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.     

Some statistical properties for a spin-(1/2) particle coupled to two spirals

In this paper we consider the problem of the interaction between two SU(2) quantum systems namely: two-level atom and multi-level atoms. The evolution operator is obtained and used to calculate the time-dependent dynamical operators. It has shown that the atomic inversion is sensitive to the change in the detuning parameter ?, the quantum numbers j_k as well as the atomic angles. The atomic squeezing is also considered and the phenomenon of squeezing is observed in both quadrature variances, however, with a periodic exchange between the quadratures. The degree of entanglement is examined by employing von Neumann entropy. It has shown that an increase in the value of the detuning parameter leads to a decrease in the degree of entanglement. However, for a weak coupling parameter the system shows reduction in the entropy. In the meantime the maximum entanglement can be reached when we increase the value for the quantum numbers j_k. Also it has shown that the atomic angles play a role for controlling the degree of entanglement.     

Entropy squeezing and entanglement of the interaction between SU(1,1) and SU(2) quantum systems

The problem of the interaction between two quantum systems namely SU(1,1) and SU(2) is considered. Using the evolution operator technique, an exact solution of the wave function and consequently the density matrix are obtained. The entropy squeezing is examined and it has shown that, different values of the relative phase angle ? as well as the coupling parameter λ lead to different observation of the squeezing in the quadratures. In the meantime, we have shown that the entropy squeezing is also sensitive to the variation in the state angle θ, the detuning parameter Δ in addition to the excitation number m. Moreover, for a large value of the detuning parameter there is a weak entanglement between the atom and the quantum system and vice versa. Furthermore, we find that the Q-function is sensitive to the variation in the excitation number m in addition to the Bargmann index k where the nonclassical effect is pronounced for the even parity.     

Entropic uncertainty for two atoms interacting with a cavity field under the influence of two photons (off-resonance case)

In this paper, we introduce a Hamiltonian model describing the interaction of two photons with two two-level atoms and a degenerate parametric amplifier. In the near-resonance case, we obtain an analytic solution of the evolution equation for the wave function in the Schr¨odinger picture and use the obtained result for discussing the atomic inversion, the purity, and the phenomenon of squeezing. We show that the phenomenon of superstructure appears in the atomic inversion in the presence of detuning (with parameter ??) and coupling (with parameter ??₃). Our study of the purity shows that the system is always in a mixed state, and the maximum value of entanglement occurs around ~0.6. Also we show that detuning leads to a reduction in the value of squeezing for all quadrature variances. In contrast, the coupling parameter leads to an increase in the value of squeezing. However, for the usual single-mode squeezing (of quadratures) the effect of detuning consists in increase in the squeezing period.     

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.     

Wigner Function of the Two-Mode Squeezing-Enhanced Vacuum State

We find the two-mode generalized squeezing operator with two parameters can be separated into the product of a ordinary squeezing operator S ₂(ξ) and a rotating operator R ₂(θ). Acting it on the two-mode vacuum state, one can get two-mode squeezing-enhanced vacuum state (TSEVS). Compared with the usual two-mode squeezed vacuum state, TSEVS exhibits stronger squeezing properties. With the help of the operator’s Weyl-ordering invariance under the similarity transformation, we derive the Wigner function of the TSEVS.     

Spin Squeezing in Superposition of Four-Qubit Symmetric State and W States

We investigate the entanglement property of a four-qubit state superposed by a four-qubit GHZ state and a symmetric state with spin squeezing. Numerically and analytic solutions for spin squeezing parameters are given. The squeezed parameters depend on the superpose coefficients and the relative phases. It is shown that there is no spin squeezing at n ₁ direction and it occurs at n ₂ direction under some conditions.     

Sudden Vanishing of Atomic Dipole-Squeezing in a Kerr Nonlinear Blackbody

The dynamics of atomic dipole momentum and atomic dipole-squeezing effect are investigated inside a Kerr nonlinear blackbody. It is found that in a Kerr nonlinear blackbody, the atomic dipole momentum and its squeezing effect are heavily dependent on the Kerr nonlinear coefficient. It is also found that below a transition temperature T _c , the dipole momentum and its squeezing effect in a Kerr nonlinear blackbody can vanish much faster with time than those in a normal blackbody. Above T _c , the Kerr nonlinear blackbody becomes a normal blackbody, and the dynamics of the atomic dipole momentum and its squeezing effect behaves as those in normal blackbody radiation. The physical origin of the sudden-vanishing phenomenon in a Kerr nonlinear blackbody is also discussed.     

An Alternative Model of the Damped Harmonic Oscillator Under the Influence of External Force

In this paper we introduce the modified time-dependent damped harmonic oscillator. An exact solution of the wave function for both Schrödinger picture and coherent state representation are given. The linear and quadratic invariants are also discussed and the corresponding eigenvalues and eigenfunctions are calculated. The Hamiltonian is transformed to SU(1,1) Lie algebra and an application to the generalized coherent state is discussed. It has been shown that when the system is under critical damping case the maximum squeezing is observed in the first quadrature F _x . However, for the overcritical damping case the maximum squeezing occurs in the second quadrature F _y . Also it has been shown that the system for both cases is sensitive to the variation in the coherent state phase.     

Photon Excitations Excitated the Sqeezing Properties of the Excited Entangled Coherent States

In our previous paper, we have introduced a new kind of continuous-variable-type entangled states, called double-mode excited entangled coherent states. In this paper, we study sum squeezing properties of such excited entangled coherent states. We focus on discussing the influence of photon excitations on sum squeezing properties. It is found that the photon excitations seriously affected sqeezing properties of the excited entangled coherent states. With increasing the number of the photon excitations m, the higher-order terms move away from its initial state |ψ ₀〉 and the degrees of sum squeezing are increasing. In this sense, it implies that the photon excitations excitated the sum sqeezing properties of the double-mode excited entangled coherent states.     

Squeezed states in resonance fluorescence of two interacting atoms

The possible existence of so-called “squeezed” states in two-atom resonance fluorescence is discussed in Lehmberg's master equation approach. It is shown that squeezing strongly depends on interatomic separations r₁₂. For large r₁₂ one of the quadrature components is squeezed, and as r₁₂ decreases its squeezing decreases in order to appear in the other quadrature component for certain value of r₁₂. For very small r₁₂ fluctuations in both components tend to zero.     

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.     

New Parameterized Coherent-Entangled State Representation and Its Applications

Based on EPR’s idea of quantum entanglement, new parameterized coherent-entangled states |α,p〉 _μ,ν are introduced in two-mode Fock space, which can be implemented by using a beam splitter. Possible superpositions of |α,p〉 _μ,ν result in some new entangled states. The asymmetric ket-bra integration from |α,p〉 _μ,ν leads to a new one- and two-mode combinatorial squeezing operator with stronger squeezing, which clearly shows the intrinsic relationship between squeezing mechanism and quantum entanglement.     

新的奇偶非线性相干态及其非经典性质

构造出了一种新的奇偶非线性相干态, 并借助于数值计算方法研究了它们的压缩、振幅平方压缩、反聚束和相位概率分布等非经典性质. 结果表明, 与通常的奇偶相干态和非线性奇偶相干态不同, 在参数|λ|的不同取值范围内, 新的奇偶非线性相干态在Y₁和Y₂两个方向均可呈现振幅平方压缩效应, 而压缩效应仅在偶非线性相干态的X₂方向上呈现, 反聚束效应仅在奇非线性相干态中呈现. 另外, 通过研究新的奇偶非线性相干态相位概率分布, 发现新的奇偶非线性相干态具有完全不同的量子干涉特性. 关键词： 新的奇偶非线性相干态 压缩效应 反聚束 相位概率分布     

Effective Mode Volume of Nanoscale Plasmon Cavities

The controlled squeezing of electromagnetic energy into nanometric volumes via surface plasmon-polariton excitations in plasmonic nanoresonators is analyzed using the concept of an effective electromagnetic mode volume V _eff, while taking careful account of the plasmon-polariton dispersion and the electromagnetic energy stored in the metal. Together with the quality factor Q of the cavity resonance, this enables a comparison with dielectric optical cavities, where V _eff is limited by diffraction. For a Fabry–Perot type planar metallic cavity, a one-dimensional analytic model as well as a three-dimensional finite-difference time-domain simulation reveal that V _eff is not bounded by diffraction, and that Q/V _eff increases for decreasing cavity size. In this picture, matter–plasmon interactions can be quantified in terms of Q and V _eff, and a resonant cavity model for the enhancement of spontaneous Raman scattering is presented.     

Photon Modulated Coherent States of a Generalized Isotonic Oscillator by Weyl Ordering and their Non-Classical Properties

We construct photon modulated coherent states of a generalized isotonic oscillator by expanding the newly introduced superposed operator through Weyl ordering method. We evaluate the parameter A ₃ and the s-parameterized quasi probability distribution function to confirm the non - classical nature of the states. We also calculate the identities related with the quadrature squeezing to explore the squeezing property of the states. Finally, we investigate the fidelity between the photon modulated coherent states and coherent states to quantify the non-Gaussianity of the states. The constructed states and their associated non - classical properties will add further knowledge on the potential.     

Higher-order properties of photon-added coherent states

We have studied a higher-order squeezing and a higher-order sub-Poissonian photon statistics in photon-added coherent states. We obtained analytic forms of the degree of higher-order squeezing and the degree of higher-order sub-Poissonian statistics. We show that the photon-added coherent state |α,m〉 exhibits both higher-order squeezing and higher-order sub-Poissonian character. For two different types of higher-order squeezing, the degree of squeezing becomes bigger when the added photon number is increased. In single-photon-added coherent state, the degree of squeezing depends upon the order of squeezing N. When N is increased, the degree of squeezing becomes bigger in the Hong-Mandel-type higher-order squeezing but becomes smaller in the Hillery-type higher-order squeezing. Also, the higher-order sub-Poissonian character is more pronounced than the usual sub-Poissonian character in the single-photon-added coherent state.     

Applications of the master equation of a two-level atom in a narrow-bandwidth squeezed vacuum

In this paper, we derive the time-dependent solution of the effective master equation for the reduced density matrix operator of a two-level atom driven by a coherent laser field and damped by a finite-bandwidth squeezed vacuum. The master equation has the standard form known from the broadband squeezing approaches but with new effective squeezing parameters and and new rate coefficients. There are also new terms, proportional to β, which are essentially narrow-bandwidth modifications determined by the parameters γ_n, δ_n and the shifts δ_N and δ_M. These parameters become zero when the squeezing bandwidth tends to infinity. The effects of the detuning parameter Δ of the driving laser field frequency ω_L from the atomic resonance ω_A and the squeezing parameters and on the atomic inversion, the von Neumann entropy and the resonance fluorescence spectrum are discussed.     

Spin Squeezing in Superpositions of GHZ State and W States

We investigate the spin squeezing in superpositions of a N-qubit GHZ state and two W states. The spin squeezing parameter is determined by the superposition coefficients and the relative phase. It is shown that there is squeezing in the n ₂ direction and there is no squeezing in the n ₁ direction. It is also shown that the state with more number of qubits has smaller spin squeezing parameter.     

Application of the two-mode squeezed coherent state representation in deriving generalized optical Collins formula

We propose a new two-mode squeezed coherent state representation |z₁, z₂〉_g which is characteristic of the correlation between the squeezing and the displacement. Based on it and using the technique of integration within an ordered product of operators we obtain a generalized two-mode Fresnel operator (GTFO), which is an image of the mapping from (z₁, z₂) to in |z₁, z₂〉_g representation. The matrix element of GTFO in the coordinate representation leads to a generalized two-dimensional Collins formula (Huygens-Fresnel integration transformation describing optical diffraction) in entangled form.