Abstract:
Some aspects of lasing at vibronic transitions in impurity crystals are theoretically studied. The threshold conditions for a vibronic laser are shown to be dependent on the strength of interaction of optical centers with a local vibration, which forms the vibronic spectrum, and the crystal lattice temperature. The theory can be easily generalized to the spectrum containing a structureless phonon sideband and well agrees with the experimental temperature dependence of the output power of a Mg2SiO4:Cr4+ forsterite laser.

Abstract:
The Dicke superradiance on vibronic transitions of impurity crystals is considered. It is shown that parameters of the superradiance (duration and intensity of the superradiance pulse and delay times) on each vibronic transition depend on the strength of coupling of electronic states with the intramolecular impurity vibration (responsible for the vibronic structure of the optical spectrum in the form of vibrational replicas of the pure electronic line) and on the crystal temperature through the Debye-Waller factor of the lattice vibrations. Theoretical estimates of the ratios of the time delays, as well as of the superradiance pulse intensities for different vibronic transitions well agree with the results of experimental observations of two-color superradiance in the polar dielectric KCl:O2-. In addition, the theory describes qualitatively correctly the critical temperature dependence of the superradiance effect.

Abstract:
We show that the Krylov-Bogoliubov-Mitropolsky averaging in the canonical formulation can be used as a method for constructing effective Hamiltonians in the theory of strongly correlated electron systems. As an example, we consider the transition from the Hamiltonians of the Hubbard and Anderson models to the respective Hamiltonians of the t-J and Kondo models. This is a very general method, has several advantages over other methods, and can be used to solve a wide range of problems in the physics of correlated systems.

Abstract:
The paper examines superradiance in impurity crystals in the field of a coherent phonon wave excited by two ultrashort laser pulses via Raman scattering processes at the moment of preparation of the initial state of an ensemble of emitters. It is shown that by varying the power of the excitation pulses and their mutual direction of propagation, one can control the superradiance parameters and extract data on the electron-phonon coupling constant and its anisotropy.

Abstract:
Multiplication of spin qubits arises at double resonance in a bichromatic field when the frequency of the radio-frequency (rf) field is close to that of the Rabi oscillation in the microwave field, provided its frequency equals the Larmor frequency of the initial qubit. We show that the operational multiphoton transitions of dressed qubits can be selected by the choice of both the rotating frame and the rf phase. In order to enhance the precision of dressed qubit operations in the strong-field regime, the counter-rotating component of the rf field is taken into account.

Abstract:
We propose an explanation for the experimentally observed temperature hysteresis of magnetization in single crystals of lanthanum manganite (La0.8Sr0.2MnO3). The phenomenon is interpreted within the framework of a double-exchange model with allowance for the interaction of the magnetic subsystem with a bistable mode of the tilting-rotational oscillations in the correlated sublattice of MnO6 octahedra.

Abstract:
We propose an explanation for the experimentally observed [JETP Lett. 74, 115 (2001)] giant temperature hysteresis of the ultrasound velocity and the internal friction in single crystals of lanthanum manganite (La0.8Sr0.2MnO3). The effect is interpreted within the framework of a phenomenological model based on the notion of two coexisting sublattices of the oxygen octahedra performing cooperative tilting-rotational oscillations in bistable potential fields.

Abstract:
The two-loop temperature hysteresis of integrated intensity of Raman scattering of light is explained theoretically for a line of frequency 50 cm-1 in a superconducting oxide Ba1-xKxBiO3 single crystal.

Abstract:
The geometric phase in the dynamics of a spin qubit driven by transverse microwave (MW) and longitudinal radiofrequency (RF) fields is studied. The phase acquired by the qubit during the full period of the "slow" RF field manifests in the shift of Rabi frequency \omega_{1} of a spin qubit in the MW field. We find out that, for a linearly polarized RF field, this shift does not vanish at the second and higher even orders in the adiabaticity parameter \omega_{rf} / \omega_{1}, where \omega_{rf} is the RF frequency. As a result, the adiabatic (Berry) phases for the rotating and counter-rotating RF components compensate each other, and only the higher-order geometric phase is observed. We experimentally identify that phase in the frequency shift of the Rabi oscillations detected by a time-resolved electron paramagnetic resonance.

Abstract:
The dynamics of a two-level spin system dressed by bichromatic radiation is studied under the conditions of double resonance when the frequency of one (microwave) field is equal to the Larmor frequency of the spin system and the frequency of the other (radio-frequency) field \omega_{rf} is close to the Rabi frequency \omega_{1} in a micro-wave field. It is shown theoretically that Rabi oscillations between dressed-spin states with the frequency \epsilon are accompanied by higher-frequency oscillations at frequencies n\omega_{rf} and n\omega_{rf}\pm \epsilon, where n = 1, 2, .... The most intense among these are the signals corresponding to n = 1. The counter-rotating (antiresonance) components of the RF field give rise to a shift of the dressed-state energy, i.e., to a frequency shift similar to the Bloch-Siegert shift. In particular, this shift is manifested as the dependence of the Rabi-oscillation frequency \epsilon on the sign of the detuning \omega{1} -\omega{rf} from resonance. In the case of double resonance, the oscillation amplitude is asymmetric; i.e., the amplitude at the sum frequency \omega_{rf} +\epsilon increases, while the amplitude at the difference frequency \omega_{rf} -\epsilon decreases. The predicted effects are confirmed by observations of the nutation signals of the electron paramagnetic resonance (EPR) of centers in quartz and should be taken into account to realize qubits with a low Rabi frequency in solids.