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中国物理B：英文版

Detaching two single-mode squeezing operators from the two-mode squeezing operator

范洪义, 笪诚

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

It has been common knowledge that the single-mode squeezing operator and the two-mode squeezing operator are independent of each other. However, in this work we find that after using the technique of integration within Q-ordering and P-ordering, we can detach two single-mode squeezing operators from the two-mode squeezing operator. In other words, we show that the two-mode squeezing operator can be split into a P-ordered two-mode squeezing operator (with a new squeezing parameter) and two single-mode squeezing operators (with another squeezing parameter). This tells us that the two-mode squeezing mechanism also involves some single-mode squeezing.

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It has been common knowledge that the single-mode squeezing operator and the two-mode squeezing operator are independent of each other. However, in this work we find that after using the technique of integration within Q-ordering and P-ordering, we can detach two single-mode squeezing operators from the two-mode squeezing operator. In other words, we show that the two-mode squeezing operator can be split into a P-ordered two-mode squeezing operator (with a new squeezing parameter) and two single-mode squeezing operators (with another squeezing parameter). This tells us that the two-mode squeezing mechanism also involves some single-mode squeezing.
It has been common knowledge that the single-mode squeezing operator and the two-mode squeezing operator are independent of each other. However, in this work we find that after using the technique of integration within -ordering and -ordering, we can detach two single-mode squeezing operators from the two-mode squeezing operator. In other words, we show that the two-mode squeezing operator can be split into a -ordered two-mode squeezing operator (with a new squeezing parameter) and two single-mode squeezing operators (with another squeezing parameter). This tells us that the two-mode squeezing mechanism also involves some single-mode squeezing.
For two unequal-mass particles, we construct the entangled state representation and then derive the corresponding squeezing operator. This squeezing operator has a natural realization in the entangled state representation, which exhibits the intrinsic relation between squeezing and quantum entanglement. This squeezing operator involves both two-mode squeezing and the direct product of two single-mode squeezings. The maximum squeezing occurs when the two particles possess equal mass. When the two particles' mass difference becomes large, the component of the two single-mode squeezings becomes dominant.
One- and two-mode successively squeezed state, obtained through re-squeezing two single mode squeezed states by the two-mode squeezing operator, is studied in terms of the technique of integration within an ordered product (IWOP) of operators. We first derive the normally ordered form of this one- and two-mode successively squeezing operator, and then investigate the quantum statistical properties of the corresponding squeezed state. Particularly, we use the Weyl ordering invariance under a similar transformation to derive the analytical expression of its Wigner function, which seems very easy and concise. Finally, the experimental generation of one- and two-mode successively squeezed state is also proposed simply.