the states are degenerate, unlinked by Hamiltonian matrix elements. The remaining Hamiltonian linkages must share the same time dependence, but are otherwise arbitrary. We apply this method to reduction of the angular momentum degeneracy of a two-level atom excited by elliptically polarized light and to multiple-laser resonant excitation of multiple levels into a common level.

Nonadiabatic excitation of degenerate two-level systems by laser radiation with a continuously variable frequency

Expressions are obtained for the probability of a nonadiabatic transition between two degenerate levels under the action of laser radiation with a continuously variable resonance frequency. It is shown that this problem reduces to the solution of the Landau?Zener problem for eigenvectors of the matrix of a transition between two degenerate levels.

On the time dependence of a degenerate two-level system interacting with a pulse of radiation

The solution of the time-dependent Schrödinger equation is presented for a degenerate two-level system interacting with a pulse of radiation. The sinusoidal limit of the solution is used to illustrate the importance of averaging transition probabilities over the phase of an applied sinusoidal field.

Transient polarization characteristics associated with resonant light scattering by a degenerate two-level system

The time dependence of the polarized and unpolarized parts of the secondary-radiation intensity, ${I}_{\mathrm{p}}$ and ${I}_{\mathrm{up}}$, and the time-dependent degree of polarization $P(t)$ are calculated. A method is based upon the Feynman-diagram technique which is extended to enable the calculation of the reduced-density matrix element. It is found that, for the step excitation, $P(t)$ does not show a simple exponential decay. Especially in the off-resonance case, $P(t)$ shows oscillatory behavior. In the case of pulse excitation, ${I}_{\mathrm{up}}$ takes its maximum value after the excitation pulse has been turned off, and in the long-time limit it decays with the radiative-damping rate. In contrast to ${I}_{\mathrm{up}}$, ${I}_{\mathrm{p}}$ quickly responds to the excitation pulse and shows rapid exponential decay with the transverse-relaxation rate. It is also found that, contrary to the nondegenerate case, the total intensity of the secondary radiation does not exhibit simple exponential decay with the radiative-damping rate.

Photon statistics of second-harmonic generation in a gaseous system

Second-harmonic generation in a degenerate two-level gaseous system is considered with atomic motion taken into account. The diagonal elements of the dipole matrix are assumed to be present. We find the photon statistics of the second-harmonic field to be considerably influenced by the detuning in the two-photon absorption. The threshold condition is discussed. We obtain the average second-harmonic photon number and thus calculate the dimensionless intensity parameter. The output variance of the second-harmonic field is discussed.