New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case

As a natural extension of Fan's paper (arXiv: 0903.1769vl [quant-ph]) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation we find new two-fold complex integration transformation about the Wigner operator (in its entangled form) in phase space quantum mechanics and its inverse transformation. In this way, some operator ordering problems can be solved and the contents of phase space quantum mechanics can be enriched.Comment: 8 pages, 0 figure

Wigner functions of thermo number state, photon subtracted and added thermo vacuum state at finite temperature

Based on Takahashi-Umezawa thermo field dynamics and the order-invariance of Weyl ordered operators under similar transformations, we present a new approach to deriving the exact Wigner functions of thermo number state, photon subtracted and added thermo vacuum state. We find that these Wigner functions are related to the Gaussian-Laguerre type functions of temperature, whose statistical properties are then analysed.Comment: 10 pages and 2 figure

Entangled Husimi distribution and Complex Wavelet transformation

Based on the proceding Letter [Int. J. Theor. Phys. 48, 1539 (2009)], we expand the relation between wavelet transformation and Husimi distribution function to the entangled case. We find that the optical complex wavelet transformation can be used to study the entangled Husimi distribution function in phase space theory of quantum optics. We prove that the entangled Husimi distribution function of a two-mode quantum state |phi> is just the modulus square of the complex wavelet transform of exp{-(|eta|^2)/2} with phi(eta)being the mother wavelet up to a Gaussian function.Comment: 7 page

Quantum mechanical photon-count formula derived by entangled state representation

By introducing the thermo entangled state representation, we derived four new photocount distribution formulas for a given density operator of light field. It is shown that these new formulas, which is convenient to calculate the photocount, can be expressed as such integrations over Laguree-Gaussian function with characteristic function, Wigner function, Q-function, and P-function, respectively.Comment: 5 pages, no figur

Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian

Based on the technique of integration within an ordered product (IWOP) of operators we introduce the Fresnel operator for converting Caldirola-Kanai Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel operator with the parameters A,B,C,D corresponds to classical optical Fresnel transformation, these parameters are the solution to a set of partial differential equations set up in the above mentioned converting process. In this way the exact wavefunction solution of the Schr\"odinger equation governed by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed number state. The corresponding Wigner function is derived by virtue of the Weyl ordered form of the Wigner operator and the order-invariance of Weyl ordered operators under similar transformations. The method used here can be suitable for solving Schr\"odinger equation of other time-dependent oscillators.Comment: 6 pages, 2 figure

Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.Comment: 4 pages no figur

Simultaneous eigenstates of the number-difference operator and a bilinear interaction Hamiltonian derived by solving a complex differential equation

As a continuum work of Bhaumik et al who derived the common eigenvector of the number-difference operator Q and pair-annihilation operator ab (J. Phys. A9 (1976) 1507) we search for the simultaneous eigenvector of Q and (ab-a^{+}b^{+}) by setting up a complex differential equation in the bipartite entangled state representation. The differential equation is then solved in terms of the two-variable Hermite polynomials and the formal hypergeometric functions. The work is also an addendum to Mod. Phys. Lett. A 9 (1994) 1291 by Fan and Klauder, in which the common eigenkets of Q and pair creators are discussed