Barut-Girardello and Gilmore-Perelomov coherent states for pseudoharmonic oscillators and their nonclassical properties: Factorization method

In this paper we try to introduce the ladder operators associated with the pseudoharmonic oscillator, after solving the corresponding Schrrdinger equation by using the factorization method. The obtained generalized raising and lowering operators naturally lead us to the Dirac representation space of the system which is much easier to work with, in comparison to the functional Hilbert space. The SU（1, 1） dynamical symmetry group associated with the considered system is exactly established through investigating the fact that the deduced operators satisfy appropriate commutation relations. This result enables us to construct two important and distinct classes of Barut-Girardello and Gilmore-Perelomov coherent states associated with the system. Finally, their identities as the most important task are exactly resolved and some of their nonclassical properties are illustrated, numerically.

Hong–Ou–Mandel interference with two independent weak coherent states

Recently, the Hong-Ou-Mandel （HOM） interference between two independent weak coherent pulses （WCPs） has been paid much attention due to the measurement-device-independent （MDI） quantum key distribution （QKD）. Using classical wave theory, articles reported before show that the visibility of this kind of HOM-type interference is 〈 50%. In this work, we analyze this kind of interference using quantum optics, which reveals more details compared to the wave theory. Analyses confirm the maximum visibility of 50%. And we conclude that the maximum visibility of 50% comes from the two single-photon states in WCPs, without considering the noise. In the experiment, we successfully approach the visibility of 50% by using WCPs splitting from the single pico-second laser source and phase scanning. Since this kind of HOM interference is immune to slow phase fluctuations, both the realized and proposed experiment designs can provide stable ways of high-resolution optical distance detection.

Generation of Multi-mode Entangled Coherent States for N Trapped Ions in Strong-Excitation Regime

We propose a scheme to generate entangled coherent states for the vibrational modes of N trapped ions.In the scheme the first ion is sequentially excited by two travelling wave laser fields tuned to the ion transition. The scheme works in the strong-excitation regime, which is of experimental importance in view of decoherence.

The Wigner function and phase properties of superposition of two coherent states with the vacuum state

This paper discusses some statistical properties of the superposition of two coherent states with a vacuum state, such as sub-Poissonian photon statistics and negativity of the Wigner function. Phase probability distribution and phase variance are calculated. Special cases of the constructed superposition states are presented. The results show that depending on the vacuum state coefficient γ and the coherent state coefficient a, it can generate a variety of nonclassical states.

Amplitude-squared squeezing of superposition of coherent states

This paper discusses the amplitude-squared squeezing for the superposition of two coherent states with their phase differences being separately π/2, 3π/2, and π1, as well as for the superposition state of two pseudoclassical states. According to the analysis, it is found that the superposition state of two coherent states with their phase differences π/2 and 3π/2, and the superposition state of two pseudoclassical states both do exhibit the amplitude-squared squeezing. Also, some specific states are found to exhibit even stronger squeezing effects when relative phase of the superposition is equal to the average photon number. Amplitude-squared squeezing is dependent on the difference in phase between two coherent states.

Quantum Properties of Two-Mode Squeezed Even and Odd Coherent States

Two new types of quantum states are constructed by applying the operator s（ξ） = exp（ξ＊ ab - ξa＋b＋） on the two-mode even and odd coherent states. The mathematical and quantum statistical properties of such states are investigated. Various nonclassical features of these states, such as squeezing properties, the inter-mode photon bunching, and the violation of Cauchy-Schwarz inequality, are discussed. The Wigner function in these states are studied in detail.

Using Coherent States to Make Physically Correct Classical-to-Quantum Procedures That Help Resolve Nonrenomalizable Fields Including Einstein’s Gravity

Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important problems including the quantization of half-harmonic oscillators [1], non-renormalizable scalar fields, such as (ϕ12)3 [2] and (ϕ12)3 [3], as well as the quantum theory of Einstein’s general relativity [4]. The features that distinguish affine quantization are emphasized, especially, that affine quantization differs from canonical quantization only by the choice of classical variables promoted to quantum operators. Coherent states are used to ensure proper quantizations are physically correct. While quantization of non-renormalizable covariant scalars and gravity are difficult, we focus on appropriate ultralocal scalars and gravity that are fully soluble while, in that case, implying that affine quantization is the proper procedure to ensure the validity of affine quantizations for non-renormalizable covariant scalar fields and Einstein’s gravity.

Quantum statistical properties of photon-added spin coherent states

The photon-added spin coherent state as a new kind of coherent state has been defined by iterated actions of the proper raising operator on the ordinary spin coherent state. In this paper, the quantum statistical properties of photon-added spin coherent states such as photon number distribution, second-order correlation function and Wigner function are studied. It is found that the Wigner function shows the negativity in some regions and the second-order correlation function is less than unity. Therefore, the photon-added spin coherent state is a nonclassical state.

Maximal entanglement from photon-added nonlinear coherent states via unitary beam splitters

In this paper, we construct photon-added f-deformed coherent states （PAf-DCSs） for nonlinear bosonic fields by discussing Klauder＇s minimal set of conditions required to obtain coherent states. Using this set of nonlinear states, we propose a very useful scheme for generating the maximal amount of entanglement via unitary beam splitters for different strength regimes of the input field α, deformation q and excitation number m. Therefore, the possibility to create highly entangled states and to control the entanglement is proposed. Moreover, the condition for a maximal and separable output beam state is obtained. Finally, we examine the statistical properties of the PAf-DCSs through the Mandel parameter and exploit a connection between this quantity and the behavior variation of the output state entanglement. Our result may open new perspectives in different tasks of quantum information processing.

Wave packet dynamics of nonlinear Gazeau–Klauder coherent states of a position-dependent mass system in a Coulomb-like potential

AD = 1 position-dependent mass approach to constructing nonlinear quantum states for a modified Coulomb potential is used to generate Gazeau–Klauder coherent states. It appears that their energy eigenvalues are scaled down by the quantum number and the nonlinearity coefficient. We study the basic properties of these states, which are found to be undefined on the whole complex plane, and some details of their revival structure are discussed.

Generation of Four-Mode Cluster-Type Entangled Coherent States in Free-Traveling Optical Fields

In this paper, we propose an optical scheme to generate four-mode cluster-type entangled coherent states （ECSs） in free traveling optical fields by using two single-photon sources, coherent state sources, beam splitters, pho- todetectors, cross-Kerr media, and phase shifters. And the success probability of the states preparation is calculated. At last we discuss the experimental feasibility of such proposal.

A New Kind of k-Quantum Nonlinear Coherent States： Their Generation and PhysicalMeaning

A new kind of k-quantum nonlinear coherent states,i.e.,the k eigenstates of the k-th power~k (k≥3) of the generalized annihilation operator=1/f() of f-oscillators,are obtained and their properties are discussed.The completeness of the k states is investigated.An alternative method to construct them is proposed.It is shown that these states may form a complete Hilbert space,and all of them can be generated by a linear superposition of k Roy-type nonlinear coherent states.Physically,they can be generated by a linear superposition of the time-dependent Roy-type nonlinear coherent states at different instants.

Coupling Between the Group—Related Coherent States

When two representations of the Lie algebra are coupled, the coupling integral kernels are presented to relate the coupled to uncoupled group-related coherent states. These kernels have a connection with usual coupling coefficients. The explicit expressions of these kernels for and are given. When the direct product of three representations is formed in two ways, the recoupling integral kernels relating to the coupled group-related coherent states corresponding to two different schemes are introduced, and the relations between these kernels and the general recoupling coefficients are obtained. The properties of these kernels are discussed.

Quantum dual signature scheme based on coherent states with entanglement swapping

A novel quantum dual signature scheme, which combines two signed messages expected to be sent to two diverse receivers Bob and Charlie, is designed by applying entanglement swapping with coherent states. The signatory Alice signs two different messages with unitary operations（corresponding to the secret keys） and applies entanglement swapping to generate a quantum dual signature. The dual signature is firstly sent to the verifier Bob who extracts and verifies the signature of one message and transmits the rest of the dual signature to the verifier Charlie who verifies the signature of the other message. The transmission of the dual signature is realized with quantum teleportation of coherent states. The analysis shows that the security of secret keys and the security criteria of the signature protocol can be greatly guaranteed.An extensional multi-party quantum dual signature scheme which considers the case with more than three participants is also proposed in this paper and this scheme can remain secure. The proposed schemes are completely suited for the quantum communication network including multiple participants and can be applied to the e-commerce system which requires a secure payment among the customer, business and bank.

Amplitude-squared squeezing of the generalized odd-even coherent states of the anharmonic oscillator in a finite-dimensional Hilbert space

This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.

Coherent States and a Path Integral for the Relativistic Linear Singular Oscillator

The SU（1,1） coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between SU（1,1） coherent states is given. Classical equations of the motion in the generalized curved phase space are obtained. It is shown that the use of quasiclassical Bohr Sommerfeld quantization rule yields the exact expression for the energy spectrum.

Study of Concurrence and D-Concurrence on Two-Qubits Resulted in Pair Coherent States in Language of SU(2) Coherent States

Pair coherent state, is a state of a two-mode radiation field that is known as a state with non-gaussian wave function. In this paper, study on the pair coherent state, we notice that with superposition of two first terms of this states, one two-qubits formed. Because of the importance of two-qubits in theory of quantum entanglement, with two different measures with the title of concurrence and D-concurrence, we have studied the amount of entanglement and discussed its details. At the end, we describe these measures for pair coherent states as a function of the amplitude of the SU（2） coherent states.

Realistic teleportation of coherent states using squeezed vacuum states

This paper presents a realistic scheme for the teleportation of coherent states in which a two-mode squeezed vacuum state serves as the quantum channel and the position-sum and momentum-difference of two local modes serve as the measuring observables. The average fidelity of the teleportation of coherent states is derived for finite squeezing parameters and it turns out that fidelity greater than 1/2 cannot be achieved by using a classical channel alone and the probability distribution of the measurement result is a Gaussian distribution around the unknown parameter of the input coherent state with a width given by the squeezing parameter.

Entanglement Properties of Two-Mode Squeezed Coherent States in Radiation Field

Entanglement properties of two-mode squeezed coherent states in the radiation field ＆re investigated according to the entanglement criterion [Phys. Rev. Lett. 84 （2000） 2722]. The dependence of entanglement on squeeze angle and squeeze parameter is discussed. It shows that the system evolves into entangled states and entanglement does not increase persistently with the increase of squeeze angle and squeeze parameter. There only exists a certain squeeze angle in which the entanglement exists continuously.

Non-locality of Entangled Coherent States and Its Evolution in a Thermal Reservoir

Regarding the necessary and sufficient condition violating Bell-CHSH's inequality as criterion for nonlocality of entangled states, we present a perturbative calculation determining non-locality of evolving entangled states.Furthermore, by means of the perturbative calculation, the non-locality and its evolution of two kinds of entangled coherent states in a thermal reservoir are discussed.