Quantum dynamics of interacting modes in the process of intracavity subharmonic generation

The dynamics of correlation between fluctuations of the number of photons of interacting modes is investigated for the process of intracavity subharmonic generation. It is demonstrated that this correlation strongly depends on the nonlinear mode coupling coefficient. For small values of the coupling coefficient, the correlation between fluctuations of the number of photons is small. With an increase in the coupling coefficient, the correlation increases (the state of subsystems becomes entangled) and, starting from a particular value of the coupling coefficient, starts to decrease with further increase in the coupling coefficient, gradually approaching zero (entanglement of subsystem states decreases). The quantum dynamics of the number of photons, quantum entropy, and Wigner function of the stationary state of the fundamental and subharmonic modes is investigated. It is demonstrated that the dynamics of these quantities also strongly depends on the coupling coefficient of the interacting modes. We show that, for large values of the mode coupling coefficient and long interaction times, the subharmonic mode becomes localized in a two-component state with equal probabilities of finding it in each component. Quantum entropy of this state is smaller than maximum entropy of the two-component state equal to ln2, which suggests that quantum-mechanical interference takes place between the subharmonic mode components.     

Quantum dynamics of intracavity third-subharmonic generation

The quantum dynamics of the mean number of photons and quantum entropy of interacting modes, as well as the Wigner function of the stationary state of the fundamental mode and the third subharmonic mode has been investigated for the intracavity third-subharmonic generation. It is shown that the quantum dynamics of the system depends strongly on the nonlinear coupling coefficient between the modes. It is also demonstrated that, in the steady-state limit, depending on the intermodal coupling coefficient, the fundamental mode can be either in a pure coherent state, or in a squeezed state, or in a pure vacuum state. The third subharmonic mode in the subthreshold regime of generation of this mode is in the vacuum state. The Wigner function is squeezed over three sides of an equilateral triangle (squeezed vacuum). The quantum entropy of this state is nonzero. It is also shown that the third subharmonic mode, depending on the nonlinear coupling coefficient in the steady-state limit, can be localized in the three-component state with the same probability of detecting a field in each coherent component of the state and with the presence of quantummechanical interference between the state components. The mean number of photons in this state is smaller than unity. Depending on the nonlinear coupling coefficient, the third subharmonic mode can also be localized in the three-component state, which is a statistical mixture of three squeezed states.     

Evolution dynamics of initial coherent states of a field in an unstable region of the behavior in the process of intracavity third harmonic generation

The quantum dynamics of the state of a field is studied for the process of intracavity third harmonic generation in the region of unstable behavior of the system in the case in which the interacting modes are developed from initial coherent states. It is shown that the Wigner functions of the states of the modes and mean values of the quadrature amplitudes of the fields can have oscillations disappearing with the transition of the system to a stable region.     

Quantum coherence and entangled states in intracavity third subharmonic generation process

The dynamics of correlation of photon number fluctuations of interacting modes for the process of intracavity third subharmonic generation is investigated. It is shown that the entangled field states by the variables of photon number can be obtained in this system. The quantum dynamics of the photons number, the quantum entropy and the Wigner function of the stationary states of the fundamental mode and the third subharmonic mode have also been studied. It is found that the dynamics of these quantities depends highly on the value of the coupling coefficient of the interacting modes. It is shown that at long interaction times and for the large values of the coupling coefficient of the modes, the mode of the third subharmonic is localized in the three-component state with the same probability of detection of the mode in each component of the state. The quantum entropy of the state is less than the maximal entropy of the three-component state ln3, which points out the presence of quantum mechanical interference between the components of the state of third subharmonic mode.     

Laser control of third-harmonic generation by means of an additional EM field

Control of the third-harmonic generation process through an external electromagnetic field is observed in atomic Ca. The conversion efficiency can be modified when the third harmonic is produced in the vicinity of an autoionizing state. A second laser is used to produce strong radiative coupling between a low-lying bound state and the autoionizing state.     

宽带三倍频混频过程的群速匹配关系

基于非线性耦合波理论分析了三倍频过程中群速度之间的关系，推导出三波混频条件下的群速匹配关系式.对超短脉冲在Ⅱ类KDP晶体中的混频过程进行了模拟分析，结果表明：当三波(基波ω，谐波2ω和3ω)的群速度满足该匹配关系式时，三倍频(3ω)的带宽和转换效率均可达最大值；而随着三波群速度对该关系式的偏离逐渐增大，带宽变窄、转换效率下降.导出的三波群速匹配关系式对寻找合适的色散晶体和选择有效的匹配措施、实现宽带三次谐波转换具有指导意义.     

Distribution of numbers of photons in the region of unstable behavior in the process of intracavity second harmonic generation

For the process of intracavity second harmonic generation we investigate in positive P-representation with simulation of Langevin noise sources the distribution functions of numbers of photons in fundamental and second harmonic modes in the region of unstable behavior of the system. It is shown that in the unstable region, as distinct from the stable, the functions of distribution have two-peak structure. We also study the joint function of distribution of photon numbers in interacting modes.     

Fluctuations in number of photons in region of unstable behavior in process of intracavity generation of second harmonic

Quantum fluctuations of the number of photons of the fundamental mode and of the second harmonic in the process of intracavity generation of the second harmonic in the unstable region of the system are studied. The distribution functions of the number of photons of interacting modes are calculated in the positive P-representation. The functions of the joint distribution of the number of photons of the fundamental mode and the number of photons in the second harmonic are also studied.     

Correlation of fluctuations of the quadrature amplitudes of interacting modes in the instability region of intracavity third-harmonic generation

Correlation of fluctuations of quadrature amplitudes of interacting modes is studied for the process of intracavity third-harmonic generation in the region of instability. It is shown that this correlation strongly depends on the value of the nonlinear mode coupling coefficient. For small values of the coupling coefficient, correlation of fluctuations of quadrature amplitudes is small. With increasing coupling coefficient, the correlation increases (states of the subsystems become entangled). Then, starting from a certain value of the coupling coefficient, it starts decreasing gradually, tending to zero (entanglement of states of the subsystems decreases). Correlation of fluctuations of quadrature amplitudes decreases also when the amplitude of the fundamental mode perturbing field is decreased.     

Sub-poissonian light in third-harmonic generation: Quantum predictions via classical trajectories

Sub-Poissonian light in the third-harmonic generation process is studied numerically and analytically. Special regime exhibiting the time-stable maximum sub-Poissonian behaviour with the Fano factorF ≈ 0.81 is found and analyzed. Theoretical prediction of the Fano factor and explanation of the extraordinary time stability of the sub-Poissonian behaviour are given using the semiclassical method of classical trajectories.     

Suppression of FM-to-AM conversion in phase modulated third-harmonic generation process

Phase modulation to amplitude modulation (FM-to-AM) conversion occurring in phase modulated third-harmonic generation (THG, process 1ω + 2ω → 3ω) process is investigated. To suppress the FM-to-AM conversion, a group-velocity-matching relationship is derived, which appears to be dependent on the ratio of modulation depth of 2ω–1ω pulses. Numerical simulations indicate that the FM-to-AM conversion in phase-modulated THG process can be suppressed effectively by satisfying that group-velocity-matching relationship.     

Quantum computation and entangled state generation through a cavity output process

We propose a protocol to realize quantum phase gates and generate entangled states between two atoms trapped in one cavity. In Lamb-Dick limits, it is not necessary to require coincidence detections, which will relax the conditions for the experimental realization. The protocol can be generalized to generate N-atom entangled states.     

Quantum state tomography of an itinerant squeezed microwave field

We perform state tomography of an itinerant squeezed state of the microwave field prepared by a Josephson parametric amplifier (JPA). We use a second JPA as a preamplifier to improve the quantum efficiency of the field quadrature measurement from 2% to 36%±4%. Without correcting for the detection inefficiency we observe a minimum quadrature variance which is 68(-7)(+9)% of the variance of the vacuum. We reconstruct the state's density matrix by a maximum likelihood method and infer that the squeezed state has a minimum variance less than 40% of the vacuum, with uncertainty mostly caused by calibration systematics.     

内腔二次谐波过程中光场强度自脉冲振荡的增强

本文利用宏观非线性极化模型,分析了相干驱动内腔二次谐波过程中光场的动力学演化行为.发现了光场的一种新的动力学不稳定性.在此基础上,提出了一个增强光场强度自脉冲振荡的可能途径.     

Imaging of Ca(2)+ intracellular dynamics with a third-harmonic generation microscope

We describe the promising development of third-harmonic generation (THG) in laser scanning microscopy for study of the functional imaging of live biological cells. The dynamics of Ca(2+) in biological cells is shown. The Ca(2+) signal consists of a transient increase in the intracellular concentration. THG microscopy allows one to temporally visualize the release of Ca(2+) from internal stores and (or) calcium influx.     

Investigation of intracavity third-harmonic generation at 1.06 μm in YCa4O(BO3)3 crystals

Intracavity sum-frequency mixing of 1.06 μm and 532 nm in YCa₄O(BO₃)₃ (YCOB) crystals cut for different type-I phase-matching directions of (θ,ϕ)=(106°,77.2°), (111°, 79.6°) and (65°, 82.8°) was investigated in a compact diode-end-pumped acousto-optical Q-switched Nd:YVO₄/KTP laser formed with a three-mirror folded resonator. The maximum 355-nm average output power of 124 mW was obtained in the phase-matching direction of (106°, 77.2°) with a pump-to-ultraviolet conversion efficiency of 3.3% at the repetition frequency of 20 kHz. Received: 17 September 2001 / Revised version: 27 November 2001 / Published online: 17 January 2002