Cascading of second-order nonlinear effects leads to an effective third-order nonlinearity. In addition to the macroscopic electric field at the intermediate frequencies another term has to be taken into account which is due to the locality of the intermediate polarization sources. Combining the correction terms at the three intermediate frequencies gives rise to a third-order susceptibility tensor, which exhibits the same symmetry properties as an intrinsic susceptibility. This particularly applies to the contributions from the rectified and the second-harmonic fields to the degenerate susceptibility.

We report a one-laser-shot measurement technique using a phase object at the entry of a $4f$ coherent imaging system to characterize the value of the nonlinear refractive index of materials placed in the Fourier plane of the setup. Experimental and simulated images are presented here in order to validate our approach. We show that the use of a quarter-wavelength dephasing object maximizes the transmission variations in the detected image. We show also that the use of phase objects increases significantly the sensitivity of the measurement compared to top-hat beams (by a factor of 6). Moreover, by adding this type of object at the entry of our imaging system it is possible to determine the sign of the refractive nonlinearity.

We explore in detail the possibility of intracavity generation of continuous-variable (CV) entangled states of light beams under mode phase-locked conditions. We show that such quantum states can be generated in a self-phase-locked nondegenerate optical parametric oscillator (NOPO) based on type II phase-matched down-conversion combined with a linear mixer of two orthogonally polarized modes of the subharmonics in a cavity. A quantum theory of this device, recently realized in the experiment, is developed for both subthreshold and above-threshold operational regimes. We show that the system providing high-level phase coherence between two generated modes, unlike the ordinary NOPO, also exhibits different types of quantum correlations between photon numbers and phases of these modes. We quantify the CV entanglement as two-mode squeezing and show that the maximal degree of the integral two-mode squeezing (which is $50\%$ relative to the level of vacuum fluctuations) is achieved at the pump field intensity close to the generation threshold of a self-phase-locked NOPO, provided that the constant of linear coupling between the two polarizations is much less than the mode detunings. The peculiarities of CV entanglement for the case of unitary, nondissipative dynamics of the system under consideration are also cleared up.

We study the influence of the preparation of an open quantum system on its reduced time evolution. In contrast to the frequently considered case of an initial preparation where the total density matrix factorizes into a product of a system density matrix and a bath density matrix the time evolution generally is no longer governed by a linear map nor is this map affine. Put differently, the evolution is truly nonlinear and cannot be cast into the form of a linear map plus a term that is independent of the initial density matrix of the open quantum system. As a consequence, the inhomogeneity that emerges in formally exact generalized master equations is in fact a nonlinear term that vanishes for a factorizing initial state. The general results are elucidated with the example of two interacting spins prepared at thermal equilibrium with one spin subjected to an external field. The second spin represents the environment. The field allows the preparation of mixed density matrices of the first spin that can be represented as a convex combination of two limiting pure states, i.e., the preparable reduced density matrices make up a convex set. Moreover, the map from these reduced density matrices onto the corresponding density matrices of the total system is affine only for vanishing coupling between the spins. In general, the set of the accessible total density matrices is nonconvex.

We propose an experimentally feasible scheme to generate general entangled states between atoms in spatially separate cavities, and then show one of the applications—a secure communication allowing asymptotically key distribution and quasisecure direct communication. The scheme involves laser manipulation of atoms in a high-$Q$ cavity, adjustable quarter- and half-wave plates, beam splitter, polarizing beam splitters, and single-photon detectors, and well fits the status of the current experimental technology.

Quantum secure direct communication is the direct communication of secret messages without first producing a shared secret key. It may be used in some urgent circumstances. Here we propose a quantum secure direct communication protocol using single photons. The protocol uses batches of single photons prepared randomly in one of four different states. These single photons serve as a one-time pad which is used directly to encode the secret messages in one communication process. We also show that it is unconditionally secure. The protocol is feasible with present-day technique.

We introduce a Gaussian version of the entanglement of formation adapted to bipartite Gaussian states by considering decompositions into pure Gaussian states only. We show that this quantity is an entanglement monotone under Gaussian operations and provide a simplified computation for states of arbitrary many modes. For the case of one mode per site the remaining variational problem can be solved analytically. If the considered state is in addition symmetric with respect to interchanging the two modes, we prove additivity of the considered entanglement measure. Moreover, in this case and considering only a single copy, our entanglement measure coincides with the true entanglement of formation.

We present an optical implementation of two programmable quantum measurement devices. The first one serves for unambiguous discrimination of two nonorthogonal states of a qubit. The particular pair of states to be discriminated is specified by the quantum state of a program qubit. The second device can perform von Neumann measurements on a single qubit in any basis located on the equator of the Bloch sphere. Again, the basis is selected by the state of a program qubit. In both cases the data and program qubits are represented by polarization states of photons. The experimental apparatus exploits the fact that two Bell states can be distinguished solely by means of linear optics. The outcome corresponding to the remaining two Bell states represents an inconclusive result.

In this work we discuss the ability of different types of ancillas to control the decoherence of a qubit interacting with an environment. The error is introduced into the numerical simulation via a depolarizing isotropic channel. The ranges of values considered are ${10}^{-4}⩽\epsilon ⩽{10}^{-2}$ for memory errors and $3\times {10}^{-5}⩽\gamma ∕7⩽{10}^{-2}$ for gate errors. After the correction we calculate the fidelity as a quality criterion for the qubit recovered. We observe that a recovery method with a three-qubit ancilla provides reasonably good results bearing in mind its economy. If we want to go further, we have to use fault tolerant ancillas with a high degree of parallelism, even if this condition implies introducing additional ancilla verification qubits.

Projectile-elastic, target-elastic, and full close-coupling approximation models have been employed to investigate scattering of ortho-positronium off Li and Na atoms at low energies. Nine different basis sets for each system have been used to find the relative importance of atomic (target and projectile) states on the elastic scattering parameters and the convergence of the predicted results with added eigen- and pseudostates. The $s$-wave elastic phase shifts, scattering lengths and cross sections of both the systems are reported upto the incident energy $k=0.5\text{a.u.}$ and compared with the corresponding existing theoretical predictions. It has been found that the van der Waals and higher order long-range interactions play a crucial role in predicting $s$-wave elastic parameters for Ps–alkali-metal-atom systems at low energies.

Using a nonperturbative scattering theory, we study the photoionization of xenon atoms irradiated by a bichromatic laser field of linear and circular polarizations. The bichromatic laser field is modulated in such a way that it comprises an infinite sequence of identical, one-cycle laser pulses. The photoelectron angular distribution (PAD) in such a field is inversion asymmetric and depends on the phase difference between laser modes, the laser polarization and intensity, and the kinetic energy of photoelectrons. By investigating the broadening effect in the PADs of lower-order peaks, we show that one can perform an effective control on the motion of electrons of high kinetic energy.

We study the collective modes of a confined gaseous cloud of bosons and fermions with mutual attractive interactions at zero temperature. The cloud consists of a Bose-Einstein condensate and a spin-polarized Fermi gas inside a spherical harmonic trap and the coupling between the two species is varied by increasing either the magnitude of the interspecies $s$-wave scattering length or the number of bosons. The mode frequencies are obtained in the collisional regime by solving the equations of generalized hydrodynamics and are compared with the spectra calculated in the collisionless regime within a random-phase approximation. We find that, as the mixture is driven towards the collapse instability, the frequencies of the modes of fermionic origin show a blue shift which can become very significant for large numbers of bosons. Instead the modes of bosonic origin show a softening, which becomes most pronounced in the very proximity of collapse. Explicit illustrations of these trends are given for the monopolar spectra, but similar trends are found for the dipolar and quadrupolar spectra except for the surface $\left(n=0\right)$ modes which are essentially unaffected by the interactions.

We present time-resolved cross-correlation measurements of extreme ultraviolet (xuv) pulses generated as high-order harmonics of intense $35\mathrm{fs}$ pulses, using a short $\left(12\mathrm{fs}\right)$ probe pulse. We modulate the ellipticity of the laser driving the generation process such that the polarization is linear for short times around the temporal peak of the pulse. Since harmonic generation is strongly suppressed for very small amounts of driving laser ellipticity, the emission of xuv radiation can therefore be confined to times much shorter than the laser pulse duration. In addition, our setup allows us to continuously confine the xuv emission as well as to determine its frequency sweep during the pulse.

The phase-space method is applied for considering continuous variable quantum teleportation. It is found that the continuous variable quantum teleportation transforms the $s$-parametrized phase-space function of an input state into the $\left(s+\delta \right)$-parametrized phase-space function, where the parameter $\delta$ is determined by the shared quantum entanglement. It is shown from this result that the Wigner function of the teleported state is always non-negative for ${\mathcal{F}}_c⩽2∕3$ and the Glauber-Sudarshan $P$ function non-negative for ${\mathcal{F}}_c⩽1∕2$, where ${\mathcal{F}}_c$ is the fidelity of the coherent-state teleportation. Furthermore the fidelity between input and output states is calculated when Gaussian states are teleported.

The generation of an entangled state for a pair of two-level atoms embedded in a bad cavity injected with a squeezed vacuum is investigated. The degree of entanglement between the two atoms strongly depends on the mean photon number and the strength of two-photon correlations of the squeezed vacuum, the cavity-induced decay rate of atoms, and the atomic separation.

In this Comment on Feng’s paper [Phys. Rev. A 63, 052308 (2001)], we show that Grover’s algorithm may be performed exactly using the gate set given, provided that small changes are made to the gate sequence. An analytic expression for the probability of success of Grover’s algorithm for any unitary operator $U$ instead of Hadamard gate is presented.

We present a procedure inspired by dense coding, which enables a highly efficient transmission of information of a continuous nature. The procedure requires the sender and the recipient to share a maximally entangled state. We deal with the concrete problem of aligning reference frames or trihedra by means of a quantum system. We find the optimal covariant measurement and compute the corresponding average error, which has a remarkably simple close form. The connection of this procedure with that of estimating unitary transformations on qubits is briefly discussed.

We study the propagation of a probe light in an ensemble of $\Lambda$-type atoms, utilizing the dynamic symmetry as recently discovered when the atoms are coupled to a classical control field and a quantum probe field [Sun et al., Phys. Rev. Lett. 91, 147903 (2003)]. Under two-photon resonance, we calculate the group velocity of the probe light with collective atomic excitations. Our result gives the dependence of the group velocity on the common one-photon detuning, and can be compared with the recent experiment of E. E. Mikhailov, Y. V. Rostovtsev, and G. R. Welch, e-print quant-ph∕0309173.

The position and momentum space information entropies, of the ground state of the Pöschl-Teller potential, are exactly evaluated and are found to satisfy the bound obtained by Beckner, Bialynicki-Birula, and Mycielski. These entropies for the first excited state, for different strengths of the potential well, are then numerically obtained. Interesting features of the entropy densities, owing their origin to the excited nature of the wave functions, are graphically demonstrated. We then compute the position space entropies of the coherent state of the Pöschl-Teller potential, which is known to show revival and fractional revival. Time evolution of the coherent state reveals many interesting patterns in the space-time flow of information entropy.