Two algorithms are presented that use the properties of twisted light to construct symmetric encryption schemes. Their possible physical realization is discussed.
The properties of quantum networks based on generalized Tavis-Cummings models are theoretically investigated. We have calculated the information transfer success rate from one node to another in a simple model of a quantum network realized with two-level atoms placed in the cavities and interacting with an external laser field and cavity photons. The method of dynamical group of the Hamiltonian and technique of corresponding coherent states were used for investigation of the temporal dynamics of the two nodes model.
We investigated numerically the time-dependent behavior of atoms populations and mean number of photons in cavities with losses. To derive the dynamic equations, we used the method of oscillator and atomic coherent states. We also took into account the various locations of the atoms in the cavity and their movement through the cavity. The losses of photons in the cavities were considered in the Wigner-Weisskopf approximation.
Method of dynamical groups and approach of coherent states have used to calculate the squeezing and multiphoton correlations in spontaneous parametric down-conversion processes. Special case of twisted photons with orbital angular momentum is considered.
Proc. SPIE. 9917, Saratov Fall Meeting 2015: Third International Symposium on Optics and Biophotonics and Seventh Finnish-Russian Photonics and Laser Symposium (PALS)
KEYWORDS: Chemical species, Photons, Computer simulations, Quantum optics, Electromagnetism, Systems modeling, Quantum communications, Quantum computing, Quantum chaos, Chaos
A coherent dynamics of a three-level atoms in the ideal cavity were investigated. This model evidently generalizes the well-known Tavis-Cummings model of two-level atoms. We have derived a system of equations for the parameters of coherent states associated with the group <i>G = W</i><sub>2</sub>˄<i>SU</i>(3). It is shown that this model gives a nontrivial example of the chaotic behavior of the parameters of coherent states, taking into account non-resonant terms in the Hamiltonian. Time dependencies of mean number of the cavity photons and level populations of atoms are computed and maximal Lyapunov coefficient is calculated.
Proc. SPIE. 9448, Saratov Fall Meeting 2014: Optical Technologies in Biophysics and Medicine XVI; Laser Physics and Photonics XVI; and Computational Biophysics
KEYWORDS: Chemical species, Photons, Physics, Computer simulations, Quantum optics, Electromagnetism, Systems modeling, Quantum communications, Quantum chaos, Chaos
A coherent dynamics of two-and three-level atoms in the ideal cavity were investigated. In particular, the investigation of the dynamics of three-level atoms (qutrits) interacting with photons in the cavity having two resonant frequencies close to the frequencies of the two allowed atomic transitions were performed. This model generalizes the well-known Tavis-Cummings model. Time dependencies of mean number of the cavity photons and level populations of atoms are computed and entanglement of atoms and photon fields states are discussed.
The influence of chaotic behavior of coherent state (CS) parameters on entanglement dynamics in system
of two level atoms and photons in cavity is investigated. The initial state of the system is chosen as factorized
production of photon and atomic coherent states. To find a solution of the Schrödinger equation, we presented
the time-dependent wave function in the form of a wave packet in CS representation. The phase portraits and
Poincare sections for classical dynamics of CS were computed, and time dependence of the mean number of
photons level populations and atomic entropy were calculated in quantum case. The analysis showed that the
chaotic behavior in quantum-optical Dicke model increases the degree of entanglement in the atomic subsystem.
At the same time greater entanglement is generated when selecting the initial atomic CS parameters near the
center of the corresponding Poincare sections. It is considered dynamics of two identical two-level atoms in
non-ideal cavity (nonideal Tavis-Cummings model). Accounting for decay showed that the generation of atomic
entanglement is accompanied by the return of the initial separable state (”death” of entanglement), but this
behavior with the increase of the initial parameter of the field CS is only at sufficiently small times. Influence of
detuning and damping constants are considered.
The dynamics of two identical two-level atoms in non-ideal cavity it is considered. Using approach developed
before by us for case of one two-level atom, the analytical expression for density matrix of the system is presented.
Dynamics of level populations, mean number of photons and correlation function for photons are calculated.
Using Peres - Horodecki criteria exact expression for entanglement dynamics of two identical two-level atoms in
cavity is given. Influence of detuning and damping constants are investigated.
It is considered dynamics of two identical two-level atoms in non-ideal cavity. Using approach developed
before by us for case of one two-level atom, analytical expression for density matrix of the system is presented.
Dynamics of level populations, mean number of photons and correlation function for photons are considered.
Using Peres-Horodecki criteria exact expression for entanglement dynamics of two identical two-level atoms in
cavity is given. Influence of detuning and damping constants are considered.
The problem of the coherent states generation with definite parameters for multilevel quantum systems is investigated.
The interaction with external environment and stochastic fields can destroy of the coherence. The
competition of these processes is considered on a base of Fokker - Planck Equations approach, deriving from master
equation for the density matrix of the system. Examples of the coherent states dynamics for two-level atoms in an
external stochastic field in the nonideal resonator are considered. Average over the realizations of stochastic fields
is performed for the case of white gaussian noise and Kubo - Anderson process. Explicit formulas for transition
probabilities, longitudinal and transversal relaxation times and shape of radiation line are obtained.
The Jaynes-Cummings model (JCM) of two-level atom interacting with the photon mode in ideal cavity plays an essential role in modern quantum optics. In previous papers <sup>1,2</sup> an exact form of density matrix of the JCM with fixed atom position and photons dissipation was found. Here, taking into account the classical motion of the atom through the cavity, it is considered a case of nonideal cavity with zero temperature. We have obtained an exact expression for density matrix and calculated photon spectra and spectra of the mean number of photons in a cavity and and time dependencies of some values relevant for the one-atom maser theory.
The Jaynes-Cummings model (JCM) of two-level atom interacting with the photon mode in ideal cavity plays an essential role in modern quantum optics. In previous papers an exact form of density matrix of the JCM with photons dissipation was found. In this article it is considered a partial case of cavity with zero temperature and obtained an exact expression for photon spectra and spectra of the mean number of photons in a cavity.
Exact analytical expression for the density matrix of atom + field system is obtained taking into account of the photons relaxation and frequency detuning (Jaynes-Cummings model with m-quantum transitions and dissipation). The photon mean number, atom population inversion and Fano Q - factor depending on initial states of the field and parameters of the one-atom maser are investigated.
An exact analytical expression for a density matrix of atom + field system is obtained taking into account of the relaxation of photons and frequency detuning (Jaynes-Cummings model with dissipation). The photon mean number, atom population inversion and Fano Q - factor depending on initial states of the field and various parameters of the one-atom maser parameters are investigated.
Examples of Berry’s and WBBZ - (D.Wojcik, I.Bialynicki-Birula and K.Zyczkowski) quantum fractal constructions are considered. The behavior of fractal dimensions of these very special superpositions of basic states of a particle in a potential box and harmonic oscillator is investigated in going from coordinate representation to momentum and coherent state representations. The mean value of quanta and dispersion for isolated quantum harmonic oscillator prepared in “fractal” state and interacting with another oscillator are calculated.
Proc. SPIE. 5067, Saratov Fall Meeting 2002: Laser Physics and Photonics, Spectroscopy, and Molecular Modeling III; Coherent Optics of Ordered and Random Media III
KEYWORDS: Superposition, Oscillators, Visualization, Particles, Photons, Physics, Fractal analysis, Quantum physics, Probability theory, Information security
Examples of Berry’s and WBBZ - (D.Wojcik, I.Bialynicki-Birula and K.Zyczkowski) quantum fractal constructions are considered. The behavior of fractal dimensions of these objects is investigated in going from coordinate representation to momentum and coherent state representations. The mean value of quanta and dispersion for isolated quantum harmonic oscillator prepared in "fractal" state and interacting with another oscillator are calculated.
Proc. SPIE. 4706, Saratov Fall Meeting 2001: Laser Physics and Photonics, Spectroscopy, and Molecular Modeling II
KEYWORDS: Molecules, Energy transfer, Oxygen, Iodine, Molecular spectroscopy, Molecular lasers, Chemical lasers, Chemical oxygen iodine lasers, Information operations, Molecular energy transfer
Relaxation of the electronic energy in the active medium of the chemical oxygen-iodine laser (COIL) causes non- equilibrium population of vibrational levels of oxygen. It is found that the fraction of vibrationally excited oxygen can reach several of percent in the oxygen stream. The rate relaxation of vibrational energy of oxygen is limited by the exchange between oxygen at the first vibrational level and the bending mode of water. A simple formulas for the population of singlet oxygen vibrational levels at the output of a singlet-oxygen generator are found. It is noted that the EE energy transfer between singlet oxygen and molecular iodine stimulated by the vibrational excitation may be of considerable importance in the kinetics of iodine dissociation.
Some quantum optical models possessing a transition from regular to chaotic dynamics and influence of 'quantum chaos' to photons statistics are investigated. Particular cases of semiclassical dynamics of a single atom and cooperative system of these atoms with (2j + 1) -- equidistant levels interacting with a quantized photon mode in an ideal cavity were considered. We take into account parametric pumping. Corresponding equations of motion are received without the rotation-wave approximation. It was demonstrated the scenario of transition to chaos, realized by doubling frequencies mechanism with growing of 'atom + field' coupling constant. Chaotic behavior and squeezing degree time dependence were obtained in computer simulations for coupling constant values of order of the atomic frequency, the calculation of the maximal Lyapunov coefficient for the dynamics of many two- level atoms interacting with photon cavity mode as function of 'atoms + field' interaction constant is performed. An influence of possible parametric instabilities of nonlinear media and effects of dissipation for atoms are discussed.
The Fokker-Planck equations (FPE) which determine the time dependence of P -- symbol of the density matrix of quantum parametric amplifiers are derived and their group properties are investigated. Exploring the coherent states method, constructing the dynamical symmetry group of FPE and generalizing the well known Wei-Norman method to the case of FPE, we have found FPE solutions exactly. The initial squeezing influence of the thermal reservoir is discussed.
Some quantum optical models possessing a transition from regular to chaotic dynamics and influence of `quantum chaos' to squeezing are investigated. Particular cases of semiclassical dynamics of a single atom and cooperative system of these atoms with (2j + 1)--equidistant levels interacting with a quantized photon mode in an ideal cavity were considered. Corresponding equations of motion are received without the rotation-wave approximation. Chaotic behavior and squeezing degree time dependence were obtained in computer simulations for coupling constant values or order of the atomic frequency.
Some quantum optical models possessing a transition from regular to chaotic dynamics and influence of 'quantum chaos' to squeezing are investigated. Exploring coherent states method and 1/N-expansion technique we have derived an appropriate system of nonlinear equations and demonstrate in computer simulations a change of squeezing degree time dependence.
The coherent state representations of the group G equals W<SUB>1</SUB> (direct product) G<SUB>0</SUB> [where G<SUB>0</SUB> equals SU(2) or SU(1,1)] are used in computer simulations of the dynamic of single two- level atom [G<SUB>0</SUB> equals SU(2)] interacting with a quantized photon cavity mode [Jaynes-Cummings Model (JCM) without the rotating wave approximation] and, in general, nonlinear in photon variables. The second case [hyperbolic Jaynes - Cummings Model (HJCM), G<SUB>0</SUB> equals SU(1,1)] corresponds to the quantum dynamics of quadratic nonlinear coupled oscillators (the parametric resonance on double field frequency and a three-wave parametric processes of nonlinear optics). Quasiclassical dynamical equations for parameters of approximately factorizable coherent states for these models are derived and regimes of motion for 'atom' and field variables are analyzed.
This work is devoted to the description of the interaction between n-level atom and a large dissipative system (heat bath). SU(n)-group coherent states as useful and convenient basis are employed. Fokker-Planck-like equations for (rho) - symbol of reduced density matrix taking into account possible squeezed fluctuations of heat bath are derived. New formulas for correlators of the transition operators between levels of system are obtained and influence of squeezing on the shape of radiation lines is discussed.