Two-mode Fock Space Research Articles

New Parameterized Coherent-Entangled State Representation and Its Applications

Based on EPR’s idea of quantum entanglement, new parameterized coherent-entangled states |α,p〉 μ,ν are introduced in two-mode Fock space, which can be implemented by using a beam splitter. Possible superpositions of |α,p〉 μ,ν result in some new entangled states. The asymmetric ket-bra integration from |α,p〉 μ,ν leads to a new one- and two-mode combinatorial squeezing operator with stronger squeezing, which clearly shows the intrinsic relationship between squeezing mechanism and quantum entanglement.

A driven damped harmonic oscillator in the ket-vector representation of the density operator

By virtue of the entangled-state basis and the ket-vector representation of the density operator, we solve the master equation of a driven damped harmonic oscillator. In this representation, the density operators are mapped to vectors of a two-mode Fock space whose first mode is the system mode and the second mode is a fictitious one. We derive the Glauber–Sudarshan P function of the quantum state.

A new class of f-deformed charge coherent states and their nonclassical properties

Two-mode charge (pair) coherent states have been introduced previously by using the 〈η| representation. In this paper, we reobtain these states by a rather different method. Then, using the nonlinear coherent state approach and based on a simple manner by which the representation of two-mode charge coherent states is introduced, we generalize the bosonic creation and annihilation operators to the f-deformed ladder operators and construct a new class of f-deformed charge coherent states. Unlike the (linear) pair coherent states, our presented structure has the potential to generate a large class of pair coherent states with various nonclassicality signs and physical properties which are of interest. For this purpose, we use a few well-known nonlinearity functions associated with particular quantum systems as some physical appearances of our presented formalism. After introducing the explicit form of the above correlated states in the two-mode Fock space, several nonclassicality features of the corresponding states (as well as the two-mode linear charge coherent states) are numerically investigated by calculating quadrature squeezing, the Mandel parameter, the second-order correlation function, the second-order correlation function between the two modes and the Cauchy–Schwartz inequality. Also, the oscillatory behaviour of the photon count and the quasi-probability (Husimi) function of the associated states will be discussed.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.

Generation of a new bipartite coherent-entangled state and its applications

A new bipartite coherent-entangled state is introduced in the two-mode Fock space, which exhibits the properties of both a coherent state and an entangled state. The set of coherent-entangled states makes up a complete and partly nonorthogonal representation. A simple experimental scheme to produce the coherent-entangled state using an asymmetric beamsplitter is proposed. Some applications of the coherent-entangled state in quantum optics are also presented.

Some applications of a new coherent-entangled state in two-mode Fock space

Using the technique of integration within an ordered product of operators, we find a new kind of coherent-entangled state (CES), which exhibits both coherent and entangled state properties. The set of CESs makes up a complete and partly nonorthogonal representation. Using a beam splitter, we propose a simple experimental scheme to produce the CES. Finally, we present some applications of CESs in quantum optics.

Wigner function evolution in a self-Kerr medium derived by entangled state representation

By introducing the thermo-entangled state representation, we convert the calculation of Wigner function (WF) of density operator to an overlap between ‘two pure’ states in a two-mode enlarged Fock space. Furthermore, we derive a new WF evolution formula of any initial state in a self-Kerr medium with photon loss and find that the photon number distribution for any initial state is independent of the coupling factor with the Kerr medium, where the number state is not affected by the Kerr nonlinearity and evolves into a density operator of binomial distribution.

The construction, properties and applications of a new bipartite coherent-entangled state in the two-mode Fock space

Using the technique of integration within an ordered product (IWOP) of operators, we find a new kind of bipartite coherent-entangled state (CES) that exhibits both coherent state and entangled state properties. The set of CESs makes up a complete and partly nonorthogonal representation. Using an asymmetric beamsplitter we propose a simple experimental scheme for producing the CES. Finally, we present some new quantum states related to the CES and some applications of the CES to quantum optics.

New bipartite coherent-entangled state in two-mode Fock space and its applications

A new bipartite coherent-entangled state (CES) is found which exhibits both coherent state and entangled state properties. The set of CESs constitute a complete and partly nonorthogonal representation. Using an asymmetric beamsplitter a experimental scheme to produce the CES is proposed. Applications of CESs in quantum optics are also presented.

A New Kind of Bipartite Coherent-Entangled State and Its Applications in Quantum Optics

A new kind of bipartite coherent-entangled state (CES) is introduced in the two-mode Fock space which exhibits the properties of both coherent state and entangled state. The set of CESs make up a complete and partly nonorthogonal representation. A simple experimental scheme to produce the CES is proposed by using a beam splitter. Some applications of the CES are also presented in quantum optics.

A Generalized Hadamard-Fresnel Complementary Transformation Derived by Virtue of New Coherent-Entangled State

The new coherent-entangled state |z,x;θ〉 is proposed in the two-mode Fock space, which exhibits both the properties of coherent and entangled states. The completeness relation of |z,x;θ〉 is proved by virtue of the technique of integral within an ordered product of operators. A generalized Hadamard-Fresnel complementary transformation derived by virtue of the coherent-entangled state |z,x;θ〉, which is unitary. The new unitary operator plays the role of both Hadamard transformation for \((\hat{a}_{1}\sin\theta -\hat{a}_{2}\cos\theta)\) and Fresnel transformation for \((\hat{a}_{1}\cos\theta +\hat{a}_{2}\sin\theta)\), respectively.

New Two-Mode Coherent-Intermediate-Entangled State and Its Squeezing Operator

The coherent-intermediate-entangled state |α, x⟩λ,ν is proposed in the two-mode Fock Space, which exhibits both the properties of the coherent and entangled states. The |α,x⟩λ,ν makes up a new quantum mechanical representation, and the completeness relation of |α,x⟩λ,ν is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operators are derived. Furthermore, Generalized P-representation is constructed in the coherent-intermediate-entangled state |α,x⟩λ,ν and the Schmidt decomposition of |α,x⟩λ,ν is investigated.

Generalized two-mode coherent-entangled state with real parameters

The coherent-entangled state |α, x; λ> with real parameters λ is proposed in the two-mode Fock space, which exhibits the properties of both the coherent and entangled states. The completeness relation of |α, x; λ> is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operator is derived, with its own squeezing properties. Furthermore, generalized P-representation in the coherent-entangled state is constructed. Finally, it is revealed that superposition of the coherent-entangled states may produce the EPR entangled state.

Phase State as a Limiting Case of SU(1,1) Coherent State

We show that the Susskind—Glogower phase state is a limiting case of a kind of SU(1,1) coherent states. By analogy, based on the bipartite entangled state representation (ESR) we demonstrate that an appropriate SU(1,1) coherent state composed of the two-mode unitary phase operator also leads to a new phase state in two-mode Fock space. is diagonalized in the ESR.

Phase Properties of Two-Mode Squeezing-Rotating Entangled Representation

By virtue of the squeezing-rotating entangled representation,we mainly establish the new two-mode phase operator and phaseangle operator, which is a general form including the foregoingformalist in two-mode Fock space. In addition, the correspondingphase distribution function is given in the entangled representation.In terms of this definition, we also analyze thephase behavior of some simple two-mode states such as squeezing-rotatingcoherent state, squeezing-rotating vacuum state, and so on. It is foundthat the results exactly agree with the foregoing phasetheory.

Application of Bipartite Entangled States to Quantum MechanicalVersion of Complex Wavelet Transforms

We introduce the bipartite entangled states to present a quantum mechanicalversion of complex wavelet transform. Using the technique of integral withinan ordered product of operators we show that the complex wavelet transformcan be studied in terms of various quantum state vectors in two-mode Fockspace. In this way the creterion for mother wavelet can be examinedquantum-mechanically and therefore more deeply.

Continuum variable entangled state generated by an asymmetric beam splitter

For an asymmetric beam-splitter a new kind of entangled state \(\left| \eta ,\theta \right\rangle \) is introduced, we then derive the integration measure with which such states can make up a complete and orthonormal representation in two-mode Fock space. We then show how to use \(\left| \eta ,\theta \right\rangle \) in finding new squeezing operator and new squeezed state, whose generation can relies on the asymmetric beamsplitter.

New two-mode coherent-entangled state and its application

We introduce the so-called coherent-entangled state in the two-mode Fock space; this state exhibits both the properties of the coherent and entangled states. Generalized -representation in the coherent-entangled state is constructed. A protocol for producing the ideal coherent-entangled state is presented. It is shown that the bipartite entangled state can be a superposition of the coherent-entangled states.

Symplectic Group Representation of the Two-Mode Squeezing Operator in the Coherent State Basis**The project supported by National Natural Science Foundation of China under Grant No. 10575057

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.

New Parametrized Entangled State Representations and Their Applications

We construct two new kinds of parametrized entangled states in two-mode Fock space. Using the technique of integration within an ordered product of operators, we prove that they span the complete space. Their applications to solving dynamic problems and finding new generalized squeezing are addressed.

SOME NEW RELATIONS BETWEEN TARGET STATE AND QUANTUM TELEPORTED STATE GAINED BY VIRTUE OF THE |η> REPRESENTATION

Based on the entangled state representation <η| in two-mode Fock space (Fan and Klauder, Phys. Rev.A49, 704 (1994)), we provide an alternative approach for analyzing quantum teleportation of continuous variables and go a step further by deriving some relations between input (target) states and teleported states. The natural representation of the two-mode squeezing operator in the |η> representation greatly simplifies our calculations.