Abstract:
We investigate theoretically the generation of squeezed states in spontaneous and stimulated six-wave mixing process quantum mechanically. It has been found that squeezing occurs in field amplitude, amplitude-squared, amplitude-cubed, and fourth power of field amplitude of fundamental mode in the process. It is found to be dependent on coupling parameter “g” (characteristics of higher-order susceptibility tensor) and phase values of the field amplitude under short-time approximation. Six-wave mixing is a process which involves absorption of three pump photons and emission of two probe photons of the same frequency and a signal photon of different frequency. It is shown that squeezing is greater in a stimulated interaction than the corresponding squeezing in spontaneous process. The degree of squeezing depends upon the photon number in first and higher orders of field amplitude. We study the statistical behaviour of quantum field in the fundamental mode and found it to be sub-Poissonian in nature. The signal-to-noise ratio has been studied in different orders. It is found that signal-to-noise ratio is higher in lower orders. This study when supplemented with experimental observations offers possibility of improving performance of many optical devices and optical communication networks. 1. Introduction Over the past three decades, particular attention has been focused on theoretical investigations and experimental observations in generation of squeezed light, for improving the performance of many optical devices and optical communication networks. The concept of squeezed light is concerned with reduction of quantum fluctuations in one of the quadrature, at the expense of increased fluctuations in the other quadrature. In general, the two important nonclassical effects, squeezing and antibunching (or Sub-Poissonian photon statistics), are not interrelated; that is, some states exist that exhibit the first but not the second and vice versa. However, squeezing can be detected using simple photon counting in higher-order sub-Poissonian statistics. A lot of work has appeared in the literature on the theoretical and experimental investigations on generation of squeezed states of electromagnetic field. Mandel [1] found squeezed state of the second harmonic when a beam of light propagates through a nonlinear crystal. Later, Hillery [2] defined amplitude-squared squeezing and showed that amplitude-squared squeezed states can be of use in reducing noise in the output of certain nonlinear optical devices. Hong and Mandel [3, 4] introduced the notion of Nth-order

Abstract:
In this Letter we study the evolution of the higher-order squeezing, namely, $n$th-order single-mode squeezing, sum- and difference-squeezing for the codirectional Kerr nonlinear coupler. We show that the amount of squeezing decreases when $n$, i.e. the squeezing order, increases. For specific values of the interaction parameters squeezing factors exhibit a series of revival-collapse phenomena, which become more pronounced when the value of $n$ increases. Sum-squeezing can provide amounts of squeezing greater than those produced by the $n$th higher-order ($n\geq 2$) squeezing for the same values of interaction parameters and can map onto amplitude-squared squeezing. Further, we prove that the difference-squeezing is not relevant measure for obtaining information about squeezing from this device.

Abstract:
Recently simpler criteria for the Hong-Mandel higher order squeezing (HOS) and higher order subpossonian photon statistics (HOSPS) are provided by us [Phys. Lett. A 374 (2010) 1009]. Here we have used these simplified criteria to study the possibilities of observing HOSPS and HOS in different intermediate states, such as generalized binomial state, hypergeometric state, negative binomial state and photon added coherent state. It is shown that these states may satisfy the condition of HOS and HOSPS. It is also shown that the depth and region of nonclassicality can be controlled by controlling various parameters related to intermediate states. Further, we have analyzed the mutual relationship between different signatures of higher order nonclassicality with reference to these intermediate states. We have observed that the generalized binomial state may show signature of HOSPS in absence of HOS. Earlier we have shown that NLVSS shows HOS in absence of HOSPS. Consequently it is established that the HOSPS and HOS of same order are independent phenomenon.

Abstract:
Higher order nonclassical properties of fields propagating through a codirectional asymmetric nonlinear optical coupler which is prepared by combining a linear wave guide and a nonlinear (quadratic) wave guide operated by second harmonic generation are studied. A completely quantum mechanical description is used here to describe the system. Closed form analytic solutions of Heisenberg's equations of motion for various modes are used to show the existence of higher order antibunching, higher order squeezing, higher order two-mode and multi-mode entanglement in the asymmetric nonlinear optical coupler. It is also shown that nonclassical properties of light can transfer from a nonlinear wave guide to a linear wave guide.

Abstract:
It is found that the two-mode output quantum electromagnetic field in two-mode squeezed states exhibits higher-order squeezing to all even orders, and the degree of higher-order squeezing is greater than that of the second-order. The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the higher-order uncertainty relations in two-mode squeezed states are presented for the first time. The product of higher-order noise moments is related to even order number N and the squeeze factor r.

Abstract:
It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the higher-order uncertainty relations in the process of non-degenerate four-wave mixing are presented for the first time. The product of higher-order noise moments is related to even order number N and the length L of the medium.

Abstract:
The higher-order fundamental quantum-mechanical fluctuation is given on the base of the higher-order uncertainty relation, from which the definition of higher-order squeezing for atomic dipole is introduced. As an example, we examine the second-, fourth-and sixth-order squeezing of atomic dipole in the two-photon Jaynes-Cummings model with the two-photon superposition state preparation.

Abstract:
In our preceding serial works, we have investigated the generation of higher-order atomic dipole squeezing (HOADS) in a high-Q micromaser cavity, discussing the effects of dynamic Stark shift, atomic damping, atomic coherence and nonlinear one-photon processes and different initial states (for example, correlated and uncorrelated states, superposition states, squeezed vacuum). In this paper, we continue to study HOADS in a high-Q micromaser cavity, but consider that the atom interacts with the optical field via a multi-photon transition process and that the initial atom is arbitrarily prepared. For a vacuum initial field, we demonstrate that HOADS cannot occur if the atom is initially prepared in a chaotic state and that a coherent atomic state generates less efficient and stable HOADS than an arbitrary one. It is found that large detuning may lead to enhanced and strong HOADS.

Abstract:
We demonstrate quantum correlations in the transverse plane of continuous wave light beams by producing -4.0 dB, -2.6 dB and -1.5 dB of squeezing in the TEM00, TEM10 and TEM20 Hermite- Gauss modes with an optical parametric amplifier, respectively. This has potential applications in quantum information networking, enabling parallel quantum information processing. We describe the setup for the generation of squeezing and analyze the effects of various experimental issues such as mode overlap between pump and seed and nonlinear losses.

Abstract:
In this paper, the properties of N-th p0wer Y-squeezing, N-th power H-squeezing, N-Yminimum uncertainty state and N-H minimum uncertainty state in the multi-mode even-coherent statelight field t W,e), is studied in detail,that is based upon utilizing the theory 0f generalized nonlinearequal-order higher-order squeezing of multi-mode radiative light field, which is proposed by YangZhiyong and Hou Xun recently, lt ls f0und that, l ), When N, the number of squeezing-order, is evennumber, the state, W, e), is always stayed in N-Y minimum uncertainty state; and when N is 0ddnumber, the state I W, e ),, under some certain c0nditi0ns, can present any order N-th p0wer Y-squeezing which changes periodically1 2 ) When q. N, the products of cavity m0des number andsqueezingxirder number, is even number, the state W, e, is also always stayed in N-H minimumuncertainty state,and when q. N is odd number under s0me other c0nditi0ns the state l W,e), can als0present any order N-th power H-squeezing that changes periodically to0 1and 3) the squeezing depthand degree of both N-th power Y-squeezing and N-th p0wer H-squeezing are related nonlinearly to theprobability amplitude ,to the squeezing parameter R,,to the initial phase of each mode or to thesum of the initial phase of each mode to the squeezing order number N and to the cavity-modenumber q,the later is more intensive than the former.