Odd Coherent States Research Articles

Locality Violation with Spin-Type W States without UsingInequalities

Using even and odd coherent states, we define a newstate, which is called the spin-type W state. With the spin-type W states, weprovide a new scheme for testing fundamental aspects of quantum mechanics andrefuting local hidden variable theory without using inequalities. Finally, a schemefor preparing the spin-type W states, and discussion of experimental possibility andthe effect of the measurement on physical observables due to a close orthogonalityof the two coherent states are given.

SU(1,1) Lie Algebra Applied to the General Time-dependent Quadratic Hamiltonian System

Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are studied. We applied our result to the Caldirola–Kanai oscillator. The probability density of these coherent states for the Caldirola–Kanai oscillator converged to the center as time goes by, due to the damping constant γ. All the coherent state probability densities for the driven system are somewhat deformed.

Continuous-variable quantum teleportation of even and odd coherent states through varied gain channels

This paper has investigated quantum teleportation of even and odd coherent states in terms of the EPR entanglement states for continuous variables. It discusses the relationship between the fidelity and the entanglement of EPR states, which is characterized by the degree of squeezing and the gain of classical channels. It shows that the quality of teleporting quantum states also depends on the characteristics of the states themselves. The properties of teleporting even and odd coherent states at different intensities are investigated. The difference of teleporting two such kinds of quantum states are analysed based on the quantum distance function.

Two mesoscopic Josephson junctions in the quantized light fields

The supercurrents in two mesoscopic Josephson junctions in the presence of the quantized light fields are studied. The states of the light fields discussed in this paper include squeezed coherent states, thermal states, even and odd coherent states. The Shapiro dc currents and the even-order fluctuations of supercurrents are discussed. The effects of the field states on the supercurrents are investigated. Interfering between the supercurrents in two junctions in time domain transforms the frequency modulating in single junction into the amplitude modulating in two junctions and forms beats. The modulating degree of amplitude depends on the states of the quantized light fields. The voltage jumps of Shapiro steps in two junctions for the squeezed coherent states and displaced thermal states are double in size in comparison with those in single junction. The fluctuations of supercurrents in two junctions are much larger than those in single junction, but the fundamental quantum fluctuations are zero. The higher-order fluctuations are larger than the lower-order fluctuations. The fluctuations exhibit oscillations with same frequency for each even order and their amplitudes are modulated synchronously.

Entropy evolvement properties in a system of Schrödinger cat state light field interacting with two entangled atoms

The field entropy can be regarded as a measurement of the degree of entanglement between the light field and the atoms of a system which is composed of two-level atoms initially in an entangled state interacting with the Schr?dinger cat state. The influences of the strength of light field and the phase angle between the two coherent states on the field entropy are discussed by using numerical calculations. The result shows that when the strength of light field is large enough the field entropy is not zero and the degrees of entanglement between the atoms and the three different states of the light fields are equal. When the strength of the light field is small, the degree of entanglement is maximum in a system of the two entangled atoms interacting with an odd coherent state; it is intermediate for a system of the two entangled atoms interacting with the Yurke?Stoler coherent state and it is minimum in a system of the two entangled atoms interacting with an even coherent state.

Quantum logical states and operators for Josephson-like systems

We give a formal algebraic description of Josephson-type quantum dynamical systems, i.e., Hamiltonian systems with a cos theta-like potential term. The two-boson Heisenberg algebra plays for such systems the role that the h(1) algebra does for the harmonic oscillator. A single Josephson junction is selected as a representative of Josephson systems. We construct both logical states (codewords) and logical (gate) operators in the superconductive regime. The codewords are the even and odd coherent states of the two-boson algebra: they are shift-resistant and robust, due to squeezing. The logical operators acting on the qubit codewords are expressed in terms of operators in the enveloping of the two-boson algebra. Such a scheme appears to be relevant for quantum information applications.

Amplitude-squared squeezing of Roy-type even and odd nonlinear coherent states in a finite-dimensional Hilbert space

The Roy-type even and odd nonlinear coherent states in a finite-dimensional Hilbert space are constructed. Their amplitude-squared squeezing effect, orthonormalized property, unitary property and completeness relations are discussed. The results reveal the existence of unitary property, completeness relations and non-orthonormalized property. There exists the amplitude-squared squeezing effect for the Roy-type even and odd nonlinear coherent states when the phase θ of parameter β meets the fixed condition. The relations between conditions of squeezing effect and parameters s,r and function f(n) are given. Finally using the numerical method, it is found that in some different ranges of r, the amplitude-squared squeezing effect exists in Roy-type even and odd nonlinear coherent states field in a finite-dimensional Hilbert space when the parameters s,θ and Lamb-Dike parameter η are given as the fixed value.

EVEN AND ODD DISPLACED NUMBER STATE

In this paper we will study the statistical properties of a generalized superposition of two displaced number states of the form, [Formula: see text] with a phase difference of φ between them. A particular case of this state is obtained when we consider n1=n2=n and α1=-α2=α, which we will call even and odd displaced number state. It will be shown that they are the generalization of the even and odd coherent states. The generation of this states, based on the dispersive interaction with a two-level atom, will also be discussed.

Two-boson algebra and quantum computing with Josephson-like systems

Our investigation concerns the class of Josephson-like systems, sharing the same nonlinear Hamiltonian. Among the latter a Josephson junction with an external biasing circuit is considered. We diagonalize the fully nonlinear Hamiltonian (in the superconductive regime of the junction) in the Fock space of the TBHA (two-boson Heisenberg algebra) and prove that such algebra leads quite naturally to the theoretical realization of codewords and logical operators: the codewords are defined as the even and odd coherent states of the TBHA, while the logical operators are expressed in terms of operators in the same algebra. Our theoretical construction corresponds to a continuous variable quantum computation scheme; the continuous variables are identified in terms of the physical operators of the junction. The link between this scheme and the technique of fermionization of bosonic systems is also discussed.

Decoherence and transfer of quantum states of field modes in a one-dimensional cavity with an oscillating boundary

We study the evolution of Wigner functions of arbitrary initial quantum states of field modes in a one-dimensional ideal cavity, whose boundary performs small harmonic oscillations at the frequency ωW = pω1 (where ω1 is the fundamental field eigenfrequency). Special attention is paid to the case of initial even and odd coherent states, which serve as models of the 'Schrodinger cat states'. We show that the strong intermode interaction (due to the Doppler upshift of the fields reflected from the oscillating mirror) results in the decoherence of initial quantum superpositions in selected modes, even in the absence of any external 'environment'. Different quantitative measures of decoherence are discussed. The analytical solutions obtained show that any initial state of the field goes asymptotically to a highly mixed and moderately squeezed state in the 'principal resonance case' p = 2 and to the vacuum state in the 'semiresonance case' p = 1. It is shown that the decoherence process has several stages. In the first one, the interference between the components of the initial superposition is rapidly destroyed during the time of the primary decoherence, which is inversely proportional to the first power of the initial distance between the components, as opposed to the second power in the case of usual dissipative reservoirs. However, some weak traces of coherence (quantumness of states), such as the regions of negativity of the Wigner function, survive for much longer times, which do not depend on the size of the initial superposition.

Generation of Entanglement Between Two Noninteracting Qubitsvia Interaction with Nonclassical Radiation Field**The project supported byNational Natural Science Foundation of China under Grant No. 10374007

We study the interaction between a single-mode quantized fieldand a quantum system composed of two qubits. We suppose that two qubitsinitially be prepared in the mixed and separable state, and studyhow entanglement between two qubits arises in the course ofevolution according to the Jaynes–Cummings type interaction with nonclassical radiation field. We also investigate the relation between entanglement and purity of qubit subsystem. We show that different photon statistics have different effects on the dynamical behavior of the qubit subsystem.When the qubits are initially prepared in the maximally mixed andseparable state, for coherent state field we cannot findentanglement between two qubits; for squeezed state fieldentanglement between two qubits exists in several short period of time; for evenand odd coherent state fields of large photon number, the dynamicalbehavior of the entanglement between two qubits shows collapseand revival phenomenon. For odd coherent state field of smallphoton number, the entanglement with both qubitsinitially prepared in maximally mixed state can be stronger than thatwith both qubits initially prepared in pure states. For fields ofsmall photon number, the entanglement stronglydepends on the states they are initially prepared in. For coherentstate field, and odd and even coherent state fields of large photonnumber, the entanglement only depends on the purity of the initialstate of qubit subsystem. We also show that during the evolutionthe unentangled state may be purer than the entangled state, andthe maximum degree of entanglement may not occur at the time whenthe qubit subsystem is in the purist state.

Interaction of mesoscopic Josephson junction with the excited even and odd coherent states

The interaction of a mesoscopic Josephson junction (MJJ) with the excited even and odd coherent states is investigated. Some properties of the supercurrent in the MJJ in the presence of nonclassical light fields, such as collapse and revival phenomenon, the current–voltage step, dc component fluctuation and quantum coherence of supercurrent, are studied. It is shown that the expectation values and the fluctuation of supercurrent can exhibit dc components. It is also shown that the static supercurrent flows, dc components of the supercurrent fluctuation and correlation function of the dc supercurrent components, are related to the phase of the light field.

Constructing Even- and Odd-Negative Binomial States

By suitably choosing the normalization factors we introduce the even-and odd-negative binomial states. In some limit cases they approach the even-and odd-coherent states, respectively. We also derive a new eigenvectorequation that the negative binomial state satisfies as a nonlinear coherent state.

Wigner functions for the photon-added and photon-depleted even and odd coherent states

By using the definition of Wigner function in Fock states representation，Wigner functions for the photon_added and photon_depleted even and odd coherent states is reconstvucted. The results show that photon_added even and odd coherent stat es always demonstrate non_classical characteristics but photon_depleted even and odd coherent states demonstrate non_classical characteristics only when k t ake odd and even number respectively.

Nonclassical Properties in Mesoscopic Josephson Junction with Excited Even and Odd Coherent States**The project supported by the Natural Science Foundation of Education Bureau of Jiangsu Province of China

Dynamic evolution of a mesoscopic Josephson junction (MJJ) interacting with excited even and odd coherent states is studied. It is shown that the supercurrent in MJJ exhibits both collapse and revival (CR) phenomenon and squeezing effect. It is also shown that the CR and squeezing of supercurrent are related to degree of excitation and average photon number.

Squeeze tomography of quantum states

A new type of tomogram, squeeze tomograms, of quantum states of light, is introduced, which is based on measuring photon statistics after the action of a squeeze operator on the states' density matrix. The introduced tomograms are photon number probability functions depending on two real parameters which are a scaling factor and a rotation angle. The rotation angle and scaling factor label the reference frame in the phase space of field quadratures in which the photon statistics is measured. The expressions of the squeeze tomogram in terms of the Wigner function and density matrix in quadrature representation are obtained. The examples of squeezed states, even and odd coherent states and thermal states are considered in detail. The multimode generalization is discussed.

A Class of Even and Odd Nonlinear Coherent States and Their Properties

A class of even and odd nonlinear coherent states are introduced. The properties of some related states, including quadrature squeezing, antibunching effect and phase probability distribution, are studied.

Two new types of quantum states generated via higher powers of Bogoliubov’s transformation

By applying higher powers of Bogoliubov’s transformation operator b†=ν*a+μ*a† to the even and odd coherent states we construct mathematically two new types of quantum states. Various special functions and mathematical formulations are used to obtain the matrix elements for the states in the coherent state representation. The nonclassical nature of these states is found to be related to their quantum coherence in phase space. The interference effects can also be regarded as a consequence of the oscillatory behavior of the special functions in the structure of the states.

Phase probability distributions of Roy-type even and odd nonlinear coherent states

Based on our previous work, with the aid of the numerical method, the phase pro bability distributions of Roy-type even and odd nonlinear coherent states are in vestigated. It is shown that the distributions for the states are rather different, and unlike the case of ordinary even and odd coherent states the Pegg-Barnett distribution clearly reflects the different characters of quantum interference in the case of Roy-type even and odd nonlinear coherent states.

Teleporting superpositions of even and odd coherent states of a cavity field via the entangled state of a degenerate Λ-type atom interacting with the cavity field

Based on the modified effective Hamiltonian for the system which is made up of a degenerate Λ-type three-level atom and a single-mode coherent state cavity field,the wave function of the system for the arbitrary initial states is derived by means of matrix forms. Through changing the interaction time,the entangled state of an atom-field is prepared. A feasible scheme is proposed to probabilistically teleport superpositions of even and odd coherent states of the cavity field by using the entangled state of a degenerate Λ-type three-level atom interacting with a coherent state cavity field of large amplitude under a far-off resonant condition. By performing Bell state measurement, the superpositions of even and odd coherent states of the cavity field can be successfully achieved with a total probability of 0.25.