Entangled State Representation Research Articles

Wigner Function of Density Operator for Negative Binomial Distribution

By using the technique of integration within an ordered product (IWOP) of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.

Husimi Operator for Describing Probability Distribution of Electron States in Uniform Magnetic Field Studied by Virtue of Entangled State Representation

For the first time we introduce an operator Δh(γ,e;κ) for studying Husimi distribution function in phase space (γ,e) for electron’s states in uniform magnetic field, where κ is the Gaussian spatial width parameter. The marginal distributions of the Husimi function are Gaussian-broadened version of the Wigner marginal distributions. Using the Wigner operator in the entangled state 〈λ| representation we find that Δh(γ,e;κ) is just a pure squeezed coherent state density operator |γ,e〉κκ〈γ,e|, which brings much convenience for studying Husimi distribution, so we name Δh(γ,e;κ) the Husimi operator. We then derive Husimi operator’s normally ordered form that provides us with an operator version to examine various properties of the Husimi distribution.

Modified Josephson equations for the mesoscopic LC circuit including two coupled Josephson junctions**Work supported by the National Natural Science Foundation of China under Grant 10574060 and the Natural Science Foundation of Liaocheng University under Grant X071049.

Based on the entangled state representation and Feynman's idea that ‘electron pairs are bosons, …, a bound pair acts as a Bose particle’, we present a cooper-pair number-phase quantization scheme for the mesoscopic LC circuit including two coupled Josephson junctions (JJs). Then we use the Heisenberg equation of motion to obtain the modified current equation and voltage equation across each JJ, as well as the equation for realizing quantum control. Besides, we investigate how the phases in two JJs are affected mutually through the capacitor coupling and the coupled JJs.

Relationship Between Wave Function and Corresponding Wigner Function Studied in Entangled State Representation

By using the explicit form of the entangled Wigner operator and the entangled state representation we derive the relationship between wave function and corresponding Wigner function for bipartite entangled systems. The technique of integration within an ordered product (IWOP) of operators is employed in our discussions.

Two-Mode Excited Squeezed Vacuum State and Its Properties

In this paper, the two-mode excited squeezed vacuum state (TESVS) is studied by using the statistical method. By calculating the normalization of the TESVS, a new form of Jacobi polynomials and some new identities are obtained. The photon number distribution of the TESVS is given and it is a simple form of Jacobi polynomials. Using the entangled state representation of Wigner operator, the Wigner function of the TESVS is obtainded and the variations of the Wigner function with the parameters m, n, and r are discussed. Here from the phase space point of view the TESVS can be well interpreted and described.

Quantum Hadamard Operators and Their Decomposition Derived by Virtue of IWOP Technique

We introduce the quantum Hadamard operator in continuum state vector space and find that it can be decomposed into a single-mode squeezing operator and a position-momentum mutual transform operator. The two-mode Hadamard operator in bipartite entangled state representation is also introduced, which involves the two-mode squeezing operator and |η⟩ ↔ ξ⟩ mutual transformation operator, where |η⟩ and ξ⟩ are mutual conjugate entangled states. All the discussions are proceeded by virtue of the IWOP technique.

Time Evolution of Density Operator for Field Damping in Squeezed Bath Calculated by Squeezing Transformation and Entangled State Representation

We find that a squeezing transformation can efficiently simplify the density operator equation of field damping in a squeezed bath. Then the entangled state representation is introduced to solve the simplified equation and the time evolution of density operator, which turns out to be a mixed coherent squeezed state.

Cooper-Pair Number-Phase Quantization for Inductance Coupling Circuit Including Josephson Junctions

Based on the entangled state representation and a bosonic phase operator formalism, we tackle with Cooper-pair number-phase quantization for the inductance coupling circuit including Josephson junctions, and then investigate how Josephson current equations change due to the presence of the coupling inductance and obtain bosonic operator Faraday formula, as well as the corresponding number-phase uncertainty relation.

Eigenfunctions of the complex fractional Fourier transform obtained in the context of quantum optics

We employ the recently established basis (the two-variable Hermite-Gaussian function) of the generalized Bargmann space (BGBS) [Phys. Lett. A303, 311 (2002)] to study the generalized form of the fractional Fourier transform (FRFT). By using the technique of integration within an ordered product of operators and the bipartite entangled-state representations, we derive the generalized generating function of the BGBS with which the undecomposable kernel of the two-dimensional FRFT [also named complex fractional Fourier transform (CFRFT)] is obtained. This approach naturally shows that the BGBS is just the eigenfunction of the CFRFT.

Energy-level and wave functions of two moving charged particles with elastic coupling derived by virtue of the entangled state representations

We derive the energy-level and wave functions for two moving charged particles with elastic coupling, using two mutually conjugate entangled state representations.

Cooper-pair number-phase quantization analysis in double-Josephson-junction mesoscopic circuit coupled by a capacitor

This paper examines the quantization of mesoscopic circuit including Josephson junctions. Following Feynman's assumption, via the Hamilton dynamic approach and by virtue of the entangled state representation, it constructs Hamiltonian operator for the double-Josephson-junction mesoscopic circuit coupled by a capacitor. Then it uses the Heisenberg equation of motion to derive the induction voltage across each Josephson junction. The result manifestly shows how the voltage is affected by the capacitance coupling.

New Three-Mode Squeezing Operators Gained via Tripartite Entangled State Representation

We show that the Agarwal–Simon representation of single-mode squeezed states can be generalized to find new form of three-mode squeezed states. We use the tripartite entangled state representations |p,y,z〉 and |x,u,v〉 to realize this goal.

Cooper-Pair Number-Phase Quantization for a Mesoscopic LCCircuit Including a Josephson Junction

By introducing the entangled state representation and Feynmanassumption that `electron pairs are bosons, …, a bound pair actsas a Bose particle', we construct an operator Hamiltonian for amesoscopic inductance-capacitance (LC) circuit including a Josephsonjunction, then we use the Heisenberg equation of motion to derive thecurrent equation and the voltage equation across the inductance as wellas across the Josephson junction. The result manifestly shows how thejunction voltage is affected by the capacitance coupling. In this waythe Cooper-pair number-phase quantization for this system is completed.

Calculation of Gaussian Perturbation on Two Harmonic Oscillators byVirtue of Entangled State Representation

The exact expressions of Gaussian-perturbation matrix elements inone- and two-mode Fock states are derived by virtue of the technique ofintegration within an ordered product of operators and theentangled state representation. It turns out that the matrixelements are just related to Gegenbauer polynomial and Hypergeometricfunction respectively. The 1st- and 2nd-order corrections tothe energy levels and the 1st-order correctionto wavefunctions of harmonic oscillator are deduced.

NEW APPROACH FOR FINDING MULTIPARTITE ENTANGLED STATE REPRESENTATIONS VIA THE IWOP TECHNIQUE

We present a new approach to finding multipartite entangled state representation by decomposing normally ordered Gaussian-form operator in completeness relation, the technique of integration within an ordered product (IWOP) of operators is essential in this searching.

Density matrix of two interacting particles with kinetic coupling derived in bipartite entangled state representation

A density matrix is usually obtained by solving the Bloch equation, however only a few Hamiltonians' density matrices can be analytically derived. The density matrix for two interacting particles with kinetic coupling is hard to derive by the usual method due to this coupling; this paper solves this problem by using the bipartite entangled state representation.

CONVOLUTION THEOREM OF THE COMPLEX FRACTIONAL FOURIER TRANSFORMATION DERIVED BY TRANSFORMATION OF ENTANGLED STATES

Based on our previous paper [H.-Y. Fan and H.-L. Lu, Int. J. Mod. Phys.19, 799 (2005)] and the two mutually-conjugate entangled state representations, we derive the convolution theorem of complex fractional Fourier transformation in the context of quantum mechanics. This approach seems convenient and neat.

BOSONIC OPERATOR HAMILTONIAN MODELS OF JOSEPHSON JUNCTIONS IN SERIES AND IN PARALLEL AND THEIR PROJECTIONS ONTO ENTANGLED STATE REPRESENTATIONS

We present the bosonic operator Hamiltonian models of two Josephson junctions which are connected in series and in parallel, respectively. By introducing the entangled state representations (|η〉 representation and Cooper pairs representation) and projecting the operator Hamiltonian onto the |η〉 representation we obtain the correct Josephson current and phase equations consistent with the classical Hamiltonian cases.

Solution to Operator Fredholm Equation in Bipartite Entangled StateRepresentation and Its Applications

Based on the bipartite entangled state representation and using thetechnique of integration within an ordered product (IWOP) of operators weconstruct the corresponding operator Fredholm equations and then derivetheir solutions. As its application we deduce some new bosonic operatoridentities and new relations about the two-variable Hermite polynomials.

MAGNETIC TRANSLATION AND DEGENERACY OF SOME LANDAU STATES STUDIED BY VIRTUE OF THE ENTANGLED STATE REPRESENTATION

By virtue of the entangled state representation, we show that a new function space for Landau state vectors can be constructed. As a result, the magnetic translation and degeneracy of some Landau states can be analyzed in a direct and transparent manner.