45,163 research outputs found
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
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