Nonclassical states generated via four-wave mixing

The nonclassical properties of quantum fields generated by four- or three-wave mixing are investigated on the basis of assumptions of two-photon coherent (squeezed) input states and the approximation of strong pumping. The influence of losses is shown supposing the model of mutually independent phonon reservoirs. The possibility of producing squeezed and sub-Poisson light outputs is demonstrated in single or superposed modes using computer solutions.The author wishes to acknowledge helpful discussions with Dr. J. Peina and Dr. M. Kárská.     

Model of a degenerate four-wave mixing phase-conjugate mirror without slowly varying envelope approximation

The exact solution to the boundary value problem for a simple conjugator model is presented. The analysis shows that, for this model, it is necessary to introduce two reflected and two transmitted waves. No SVEA approximation is used to obtain the exact formulae for the amplitudes of the reflected waves. The role of the boundaries in the phase-conjugation process is stressed.     

Reduction to the Fock state via a degenerate four-wave mixing

A scheme to generate the Fock state via a degenerate four-wave mixing and partial measurement is proposed. A conditional state of the signal mode of a degenerate four-wave mixer will be shown to reduce to the Fock state when the outcome of the measurement on the reference mode satisfies a certain condition. The photon number of the Fock state is distributed when the measurement is repeated many times. Conditioning for the quantum state of the signal mode is carried out by the photon counting measurement on the reference mode whose input state is assumed to be the vacuum. The phase coherence of the conditional signal state is also considered. Furthermore conditioning for the signal mode by means of heterodyne and homodyne detections are briefly considered.     

简并四波混频实现全光信号幅度整形的系统设计

对光纤中简并四波混频(DFWM)耦合波方程进行数值求解,通过分析发现:泵浦光功率的增大会导致泵浦光与反斯托克斯光之间能量交换周期减小。阐述了优化光纤中DFWM实现全光信号幅度整形的机理。在此基础上设计了一个优化的全光信号幅度整形系统,并进行了系统仿真,结果表明:通过再生系统后,信号的消光比从9.46 dB提升到30.40 dB,品质因子从15.95提升到了180.40。     

简并四波混频实现全光信号幅度整形的系统设计

对光纤中简并四波混频(DFWM)耦合波方程进行数值求解,通过分析发现:泵浦光功率的增大会导致泵浦光与反斯托克斯光之间能量交换周期减小。阐述了优化光纤中DFWM实现全光信号幅度整形的机理。在此基础上设计了一个优化的全光信号幅度整形系统,并进行了系统仿真,结果表明:通过再生系统后,信号的消光比从9.46 dB提升到30.40 dB,品质因子从15.95提升到了180.40。     

Deflection of a phase-conjugate wave in nondegenerate four-wave mixing

The boundary problem for signal phase conjugation at nondegenerated four-wave mixing (FWM) is considered. In contrast to the statements of some authors it is shown that noncollinearity of the incident and the phase-conjugate waves occur. Expressions have been obtained for the deflection angle for a number of configurations of practical importance. Useful analogy between linear and nonlinear reflection at the FWM is noted.     

Large signal analysis of phase variations and bistability in degenerate four-wave mixing

Optical and Quantum Electronics -     

Quantum atomic-fluctuations reduction and squeezed-state generation via forward degenerate four-wave mixing

It is shown that correlation of quantum atomic fluctuations for coupled modes at forward degenerate four-wave mixing leads to atomic noise reduction from the in-phase quadrature variance of the mode which is a linear combination of the coupled signal and probe modes. Thus, quantum atomic fluctuations are not an obstacle for the squeezed-state generation via degenerate four-wave mixing.     

Transient degenerate four-wave mixing in molecular systems

The dependence of the degenerate four-wave mixing (DFWM) signal on laser intensity, molecular transition moment and molecular concentration were examined experimentally by taking the iodine molecule (l₂) as a testing example. The experimental results will be interpreted by a non-steady-state DFWM theory, an extension of the non-degenerate two-level system previously proposed. The distinctive physical feature of this mechanism is that the present observation is the result of non-stationary evolution of the excited-state population, in contrast to the conventional theory based on the steady-state treatment. In this study, we have also taken into account the magnetic sub-levels of molecular rovibronic quantum states. The non-steady-state model we developed in this paper is applicable to fast pump and slow relaxation conditions, thus being more suitable for gas-phase systems than the condensed-phase where fast relaxations usually take place.     

Optical chaos in multiple degenerate four-wave mixing

Spatial evolution has been studied of an ensemble of equal-frequency light waves involved in several four-wave mixing processes under linear photoabsorption. It is shown that this system may exhibit spatial chaos caused by competition of optical mixing processes with strong energy exchange between the waves. For pulsed radiation, the temporal envelopes of interacting waves undergo modulations which may also be of chaotic character. Also discussed are possible variants of identifying chaos in systems of interacting light waves experimentally and the role of accompanying photoprocesses (photoabsorption, self-action of radiation).     

Probe gain via four-wave mixing based on spontaneously generated coherence

We have studied the probe gain via a double-Λ atomic system with a pair of closely lying lower levels in the presence of two probe and two coherent pump fields. The inversionless gain can be realized by using nondegenerate four-wave mixing under the condition of spontaneously generated coherence(SGC) owing to near-degenerate lower levels. Note that by using SGC, two probe fields can be amplified with more remarkable amplitudes, and the gain spectra of an extremely narrow linewidth can be obtained. Last but not least, our results show that the probe gain is quite sensitive to relative phases due to the SGC presence which allows one to modulate the gain spectra periodically by phase modulation, and can also be influenced by all laser field intensities and frequencies, and the angles between dipole elements.     

Quantum statistics of the degenerate four-wave mixing process

A quantum mechanical treatment is given of the degenerate four-wave mixing process. The approximate Heisenberg equation of motion for creation and annihilation operators is solved taking into account attenuation and noise. The solution and the statistics of the modes are discussed both below and above the threshold condition.     

Gas-phase velocimetry by nearly degenerate four-wave mixing

We demonstrate a new velocimetry technique for gas flows based on Nearly Degenerate Four-Wave Mixing (NDFWM). Measurements were performed on nitric oxide in a free-jet expansion using helium and argon as carrier gases, at flow velocities on the order of 1000 m/s. We obtained velocities by analyzing experimental spectra from the jet using a perturbative treatment of NDFWM that we extended to include an arbitrary bulk velocity. The results agreed with independent velocity measurements based on Laser-Induced Fluorescence (LIF), as well as with theoretical flow-field velocities, to better than 5% in all cases studied.     

Slow light with degenerate backward-wave four-wave mixing

We report on a slowing down of light pulses using degenerate backward-wave four-wave mixing in a photorefractive crystal. The delay and width of the output pulse for the amplified transmitted beam and for the phase-conjugated beam are studied as a function of the input pulse width. We demonstrate that the four-wave mixing process ensures a larger slowing down of short pulses compared to the photorefractive two-beam coupling scheme and guarantees the elimination of forerunners, which are among the principal drawbacks for slowing down of short pulses with two-beam coupling. The technique may be extended to slowing down of light with degenerate or nearly degenerate backward-wave four-wave mixing based on other types of nonlinearities.     

Theory of degenerate four-wave mixing in three-level atoms

We derive a theoretical model for phase conjugation in three level atoms. The atoms are assumed to be at rest and the intensities I₁ and I₂ of the pump beams can take arbitrary large values. We calculate the lineshape for a thin optical medium in the case of plane waves and of gaussian beams. In the case of a thick optical medium, we show that the gain saturates if I₁ ≠ I₂.     

Doppler-free two-photon spectroscopy using degenerate four-wave mixing

Using recently developed techniques of degenerate, four-wave mixing, Doppler-free two-photon spectra can be obtained. The signal level for such an experiment in xenon is calculated and found to be readily detectable as well as competing favorably with the method of observing fluoresence following two-photon absorption.     

On the finesse of a phase-conjugate Fabry-Perot resonator using nearly-degenerate four-wave mixing

We consider a Fabry-Perot cavity in which one of the mirrors is a phase-conjugate mirror (PCM) using near-degenerate four-wave mixing. We show that when taking pump depletion into account, the divergence in finesse of the resonator predicted by linear theories for a resonator round trip gain approaching unity is eliminated. The saturation of the finesse as a function of pump intensity leads to a new kind of bistability in the transmission characteristics of the system.