Bosonic Operator Realization Research Articles

New angular momentum state via the bosonic operator realization and its nonclassical property

We theoretically introduce a new angular momentum state via the bosonic operator realization of angular momentum operators on a number state, and study its nonclassicality based on the sub-Poissonian distribution, photon number distribution, entanglement entropy and Wigner distribution. The results show that the nonclassicality of the new state for odd q is more stronger than that for even q, and the nonclassicality for any q always enhances first and then weakens with increasing g. Besides, the entanglement always increases with the increase of q for all of g, and finally reaches a maximum when g and h are in certain value ranges and q is large enough.

The New Multipartite Squeezing Operator and Some of its Properties

In this paper, we introduce a pair of mutually conjugate multipartite entangled state representations for defining the squeezing operator of entangled multipartite Sn(λ) which involves an n-mode bosonic operator realization of the SU(1,1) Lie algebra. This operator squeezes the multipartite entangled state in a natural way. We discuss the transform properties of aj and \(a_{j}^{\dagger }\) under the operation of Sn(λ) and derive the interaction Hamiltonian which can generate such an evolution. In addition, the corresponding multipartite squeezed vacuum state |λ〉 is obtained. Based on this, the variances of the n-mode quadratures in |λ〉 are evaluated and the violation of the Bell inequality for |λ〉 is examined by using the formalism of Wigner representation.

Parametric Amplifier Studied as Time Evolution of Angular Momentum System in Entangled State Representation

We present a new approach for studying theoretical model of a parametric amplifier. We show that time-evolution of parametric amplifier can be treated as formalism of angular momentum system by using the newly found bosonic operator realization of three generators (J +, J −, J z ). The entangled state representation is essential in this approach. The transition probability from vacuum state to two-mode squeezed state in a parametric amplifier can be directly evaluated.

New 3-mode bosonic operator realization of SU(2) Lie algebra: From the point of view of squeezing

We consider the quantum mechanical SU(2) transformation e2λJzJ±e−2λJz = e±2λJ± as if the meaning of squeezing with e±2λ being squeezing parameter. By studying SU(2) operators (J±,Jz) from the point of view of squeezing we find that (J±,Jz) can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation (the eigenvectors of J+ or J−) of the 3-mode squeezing operator e2λJz. The idea of considering quantum SU(2) transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU(2) and new squeezing operators.

New Pair of Mutually Conjugate 3-Mode Entangled State Representations and the Corresponding Fractional Fourier Transformation

Based on constructing a new pair of mutually conjugate 3-mode entangled state representations (ESR), we find new 3-mode bosonic operator realization of angular momentum. Using the properties of 3-mode ESR we formulate the new fractional Fourier transformation in entangled form. The method of integration within an ordered product of operators plays an important role in establishing the ESR.

Virial Theorem for Angular Displacement and Torque

The usual Virial theorem is expressed through the coordinate and the force, \(2\langle T\rangle =\langle X\frac{dV}{dX}\rangle =-\langle XF\rangle \), \(F=-\frac{dV}{dX}\), XF is the work done by the force F, T is the kinetic energy. In this paper we extend the usual discussion on the Virial theorem about coordinate-force variables to the case of angular displacement-torque variables. By virtue of introducing the entangled state representation and the bosonic operator realization of the Hamiltonian of quantum pendulum system we derive the Virial theorem for angular variable and torque.

Optical entangled fractional Fourier transform derived via non-unitary SU(2) bosonic operator realization and its convolution theorem

Based on the two mutually conjugate tripartite entangled state representations (TESR), we introduce the 3-mode optical entangled fractional Fourier transform (EFrFT) through a new non-unitary bosonic operator realization of the SU(2) generators and the tripartite squeezing operator. The EFrFT, which is characteristic of the eigenmodes being three-variable Hermite polynomials, is not the direct product of three single-variable FrFTs. We show that the EFrFT adapts to the transform between two mutually conjugate quantum mechanical TESR, i.e., we can recast the EFrFT into the matrix element of expiπ2−αJ++J− in the TESR. In addition, we define the two functions' convolution in the EFrFT scheme and obtain the convolution theorem using the TESR. The derivation is concise and rigorous because our calculation is based on Dirac's powerful representation theory.

Pseudo-Classical Partition Function of Spin One-Half Derived by Coherent State Method

Using the bosonic coherent state representation and the Schwinger bosonic operator realization of angular momentum we find the formula for the quantum Hamiltonian H = ia†iU̇ijU†jlal for SU(2) rotation U, in this way we further specify the angular velocity , where is the Pauli matrix. Though the spin as a quantum observable has no classical correspondence, we may still mimic it as a rigid body rotation characterized by 3 Euler angles, and calculate its Pseudo-classical rotational partition function of spin one-half.

ENTANGLED STATE REPRESENTATION FOR A PARTICLE ON A CIRCLE STUDIED IN TERMS OF BOSONIC OPERATOR REALIZATION OF ANGULAR MOMENTUM

By introducing the bosonic operator realization of angular momentum, we establish the entangled state representation for describing quantum mechanics of a particle on a circle. The phase operator, the angular momentum eigenstates, the lowering and ascending operators for angular momentum are all well expressed in the bosonic realization with the aid of appropriate entangled states, i.e. we establish a new formalism for the quantum mechanics of a particle on a circle.

Fractional Hankel transform gained via non-unitary bosonic operator realization of angular momentum generators

By proposing new non-unitary Bose operator realization of angular momentum generators ( J − , J + , J 0 ) and finding that the charge-amplitude entangled states (CAES) introduced in [H.-y. Fan, Phys. Lett. A 313 (2003) 343] carry the representative space of them, we derive the integral kernel of optical fractional Hankel transform (FHT) by calculating the matrix element of exp { i θ ( J + + J − ) } in the CAES.

Multi-Partite EPR Entangled State Representation for ContinuousVariables and Its Application in Squeezing Theory

By extending the Einstein–Podolsky–Rosen (EPR) bipartite entanglement toan n-partite case, we construct the common eigenstate of the n-partitetotal coordinate and relative momenta for the continuous variables. Theentanglement property of the state is shown. The classical dilationtransform of variables in such a state induces a new n-mode squeezingoperator related to an n-mode bosonic operator realization of SU(1,1) Liealgebra.

Bosonic Operator Realization of Hamiltonian for a Superconducting Quantum Interference Device**The project supported by National Natural Science Foundation of China under Grant No. 10175057 and the President Foundation of the Chinese Academy of Sciences

Based on the appropriate bosonic phase operator diagonalized in the entangled state representation we construct the Hamiltonian operator model for a superconducting quantum interference device. The current operator and voltage operator equations are derived.

WAVE FUNCTION REPRESENTATION FOR THE GENERALIZED EIGENSTATES OF SU(1, 1) NONCOMPACT GENERATORS

The SU(1, 1) algebra is represented by a two bosonic operator realization. This allows one to obtain a remarkable simplification of the SU(1, 1) noncompact generator eigenvectors by representing the Hilbert space basis in terms of two harmonic oscillator wave functions.

Bosonization, τ-functions and operator formalism on Riemann surfaces

We propose an operator bosonization of generalized ghost systems of closed string theory (the bc-system of spin J) on Riemann surfaces of arbitrary genus. The bosonization is carried out at the operator level in terms of Bose conformal field theory operators which are well-defined globally on the Riemann surface and are essentially given by operator-valued Baker-Akhiezer functions. The formalism yields an elementary derivation of higher-loop bc-correlation functions as well as a bosonic operator realization of the algebro-geometric tau function of arbitrary Riemann surfaces. It also enables us to construct explicitly an operator that glues a handle to Riemann surfaces.