Chen Jun-Hua

Coherent State Projection Operator Representation of Symplectic Transformations as a Loyal Representation of Symplectic Group

We find that the coherent state projection operator representation of symplectic transformation constitutes a loyal group representation of symplectic group. The result of successively applying squeezing operators on number state can be easily derived.

Symplectic Group Representation of the Two-Mode Squeezing Operator in the Coherent State Basis*

We find that the coherent state projection operator representation of the two-mode squeezing operator constitutes a loyal group representation of symplectic group, which is a remarkable property of the coherent state. As a consequence, the resultant effect of successively applying two-mode squeezing operators are equivalent to a single squeezing in the two-mode Fock space. Generalization of this property to the 2n-mode case is also discussed.

Fractional Radon Transform and Transform of Wigner Operator

Based on the Radon transform and fractional Fourier transform we introduce the fractional Radon transformation (FRT). We identify the transform kernel for FRT. The FRT of Wigner operator is derived, which naturally reduces to the projector of eigenvector of the rotated quadrature in the usual Radon transform case.

Wave functions of a new kind of nonlinear single-mode squeezed state

We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear single-mode squeezing operators. We derive the wave functions of exp[−(ig/2)(P + P)|0 in the coordinate representation. A new operators disentangling formula is derived as a by-product.

Long-time limit behavior of the solution to an atom's master equation

We study the long-time limit behavior of the solution to an atoms master equation. For the first time we derive that the probability of the atom being in the α-th (α = j + 1 − jz, j is the angular momentum quantum number, jz is the z-component of angular momentum) state is {(1 − K/G)/[1 − (K/G)2j+1]}(K/G)α−1 as t → +∞, which coincides with the fact that when K/G > 1, the larger the α is, the larger the probability of the atom being in the α-th state (the lower excited state) is. We also consider the case for some possible generalizations of the atomic master equation.

Squeezing-Displacement Dynamics for One-Dimensional Potential Well with Two Mobile Walls where Wavefunctions Vanish

We show that the dynamics for a particle confined in a one-dimensional potential well with two mobile boundaries where wavefunctions vanish can be converted to the case as if the boundary was time-independent at the expense of an appropriate time-dependent Hamiltonian. The squeezing-displacement operator can be derived, and the corresponding Hamiltonian is determined by the situation of mobile boundaries.

Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian

For classical Hamiltonian with general form we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator (IEO) method (Fan et al. 2004 Phys. Lett. A 321 75) to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.

Radon transforms of the Wigner operator on hyperplanes

The generalization of tomographic maps to hyperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distribution—a mixed-state density operator. Reconstruction of the Wigner operator is also feasible. The normally ordered form and the Weyl ordered form of the Wigner operator are used in our derivation. The operator quantum tomography theory is expressed in terms of some operator identities, with the merit of revealing the essence of the theory in a simple and concise way.

A theorem for quantum operator correspondence to the solution of the Helmholtz equation

We propose a theorem for the quantum operator that corresponds to the solution of the Helmholtz equation, i.e., ∫∫∫V(x1,x2,x3)|x1,x2,x3x1,x2,x3|d3x = V(X1,X2,X3) = e−λ2/4:V(X1,X2,X3):, where V(x1,x2,x3) is the solution to the Helmholtz equation 2V + λ2V = 0, the symbol: : denotes normal ordering, and X1,X2,X3 are three-dimensional coordinate operators. This helps to derive the normally ordered expansion of Diracs radius operator functions. We also discuss the normally ordered expansion of Bessel operator functions.

A Few Remarks on Milburn Equation

After presenting the infinite operator-sum form solution to the Milburn equation dρ/dt = γ(UρU† – ρ) = γU[ρ,U†], where U = e-iH/γ, and verifying that this equation preserves the three necessary conditions of density operators during time evolution, we prove that the von Neumann entropy increases with time. We also point out that if A and B both obey the Milburn equation, then the product AB obeys (d/dt) (AB) = γU[AB, U†] – (1/γ) (dA/dt) (dB/dt), which violates the Milburn equation, this reflects that a pure state will evolve to a mixture in general.