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International Journal of Optics

Sum Squeezing of the Field Amplitude in Frequency Upconversion Process

Dilip Kumar Giri, Binod Kumar Choudhary

Published Feb 1, 2020• 4 citations
Publisher

Abstract

Sum squeezing of the field amplitude is studied in the nondegenerate and degenerate frequency upconversion process under the short interaction time. It is shown that sum squeezing can be converted into normal squeezing via sum-frequency generation in the nondegenerate frequency upconversion process, while the amplitude-squared squeezing of the fundamental mode directly changed into the squeezing of the harmonic in the degenerate frequency upconversion process. All reachable conditions of uncorrelated modes for obtaining a sum squeezing in two modes and its dependence on the squeezing of individual field modes are investigated. It is found that the squeezed states are associated with large number of pump photons. It is also confirmed that the higher-order squeezing (sum squeezing) is directly associated with coupling of the field and interaction time.

DOI
10.1155/2020/1483710

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Sum squeezing of the field amplitude is studied in the nondegenerate and degenerate frequency upconversion process under the short interaction time. It is shown that sum squeezing can be converted into normal squeezing via sum-frequency generation in the nondegenerate frequency upconversion process, while the amplitude-squared squeezing of the fundamental mode directly changed into the squeezing of the harmonic in the degenerate frequency upconversion process. All reachable conditions of uncorrelated modes for obtaining a sum squeezing in two modes and its dependence on the squeezing of individual field modes are investigated. It is found that the squeezed states are associated with large number of pump photons. It is also confirmed that the higher-order squeezing (sum squeezing) is directly associated with coupling of the field and interaction time.
Sum squeezing of the field amplitude is studied in the nondegenerate and degenerate frequency upconversion process under the short interaction time. A state is squeezed when the quantum fluctuation (amplitude noise or phase noise) in one variable is reduced below the symmetric limit at the expense of the increased quantum fluctuation in the conjugate variable such that the Heisenberg uncertainty relation is not violated. It is shown that sum squeezing can be converted into normal squeezing via sum-frequency generation in the nondegenerate frequency upconversion process, while the amplitude-squared squeezing of the fundamental mode directly changed into the squeezing of the harmonic in the degenerate frequency upconversion process. All reachable conditions of uncorrelated modes for obtaining a sum squeezing in two modes and its dependence on the squeezing of individual field modes are investigated. It is found that the squeezed states are associated with large number of pump photons. It is also confirmed that the higher-order squeezing (sum squeezing) is directly associated with coupling of the field and interaction time. The results obtained in this chapter are of interest for new experiments on the study of nonlinear optical processes in dielectric media using ultrashort intense laser pulses as exciting radiation, and the effects of damping and decoherence as well as higher-order time terms could be investigated.
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Squeezing in the difference of the fields in degenerate four- and five-wave interaction processes is studied. It is shown that the difference squeezing can be led to normal squeezing of the field for uncorrelated modes. It is found that the amplitude-squared squeezing of the fundamental mode directly converted into the normal squeezing of the signal mode in the four-wave interaction process and amplitude-cubed of the fundamental directly converted into the normal squeezing of the signal mode in the five-wave interaction process. Detection of higher-order squeezing in these processes is also studied. It is observed that difference squeezing responds nonlinearly to the number of pump photons and found greater in the stimulated process than in spontaneous one. Difference squeezing exists only in certain domain value of pump photons. It is inferred that the multi-photon absorption process is more suitable for the generation of optimum squeezed light.
We studied squeezing in the difference of the field amplitude in degenerate six wave interaction process, which is a higher-order squeezing effect.It is shown that for uncorrelated modes the normal squeezing in the difference-frequency field directly depends on the difference squeezing of input field modes.It is established that the amplitude-squared squeezing of the fundamental feeds directly into the normal squeezing of the signal mode.Detection of difference and amplitude-squared squeezing in this process is also studied.It is found that squeezing is greater in stimulated process than in spontaneous interaction.
Squeezing of electro-magnetic field, which is a purely quantum phenomenon has attracted considerable attention owing to its low noise property with applications in high quality telecommunication. This quantum effect is expected to manifest itself in optical processes in which the nonlinear response of the system to the radiation field plays an important role. In this paper squeezing of electro- magnetic field in some multi-photon processes are investigated under short-time approximation. The processes studied include Raman and hyper Raman processes and sum- frequency generation. The coupled Heisenberg equations of motion for field operators are set up and solved under short-time approximation. The occurrence of squeezing of field is investigated using the required conditions of squeezing in each of the cases. The squeezing is found to exist in the fundamental mode and the squeezing in the generated field depends on squeezing in fundamental mode. Squeezing in higher order amplitudes are also studied. This corresponds to the squeezing of the variables which describe the real and imaginary parts of square and cube of the complex amplitudes of the radiation field. The higher order multimode sum squeezing of radiation field is dealt with for harmonic and sum frequency generation. It s shown that squeezing in the sum frequency field depends directly on the sum squeezing of fundamental modes. The results can be utilized in selecting a suitable process which will generate a radiation field with optimum squeezing and can be useful in high quality telecommunication.
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.