Sergey M. Chumakov

Supersymmetry in Helmholtz optics

Abstract A planar waveguide with a specific refractive index profile admits supersymmetry. Physically, optical supersymmetry describes two light beams of different colors that form a standing periodic interference pattern along the waveguide axis. The supersymmetry is exact in the paraxial approximation and broken beyond.

Dicke model: quantum nonlinear dynamics and collective phenomena

We study the resonant interaction of A initially unexcited two-level atoms with single-mode Fock, coherent and thermal cavity fields of arbitrary intensity. Two mechanisms lead to a spread of the eigenfrequencies: one is due to the photon-number distribution in the initial state and the other reflects the cooperativity of the system. Both affect the evolution of the photon number and photon statistics. We present approximate expressions for the eigenvalues and eigenvectors of the system. Its regular dynamical regions are found and the difference in shape of the collapses and revivals connected with the above mechanisms is discussed.

On the phase space description of quantum nonlinear dynamics

Abstract We analyze the difference between classical dynamics (geometric optics) and quantum dynamics (wave optics) by calculating the time history of the Wigner function for the simplest nonlinear Hamiltonians which are fourth-degree polynomials in p and q . It is shown that the moments of the Wigner function carry important information about the state of a system and can be used to distinguish between quasiclassical and quantum evolution.

Semiclassical quantization of the evolution operator for a class of optical models

Abstract We consider an arbitrary atomic system ( n -level atom or many such atoms) interacting with a strong resonant quantum field. The approximate evolution operator for a quantum field case can be obtained from the atomic evolution operator in an external classical field by a “quantization prescription”, passing the operator arguments to Wigner D -functions. Some applications are discussed.

Many-atom spontaneous emission in a lossless cavity

Applying a perturbation method, constructed in terms of SU(2)-group representations, we investigate the anharmonic dynamics of spontaneous emission of a system of N identical two-level atoms immersed in a single-mode ideal cavity with s atoms initially inverted. The phenomenon of collective collapses and revivals is revealed.

Revivals in a two-atom single-mode system

Abstract We show that only one series of revivals is still possible for two two-level atoms interacting with a quantized coherent cavity field mode on the condition of initial excitation of one of the atoms.

Gaussians on the circle and quantum phase

Abstract We show that the phase distribution function for a strong quantum radiation field can be represented in terms of the Jacobi elliptic function Θ 3 ( z | q ). This representation simplifies calculation of phase properties of the field.

Nonspreading Wave Packets in Cavity QED

We consider a single quantized mode interacting simultaneously with resonant two-level atoms and a Kerr medium.

Evolution Operator for Quantum Optical Systems in a Strong Field Limit

We consider a class of optical models describing the interaction of an atomic system with a resonant mode of the quantized field under RWA.

Squeezed Vacuum as an Accelerator of Revivals

In the Dicke model (DM) of a system of A two-level atoms coupled in a high-Q cavity to a single-mode radiation field the total number of excitations N (the number of photons n plus the number of excited atoms) is an integral of motion. There are two limits when the model has an approximately equidistant eigenvalues spectrum: N 《 A (“weak-field” limit) and N 》 A (“strong-field” limit). The atomic inversion response to a photon number state is then truly periodic. According to the above distinction the Jaynes-Cummings model (JCM) belongs to the “strong-field” limit. For an initial field state being a superposition of photon number states the atomic inversion response is a sum of the responses to each of these states weighted with a corresponding photon number distribution P n. If the initial field is in a thermal or squeezed vacuum state the summation over the photon number always includes the region of small n’s with the greatest weights.