Effects of correlations between the real and imaginary parts of quantum noise on intensity fluctuation for a saturation laser model

This paper studies the effects of cross-correlations between the real and imaginary parts of quantum noise on the laser intensity in a saturation laser model. It derives the analytic expressions of the intensity correlation function ${C(\tau)}$ and the associated relaxation time ${T({C})}$ in the case of a stable locked phase resulting from the cross-correlation ${\lambda_q}$ between the real and imaginary parts of quantum noise. Based on numerical computations it finds that the presence of cross correlations between the real and imaginary parts of quantum noise slow down the decay of intensity fluctuation, i.e., it causes the increase of intensity fluctuation.     

Effects of correlations between the real and imaginary parts of quantum noise on intensity fluctuation for a saturation laser model

This paper studies the effects of cross-correlations between the real and imaginary parts of quantum noise on the laser intensity in a saturation laser model. It derives the analytic expressions of the intensity correlation function C（τ） and the associated relaxation time T（C） in the case of a stable locked phase resulting from the cross-correlation λq between the real and imaginary parts of quantum noise. Based on numerical computations it finds that the presence of cross correlations between the real and imaginary parts of quantum noise slow down the decay of intensity fluctuation, i.e., it causes the increase of intensity fluctuation.     

Statistical properties of the laser emission in a low-Q cavity

We investigate theoretically the stationary statistical properties of the laser radiation in a low-Q cavity with field, polarization, and population fluctuations. Eliminating adiabatically the electric field from the Maxwell-Bloch equations, coupled Langevin equations with bothadditive andmultiplicative noises are derived and are transformed into the multivariable Fokker-Planck equation of a probability density of the light intensity and the population difference. It is solved by the expansion into orthonormal sets, and a vector recurrence equation of motion of the expansion coefficients is given whose stationary solutions are analytically obtained in theMatrix continued-fraction. The stationary distribution function of the radiation intensity are calculated with several values of control parameters. We discuss the variance of the intensity distribution, the photon-counting coefficient, and the cross-correlation between intensity and population as a function of the pump parameter, and reveal the novel and characteristic features of the bad-cavity laser system. The comparison with the good-cavity (high-Q cavity) case is also made.     

Phase dynamics of a detuned single-mode laser

We report measurements on the phase dynamics of a detuned single mode laser which has in the past shown correspondence to the complex Lorenz equation. The corresponding ranges of periodic pulsing, of detuned chaos and of windows within the chaotic domain are investigated.Invited paper     

The statistical fluctuation of a single-mode laser system driven by coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts

Using the linear approximation method, this paper studies the statistical property of a single-mode laser driven by both coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts, and calculates the steady-state mean normalized intensity fluctuation and intensity correlation time. It analyses the influences of the modulation signal, the net gain coefficient, the noise and its correlation form on the statistical fluctuation of the laser system respectively. It is found that the coloured pump noise modulated by the signal has a great suppressing action on the statistical fluctuation of the laser system; the pump noise self-correlation time and the specific frequency of modulation signal have the result that the statistical fluctuation tends to zero. Furthermore, the `colour' correlation of pump noise has much influences on the statistical fluctuation of the laser system. Increasing the intensity of pump noise will augment the statistical fluctuation of the laser system, but the intensity of quantum noise and the coefficient of cross-correlation between its real and imaginary parts have less influence on the statistical fluctuation of the laser system. Therefore, from the conclusions of this paper the statistical property can be known and a theoretical basis for steady operation and output of the laser system can be provided.     

信号调制色泵噪声和实虚部间关联量子噪声驱动下单模激光的随机共振现象

计算了受信号调制的色泵噪声和实虚部间关联的量子噪声驱动的单模激光损失模型的输出光强信噪比.发现信噪比R随泵噪声自关联时间τ、调制信号频率Ω和量子噪声实虚部间关联系数λq的变化均存在随机共振,这种现象扩展了“信噪比R对噪声强度的变化曲线具有极大值”的典型随机共振. 若以Ω为参数,当Ω增加时,Ｒ随τ的关系曲线经历了从同时出现共振和抑制到单峰共振,最后到单调上升的变化,呈现多种形式的随机共振．若以τ为参数,当τ增加时,Ｒ随Ω的关系曲线经历了从单调上升到同时出现共振和抑制,最后又到单调下降的变化过程．Ｒ随λq的关 关键词： 噪声 信噪比 随机共振     

Four-photon processes stimulated by a fluctuating pump

Four-photon parametric light amplification stimulated by noisy pump in a dispersive medium, is theoretically analyzed. The model of the fluctuating phase is used. The increments in case of temporal as well as of spatial laser pump modulation are considered. It is shown that the efficiency of the four-photon process due to a broad-band pump is comparable to that of monochromatic pump. Quantitative estimates for the medium of metal vapor are given, too.     

Moments of the intensity of a single-mode laser driven by coloured pump noises with a cross-correlation between the real and imaginary parts of the quantum noise

By means of the unified coloured noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser cubic model driven by coloured pump noise with cross-correlation between the real and imaginary parts of the quantum noise. We present a thorough discussion of how the cross-correlation λ_q between the real and imaginary parts of the quantum noise and the self-correlation time τ of the pump noise determine the behaviours of the mean intensity 〈I〉 and variance λ_2 (0) for both below and above the threshold operation, and many new phenomena are discovered. When the laser is operated above the threshold, increasing the cross-correlation intensity λ_q makes the 〈I 〉－τ curves exhibit a "re-entrant phase transition". Whether the laser is above or below the threshold, the whole 〈I 〉－τ curve moves down as λ_q increases; however, when λ_q=1 (perfect cross-correlation), the curve abruptly runs up. A nonzero value of cross-correlation time τ (τ≠0) leads to the entire λ_2(0)－p′ curve being suppressed (here p′ is the pump noise intensity). This indicates the increasing precision of the laser beam due to the existence of the self-correlation time τ. The behaviour of the λ_2 (0)－p′ curve as a function of λ_q is similar to that of the 〈I 〉－τ curve against λ_q: that is, whether the laser is above or below the threshold, the λ_2 (0)－p′ curve moves up as λ_q increases; however, when λ_q=1, the curve suddenly moves down. Through the study in this paper, we can find a way to optimize for output laser intensity.τ     

Stochastic resonance in a gain--noise model of a single-mode laser driven by pump noise and quantum noise with cross-correlation between real and imaginary parts under direct signal modulation

Stochastic resonance (SR) is studied in a gain--noise model of a single-mode laser driven by a coloured pump noise and a quantum noise with cross-correlation between real and imaginary parts under a direct signal modulation. By using a linear approximation method, we find that the SR appears during the variation of signal-to-noise ratio (SNR) separately with the pump noise self-correlation time \tau , the noise correlation coefficient between the real part and the imaginary part of the quantum noise \lambda_q , the attenuation coefficient \gamma and the deterministic steady-state intensity I_0 . In addition, it is found that the SR can be characterized not only by the dependence of SNR on the noise variables of \tau and \lambda_q, but also by the dependence of SNR on the laser system variables of \gamma and I₀. Thus our investigation extends the characteristic quantity of SR proposed before.     

Colored noise in a two-dimensional nonlinear system

A two-dimensional decoupling theory is developed when colored noise is included in a nonlinear dynamical system. By a functional analysis, the colored noise is transformed to an effective noise that includes the noise correlation time, the mean dynamical variable, and the original noise strength. When the two-dimensional decoupling theory is applied to single-mode and two-mode dye laser systems, the mean, variance, and effective eigenvalue of laser intensity are calculated. Excellent agreement between theoretical analysis, numerical simulations, and experimental measurements are obtained. It is seen that the increase of noise correlation time can reduce the fluctuations in the laser system. It is also shown that there is relatively large fluctuation in the phase when the laser undergoes from thermal light to coherent light when the theory is applied to a single mode dye laser. Received 20 August 2001 and Received in final form 4 December 2001     

Dynamics of a quantum oscillator strongly and off-resonantly coupled with a two-level system

Beyond the rotating-wave approximation, the dynamics of a quantum oscillator interacting strongly and off-resonantly with a two-level system exhibit beatings, whose period equals the revival time of the two-level system. On a longer time scale, the quantum oscillator shows collapses, revivals and fractional revivals, which are encountered in oscillator observables like the mean number of oscillator quanta and in the two-level inversion population. Also the scattered oscillator field shows doublets with symmetrically displaced peaks.     

实虚部关联的量子噪声和泵噪声对单模激光动力学性质的影响

采用具有实虚部关联的量子噪声和泵噪声驱动的单模激光损失模型，用线性化近似方法研究了反映激光动力学性质的光强关联函数，讨论了光强关联函数随时间的演化；并对线性化近似方法的适用范围进行了详细分析，分别讨论了量子噪声强度、泵噪声强度、量子噪声实虚部关联系数对光强相对涨落的影响，得出在小噪声、远离阈值时，线性化近似方法适用范围扩大；小噪声、远离阈值且当量子噪声实虚部无关联时，线性化近似方法适用范围最大的结论. 关键词： 单模激光 光强关联函数 光强相对涨落     

Spatio-temporal coupling of laser fluctuations — Observations on a laser with internal frequency conversion

The amplitude of standing wave solid state lasers with frequency conversion inside the resonator can become unstable. We investigated the amplitude fluctuations of an end-pumped Nd:YAG-laser at low pump rates (below 160% threshold pump power) and also above. Detecting the individual mode instabilities separately and comparing them with a theoretical laser model, we can trace the origin of the mechanism leading to the observed fluctuations. At certain well defined discrete pump levels above 160% threshold the instabilities disappear. These stable emission states are associated with particular nonconventional mode patterns, some of them exhibiting a helical phase structure. Based on experimental observations and computer simulations of pump induced resonator aberrations we describe a mechanism for the emergence of the peculiar transversal modes and laser fluctuations.     

Non-universality of dephasing in quantum transport

We investigate the influence of the environment on coherent quantum transport. While random processes with classical stochastic potentials can be treated in the concept of phase memory, this is not possible for fully quantized system-plus-reservoir models. In the latter case, the decay of coherences is not only depending on the coupled dynamics, but also crucially on the special geometry of the physical system in regard. We introduce a microscopic model with localized environmental modes where the geometry dependence is removed and calculate the coherence length.     

The distribution of quantum fidelities

When applied to different input states, an imperfect quantum operation yields output states with varying fidelities, defined as the absolute square of their overlap with the desired states. We present an expression for the distribution of fidelities for a class of operations applied to a general qubit state, and we present general expressions for the variance and input-space averaged fidelities of arbitrary linear operations on state vectors in finite-dimensional Hilbert spaces.     

Analysis of nonclassical behavior for a two-mode coupled-photon system

We consider a model two-mode coupled-photon system and verify that the photon distribution for this system is exactly super-Poissonian. We calculate the Glauber–Sudarshan diagonal P representation for both the individual photon subsystem and the complete photon–photon complex. We present the detailed analysis on the threshold temperature of the nonclassical behavior for the both cases. We discuss the effect of the interaction between two photons on the threshold temperature.     

Threshold and saturation properties of a solid-state XeF (C-A) excimer laser

A dielectric laser cavity of 1 cm length has been optimized for high gain (7 cm^–1) operation which is achieved in XeF doped Ar crystals. Mode structures on the C-A spectral distribution around 540 nm and far field transverse mode patterns are reported. Photchemical gain burning is observed in the spectral mode structures. The dependence of the laser threshold on pump energy, pumped length and on cavity losses is studied. XeF densities of 7×10¹⁷ cm^–3 and distributed losses of 1.2 cm^–1 are derived. The measured quantum efficiency of 14% and the saturation behaviour are consistently described. Losses by transient aborption and two photon absorption are discussed.     

Long time tails in the quantum Hall effect

Velocity correlation functions in the time domain offer a new approach to the dissipative conductivity in the quantum Hall effect at half-filled Landau bands. We describe two methods of calculating these functions directly by wave packet propagation techniques. We address the question whether quantum effects modify the high field diffusion described within the semiclassical percolation picture of the QHE. We investigate a number of random potentials with finite correlation length. Coupling to higher Landau levels leads to damped cyclotron oscillations in the velocity correlation. Besides that, we observe a long time tail (t)t ^– with 2.3 for all potential ranges investigated. Within the statistical uncertainty and the time interval considered, this power law is consistent with the semiclassical result obtained by averaging over all cluster sizes. Our findings imply detectable deviations from Drude's law for the AC conductivity.     

Time evolution of the intensity correlation function in a single-mode laser driven by both the coloured pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts

Using the linear approximation, we have studied the time evolution of intensity correlation function C（t） in a single-mode laser driven by both the colored pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts. In the case of the pump noise self-correlation time, we find that the time evolution of C（t） varies with modulation signal frequency Ω, amplitude B, and net gain ɑ0. (i) As the Ω increases, the time evolution of C（t） experiences a process changing from the monotonous descension to the descension with a flat appearing initially, and finally to the a form of damping oscillation; (ii) As the B increases, it experiences from monotonous descension to the appearance of a maximum; (iii) As the net gain ɑ0 increases, it experiences a process repeatedly changing from the monotonous descension to monotonous ascension, and to the appearance of a maximum, finally to monotonous descension again. However, in the case of, the time evolution of C（t） only exhibits a form of damping oscillation .