Einstein——Podolsky——Rosen entanglement in time-dependent periodic pumping non-degenerate optical parametric amplifier

The solution of the time-dependent periodic pumping non-degenerate optical parametric amplifier (NOPA) is derived when the pump depletion is considered both above and below thresholds. Based on this solution, the quantum fluctuation calculated shows that a high entanglement and a good squeezing degree of the parametric light beams are achieved near and above thresholds. We adopt two kinds of pump fields: (i) a continuously modulated pump with a sinusoidal envelope; (ii) a sequence of laser pulses with Gaussian envelopes. We analyse the time evolution of continuous variable entanglement by analytical and numerical calculations, and show that the periodic driven pumping also improves the degree of entanglement. The squeezing and Einstein-Podolsky-Rosen (EPR) entanglement by using the two pumping driven functions are investigated from below to above the threshold regions, the tendencies are nearly the same, and the Gaussian driven function is superior to that of the sine driven function, when the maximum squeezing and the minimum variance of quantum fluctuation are considered. In the meantime, the generalization of frequency degenerate OPA to frequency non-degenerated OPA problem is investigated.     

Theorie der parametrischen Vier-Photonen-Wechselwirkung. III. Verstärkung und Oszillation bei Berücksichtigung der Rückwirkung auf die Pumpwelle

The processes of parametric amplification and oscillation in a medium with cubic polarization are investigated theoretically taking into consideration the depletion of the pump wave. We suppose that phase-matching is realized exactly (a possible nonlinear detuning of the exact phase-matching should be compensated by a suitable subsequent adjustment of the frequencies). A consequence of linear losses is the appearance of a threshold for the parametric amplification. There exist a maximum length, a minimum length and an optimum length of the nonlinear medium for the process of parametric amplification. The threshold intensity, the optimum length of the nonlinear medium and the optimum reflection coefficient for outcoupling are determined for two arrangements of the double resonant parametric four-photon oscillator (ring resonator, FABRY -PEROT resonator). It is shown that for the above mentioned arrangements of the single resonant and the double resonant four-photon oscillator the efficiency is a monotonous function of the threshold excess. On the contrary in case of the three-photon oscillator there exists an optimum value of the threshold excess.     

Theorie der parametrischen Vier-Photonen-Wechselwirkung. II., Verstärkung und Oszillation in der Näherung des vorgegebenen Pumpfeldes)

The processes of parametric amplification and oscillation in a medium with cubic polarization is investigated in parametric approximation. For the case of amplification the threshold power of the pump wave is calculated. The influence of a finite phase mismatching and of the initial phases on the amplification process is discussed. For larger values of mismatching a periodical change between amplification and depletion may appear. For the cases of a single resonant oscillator (for the signal wave only), a double resonant oscillator (for both signal and idler wave) and a double resonant oscillator with the pump wave reflected at the second mirror the threshold power of the pump wave and the rise time are calculated. Characteristic differences between four-photon and three-photon parametric oscillators are discussed. A numerical estimation of the threshold power for some media with nonlinear susceptibilities known from literature leads to the conclusion that the realization of a four-photon parametric oscillator should be possible. In the appendix we discuss the influence of diffraction, focussing, birefrigence, nonstationarity and depletion of the pump wave on the studied process as well as the conditions under which these effects can be neglected.     

利用三平面腔镜共焦腔产生多模压缩光束

设计了一种阈值下的简并光学参量振荡腔用于产生多模压缩光束,并且利用"薄晶体近似"的方法分析了这个光学参量振荡腔,得到了输出多模压缩光束的噪声谱.数值模拟了多模压缩光束的压缩度和抽运光场或者振荡腔的失谐量之间的关系,得出只有适当选择本底光的相位,抽运光的幅度以及共焦腔的失谐量时,才可以探测到好的信号场噪声谱压缩度.     

Generation of pulsed squeezed light in a mode-locked optical parametric oscillator

The generation of pulsed squeezed light using an optical parametric oscillator (OPO) is discussed. This mode-locked optical parametric oscillator consists of a nonlinear crystal in a cavity which is resonant for both signal and idler waves and which is synchronously pumped by the second-harmonic of an acousto-optically mode-locked cw Nd: YAG laser. The fundamental wavelength of the pump laser provides local oscillator pulses for balanced homodyne detection of squeezed vacuum pulses emitted by the oscillator when operated below oscillation threshold. Photocurrent noise reduction to 30% below the classical shot-noise limit is observed, corresponding to squeezing of the field to a level approximately a factor of two below the mean square vacuum noise.     

飞秒脉冲正交位相压缩光的产生

利用锁模飞秒脉冲激光二次谐波为抽运源, 同步抽运单共振光学参量振荡器, 抽运光中心波长为425 nm, 重复率为76 MHz, 脉宽180 fs, 光学振荡器下转换晶体采用Ⅰ类共线PPKTP, 实验上实现了压缩度为2.58 dB的正交位相压缩光.考虑到实验系统的效率, 可以推知光学参量振荡器输出的下转换光压缩度为 4.48 dB. 关键词： 同步抽运光学参量振荡器 压缩光 锁模飞秒脉冲     

三共振准相位匹配光学参量振荡器反射抽运场的正交位相压缩

利用全固化单频Nd∶YVO₄激光器抽运由periodically poled lithium niobate(PPLN)准相位匹配晶体组成的光学参量振荡器,通过调节晶体的温度,在信号模与闲置模近简并的情况下,完成了抽运场与两个亚谐波模在腔内同时共振,实现了光学参量振荡器的极低阈值运转(阈值为1.2mW);当抽运功率为阈值抽运功率的2.8倍时,观察到反射抽运光的正交位相压缩,压缩度达1.1dB.数值计算与实验结果一致     

Widely tunable photonic crystal fiber Fabry-Perot optical parametric oscillator

We present a widely tunable low-threshold chi(3) optical parametric oscillator. The oscillator cavity is formed by butt coupling dichroic mirrors to either end of a highly nonlinear index-guiding photonic crystal fiber. This yields a singly resonant Fabry-Perot oscillator with a high feedback fraction for the resonant parametric sideband. The tuning range of the output parametric sideband stretches from 23 to 164 THz above the pump frequency. The threshold power of the oscillator is only 15 W.     

中红外连续波单谐振光学参量振荡器热致相位失配

为了研究热致相位失配对中红外连续波单谐振光学参量振荡器(CW-SRO)输出效率的影响, 结合CW-SRO计算模型和热传导方程,利用有限元分析方法,重点对输出3.3 m波长闲频光的CW-SRO进行了分析。计算了不同信号光输出耦合率及不同泵浦功率下CW-SRO晶体输出截面上热致相位失配量的分布。由计算结果可以看出:晶体吸收腔中振荡信号光是导致晶体热效应的主要因素;在相同的输入条件下,泵浦功率在30 W以上时CW-SRO的热致相位失配将会大大降低其泵浦损耗率;通过增加信号光输出耦合率的方法,可以减少热致相位失配对CW-SRO输出效率的影响,但CW-SRO的振荡阈值会增加。     

含时的线性驱动简并参量放大系统的量子起伏

导出在P表象中含时的线性驱动简并参量放大Fokker-Planck方程，并求其解.在阈值以下或阈值附近，含时驱动Fokker-Planck方程的解与线性理论或阈值附近的微扰理论预言的基本相符.在阈值以上，含时驱动Fokker-Planck方程解的短期行为也与线性近似解相近，但当τ增大后的长期行为完全区别于线性理论的结果. 关键词： 含时的线性驱动简并参量放大 Fokker-Planck方程 量子起伏     

Multimode squeezed states produced by a confocal parametric oscillator

We investigate the spatial behaviour of the quantum-noise-reduction spectrum of the vacuum state emitted by a degenerate optical parametric oscillator below threshold. In view of possible experimental implementations, we consider a mode-degenerate resonator and two matching lenses and show that, for the realistic case of a finite-width pump, significant level of squeezing can be observed in a very small region of the beam. Received 25 September 2002 Published online 11 February 2003     

Generation of optical frequency comb squeezed light field with TEM_(01) transverse mode

Nonclassical optical frequency combs find tremendous utility in quantum information and high-precision quantum measurement. The characteristics of a type-I synchronously pumped optical parametric oscillator with the TEM_(01) transverse mode below threshold are investigated and a squeezing of 0.7 dB for an optical frequency comb squeezed light field with the TEM_(01) transverse mode is obtained under the pump power of 130 m W. This work has a promising application in three-dimensional space-time measurement.     

Squeezing in the audio gravitational-wave detection band

We demonstrate the generation of broadband continuous-wave optical squeezing from 280 Hz-100 kHz using a below-threshold optical parametric oscillator (OPO). The squeezed state phase was controlled using a noise locking technique. We show that low frequency noise sources, such as seed noise, pump noise, and detuning fluctuations, present in optical parametric amplifiers, have negligible effect on squeezing produced by a below-threshold OPO. This low frequency squeezing is ideal for improving the sensitivity of audio frequency measuring devices such as gravitational-wave detectors.     

Quantum correlations of pulses of optical parametric oscillator synchronously pumped above threshold

The quantum analysis of radiation from a degenerate optical parametric oscillator synchronously pumped above its oscillation threshold is presented. It is shown that pulses of signal and pump fields at the output of the oscillator have the following properties: quantum fluctuations of the fields are independent in each individual pulse, but correlated in pulses of the pulse train with a temporal step multiple of the pulse period. The number of essentially correlated pulses is on the order of the oscillator cavity finesse. Cross-correlations between the pump and signal pulses are established above the oscillation threshold. These correlations lead to a significant quantum effect in the integral characteristics of the fields. A theoretical analysis revealed that the spectrum of field fluctuations measured using a balanced homodyne detection technique of phase quadratures of the fields with a pulsed local oscillator reveals quantum noise suppression in the vicinity of frequencies that are multiples of the pulse repetition rate.     

Broadband radiation of a degenerate optical parametric oscillator operating above threshold in information applications

Information applications of the essentially multimode (in time) radiation of a degenerate optical parametric oscillator operating above the oscillation threshold, such as protocols of quantum parallel dense coding and multimode quantum teleportation, have been considered. The stream of Shannon mutual information as a function of the spectral width of Alice’s signal and the spectral fidelity of transmission of a multimode quantum signal are evaluated from the estimates of the achievable radiation squeezing that occurs as the oscillation threshold is approached. The advantages of the multimode scheme over the single-mode scheme are discussed.     

三模共振光学参量振荡腔抽运场的压缩

利用半经典理论分析了由于级联非线性过程,三模共振光学振荡腔反射场的相位压缩,讨论了压缩与各参量的关系,并与结果比较,理论与实验基本吻合。     

Spectral analysis of a four mode cluster state

We theoretically evaluate the squeezed joint operators produced in a single optical parametric oscillator which generates quadripartite entangled outputs, as demonstrated experimentally by Pysher et al. [1]. Using a linearized fluctuation analysis we calculate the squeezing of the joint quadrature operators below threshold for a range of local oscillator phases and frequencies. These results add to the existing theoretical understanding of this potentially important system.     

A degenerate three-level laser with a parametric amplifier

The aim of this paper is to study the squeezing and statistical properties of the light produced by a degenerate three-level laser whose cavity contains a degenerate parametric amplifier. In this quantum optical system the top and bottom levels of the three-level atoms injected into the laser cavity are coupled by the pump mode emerging from the parametric amplifier. For a linear gain coefficient of 100 and for a cavity damping constant of 0.8, the maximum intracavity squeezing is found at steady state and at threshold to be 93%.     

Approximation Analytical Solution for a Current-Carrying Ion Sheath and its Chaos Control

The fourth-order quantum interference of squeezed fields generated by two independent optical parametric oscillators(OPOs) is discussed based on the semi-classical theory. It is shown that at the oscillation threshold of OPOs the squeezing of two output fields is the highest but the fringe visibility of fourth-order interference is the lowest(33.3%). When the pump power is away from the threshold, the squeezing decreases while the correlation between them increases.     

Generation of bright two-color continuous variable entanglement

We present the first measurement of squeezed-state entanglement between the twin beams produced in an optical parametric oscillator operating above threshold. In addition to the usual squeezing in the intensity difference between the twin beams, we have measured squeezing in the sum of phase quadratures. Our scheme enables us to measure such phase anticorrelations between fields of different frequencies. In the present measurements, wavelengths differ by approximately 1 nm. Entanglement is demonstrated according to the Duan et al. criterion [Phys. Rev. Lett. 84, 2722 (2000)] Delta2p- + Delta2q+ = 1.41(2) < 2. This experiment opens the way for new potential applications such as the transfer of quantum information between different parts of the electromagnetic spectrum.