Photon Statistics of Photon-Added and Photon-Subtracted Two-Mode Squeezed Vacuum State

We introduce states a^(†m) |ξ〉and a^(m)|ξ〉, where |ξ〉is a two-mode squeezed vacuum state. We examine the properties of these states by analytic derivation. Because of the entanglement between the modes of the field, photon adding (or subtracting) for one of the modes results in interesting outcomes. For a two-mode squeezed vacuum state, the effect of annihilation of m a-photons is just the same as creation of m b-photons. Annihilation of photons of mode a (or mode b) actually increases the mean number of photons of mode a and mode b. We also calculate Mandel Q parameter, cross-correlation function and squeezing of the field.

Dissipation of a two-mode squeezed vacuum state in the single-mode amplitude damping channel

We explore how a two-mode squeezed vacuum state sechθeab tanh θ[00） evolves when it undergoes a single- mode amplitude dissipative channel with rate of decay k. We find that in this process not only the squeezing parameter decreases, tanhθ → e-kt tanh θ, but also the second-mode vacuum state evolves into a chaotic state exp{bbln[（1 - e-2kt） tanh2 θ]}. The outcome state is no more a pure state, but an entangled mixed state.

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.

Some Properties of Two-mode Displaced Excited Squeezed Vacuum States

In this paper,two-mode displaced excited squeezed vacuum states (TDESVS) are constructed and theirnormalization and completeness are investigated.Using the entangled state representation and Weyl ordering formof the Wigner operator,the Wigner functions of TDESVS are obtained and the variations of Wigner functions withthe parameters m,n and r are investigated.Besides,two marginal distributions of Wigner functions of TDESVS areobtained,which exhibit some entangled properties of the two-particle's system in TDESVS.

Entanglement Transfer from Two-Mode Squeezed Vacuum State Field to Two Spatially Separated Atoms in Two-Photon Processes

We investigate the influence of the Stark shift on the entanglement transfer from the two-mode squeezed vacuum state field to two spatially separated atoms in two-photon processes. Our results show that the Stark shift plays an important role in such entanglement transfer. We find that when the Stark shift parameter r is small, the degree of entanglement between the two atoms increases with the increasing of the squeezing parameter ξ first, and after achieving its maximal value, the degree of entanglement will decrease to zero with the increasing of ξ; while for big r, E will increase with the increasing of ξ.

A scheme for approximate conditional teleportation of entangled two-mode cavity state without Bell state measurement

An alternative scheme to approximately conditionally teleport entangled two-mode cavity state without Bell state measurement in cavity QED is proposed. The scheme is based on the resonant interaction of a ladder-type three-level atom with two bimodal cavities. The entangled cavity state is reconstructed with only one atom interacting with the two cavities successively.

Quantum-enhanced optical precision measurement assisted by low-frequency squeezed vacuum states

Stable low-frequency squeezed vacuum states at a wavelength of 1550 nm were generated.By controlling the squeezing angle of the squeezed vacuum states,two types of low-frequency quadrature-phase squeezed vacuum states and quadrature-amplitude squeezed vacuum states were obtained using one setup respectively.A quantum-enhanced fiber Mach–Zehnder interferometer(FMZI)was demonstrated for low-frequency phase measurement using the generated quadrature-phase squeezed vacuum states that were injected.When phase modulation was measured with the quantumenhanced FMZI,there were above 3 dB quantum improvements beyond the shot-noise limit(SNL)from 40 kHz to 200 kHz,and 2.3 dB quantum improvement beyond the SNL at 20 kHz was obtained.The generated quadrature-amplitude squeezed vacuum state was applied to perform low-frequency amplitude modulation measurement for sensitivity beyond the SNL based on optical fiber construction.There were about 2 dB quantum improvements beyond the SNL from 60 kHz to 200 kHz.The current scheme proves that quantum-enhanced fiber-based sensors are feasible and have potential applications in high-precision measurements based on fiber,particularly in the low-frequency range.

Teleportation of Two-Mode Quantum State of Continuous Variables

Using two Einstein-Podolsky Rosen pair eigenstates |η) as quantum channels, we study the teleportationof two-mode quantum state of continuous variables.

Generation and Properties of Two-Mode Circular States

Two-mode circular states,which are superposition states from some two-mode coherent states,are studiedtheoretically.It is shown that under certain conditions two-mode circular states may exhibit nonclassical effects,suchas sub-Poissonian statistics and intermode correlation.We propose schemes to generate two-mode circular states by theinteraction of a trapped ion with traveling wave lasers.

Preparation and control of entangled states in the two-mode coherent fields interacting with a moving atom via two-photon process

We investigate the preparation and the control of entangled states in a system with the two-mode coherent fields interacting with a moving two-level atom via the two-photon transition. We discuss entanglement properties between the two-mode coherent fields and a moving two-level atom by using the quantum reduced entropy, and those between the two-mode coherent fields by using the quantum relative entropy. In addition, we examine the influences of the atomic motion and field-mode structure parameter p on the quantum entanglement of the system. Our results show that the period and the duration of the prepared maximal atom-field entangled states and the frequency of maximal two-mode field entangled states can be controlled, and that a sustained entangled state of the two-mode field, which is independent of atomic motion and the evolution time, can be obtained, by choosing appropriately the parameters of atomic motion, field-mode structure, initial state and interaction time of the system.

Security of quantum key distribution using two-mode squeezed states against optimal beam splitter attack

For the beam splitter attack strategy against quantum key distribution using two-mode squeezed states, the analytical expression of the optimal beam splitter parameter is provided in this paper by applying the Shannon information theory. The theoretical secret information rate after error correction and privacy amplification is given in terms of the squeezed parameter and channel parameters. The results show that the two-mode squeezed state quantum key distribution is secure against an optimal beam splitter attack.

New formulas for normalizing photon-added(-subtracted) two-mode squeezed thermal states

For the first time,we derive the compact forms of normalization factors for photon-added（-subtracted） two-mode squeezed thermal states by using the P-representation and the integration within an ordered product of operators（IWOP） technique.It is found that these two factors are related to the Jacobi polynomials.In addition,some new relationships for Jacobi polynomials are presented.

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.

Evolution of a two-mode squeezed vacuum in the amplitude dissipative channel

For the first time we derive the dissipating result of an initial two-mode squeezed pure vacuum state passing through a two-mode amplitude dissipative channel described by the direct product of two independent single-mode master equations. Although these two master equations do not mix the two modes （there is no coupling between them）, since the two-mode squeezed state is simultaneously an entangled state, the final state which emerges from passing this channel is a two-mode mixed density operator. The compact expression of the outcoming state is obtained, which manifestly shows that as time evolves, the squeezing effect decreases.

Realization of Nonclassical States and Two-Mode Coupling in the Motion of Two Trapped Ions

We propose a scheme to generate various nonclassical vibrational states in the collective motion of twotrapped ions, such as squeezed states, Schrodinger cat states, and SU(2) states. It is based on Raman-type excitations.Two-mode coupling between the center-of-mass and relative vibrational modes can also be realized.

Statistical properties of coherent photon-subtracted two-mode squeezed vacuum and its application in quantum teleportation

We introduce a kind of non-Gaussian entangled state, which can be obtained by operating a non-local coherent photon-subtraction operation on a two-mode squeezed vacuum. It is found that its normalization factor is only related to the Legendre polynomials, which is a compact expression. Its statistical properties are discussed by the negative region Wigner function with the analytical expression. As an application, the quantum teleportation for coherent states is considered by using the non-Gaussian state as an entangled channel. It is found that the teleportation fidelity can be enhanced by this non-Gaussian operation.

Single-mode quadrature-amplitude measurement for generalized two-mode squeezed states studied by virtue of the entangled state representation

The result of one-mode quadrature-amplitude measurement for some generalized two-mode squeezed states has been studied by virtue of the entangled state representation of the corresponding two-mode squeezing operators. We find that the remaining fleld-mode simultaneously collapses to the single-mode squeezed state with more stronger squeezing. The measurement result caused by a single-mode squeezed state projector is also calculated, which indicates quantum entanglement in squeezing.

Nonlinear two-mode squeezing obtained by analysing two-mode exponential quadrature operators in entangled state representation

By analysing the properties of two-mode quadratures in an entangled state representation （ESR） we derive from ESR some complicated exponential quadrature operators for nonlinear two-mode squeezing, which directly leads to wave function of the nonlinear squeezed state in ESR.

Entanglement of Generalized Two-Mode Binomial States and Teleportation

The entanglement of the generalized two-mode binomial states in the phase damping channel is studied by making use of the relative entropy of the entanglement. It is shown that the factors of q and p play the crucial roles in control the relative entropy of the entanglement. Furthermore, we propose a scheme of teleporting an unknown state via the generalized two-mode binomial states, and calculate the mean fidelity of the scheme.

Two-mode squeezed state of nanomechanical resonators

In this paper, we introduce a flexible model for the control and measurement of NAMRs （nanomechanical resonators）. We obtain the free Hamiltonian of the dcSQUID （direct current superconducting quantum interference device） and the interaction Hamiltonian between these two NAMRs and the dc-SQUID by introducing the annihilation and creation operators under the rotating wave approximation. We can treat the mode of the dc-SQUID as a classical field. In the Heisenberg picture, the generation of two-mode squeezed states of two nanomechanical resonators is shown by their collective coordinate and momentum operators.