Hiroshi Iwasawa

Emission Spectra of an Atom for Multiphoton Jaynes-Cummings Model

The emission spectra of an atom in a cavity for the multiphoton Jaynes–Cummings model are investigated. Using Eberlys formula for the time-dependent physical spectrum, the analytical expression for the atomic emission spectrum is obtained from the two-time dipole-moment correlation function of the atom. The appearance of two strong peaks in the spectrum is explained in detail, and the relationship between the initial photon distributions and the shapes of the spectra are examined. The fundamental differences in the atomic emission spectra for the two-photon and multiphoton models are specified. Furthermore, the role of the detector filter is thoroughly studied. It is explicitly shown that the atomic emission spectra can be obtained by averaging over the convolution integrals between the Fourier transform of the atomic dipole-moment correlation function associated with a pure number state and the detector filter function on frequency domain. The comparisons of the spectra for a coherent initial field to those for a thermal initial field are presented.

Heisenberg-Picture Operators for Two-Photon Jaynes-Cummings Model.

The dynamics of the degenerate two-photon Jaynes-Cummings model in Heisenberg picture is investigated. By solving the Heisenberg equations, the exact solutions of the photon annihilation operator a( t), the atomic dipole moment operator σ-( t), and the population difference operator σz ( t) are obtained. We demonstrate that the correlation functions for the photon annihilation and dipole moment operators can be directly evaluated from these exact solutions. The solutions of the time-evolution operators are shown to be quite useful in the calculation of two-time correlation functions. Furthermore, some results of the dynamical behavior of the average values for the photon number , the in-phase field component , and the population difference are demonstrated by computer simulations.

Slow Relaxation Processes in SF6 Gas After Pumping by a CO2 Laser Pulse

The vibrational energy relaxation and distribution in SF6 at the collisional condition of 2 Torr was measured with the pump-probe method by use of two tunable CO2 300 ns-pulse lasers at the delay time up to 400 μs. The 10.6 μs P(30) pump intensity was 0.4 J/cm2. The probed spectra, divided into two parts, the induced transmission at the P(10)–P(22) and the absorption at the P(24)–P(32), were red-shifted by 50 μs and then slowly back to the initial. The time variation of induced signals was divided into the four regions due to the following processes; (I) the formation of nonthermal distribution in the ν3 mode and quasi-continuum with 1 μs, (II) the broad redistribution by the rise-up of vibrational temperature in 50 μs-duration, (III) the molecular diffusion or expansion out of the pumped region locally heated up by the V–T relaxation in another 60 μs, (IV) the gas cooling corresponding to the energy relaxation or population depletion over 400 μs. So, this pump-probe method at the collisional conditions will easily give us some informations, with a short gas cell and a suitable time scale, on those slow processes.

Exact Solutions for Two-Photon Jaynes-Cummings Model with Dynamic Stark-Shifts.

The solutions for the degenerate two-photon Jaynes-Cummings model are investigated in the presence of the dynamic Stark-shifts. By using the Heisenberg equations of motion, the operator differential equations are established from the effective Hamiltonian. The exact solutions for these operators are derived and the effects of the Stark-shifts on the atomic and field dynamics are discussed. Especially, the behavior of the atomic population difference for the simplest case is demonstrated.

Exact Solutions for Non-degenerate Two-Photon Jaynes–Cummings Model in the Presence of Dynamic Stark-Shifts

The exact solutions for the non-degenerate tow-photon Jaynes–Cummings model in the presence of the dynamic Stark-shifts are investigated. The Heisenberg equations of motion for the respective operators are established and the exact solutions are obtained. It will be shown how the presence of the Stark-shifts in the model influences the solutions of the operator differential equation.

Dynamical behaviors of two-photon non-degenerate Jaynes-Cummings model by Heisenberg picture

Abstract The two-photon non-degenerate Jaynes-Cummings models are investigated by Heisenberg picture. By solving the Heisenberg equations, the exact solutions are obtained. The dynamical behaviors of the relevant operators are analyzed and demonstrated as a function of the interaction time. It is shown that cross-correlation functions between two different modes can be easily derived from our solutions.

Induced Transmission and Absorption of SF6

The vibrational energy relaxation was measured in several Torr SF6 by a pump-probe method using two tunable TE CO2 lasers. The transmitted intensity of the probe beam through an SF6 gas cell was measured by changing the probe wavelength and the time delay up to 400μs between the pump and probe pulses. The 10.6μm P (30) pump intensity was 0.4J/cm2. The probed spectra are divided into two parts: induced transmission at P(8)-P(22) and absorption at P(24)-P(36). The time dependence of induced signals are composed of 4 regions: Ist period (≤1μs) related to multiphoton excitation, IInd (1-50μs) due to collisional V-T relaxation, IIIrd (50-110μs) from molecular expansion and diffusion, and IVth (≥100μs) restricted by gascooling. The effects of a gas pressure and a pump intensity on the induced signals were also investigated with the P(30) (or P(14)) pump line.