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.
By analyzing theoretical scheme of quantum controlling through photon addition,we propose a new optical field whose density operator asρ=λ(1-λ)l:Ll(-λ2aa/1-λ)e-λaa:(here::denotes normal ordering symbol),which is named Laguerre-polynomialweighted chaotic state.We show that such state is the solution to the master equation d/dtρ=-κ(aaρ+ρaa-aρa-aρa),describing a diffusion channel,with the initial number state|l l|,andλ=1/(1+κt).This new state is characteristic of possessing photon number l+κt at time t,so the photon number by adjusting the diffusion parameterκcan be controlled.This master equation is solved using the summation method within ordered product of operators and the entangled state representation.The physical difference between the diffusion and the amplitude damping is noted.
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.
The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state＇s evolution during the diffusion process, fully utilizing the technique of integration within an ordered product （IWOP） of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dp/dt = -κ[a＋ap -a＋pa -apa＋ ＋ paa＋]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.
For the first time we derive the evolution law of the negative binomial state In） （nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state is still a negative binomial state, however the parameter γ evolves into The decay law of theaverage photon number is also obtained.
By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral （dyduexp [iu（q-Q）＋iy（p-P）＋is/2yu]） from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.
We find the time evolution law of a negative binomial optical field in a diffusion channel. We reveal that by adjusting the diffusion parameter, the photon number can be controlled. Therefore, the diffusion process can be considered a quantum controlling scheme through photon addition.
Following the spirit of thermo field dynamics initiated by Takahashi and Umezawa, we employ the technique of integration within an ordered product of operators to derive the thermal vacuum state （TVS） for the Hamiltonian H of the two-coupled-oscillator model. The ensemble averages of the system are derived conveniently by using the TVS. In addition, the entropy for this system is discussed based on the relation between the generalized Hellmann-Feynman theorem and the entroy variation in the context of the TVS.
