Squeezing in multi mixing process was studied by number of authors using perturbation method. In this paper we obtained squeezing in six wave mixing process with a high coherent pump beam. We used a very good approximation and found larger squeezing at large interaction times
Squeezing in four wave mixing process was studied recently using perturbation method by Giri and Gupta [D. K. Giri and P. S. Gupta, J. Opt. B: Quantum Semiclass. Opt.6 (2004) 91.] We reexamine this using a coherent intense pump mode and with a much better approximation which results in validity of our results for much larger interaction times. We find that for the range of phase where these authors obtained squeezing, only a small squeezing is obtained for a brief period but larger squeezing at large times is obtained in the other range of phase. We also obtain larger amplitude squared squeezing.
The concept of fourth-order squeezing of the electromagnetic field is investigated in the fundamental mode in spontaneous and stimulated four- and six-wave mixing processes under the short-time approximation based on a fully quantum mechanical approach. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The possibility of obtaining fourth-order squeezing is studied. The dependence of fourth-order squeezing on the number of photons is also investigated. It is shown that fourth-order squeezing, which is a higher-order squeezing, allows a much larger fractional noise reduction than lower-order squeezing. It is shown that squeezing is greater in a stimulated process than the corresponding squeezing in spontaneous interaction. The conditions for obtaining maximum and minimum squeezing are obtained. We have also established the non-classical nature of squeezed radiation using the Glauber–Sudarshan representation.
The amplitude squeezing properties of the electromagnetic field is investigated in the fundamental, Stokes (probe) and signal mode in six-wave mixing process under short-time approximation based on a fully quantum mechanical approach. The interaction is looked upon as a process involving absorption of two pump photons and emission of three probe photons and one signal photon at different frequencies. The coupled Heisenberg quantum mechanical equations of motion involving real and imaginary parts of the quadrature operators are established and solved under short-time scale. The occurrence of amplitude squeezing effects in both the quadrature of the radiation field in the fundamental mode as well as in the Stokes (probe) mode is investigated using the required conditions of squeezing in each of the cases. It is also shown that the squeezing in the signal mode is found to be dependent on amplitude-squared squeezing of the initial pump field. This gives a method of converting higher-order (amplitude-squared) squeezing into normal squeezing.
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.
Multipartite entanglement is one of the most fundamental and important resources for quantum information processing in both discrete variable and continuous variable (CV) regimes. For its applications in the CV regime, such as the realization of quantum teleportation networks and quantum dense coding, the quadrature squeezing of multipartite entanglement plays a significant role. Here, we report the first, to the best of our knowledge, experimental measurement of the quadrature squeezing in the quadripartite entanglement generated by the two-beam pumped cascaded four-wave mixing process in a 85 Rb vapor cell. Moreover, we find that the quadrature squeezing is nonexistent in each pair of beams, but exists in the whole quadripartite entanglement. Our results may find potential applications in building a multi-user quantum secret sharing network.
We study a single-mode squeezing, sub-Poissonian and total noise in degenerate six-wave mixing process.We establish the analytic expression of first-order and second-order squeezing in terms of total noise under short-time approximation in degenerate six-wave mixing process.It shows that higher-order squeezing allows a much larger fractional noise reduction than lower-order squeezing.We observe that the squeezed states are associated with large number of photons.We find that squeezing is greater in stimulated process than corresponding squeezing in spontaneous interaction.The photon statistics of the pump mode in the process is investigated and found to be sub-Poissonian in nature.The effect of sub-Poissonian nature of an optical field in terms of total noise is also incorporated.We show that the depth of nonclassicality directly depends on the amount of total noise present in the system.This suggests that the more squeezed the state is, the greater is its total noise in the system.