We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±,...We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±, Jz） from the point of view of squeezing we find that （J±,Jz） can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation （the eigenvectors of J＋ or J-） of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU（2） transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU（2） and new squeezing operators.展开更多
We study the optical field＇s quadrature excitation state Xm 10）, where X = （a ＋ at）/x/2 is the quadrature operator. We find it is ascribed to the Hermite-polynomial excitation state. For the first time, we determ...We study the optical field＇s quadrature excitation state Xm 10）, where X = （a ＋ at）/x/2 is the quadrature operator. We find it is ascribed to the Hermite-polynomial excitation state. For the first time, we determine this state＇s normalization constant which turns out to be a Laguerre polynomial. This is due to the integration method within the ordered product of operators （IWOP）. The normalization for the two-mode quadrature excitation state is also completed by virtue of the entangled state representation.展开更多
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 with...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 Ω-ordering and β-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 β-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.展开更多
We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）...We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）]｜0 in the coordinate representation. A new operator＇s disentangling formula is derived as a by-product.展开更多
基金Supported by the National Natural Science Foundation of China(11471304,11401556)the Fundamental Research Funds for the Central Universities(WK2040000012)
基金supported by the National Natural Science Foundation of China(Grant Nos.11175113 and 11275123)the Key Project of Natural Science Fund of Anhui Province,China(Grant No.KJ2013A261)
文摘We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±, Jz） from the point of view of squeezing we find that （J±,Jz） can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation （the eigenvectors of J＋ or J-） of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU（2） transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU（2） and new squeezing operators.
基金supported by the National Natural Science Foundation of China(Grant Nos.11175113 and 11275123)
文摘We study the optical field＇s quadrature excitation state Xm 10）, where X = （a ＋ at）/x/2 is the quadrature operator. We find it is ascribed to the Hermite-polynomial excitation state. For the first time, we determine this state＇s normalization constant which turns out to be a Laguerre polynomial. This is due to the integration method within the ordered product of operators （IWOP）. The normalization for the two-mode quadrature excitation state is also completed by virtue of the entangled state representation.
基金supported by the Fundamental Research Funds for the Central Universities of China (Grant No. WK2060140013)
文摘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 Ω-ordering and β-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 β-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.
基金Project supported by the National Natural Science Foundation of China(Grant No.11175113)
文摘We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）]｜0 in the coordinate representation. A new operator＇s disentangling formula is derived as a by-product.
