Ryszard Tanas

Dark periods and revivals of entanglement in a two-qubit system

In a recent paper Yu and Eberly [Phys. Rev. Lett. 93, 140404 (2004)] have shown that two initially entangled and afterward not interacting qubits can become completely disentangled in a finite time. We study transient entanglement between two qubits coupled collectively to a multimode vacuum field, assuming that the two-qubit system is initially prepared in an entangled state produced by the two-photon coherences, and find the unusual feature that the irreversible spontaneous decay can lead to a revival of the entanglement that has already been destroyed. The results show that this feature is independent of the coherent dipole-dipole interaction between the atoms but it depends critically on whether or not collective damping is present.

Delayed sudden birth of entanglement

The concept of time delayed creation of entanglement by the dissipative process of spontaneous emission is investigated. A threshold effect for the creation of entanglement is found where the initially unentangled qubits can be entangled after a finite time despite the fact that the coherence between the qubits exists for all times. This delayed creation of entanglement, which we call sudden birth of entanglement, is opposite to the currently extensively discussed sudden death of entanglement and is characteristic for transient dynamics of one-photon entangled states of the system. We determine the threshold time for the creation of entanglement and find it is related to time at which the antisymmetric state remains the only excited state being populated. It is shown that the threshold time can be controlled by the distance between the qubits and the direction of initial excitation relative to the interatomic axis. This effect suggests an alternative for the study of entanglement and provides an interesting resource for creation on demand of entanglement between two qubits.

Generation of discrete superpositions of coherent states in the anharmonic oscillator model

The problem of generating discrete superpositions of coherent states in the process of light propagation through a nonlinear Kerr medium, which is modelled by the anharmonic oscillator, is discussed. It is shown that under an appropriate choice of the length (time) of the medium the superpositions with both even and odd numbers of coherent states can appear. Analytical formulae for such superpositions with a few components are given explicitly. General rules governing the process of generating discrete superpositions of coherent states are also given. The maximum number of well distinguished states that can be obtained for a given number of initial photons is estimated. The quasiprobability distribution Q( alpha , alpha *,t) representing the superposition states is illustrated graphically, showing regular structures when the component states are well separated.

Teleportation with insurance of an entangled atomic state via cavity decay

We propose a scheme to teleport an entangled state of two {lambda}-type three-level atoms via photons. The teleportation protocol involves the local redundant encoding protecting the initial entangled state and allowing for repeating the detection until quantum information transfer is successful. We also show how to manipulate a state of many {lambda}-type atoms trapped in a cavity.

Comparative study of photon antibunching of non-stationary fields

Two standard criteria of the photon antibunching for non-stationary fields are compared. A new criterion, obtained by direct application of the Cauchy-Schwarz inequality, is proposed. All three definitions, based on the two-time correlation functions, are equivalent for stationary fields. However, the photon antibunching in the non-stationary regime is demonstrated to be not uniquely defined, since different criteria can lead to self-contradictory predictions. As an example, photon correlations of the signal mode in the parametric frequency converter are analysed analytically.

Discrete superpositions of coherent states and phase properties of the m-photon anharmonic oscillator

The formation of discrete superpositions of coherent states via the unitary evolution of the m-photon anharmonic oscillator is studied. Exact analytical formulae for the superposition coefficients are obtained. It is shown that, in contrast to the two-photon anharmonic oscillator, for m>2 the superposition components enter the superposition with different amplitudes. The Pegg-Barnett phase formalism is used to calculate the phase distributions for the resulting states and to visualize their symmetry.

Role of the higher optical Kerr nonlinearities in self-squeezing of light

The part played by higher-order optical nonlinearities in self-squeezing of intense light propagating in a nonlinear Kerr medium is discussed. An analytical formula for the normally ordered variances of the field is derived under the assumption that the nonlinearity parameters of the medium are small and the number of photons is very great. The saddle-point approach is used to evaluate the sums over large numbers of photons. The analytical formula is illustrated graphically for several sets of nonlinearity coefficients. It is shown that, for large numbers of photons, the higher-order contributions are substantial and can modify the magnitude of squeezing as well as the range of the parameters over which squeezing can be observed.

The effect of a non-zero spontaneous decay rate on teleportation

We discuss the influence of the spontaneous decay rate of the excited state on teleportation of the atomic state via cavity decay in the scheme of Bose et al (Bose S, Knight P L, Plenio M B and Vedral V 1999 Phys. Rev. Lett. 83 5158). We show that even a small but non-zero decay rate of the excited state leads to significant effects such as lowering the probability of successful teleportation if the product of the saturation parameter and the spontaneous decay rate is not negligible in comparison with the cavity mode decay rate. We compare analytical results obtained using adiabatic elimination with the results calculated numerically.

Quantum phase correlations in nonlinear optical processes

A review of recent results obtained with application of the Hermitian phase formalism of Pegg and Barnett is given. Various states of the field obtained in nonlinear optical processes are discussed from the point of view of their phase properties.

Quantum properties of the two-mode Kerr states

Quantum properties of the two-mode Kerr states such as squeezing, sub-Poissonian photon statistics, Schoedinger cats, quantum correlations between the modes, polarization and quantum depolarization as well as quantum noise in the Stokes parameters are reviewed. The role of dissipation is also discussed.