Hong-yi Fan

NEW REPRESENTATION OF THERMAL STATES IN THERMAL FIELD DYNAMICS

Abstract We introduce a new state representation /vbη〉 for thermal field dynamics, which possesses orthonormal and completeness relations. The thermal operator, which engenders the transition from zero temperature to finite temperature, is shown to have a natural representation in the representation manifestly exhibiting squeezing. The relationship between temperature evolution dynamics and the squeezing is also discussed.

New representation for thermo excitation and de-excitation in thermofield dynamics☆

Abstract For quantum field theory at finite temperature we construct a new thermal excitation representation |E,g〉, which is the common eigenvector of Hamiltonian operator of total system (including the reservoir) and the operator (α(β)− α † (β))(α † (β)− α (β)) , where α † (β) ( α † (β)) creates a quantum of energy ℏω(β) (−ℏω(β)), respectively, β=ℏ/kT, k is the Boltzmann constant. The explicit from of |E,g〉 is derived by virtue of the common eigenvector α(β)− α † (β) and α † (β)− α (β) . The thermo excitation and de-excitation operations are manifestly displayed in |E,g〉 representation. As an application, the |E,g〉 representation of thermal squeezing operator is obtained.

A CONVENIENT REPRESENTATION FOR THE TWO-MODE PHASE OPERATOR (A+B)/(A+B)

Abstract We find a representation in which the two-mode phase operator ( a + b † ) ( a † + b ) manifestly exhibits its phase behavior. With this representation, the phase operator is more applicable to further illustrating the Shapiro-Wagner phase measurement approach. The technique of integration within an ordered product of operators is essential in our discussion.

EPR entangled state and generalized Bargmann transformation

Abstract In similar to the relation between the coherent state and the Bargmann transform, we find a generalized Bargmann transformation naturally accompanying Einstein–Podolsky–Rosen (EPR) entangled state of continuous variables. The new Bargmann transform kernel is introduced which can naturally lead to the entangled state. The generalized Bargmann representation of two-mode Fock state is a two-variable Hermite polynomial.

Quasi-probability distribution in the coherent thermal state representation and its time evolution

We find that the coherent thermal state |η〉 (H.-y. Fan et al., Phys. Lett. A 246 (1998) 242) can provide a new approach for studying quasi-probability distribution of density operators and their time evolution. This approach is convenient and concise because the |η〉 state possesses well-behaved properties and is based on the thermal field dynamics.

A special type of squeezed coherent state

Abstract We introduce a new type of single-mode squeezed coherent states | z 〉 g , which differs from the conventional squeezed states in that its displacement parameter depends on its squeezing parameter. By tuning the relative strength of the two complex parameters involved, this new state | z 〉 g can reduce to the simple coherent state, the coordinate eigenstate, or the momentum eigenstate. The properties of the new state | z 〉 g including its overcompleteness relation are investigated.

Hermite polynomial states in two-mode Fock space☆

Abstract We find that the state S(ξ)H p,q (μa † 1 , μa † 2 )|00〉 , where S (ξ) is a two-mode squeezing operator and H p , q ( x , y ) is a two-variable Hermite polynomial, is a minimum uncertainty state for sum squeezing.

NUMBER-DIFFERENCE-PHASE UNCERTAINTY RELATION FOR NFM OPERATIONAL QUANTUM PHASE DESCRIPTION

For the Noh, Fougers, and Mandel (NFM) operational quantum phase description, which is based on an eight-port homodyne-detection, we propose the number-difference-phase (ND-P) uncertainty relation and, then, discuss the mechanism of generation of ND-P squeezed states.

A KQ-ANALOGUE REPRESENTATION FOR A BLOCH ELECTRON IN A UNIFORM MAGNETIC FIELD

Abstract We employ the state-vector |λ〉, λ = λ 1 + i λ 2 , which is suitable for describing the wave function of the quantum Hall effect [Fan Hong-Yi, Ren Yong, Mod. Phys. Lett. B 10 (1996) 523], to construct a kq -analogue representation | λ , k 〉 for a Bloch electron in a uniform magnetic field, which is defined on both the rectangular cell of ( λ 1 , λ 2 ) and its reciprocal ( k 1 , k 2 ) zone. We show that | λ , k 〉 is the common eigenvector of the magnetic translation operators. The simple application of the | λ , k 〉 representation is briefly discussed.

An alternative approach for deriving a positive P-representation

Abstract Using the technique of integration within an ordered product of operators and adopting similar procedures as for the theory for quantizing a gauge field, we derive the Drummond-Gardiner positive P -representation directly from the Glauber-Sudarshan P -representation. The analogy between the extra phase-space dimensions in the positive P -representation and the gauge transformation freedoms for gauge field quantization is pointed out.