Two-photon Optical Bistability Research Articles

Quantum Nondemolition Measurement in Two-Photon Optical Bistability**The project supported by National Natural Science Foundation of China

We evaluate the effectiveness of the quantum nondemolition (QND) measurement scheme in an effective two-level atomic configuration by using the input–output formalism and the quantum regression theorem. The QND capability can be promoted greatly as the cavity detuning is swept towards the bistability threshold.

Nearly ideal squeezing in degenerate two-photon optical bistability in three-level atoms

Two-photon bistability in a system of three-level atoms driven by a single-frequency field shows nearly ideal squeezing close to a dynamic instability threshold, occurring in the lower branch of the steady-state bistability curve. The squeezing is maximized and becomes very broad band in the bad cavity limit. Such results which were previously predicted on the basis of an effective two-level model, are demonstrated here and analysed by a full three-level treatment of the atoms. In addition, important restrictions and new features are found.

Nonlinear dynamics of a class-A two-photon laser with injected signal

Abstract We performed a comprehensive study of the temporal dynamics of a two-photon laser with resonant injected signal in the high-Q cavity limit (class-A laser). The stationary solutions as well as their stability are completely characterized. In particular it is shown that tristable behaviour is possible, in contrast with two-photon optical bistability. It is also shown that there are two independent Hopf bifurcations, the sub- or supercritical character of which is analytically determined. The dynamics of the system far from the bifurcation points is classified through a numerical study.

Swift - Hohenberg-type equation for nascent two-photon optical bistability in the weakly dispersive limit

Two-photon optical bistability under the influence of transverse effects is considered near the onset of bistability in the weakly dispersive limit. A reduced-field equation of the Swift - Hohenberg type is then obtained, showing the equivalence between two-photon and the usual one-photon optical bistability in the considered limits.

Squeezing in the self-pulsing domain of lasers with two-photon saturable absorbers

Lasers with two-photon saturable absorbers exhibit a phase instability similar to that of two-photon optical bistability. Beyond the phase instability threshold the output intensity breaks into spontaneous oscillations. Analytical perturbative solutions have been found and we have linearized the Fokker-Planck equation around these solutions. The drift and diffusion matrices have been perturbatively developed and we obtained a time-dependent Ornstein-Uhlenbeck stochastic process. We have calculated the amplitude correlations and squeezing spectrum near but above the threshold for a Hopf bifurcation in bad cavity conditions.

Two-photon optical bistability in polar molecules: vibrational coupling effects

Single-beam two-photon optical bistability in a two-level system where the levels have unequal electric dipole moments is analyzed theoretically. By means of unitary transformations the system is transformed into a two-level nonpolar system with a field-dependent effective transition dipole moment. Two-photon optical bistability is found to be favored as the difference between the dipole moments grows. When the excited electronic system is coupled to a vibrational normal mode of the nuclei, the susceptibility becomes three-valued and consequently a different type of optical bistability appears, which can coexists with the previous one.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Generation of nonclassical states by nonlinear optical systems

We review the main results obtained recently by our group in the field of quantum noise reduction in nonlinear optical systems. We illustrate the possibility of obtaining significant effects in degenerate parametric oscillators, intracavity second-harmonic generation, nondegenerate four-wave mixing, and one- and two-photon optical bistability.

Phonon effects on optical bistability in a two-photon resonant absorber

Single beam two-photon optical bistability in a Fabry-Perot cavity is analyzed taking into account phonon effects. The Maxwell-Bloch equations of the system are further coupled by a term that is dependent on the electron-phonon interaction. It is shown that such an interaction can lead to a new type of optical bistability which competes with the ordinary absorptive one.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

THE ATOM SQUEEZING EFFECT FOR OFF-RESONANT TWO-PHOTON OPTICAL BISTABILITY IN BAD-CAVITY CASE

The atom squeezing effect for off-resonant two-photon optical bistability in bad-cavity limit is studied by means of Fokker-Planck equation of the generalized Wigner distribution. The distribution of the squeezing region in Δ-θ plane is described. As atom-detuning is sufficiently large, the squeezing effect of the atom operator R2 may appear.

TEMPORAL ASPECTS OF ABSORPTIVE TWO-PHOTON OPTICAL BISTABILITY

We investigate the temporal aspects of absorptive two-photon optical bistability described by a semiclassical theory in the limit of a fully developed hysteresis cycle and when all decay rates have comparable magnitude. We show by multiple time-scale perturbation analysis that near the high-transmission branch the behavior of the system is governed by an equation for the field amplitude which determines the long-time evolution of the system, whereas, near the low-transmission branch all dynamical variables vary on the long time scale, and it is possible to describe the transition between the two stable branch by simple equations.

Phase sensitivity in two-photon optical bistability.

Phase sensitivity in two-photon optical bistability.

Phase instability and intensity squeezing in lasers with two-photon saturable absorbers

It is shown that a laser with a two-photon saturable absorber exhibits a phase instability similar to that of two-photon optical bistability. The authors calculate the spectrum of the intensity fluctuations in the output field under conditions of exact resonance between the amplifier and the absorber. In the bad-cavity limit the relevant part of the spectrum assumes a simple Lorentzian form; as the phase-instability threshold is approached, the reduction of quantum noise becomes perfect for small frequencies.

Periodic attractors in two-photon processes

We consider three nonlinear optical models that display a two-photon process and exhibit a Hopf bifurcation corresponding to a phase instability. The three models describe second-harmonic generation, two-photon optical bistability, and degenerate four-wave mixing in resonant cavities. In all three cases we consider only the resonant configuration and analyze the attractors which emerge when the driving field is increased beyond the Hopf bifurcation threshold. At a finite distance from threshold, we find a hysteresis domain that involves a pair of periodic attractors. For all three models, each of the two solutions has the same ``field portrait'' i.e., the same representation in a plane whose axes are the imaginary and the real parts of the electric field. This suggests that the scenario is generic for this class of systems. On the other hand, the models for two-photon optical bistability and degenerate four-wave mixing in resonant cavities exhibit additional nongeneric attractors when the driving field is further increased.

Universal normal-form description of squeezing and instabilities in two-photon processes

We consider a class of optical systems, consisting of an electromagnetic resonator, a two-photon medium and a single-mode cavity field, in the limit when the field decay constant out of the cavity greatly exceeds the remaining relaxation rates. Under rather general conditions, this limit favors the emergence of self-oscillations over a finite domain of parameter space where, for resonant interaction, the instability has a pure phase or amplitude character. The squeezing of the quadrature component of the output field that is orthogonal to the unstable component approaches the ideal limit in the vicinity of the instability threshold and its spectrum can be described by a simple and universal normal-form. We analyze selected configurations of experimental interest and identify a new type of instability that should emerge in four-wave mixing cavities with a concomitant large squeezing effect; we show also that the phase instability and squeezing recently predicted in two-photon optical bistability persist even after inclusion in the model of the effects associated with the intensity-dependent Stark shift.

Two-photon optical bistability of polar molecules inserted in a solid matrix: Phonon effects

Single-beam two-photon optical bistability in a Fabry-Perot cavity filled with molecules which change permanent dipole moment upon electronic excitation is analysed under the mean-field and plane-wave approximations. One-photon resonances are discarded. These molecules are assumed to be in a solid matrix. Phonon effects are then taken into account. The Bloch equations of the system are further coupled by a term that is dependent on the electron-phonon interaction, leading to shifts in the switching thresholds which modify the optical bistability character. Such a term becomes irrelevant when the difference between the dipole moments is much greater than the transition dipole moment.

Double-beam two-photon optical bistability in a Fabry-Perot cavity with polar molecules

Optical bistability in a micrometre-sized Fabry-Perot cavity, filled with appropriate polar molecules, is analysed after two incident beams (with frequenciesgw1 andgw2) produce in the system a two-photon resonance at frequencygw1 +gw2. One-photon resonances at the frequenciesgw1 andgw2 are discarded. It was not necessary to assume a particular relationship betweengw1 andgw2, and the single-beam two-photon optical bistability whengw1 andgw2 are of the same order or equal is emphasized.

Squeezing and quantum noise correlations in dispersive two-photon optical bistability

Presents an analysis of a two-photon double-beam bistable device, in the dispersive and high-finesse limits. The expressions for the mean fields inside the cavity are given above the destabilization thresholds, and quantum fluctuations of the outcoming fields are analyzed below these thresholds. It appears that this device yields several new quantum noise reduction schemes, which are closely related to the mean fields behaviour.

Squeezing in two-photon optical bistability and laser with injected signal

We show that, on approaching the threshold for the phase instability of two-photon optical bistability, the spectrum of squeezing exhibits the onset of a large squeezing on a frequency region on the order of the cavity linewidth. The squeezing becomes perfect in the bad-cavity limit. This phenomenon does not require detuning nor a large value of the bistability parameter, and occurs for values of the input intensity well below the saturation level, and much smaller than that corresponding to the turning point of the steady-state curve. In the resonant configuration the best squeezing arises in the amplitude quadrature component and is therefore accompanied by a strongly subpoissonian photon statistics. We show that in the bad-cavity limit the two-photon laser with injected signal exhibits a significant squeezing in the phase quadrature component.

Phase instability in two-photon optical bistability

We analyze the problem of single-mode two-photon optical bistability using a model which neglects the intensity-dependent Stark shift. We demonstrate the existence of a phase instability which arises in bad-cavity conditions in the lower branch of the steady-state curve, and study the spontaneous oscillations which emerge from this instability.

THE MULTI-PHOTON QUANTUM STATISTICAL THEORY OF DRIVEN OPTICAL SYSTEMS (Ⅰ)——FOKKER-PLANCK EQUATION AND GOOD CAVITY CASE

The systematic method of Fokker-Planck equation (FPE) for the generalized Wigner distribution is used to study the multi-photon transition process of a driven optical system. The general multi-photon FPE, the state equation and the spectrum of transmitted light in good cavity limit are obtained- The two-photon optical bistability spectrum of transmitted light is calculated and compared with single-photon case. It is shown that for multi-photon case, the atom -atom correlation is also negligible in the good cavity limit.