Higher-order squeezing and photon statistics in fourth harmonic generation

Squeezing of the electromagnetic field is investigated in fundamental mode in fourth harmonic generation under a short time approximation based on quantum mechanical approach. The occurrence of squeezing in field amplitude and in higher power amplitude (up to fourth-order) in fundamental mode has been studied. It is found to be dependent on phase of field amplitude of the fundamental mode. The dependence of squeezing on the photon number has also been investigated. It is found that squeezing increases non-linearly. It has also been found that the photon statistics of the field in fundamental mode is sub-Poissonian. The signal to noise ratio has been studied in different order. It is found that signal to noise ratio is higher in lower order.     

Squeezing and photon statistical effects in spontaneous and stimulated eight-wave mixing process

Eight-wave mixing is a process which involves absorption of four pump photons and emission of three probe photons of same frequency and a signal photon of different frequency. Squeezing is investigated in the fundamental mode in spontaneous and stimulated eight-wave mixing process using quantum mechanical approach. The presence of squeezing in field amplitude, amplitude-squared and amplitude-cubed in the fundamental mode has been probed. The dependence of squeezing on photon number is established with investigations into degree of squeezing in the first and higher order of field amplitude. The photon statistics of the field in the fundamental mode has also been investigated. It has been found that the field shows sub-Poissonian behaviour in the fundamental mode.     

Effects on squeezing and sub-poissonian of light in fourth harmonic generation up to first-order Hamiltonian interaction

The effects on squeezing and sub-poissonian of light in fourth harmonic generation (FHG) are investigated based on the fully quantum mechanically up to the first order Hamiltonian interaction in gt, where g is the coupling constant between the modes per second and t is the interaction time between the waves during the process in a nonlinear medium. FHG is a process in which an incident laser beam of the fundamental frequency ω interacts with a nonlinear medium to produce the harmonic frequency at 4ω. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The occurrence of amplitude squeezing effects in both the quadratures of the radiation field in the fundamental mode is investigated and found to be dependent on the selective phase values of the field amplitude. The photon statistics of the pump mode in this process have also been investigated and found to be sub-poissonian in nature. It is found that there is no possibility to produce squeezed light in the harmonic mode up to first-order interaction in gt. Further, we have found the case up to second-order Hamiltonian interaction in gt that the normal squeezing in the harmonic mode is directly depends upon the fourth-order squeezing of the initial pump field. This gives a method of converting higher-order (fourth-order) squeezing into normal squeezing in the harmonic mode and vice versa.     

Higher-order squeezing and sub-poissonian photon statistics in CARS and CAHRS

The Squeezing and sub-poissonian photon statistics of an optical field are a purely quantum mechanical phenomenon and has been accepted as means of achieving noise below the quantum shot-noise limit. The effect of higher-order squeezing and sub-poissonian nature of an optical field in coherent anti-Stokes Raman scattering (CARS) and coherent anti-Stokes hyper Raman scattering (CAHRS) are investigated under short-time approximation. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established and solved under short-time scale. The dependence of squeezing on the number of photons is also investigated. It is also shown that higher-order squeezing allows a much larger fractional noise reduction than lower-order squeezing. The occurrence of amplitude squeezing effects of the radiation field in the fundamental mode is investigated in both the processes. The present work shows that squeezing is greater in CAHRS than the corresponding squeezing in CARS. It is also shown that squeezing is greater in stimulated process than corresponding squeezing in spontaneous interaction. The conditions for obtaining maximum and minimum squeezing are obtained. The photon statistics of the pump mode in the processes has also been investigated and found to be sub-poissonian in nature.     

Minimum total noise is a measure of higher order squeezing

The possibility of observing higher order squeezing in different optical processes, such as six-wave mixing and four-wave mixing, has been studied and it is shown that amplitude squared squeezing appears in all these cases. It is also shown that the minimum total noise (T_min) of a higher order squeezed state, which is a measure of the total fluctuations in the field amplitude, always increases with the increase in depth of nonclassicality associated with higher order squeezing. Thus we can use T_min as an indirect measure of higher order squeezing.     

Squeezing up to fourth-order in the pump mode of eight-wave mixing process

Squeezing of the electromagnetic field is investigated in the pump mode during an eight-wave mixing process under short time approximation on the basis of quantum mechanical approach. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operator are established. Occurrence of squeezing in the first, second, third and fourth-order field amplitude in the pump mode has been investigated. It depends upon the coupling constant ‘g’ and the phase values of the field amplitude. The process involves absorption of three pump photons of the same frequency, one pump photon of a different frequency and emission of four probe photons of the same frequency. The dependence of squeezing on photon number is established with investigations into the degree of squeezing in the first and higher order. The photon statistics of the pump mode in the process has also been investigated and found to be sub-Poissonian in nature.     

在两个耦合的量子点和腔QED系统中的双模激子的压缩性质(英文)

本文研究了在两个耦合的量子点和腔QED系统中的双模激子的压缩性质.讨论了不同的初始光场对双模激子的正常压缩与和压缩的影响.计算表明,当初始态光场制备在相干态时,双模激子既不存在正常压缩,也不存在和压缩,这说明双模激子振辐的两个正交分量具有相同的量子涨落;然而,当初始腔场处于压缩真空态时,无论是正常压缩还是和压缩,双模激子振辐的两个正交分量总有一个存在压缩.这意味着量子噪声能被有效的得到抑制.此外,两种情形下的最大压缩都由初始腔场的压缩因子r决定.经过比较,我们还发现双模激子的正常压缩比和压缩大.     

Detection of weak signals based on a new class of transformations of random series

For detecting weak signals (when their amplitude is comparable with the amplitude of the noise track) a new class of transformations of random series to a straight line has been suggested. It has been shown that these transformations are quasi-linear and can be defined as a signal-to-staircase transformation (SST). The height of a step defines an amplitude of the detected signal and the step length its duration. The SST can be applicable for a wide class of random series having different statistical nature. The verification of this new method based on the analysis of the real signal/noise tracks containing registration of different earthquakes with small amplitudes has been realized. It has also been shown that different situations which have been found from the real-data analysis demonstrate the high sensitivity and efficiency of the new method suggested.     

Light squeezing in optical parametric amplification beyond the slowly-varying amplitude approximation

Optical parametric amplification (OPA) described usually by the coupled-wave equations with the first-order derivatives of the signal and idler waves, is solved under the slowly-varying amplitude approximation (SVA). In this article, by keeping the second-order derivatives in the coupled-wave equations, we obtained an analytical solution for the output signal and idler waves up to the first order of (κ/k)¹; the ratio of coupling constant to the wave number. Furthermore, here the signal and the idler waves are distinguished only by their polarizations with the same frequency. Light squeezing is observed in normally ordered variances of the two quadrature operators of the output combined mode when plotted against κL, where κ is the coupling constant and L the interaction length. The variances have different signs for a range of values of κL and their variations are in opposite directions. We also show that this property is strongly dependent on the relative refractive index of the medium (n). It is worth mentioning that the relative index dependency is not an explicit feature in squeezing of OPA under SVA approximation. Furthermore, the squeezing vanishes when n → 1 and κ/k → 0.     

Generation and Preparation of the Sustained Optimal Entropy Squeezing State of a Motional Atom Inside Vacuum Cavity

Considering two two-level atoms initially in Bell state, we send one atom into a vacuum cavity while leaving the other outside, and consider the motion of atom inside the cavity. Using quantum information entropy squeezing theory, the time evolution of the entropy squeezing factor of atom inside the cavity is discussed for two cases, i.e., before and after performing rotation operations and measuring atom outside, the influences of the field mode structure and atomic motions on the atomic entropy squeezing are evaluated. It is shown that atom inside the cavity has no entropy squeezing phenomenon before operating atom outside the cavity. However, the optimal entropy squeezing phenomenon of period T = 2π/p emerges and constant entropy squeezing phenomenon can occur by adjusting rotation operation to R(π/4), and setting the field mode structure parameter 0 < p < 50. In particular, if choosing p > 50, a sustained optimal entropy squeezing state (SOESS) can be generated. We also present the schematic circuit diagram of preparation of SOESS. Our proposal provides a possible way for the initial decoherent state recovering into sustained maximal coherent superposition state of single atom in the quantum noise environment.     

The Spectrum of Squeezing in Degenerate Four-Wave Mixing

We analyze a simple model for degenerate four wave mixing, introduced by Savage and Walls. In the resonant case, the system exhibits a phase instability when the pump intensity is increased well beyond the threshold for generation of the signal mode. Still in the resonant configuration, we calculate the amplitude and phase squeezing spectra both for the signal and the pump mode. In the signal (pump) mode, the squeezing becomes especially large when the signal (pump) mode is much more damped than the pump (signal) mode. The signal field can exhibit both phase and amplitude squeezing, in distinct domains of the parameter space. On the other hand, the pump field can show squeezing only in the amplitude quadrature component. In general, the model exhibits sizable squeezing over very extended regions of the parameter space.     

Research on detection method of multi-frequency weak signal based on stochastic resonance and chaos characteristics of Duffing system

Weak signal detection has been widely used in many fields such as military and national economy. Aiming at the problem that the traditional stochastic resonance (SR) method can’t obtain the signal amplitude when detecting weak signals, the frequency and amplitude of the weak signal are obtained by combining the SR and chaos characteristics of the two-dimensional Duffing system. Firstly, the effects of two-dimensional Duffing system parameters a, b, k, noise intensity D on the Kramers rate and signal-to-noise ratio (SNR) are analyzed under the Gaussian white noise environment. The results show that the damping ratio K can hinder the SR effect of the system to some extent. Secondly, to solve the misjudgment of the state method of the weak signal amplitude in the detection, the Lyapunov exponent is used to assure the threshold's range, and the threshold of the chaotic critical state is found. Finally, the paper gives the processes of frequency and amplitude detection of multiple high-frequency signals, which realizes the effective detection of the frequency and amplitude of multiple high-frequency signals in a Gaussian white noise environment, and successfully applies the method to the accurate detection of boundary voltage amplitude in electrical impedance tomography.     

A quasi-energy operator in the Jaynes-Cummings model in a polychromatic classical field

A perturbation theory is developed for constructing the quasi-energy operator Q of the Tavis-Cummings Hamiltonian, which includes the interaction of atoms with a classical quasi-monochromatic field. The operator Q of the first order in the interaction δ of an atom with a resonator mode has a form of the generalized Tavis-Cummings Hamiltonian (in the interaction representation) to which the oppositely rotating terms with a changed interaction constant are added. Such a Hamiltonian has a singularity in the dimensionless amplitude σ of a classical field. In the vicinity of this singularity, the Hamiltonian spectrum tends to a continuous one, while the degree of squeezing of field quadratures (in its eigenstates) increases infinitely. In the case of one atom and the biharmonic perturbation, the operator Q is obtained up to the third order of the perturbation theory. The spectral problem for Q is studied. The features of the dependence of the quasi-energy spectrum on σ are explained by the presence of an efficient barrier between the regions of the “coordinate” space. It is found that the above-mentioned singularity corresponds to the beginning of the parametric resonance zone. Analytic expressions for the top and bottom of this zone in the δσ plane are presented.     

双模Jaynes-Cummings模型中原子偶极压缩与双模光场压缩间的关联

通过考察双模Ｊａｙｎｅｓ－Ｃｕｍｍｉｎｇｓ（Ｊ－Ｃ）模型中原子偶极压缩和双模光场二阶压缩以及原子振幅平方压缩与双模光场高阶压缩随时间的演化规律，研究了原子偶极压缩和双模光场二阶压缩之间的关系，讨论了原子振幅平方压缩与双模光场高阶压缩之间的联系，并探讨了原子偶极压缩与双模光场压缩之间相互转化的特征。     

Two-photon Jaynes-Cummings systems interacting with a classical field

If a two-level atom is in the two-photon resonance with a quantized mode and simultaneously inter-acts with a quasi-resonance classical field, then a photon exchange is observed in this system between the quantized and classical modes. It is demonstrated that such a physical system can serve as a source of squeezed radiation in the quantized mode. The squeezing can be arbitrarily close to unity, while the radiation amplitude can be relatively large. A situation is discussed when N atoms are in the two-photon resonance with a quantized mode and simultaneously interact with a classical field. The phenomenon of exponential superradiation is described when the number of photons in the quantized mode exponentially depends on the number N of atoms.     

Performance evaluation of path-averaged soliton pulses in loss-managed 10-Gbps soliton transmission link over a long haul

In this paper, the performance evaluation of path-averaged soliton transmission link for various performance measures viz. OSNR, optical power, extinction ratio, bit error rate (BER) and Q factor at different levels of noise figure and values of pulse width (FWHM) has been carried out. The performance of soliton transmission link is studied, taking into account soliton interaction, amplified spontaneous emission (ASE) noise and noise figure. The model presented considers interaction in a random sequence of solitons and the effect of the ASE noise added in each amplification stage. The influence of ASE noise, noise figure and pulse width with different amplifier spacing on the BER and quality factor has been investigated. It has been shown that these play dominant roles in degrading the performance measures. We have demonstrated the capability of path-averaged (guiding-centre) soliton for a long-haul distance of 17,000 km at a bit rate of 10 Gbps without ASE effect and noise figure in each amplifier span length of 500 km. The average value of quality factor is found to be 16.6 dB and the average BER is of the order of 10⁻¹² over the transmission distance of 17,000 km. Further, it has been investigated that a severe system penalty results on the inclusion of ASE effect and noise figure in order to achieve the same level of performance. Thus, the investigations ascertain that in order to maintain the same level of BER and Q factor, the amplifier spacing and total transmission distance reduce considerably.     

Higher-order amplitude squeezing of photons propagating through a semiconductor

Kth power photon amplitude squeezing is studied when the coherent photon propagates through a semiconductor containing the exciton. If the exciton is prepared initially in a coherent state, the photon may become Kth power amplitude squeezed. It is shown that, in the short-time limit, the photon squeezing in the P direction does not appear at all while that in the X direction is possible for all the amplitude powers K. In the latter case, the amount of squeezing is larger for higher power K. The dependences on all the system parameters as well as on the output light detection moment are investigated in detail.     

频率变化场与原子相互作用系统中原子的信息熵压缩

利用J-C模型,考虑场频率随时间以正弦函数形式作小量变化,在旋波近似下,研究了二能级原子与单模辐射场相互作用系统中原子的信息熵压缩特性.利用数值计算方法给出原子的信息熵压缩因子随时间的演化曲线.研究结果表明:原子的信息熵仅在演化的初期呈现压缩效应,初始的原子分布角、光场强度和场频率随时间的变化对原子的信息熵压缩有明显影响.场频率随时间的变化对原子的信息熵压缩因子的演化具有调制作用,随场频率变化的幅值增大,调制作用增强,压缩效应减弱.     

The difference in noise property between the Autlerben Townes splitting medium and the electromagnetically induced transparent medium

The quantum noise of squeezed probe light passing through an atomic system with different electromagnetically induced transparency and Autler-Townes splitting effects is investigated theoretically. It is found that the optimal squeezing preservation of the outgoing probe beam occurs in the strong-coupling-field regime rather than in the weak-coupling-field regime. In the weak-coupling-field regime, which was recently recognized as the electromagnetically induced transparency regime (Abi-Salloum T Y 2010 Phys. Rev. A bf81 053836), the output amplitude noise is affected mainly by the atomic noise originating from the random decay process of atoms. While in the strong-coupling-field regime, defined as the Autler-Townes splitting regime, the output amplitude noise is affected mainly by the phase-to-amplitude conversion noise. This is useful in improving the quality of the experiment for efficient quantum memory, and hence has an application in quantum information processing.     

Statistical properties of the nonlinear negative binomial state

In this context, we introduce and investigate the properties of the nonlinear negative binomial state (the state which interpolates between the nonlinear coherent and the number states). Mainly we concentrate on the statistical properties for such state where we have discussed two different cases of squeezing phenomenon. The first case is the normal squeezing while the second is the amplitude squared squeezing, further the second order correlation function is also considered. Our discussion have been extended to include the quasi-probability distribution functions (W-Wigner and Q-functions). The quadrature distribution and the phase properties in Pegg-Barnett formalism besides the phase variances are considered. Examination of the resonance fluorescence against the present state is given (single atom and thermodynamic limit). It has been shown that the atomic inversion is sensitive to any variation in the nonlinear negative binomial number m.