Crossing of quasilevels in the open Jaynes-Cummings model

The nonlinear dynamics of an open quantum system consisting of a “dressed” atom, i.e., an atom coupled with an external multifrequency electromagnetic field, and a single quantized mode of an electromagnetic field is studied. At different crossing points of the quasilevels of the dressed atom, the average number of photons in the quantized mode may either increase without limit with the passage of time or oscillate within finite limits. In the latter case a decrease of the number of photons is accompanied by regularization of their statistics, which may become sub-Poissonian. Zh. éksp. Teor. Fiz. 114, 474–483 (August 1998)     

Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field

We consider systems of static nuclei and electrons – atoms and molecules – coupled to the quantized radiation field. The interactions between electrons and the soft modes of the quantized electromagnetic field are described by minimal coupling, p→p−e A (x), where A(x) is the electromagnetic vector potential with an ultraviolet cutoff. If the interactions between the electrons and the quantized radiation field are turned off, the atom or molecule is assumed to have at least one bound state. We prove that, for sufficiently small values of the fine structure constant α, the interacting system has a ground state corresponding to the bottom of its energy spectrum. For an atom, we prove that its excited states above the ground state turn into metastable states whose life-times we estimate. Furthermore the energy spectrum is absolutely continuous, except, perhaps, in a small interval above the ground state energy and around the threshold energies of the atom or molecule. Received: 3 September 1998 / Accepted: 17 March 1999     

Effect of the state of a quantized electromagnetic field on the interaction with an atom with allowance for the continuum

This paper studies the effect of a transition into the continuous spectrum on the “collapse” and “revival” of population oscillations in an atom. It is shown that at large values of the mean number of photons in a radiation field and in conditions of weak ionization the phenomena of collapse and revival can still be observed, but the amplitude of population oscillations decreases exponentially because of the damping of the level. The interaction of a quantized electromagnetic field with a Λ system of an atom when one state is continuous is examined. Expressions are derived for the probability of “survival” of the atom when the quantized field was initially in a state with a given number of photons and when it was in a coherent state. An approximate calculation of the sum in averaging over the photon number distribution in the case of a coherent field leads to expressions for the probabilities of survival of the atom that transform into expressions, as the mean number of photons tends to infinity, corresponding to the case of a field in the representation of a fixed number of photons. The possibility of a stable state existing in a coherent quantized field is examined. It is found that for a Λ system the condition for the existence of a stable state remains valid in the case of a coherent state of the field when the photon number is large. Zh. éksp. Teor. Fiz. 113, 1193–1205 (April 1998)     

Strong field effects in the system of two interacting Rydberg atoms

The ionization dynamics of two interacting Rydberg atoms in a strong laser field has been investigated. Each atom has been described in the “two discrete levels + continuum” model. Quasienergy states in this system, which describe field-dressed atoms, have been studied. It has been shown that one of the quasienergy states corresponds to the formation of an atomic state stable against ionization, which leads to the interference stabilization regime first observed in the case of individual atoms in [M. V. Fedorov and A. M. Movsesian, J. Phys. B 21, L155 (1988)]. Methods for creating entangled states in this system have been proposed and the dynamics of entanglement in the process of interaction with the laser field has been analyzed.     

Dynamics of atom-field entanglement in a bimodal cavity

In this paper we investigate some aspects of the dynamics and entanglement of bipartite quantum system (atom-quantized field), coupled to a third “external” subsystem (quantized field). We make use of the Raman coupled model; a three-level atom in a lambda configuration interacting with two modes of the quantized cavity field. We consider the far off resonance limit, which allows the derivation of an effective Hamiltonian of a two-level atom coupled to the fields. We also make a comparison with the situation in which one of the modes is treated classically rather than prepared in a quantum field (coherent state).     

Multiphoton excitation of molecules and the quasienergy spectrum of the anharmonic oscillator

The quasienergy levels of an anharmonic oscillator in a strong external alternating field form two families, transitions between which are forbidden because of the large value of the quasiclassicality parameter of the forced oscillations caused by the external field. This makes it possible to explain the results of a number of experiments on the multiphoton excitation of molecules by infrared radiation. Pis'ma Zh. éksp. Teor. Fiz. 64, No. 1, 13–18 (10 July 1996)     

Berry phases in the three-level atoms driven by quantized light fields

A theoretical analysis of Berry’s phases is given for the three-level atoms interacting with external one-mode and two-mode quantized light fields. Three main results are obtained: (i) There is a Berry phase which vanishes in the classical limit or this Berry phase is completely induced by the field quantization; (ii) Berry’s phases for the one-mode field and the two-mode field can be equal so long as the photon numbers of the two-mode field are properly chosen; (iii) In the two-mode case, Berry phases of the atom interacting with one mode is affected by the other mode even if the photon number of the other mode is zero.      

Electron polarization in quantum wells in a strong variable field

The wave function of an electron in a symmetric double quantum well placed in a strong time-periodic electric field is found, expressions for quasienergy functions are derived, and the dependence of the dipole moment on the average electric field is analyzed for the case where the average field remains constant. In the case of slow monotonic variation of the “constant” component of the electric field, the Schro dinger equation is solved by the WKB method. It is found that the dependence of the dipole moment on the average field is of a clearly nonlinear almost-periodic nature and that in the event of adiabatic monotonic variation of the average field there is a periodic relocation of the electron density from well to well with a small frequency proportional to the rate of variation of the average field. Zh. éksp. Teor. Fiz. 116, 217–235 (July 1999)     

Two-photon Jaynes-Cummings systems interacting with a classical field

If a two-level atom is in the two-photon resonance with a quantized mode and simultaneously inter-acts with a quasi-resonance classical field, then a photon exchange is observed in this system between the quantized and classical modes. It is demonstrated that such a physical system can serve as a source of squeezed radiation in the quantized mode. The squeezing can be arbitrarily close to unity, while the radiation amplitude can be relatively large. A situation is discussed when N atoms are in the two-photon resonance with a quantized mode and simultaneously interact with a classical field. The phenomenon of exponential superradiation is described when the number of photons in the quantized mode exponentially depends on the number N of atoms.     

Two-level electron dynamics in a strong variable external field

This paper studies the quantum dynamics of an electron in a double-well potential subject to a strong time-periodic nonharmonic external field. The quasienergy spectrum of the system is calculated and an expression for the electron density distribution is derived. It is found that under certain conditions imposed on the shape of the excitation, the electron wave packet gets locked, into one potential well, as it were, and is unable to tunnel through the potential barrier. Zh. éksp. Teor. Fiz. 112, 1209–1225 (October 1997)     

Discrete photodetection of quantum jumps on the V configuration of atomic levels

A theory of the discrete photodetection of quantum jumps on the V configuration of atomic levels has been developed. A three-level source atom is placed in a cavity excited by a resonance fluorescence field. The cavity is tuned to exact resonance with an atomic transition. The cavity mode state is tested by a flux of unexcited (at the entrance) probe atoms passing through the cavity. The energy states of the outgoing probe atoms are detected by ionization chambers, which are assumed ideal. This a posteriori statistical information is indirectly related to the numerical characteristics of a measured quantum system consisting of the source atom and cavity mode. The “tuning” conditions for a discrete photodetector, i.e., the rules for choosing the parameters and durations of the interactions of the cavity mode with the probe and source atoms, intensities of the pump and probe fields that are necessary for observing quantum jumps from the “bright” state to the “dark” one and vice versa, have been determined. A two-state model that describes the dynamics of a quantum jump has been analyzed. The formulas have been obtained for the observable characteristics of quantum jumps: the mean residence time of the quantum system in quasistationary states (durations of the bright and dark periods), probabilities of quantum jumps, mean excitation levels of the quantized cavity mode, etc.     

Parametrization of Projector-Based Witnesses for Bipartite Systems

Entanglement witnesses are nonpositive Hermitian operators which can detect the presence of entanglement. In this paper, we provide a general parametrization for orthonormal basis of ℂ ⁿ and use it to construct projector-based witness operators for entanglement detection in the vicinity of pure bipartite states. Our method to parameterize entanglement witnesses is operationally simple and could be used for doing symbolic and numerical calculations. As an example we use the method for detecting entanglement between an atom and the single mode of quantized field, described by the Jaynes-Cummings model. We also compare the detection of witnesses with the negativity of the state, and show that in the vicinity of pure stats such constructed witnesses able to detect entanglement of the state.     

Stochastic ionization of a relativistic hydrogenlike atom

The stochastic ionization of a relativistic hydrogenlike atom in a monochromatic field is investigated. Using Chirikov’s criterion for stochasticity, an analytical formula is obtained for the critical value of the external field for which stochastic ionization of a relativistic atom occurs. Zh. Tekh. Fiz. 69, 127–129 (March 1999)     

Resonance fluorescence in an atom + dielectric microsphere system excited by a single photon

The resonance interaction of a two-level atom with a continuum of free-space modes modified by the presence of a dielectric microsphere (modified free-space modes — MFSMs) is studied. In the case that quantized MFSMs are initially excited within the contour of one of the resonance modes of the microsphere, the spectrum of emitted photons depends strongly on the excitation method. Under optimal excitation conditions efficient excitation of the atom accompanied by the formation of a Rabi doublet in the fluorescence spectrum occur. As the excitation conditions depart from optimality, the spectrum becomes a triplet. If the departure from optimality of excitation is large, the atom remains essentially unexcited, and the fluorescence spectrum has a singlet character. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 2, 115–120 (25 July 1998)     

Stimulated superradiance

If N atoms simultaneously interact with quasiresonant classical and quasiresonant quantized fields, the modes exchange photons. This processes exhibits cooperative properties, i.e., the number of photons in the quantized mode oscillates, and the amplitude of these oscillations is proportional to N ². Zh. éksp. Teor. Fiz. 116, 858–869 (September 1999)     

Dynamics of cascade three-level system interacting with the classical and quantized field

We study the exact solutions of the cascade three-level atom interacting with a single mode classical and quantized field with different initial conditions of the atom. For the semiclassical model, it is found that if the atom is initially in the middle level, the time-dependent populations of the upper and lower levels are always equal. This dynamical symmetry exhibited by the classical field is spoiled on quantization of the field mode. To reveal this non-classical effect, a Euler matrix formalism is developed to solve the dressed states of the cascade Jaynes-Cummings model (JCM). Possible modification of such an effect on the collapse and revival phenomenon is also discussed by taking the quantized field in a coherent state     

Optical exciton Stark effect and quantum beats at exciton quasienergy levels in quantum wells

The optical Stark effect and quantum beats in a GaAs/AlGaAs quantum well are investigated theoretically for the case when the first two electron size-quantization levels are mixed dynamically by a high-intensity CO₂ laser pulse polarized perpendicular to the plane of the quantum well. The quasienergy spectrum of heavy-hole excitons and the ratio between the probabilities of exciton transition with and without a strong electromagnetic field are obtained. The time-dependent intensity of absorption of the sensing light is determined. It exhibits quantum beats at twice the electron Rabi frequency. Fiz. Tverd. Tela (St. Petersburg) 39, 1291–1294 (July 1997)     

Scattering of atoms in the field of counterpropagating light waves. Effect of initial conditions

The scattering of an atom in the field of counterpropagating light waves is studied under conditions such that the state of the atom is a superposition of the ground and excited states. For the case in which this superposition is created by the field of a traveling wave, the momentum distribution function of the atom after scattering by a standing wave is found analytically in the approximation of a short interaction time, when the atom’s motion can be neglected. Longer interactions of the atom with the field are studied numerically. We also consider the case of counterpropagating light waves consisting of Gaussian or supergaussian pulses. Zh. éksp. Teor. Fiz. 113, 563–572 (February 1998)     

High-order perturbation theory for the hydrogen atom in a magnetic field

The states of a hydrogen atom with principal quantum numbers n⩽3 in a constant uniform magnetic field ℋ are studied. Coefficients in the expansion of the energy of these states in powers of ℋ² up to the 75th order are obtained. Series for the energies of the states and the wave functions are summed to values of ℋ on the order of the atomic magnetic field. A generalization of the moment method upon which these calculations are based can be used in other cases in which a hydrogen atom is perturbed by a potential with a polynomial dependence on the coordinates. Zh. éksp. Teor. Fiz. 113, 550–562 (February 1998)     

Dirac Operators Coupled to the Quantized Radiation Field: Essential Self-adjointness à la Chernoff

We study the Dirac operator D ₀ in an external potential V, coupled to a quantized radiation field with energy H _f and vector potential A. Our result is a Chernoff-type theorem, i.e., we prove, for the operator D ₀+α · A+V +λ H _f with λ ∈{0, 1}, that the essential self-adjointness is not affected by the behavior of V at ∞.