Analysis of the master equation for the Dicke model in squeezed vacua

The master equation for the reduced atomic density operator for the Dicke model (N_a 2-level atoms on the same single site) interacting with a broad-band squeezed vacuum state field is derived using operator reaction field theory. The analysis through reaction field theory is presented first of all for the normal vacuum and then for the squeezed vacuum, both within the Markov and Born approximations. In the case of the squeezed vacuum field a statistical decorrelation between matter and field variables is also necessarily adopted in order to close the system of equations: this is also the case for the broad-band black-body field, and the theory contrasts with that which employs projection operator techniques and uses weak coupling. Models involving a both axially symmetrical and wholly isotropic distribution of the squeezed vacuum modes are compared.     

Dynamical switching and memory via incoherent pump assisted optical bistability

We analyze the dynamical behavior of all-optical switching and memory based on tunable optical bistability in a three-level Λ-type atomic system driven by a probe field circulating in an optical ring cavity, a coherent coupling field and an incoherent pump field outside cavity. Owing to the incoherent pump process, the absorption and Kerr nonlinearity near the atomic resonance change dramatically as a result of varied population distribution and atomic coherence, and then the switch-up and switch-down thresholds, as well as the width (or area) of bistable curve, can be manipulated effectively. By tuning the intensity of either coherent coupling field or incoherent pump field, we can make the system output flip between the lower and upper branches of different bistable hysteresis loops while the cavity input keeps to a constant value. Accordingly, all-optical switching and memory can be implemented via dynamical control of the bistable behavior under the assistance of incoherent pump. The proposed scheme can find potential applications in all-optical communication and computation.     

布里渊光时域分析传感器的消偏振衰落技术

在布里渊光时域分析(BOTDA)光纤传感器中,由于受激布里渊散射的偏振相关性的影响,激励光和探测光的偏振态随机变化引起的信号起伏严重影响布里渊散射光信号的稳定测量。通过建立与偏振态有关的激励光和探测光的耦合方程,推导出接收探测光光强关于激励光和探测光偏振态的理论公式,并由此提出偏振扩展接收技术。理论分析表明,偏振扩展接收技术可以有效地抑制偏振相关信号衰落。通过对耦合方程进行模拟,验证了理论分析的正确性和偏振扩展接收技术的可行性。最后给出了采用偏振扩展接收的布里渊光时域分析实验结果,与理论分析和模拟具有较好的一致性。     

Electromagnetically Induced Grating Without Absorption Using Incoherent Pump

We propose a scheme for creating electromagnetically induced grating in a four-level double- Λ atomic system driven by a coupling field and an incoherent pump field. Owing to the incoherent pumping process, large refractivity accompanied with vanishing absorption or even gain across the probe field can be built up in the atoms, thus phase grating or gain-phase grating, which diffracts a probe light into different directions, can be formed with the help of a standing-wave coupling field. The diffraction efficiency of the gratings can be tuned by the coupling field intensity and the incoherent pump rate, hence the proposed gratings should be suitable for beam splitter and optical switching in optical communication and networking.     

三能级三模量子系统中探测场的增益研究

研究了三能级原子与多模光场相互作用的量子系统,从系统的密度矩阵运动方程出发讨论了无粒子数反转探测场的增益条件,发现当驱动场拉比频率取5,探测场拉比频率取1,非相干抽运取3,驱动场失谐量取3时,系统可以在偏离共振的两端获得粒子数无反转而相应的探测场获得了增益,即实现了无粒子数反转激光,其在光通信方面具有重要的应用价值。     

Simultaneous parametric generation and up-conversion of entangled optical images

A quantum theory of parametric amplification and frequency conversion of an optical image in coupled nonlinear optical processes that include one parametric amplification process at high-frequency pumping and two up-conversion processes in the same pump field is developed. The field momentum operator that takes into account the diffraction and group velocities of the waves is used to derive the quantum equations related to the spatial dynamics of the images during the interaction. An optical scheme for the amplification and conversion of a close image is considered. The mean photon number density and signal-to-noise ratio are calculated in the fixed-pump-field approximation for images at various frequencies. It has been established that the signal-to-noise ratio decreases with increasing interaction length in the amplified image and increases in the images at the generated frequencies, tending to asymptotic values for all interacting waves. The variance of the difference of the numbers of photons is calculated for various pairs of frequencies. The quantum entanglement of the optical images formed in a high-frequency pump field is shown to be converted to higher frequencies during the generation of sum frequencies. Thus, two pairs of entangled optical images are produced in the process considered.     

Isothermal resistivity for interacting charged particles in contact with a bath

To calculate the stationary resistivity, the role of the coupling to a bath is pointed out. In the case of two kinds of interacting charged particles, the coupling to a bath is taken into account by relaxation terms in the equation of motion of the density operator so that the correct balance equations for the impuls transfer are obtained. Higher orders of a perturbation expansion of the resistivity with respect to the coupling constant are given. For special cases the Matthiesen rule is derived, and deviations from the Matthiesen rule are discussed.     

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.     

Entangled photon states in consecutive nonlinear optical interactions

Quantum theory of two consecutive light-wave parametric interactions with aliquant frequencies produced by a common pump wave in a crystal is developed. Using the differentiation method, the unitary evolution operator of the system is reduced to an ordered form that allows the calculation of the field state and the statistical characteristics of interacting waves. It is shown that, for the initial vacuum field state, the created photons obey the super-Poisson statistics at the interacting frequencies and are in a multiparticle entangled state.     

Enhanced Kerr nonlinearity in a quantized four-level graphene nanostructure

In this paper, a new model is proposed for manipulating the Kerr nonlinearity of right-hand circular probe light in a monolayer of graphene nanostructure. By using the density matrix equations and quantum optical approach, the third-order susceptibility of probe light is explored numerically. It is realized that the enhanced Kerr nonlinearity with zero linear absorption can be provided by selecting the appropriate quantities of controllable parameters, such as Rabi frequency and elliptical parameter of elliptical polarized coupling field. Our results may be useful applications in future all-optical system devices in nanostructures.     

Effects of the spectral inhomogeneity on the optical properties in the four-wave mixing signal

Effects of the inhomogeneous broadening on the optical responses of a two-level system in the four-wave mixing signal (FWM) were studied in this work. In this model, we introduced in the optical Bloch equations a stochastic Bohr frequency, generated as a consequence of the solute-solvent molecular collisions. These expressions are averaged in the statistical ensemble over all realizations of the random variables. Using the convolution theorem, it is possible to incorporate the saturation effects of the electromagnetic field treated at all orders of perturbation. For the averages, we have considered two distributions of linewidth. From the analytical expressions, for both linear and nonlinear responses, numerical calculations were carried out to obtain surfaces as a function of the magnitude of the pump field and the detuning factor. Saturation effect is shown in the linear and the coupled nonlinear responses. In this work, we have already considered the inhomogeneous spectral line and studied the cases in which all the fields propagate through the medium.     

Time-resolved two-beam coupling in silicon

The analytical solution of the optical field equations and the material equations for two-beam coupling in a medium with real excitation of quasiparticles is given. Transient energy transfer is analyzed throughout the range of the coherent overlapping of the excitation and probe pulses for a hypothetical medium with variable relation between the real part and the imaginary part of the nonlinear response. A detailed comparison between the theory and the model experiments for two-beam coupling in silicon is given.     

Triple optomechanical induced transparency in a two-cavity system

We theoretically investigate the optomechanical induced transparency(OMIT) phenomenon in a two-cavity system which is composed of two optomechanical cavities. Both of the cavities consist of a fixed mirror and a high-Q mechanical resonator, and they couple to each other via a common waveguide. We show that in the presence of a strong pump field applied to one cavity and a weak probe field applied to the other, a triple-OMIT can be observed in the output field at the probe frequency. The two mechanical resonators in the two cavities are identical, but they lead to different quantum interference pathways. The transparency windows are induced by the coupling of the two cavities and the optical pressure radiated to the mechanical resonators, which can be controlled via the power of the pump field and the coupling strength of the two cavities.     

Electromagnetically induced transparency and electromagnetically induced absorption in Y-type system

The propagation of a probe field through a four-level Y-type atomic system is described in the presence of two additional coherent radiation fields, namely, the control field and the coupling field. An expression for the probe response is derived analytically from the optical Bloch equations under steady state condition to study the absorptive properties of the system under probe field propagation through an ensemble of stationary atoms as well as in a Doppler broadened atomic vapor medium. The most striking result is the conversion of electromagnetically induced transparency(EIT) into electromagnetically induced absorption(EIA) as we start switching from weak probe regime to strong probe regime. The dependence of this conversion on residual Doppler averaging due to wavelength mismatch is also shown by choosing the coupling transition as a Rydberg transition.     

Controlling the optical bistability beyond the multi-photon resonance condition in a three-level closed-loop atomic system

We investigate the optical bistability behavior of a three-level closed-loop atomic system beyond the multi-photon resonance condition. Using the Floquet decomposition, we solve the time-dependent equations of motion, beyond the multi-photon resonance condition. By identifying the different scattering processes contributing to the medium response, it is shown that in general the optical bistability behavior of the system is not phase-dependent. The phase dependence is due to the scattering of the driving and coupling fields into the probe field at a frequency, which, in general, differs from the probe field frequency.     

Kinetics and Optical Properties of the Strongly Driven Gas Medium of Interacting Atoms

This paper investigates stimulated emission and absorption near resonance for a driven system of interacting two-level atoms. Microscopic kinetic equations for the density matrix elements of N-atom states including atomic motion are built, taking into account atom-field and atom-atom interactions. Analytical solutions are given for the resulting macroscopic equations in different limits, for a system composed of a strong coherent “pump” field and a weak counter-propagating “probe” field. It was shown that the existence of a dipole-dipole (long-range) interaction between atoms separated by distance less than the pump wave-length can cause the formation of periodic polarization and population structures (gratings in time and space) in the pumped medium without a probe field. The magnitude of pump induced population grating can have a strong dependence on the relation between the pump field detuning and the polarization decay rate. The “interaction” between pump and probe induced polarization/population gratings through a dipole-dipole interaction mechanism causes the absorption line shape asymmetry. Under certain conditions, this asymmetry is revealed in increasing probe gain for the “red”-shifted (relative to pump) probe and suppressing the gain for the “blue”-shifted probe field when pump is “red”-shifted relative to the ensemble averaged resonant frequency. The theoretical results are consistent with experimental data for the probe gain or absorption as the function of frequency and the dependance of the gain on atomic density for sodium vapor when the pump laser is tuned near the D ₂ line. Here the dependance of gain on particle density was explained in the terms of the long-range interaction between the atoms.     

Collective excitations and instability of an optical lattice due to unbalanced pumping

We solve self-consistently the coupled equations of motion for trapped particles and the field of a one-dimensional optical lattice. Optomechanical coupling creates long-range interaction between the particles, whose nature depends crucially on the relative power of the pump beams. For asymmetric pumping, traveling density wavelike collective oscillations arise in the lattice, even in the overdamped limit. By increasing the lattice size or pump asymmetry, these waves can destabilize the lattice.     

光纤拉曼放大器中增益的偏振相关特性研究

提出了一种改进的、可用于计算偏振相关拉曼增益的光纤拉曼放大器的非线性耦合波方程。建立了单模双折射光纤拉曼增益的数学模型,分析了线偏振抽运光以与光纤快轴成45°激励的单模双折射光纤拉曼放大器模型与实际具有随机双折射的光纤拉曼放大器的拉曼增益偏振相关特性的等价性。基于上述模型,提出了一个可定量表征单模光纤偏振模色散统计特性的拉曼增益偏振相关因子,用以替代常规的光纤拉曼放大器非线性耦合波方程中的偏振相关因子。计算结果与已报道文献的实验数据非常吻合。同时对抽运增益在同向和反向抽运方式下截然不同的增益偏振相关特性给出了合理的解释。