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High-order squeezing of the quantum electromagnetic field and the generalized uncertainty relations in two-mode squeezed states

Xi-Zeng Li, Bao-Xia Su

Published May 1, 1994• 0 citations
OpenAlex

Abstract

It is found that two-mode output quantum electromagnetic field in two-mode squeezed states exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations are also presented for the first time. The concept of higher-order squeezing of the single-mode quantum electromagnetic field was first introduced and applied to several processes by Hong and Mandel in 1985. Lately Li Xizeng and Shan Ying have calculated the higher-order squeezing in the process of degenerate four-wave mixing and presented the higher-order uncertainty relations of the fields in single-mode squeezed states. In this paper we generalize the above work to the higher-order squeezing in two-mode squeezed states. The generalized uncertainty relations are also presented for the first time.

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It is found that two-mode output quantum electromagnetic field in two-mode squeezed states exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations are also presented for the first time. The concept of higher-order squeezing of the single-mode quantum electromagnetic field was first introduced and applied to several processes by Hong and Mandel in 1985. Lately Li Xizeng and Shan Ying have calculated the higher-order squeezing in the process of degenerate four-wave mixing and presented the higher-order uncertainty relations of the fields in single-mode squeezed states. In this paper we generalize the above work to the higher-order squeezing in two-mode squeezed states. The generalized uncertainty relations are also presented for the first time.
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 .
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.
It is found that the field of the combined mode of the probe wave and the phase-conjugate wave in the process of degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The degree of squeezing increases with the order N, and the higher-order squeeze parameter qN{q}_{N}qN​ may approach -1.
We consider squeezing of the electromagnetic field resulting from the interaction of the three-level ssV-shaped atom with two modes initially taken in coherent-state representation. We also consider higher-order squeezing in the sense of Hong and Mandel [Phys. Rev. Lett. 54, 323 (1985)] and then in the sense of Hillery [Phys. Rev. A 36, 3796 (1987)]. We calculate the two-mode squeezing proposed in [J. Mod. Opt. 34, 709 (1987)] and the sum squeezing defined by Hillery [Phys. Rev. A 40, 3147 (1989)] for an atom starting initially at its ground state.
The concept of Nth-order squeezing and intrinsic Nth-order squeezing is introduced and applied to several physical situations that are known to exhibit second-order squeezing. It is shown that the field produced in degenerate parametric down-conversion is squeezed to all orders, as well as being intrinsically squeezed to orders 2,6,10,. . . . The same is true for the fundamental mode in second-harmonic generation within the short-time approximation, but in this case there is only intrinsic second-order squeezing. In resonance fluorescence from a two-level atom squeezing is again found to be intrinsically a second-order phenomenon, although an intrinsic second-order effect can give rise to a weak form of higher-order squeezing.