The work by T. K. Ghosh and K. Machida [Phys. Rev. A 73, 013613 (2006) and cond-mat/0510160] on the sound velocity in a cylindrically confined Fermi superfluid obeying a power-law equation of state is shown to make use of an improper projection of the sound wave equation. This inaccuracy fully accounts for the difference between their results and those previously reported by Capuzzi et al. [Phys. Rev. A 73, 021603(R) (2006) and cond-mat/0509323]. In this Comment, we show that both approaches lead exactly to the same result when the correct weight function is used in the projection. Plots of the correct behavior of the phonon and monopole-mode spectra in the BCS and unitary limits and in the BEC regime are also shown.

We are providing a Reply to the preceding Comment.

We study the bipartite entanglement dynamics in an anisotropic two-qubit Heisenberg $XYZ$ model under the influence of population relaxation and in the presence of various types of magnetic fields. We find that the maximal value of the concurrence has an intrinsic rigidity for the different external magnetic fields. Moreover, our results demonstrate that it is possible to produce entangled states and to control or to modulate the concurrence within the intrinsic maximal value with the help of external time-varying fields despite the existence of dissipation.

We introduce a flow condition on open graph states (graph states with inputs and outputs) which guarantees globally deterministic behavior of a class of measurement patterns defined over them. Dependent Pauli corrections are derived for all such patterns, which equalize all computation branches, and only depend on the underlying entanglement graph and its choice of inputs and outputs. The class of patterns having flow is stable under composition and tensorization, and has unitary embeddings as realizations. The restricted class of patterns having both flow and reverse flow supports an operation of adjunction, and has all and only unitaries as realizations.

We obtain a four-photon polarization-entangled state with a visibility as high as $(95.35\pm 0.45)\%$ directly from a single down-conversion source. A success probability of $(81.54\pm 1.38)\%$ is observed by applying this entangled state to realize a four-party quantum communication complexity scenario, which comfortably surpasses the classical limit of 50%. As a comparison, two Einstein-Podolsky-Rosen pairs are shown to implement the scenario with a success probability of $(73.89\pm 1.33)\%$. This four-photon state can also be used to fulfill decoherence-free quantum information processing and other advanced quantum communication schemes.

We derive fidelity tradeoffs for probabilistic minimal disturbance measurements for certain discrete sets of symmetrical single qubit states. We propose and experimentally demonstrate a simple linear optical scheme saturating these tradeoffs in which the degree of disturbance is controlled only by measurement of a single ancillary photon.

We model sequential double detachment of ${\mathrm{Ag}}^{-}$, ${\mathrm{C}}^{-}$, ${\mathrm{I}}^{-}$, and ${\mathrm{Al}}^{-}$ irradiated by $1064\mathrm{nm}$ light by using a strong-field model and compare the theoretical double-detachment yields with experimental ones. The symmetry of the ${\mathrm{Al}}^{-}$ and ${\mathrm{C}}^{-}$ ground states ensures that the outermost electrons have different magnetic quantum numbers $m$. The difference in detachment rate for electrons with different $m$ values leads to a 50% higher saturation intensity than expected from application of the strong-field model with ionization rates for $m=0$ electrons only. For ${\mathrm{I}}^{-}$, emission of two $m=0$ electrons requires that the ${\mathrm{I}}^{+}$ ion is left in an excited state, and this leads to an increase of 20% in the saturation intensity. Good agreement is obtained with experiment for ${\mathrm{Ag}}^{-}$, ${\mathrm{C}}^{-}$, and ${\mathrm{I}}^{-}$, but a large discrepancy is observed for ${\mathrm{Al}}^{-}$. The calculations thus indicate that rearrangement of electrons over the available $m$ values may not occur for double detachment at low intensities. Finally, we explain why ${\mathrm{C}}^{-}$ and ${\mathrm{Al}}^{-}$ are well suited for further investigations on the effect of the distribution over $m$ values on sequential double detachment.

Above-threshold detachment (ATD) rates for ${\mathrm{H}}^{-}$ and ${\mathrm{F}}^{-}$ ions in the high-energy plateau region are calculated as functions of photon number and laser intensity by solving the time-dependent Schrödinger equation within the Sturmian-Floquet approach. Pronounced enhancements of the ATD rates are found (up to an order of magnitude) as the laser-field intensity passes across ponderomotive-potential-induced channel closings. We confirm the zero-range potential model results of Borca et al. [Phys. Rev. Lett. 88, 193001 (2002)] for negative ions whose initial states have $s$ symmetry, and we investigate here the case of initial states having $p$ symmetry. Depending on the symmetry of the initial state, the enhancement is found to be most pronounced for even- or odd-channel closures, which is consistent with threshold laws applicable at the closing of particular multiphoton channels. Variations of ATD electron angular distributions as functions of laser intensity near channel closings are also investigated and found to be sensitive to initial-state symmetry.

Cold atoms may travel along narrow waveguides with a strong transverse confinement, perpendicular to the longitudinal propagation axis, in a given transverse oscillation mode and having a well-defined internal state. A laser beam perpendicular to the logitudinal axis may change the internal state and/or the transverse mode. For weak transversal coupling (Lamb-Dicke regime) and the laser on resonance with an internal atomic transition, transverse excitation occurs at “Rabi resonances”—i.e., when the Rabi frequency coincides with the transition frequency between the transverse modes. This provides a route for atomic-state preparation and control in waveguides.

We consider optimization of a rubidium atom clock that uses magnetically trapped Bose condensed atoms in a highly elongated trap, and determine the optimal conditions for minimum Allan variance of the clock using microwave Ramsey fringe spectroscopy. Elimination of magnetic field shifts and collisional shifts are considered. The effects of spin-dipolar relaxation are addressed in the optimization of the clock. We find that for the interstate interaction strength equal to or larger than the intrastate interaction strengths, a modulational instability results in phase separation and symmetry breaking of the two-component condensate composed of the ground and excited hyperfine clock levels, and this mechanism limits the clock accuracy.

A different computational scheme, based on the complex-rotation method combined with a mixed Slater-Landau basis expansion, has been developed to calculate photoionization of atomic hydrogen in strong magnetic fields typical of magnetic white dwarf stars. Photoionization cross sections are presented for the ground and the $2p$ excited states for selected magnetic-field strengths and found to be in good agreement with available theoretical results. The current scheme is more efficient than previously reported methods as the basis expansion explicitly incorporates the physics of the strong-field regime. The method is particularly advantageous to quantitatively elucidate complex features of positive-energy spectra and to compute continuum absorption parameters for magnetic white dwarfs.

We present a family of Bell inequalities involving only two measurement settings of each party for $N>2$ qubits. Our inequalities include all the standard ones with fewer than $N$ qubits and thus give a natural generalization. It is shown that all the Greenberger-Horne-Zeilinger states violate the inequalities maximally, with an amount that grows exponentially as $2^{(N-2)∕2}$. The inequalities are also violated by some states that do satisfy all the standard Bell inequalities. Remarkably, our results yield in an efficient and simple way an implementation of nonlocality tests of many qubits favorably within reach of the well-established technology of linear optics.

We present an application of the genetic algorithmic computational method to the optimization of the concurrence measure of entanglement for the cases of one dimensional chains, as well as square and triangular lattices in a simple tight-binding approach in which the hopping of electrons is much stronger than the phonon dissipation.

We review the notion of a classical random cipher and its advantages. We sharpen the usual description of random ciphers to a particular mathematical characterization suggested by the salient feature responsible for their increased security. We describe a concrete system known as $\alpha \eta$ and show that it is equivalent to a random cipher in which the required randomization is affected by coherent-state quantum noise. We describe the currently known security features of $\alpha \eta$ and similar systems, including lower bounds on the unicity distances against ciphertext-only and known-plaintext attacks. We show how $\alpha \eta$ used in conjunction with any standard stream cipher such as the Advanced Encryption Standard provides an additional, qualitatively different layer of security from physical encryption against known-plaintext attacks on the key. We refute some claims in the literature that $\alpha \eta$ is equivalent to a nonrandom stream cipher.

For a dilute atomic gas in a strong transverse trapping potential, one normally expects that, in the ground state, the gas will populate only the lowest transverse level. We show, however, that for the strongly interacting gas under a Feshbach resonance, the ground state includes a large fraction of atoms in excited levels of the trap, even if the gas is in the dilute limit and the trap is very strong. This is because the effective atom-molecule coupling is typically enhanced to many times the trap mode spacing by an induced confinement along the untrapped dimension(s). Thus one cannot “freeze out” the transverse degrees of freedom except under certain conditions.

We have studied one-body and two-body correlation functions in a ballistically expanding, noninteracting atomic cloud in the presence of gravity. We find that the correlation functions are equivalent to those at thermal equilibrium in the trap with an appropriate rescaling of the coordinates. We derive simple expressions for the correlation lengths and give some physical interpretations. Finally a simple model to take into account finite detector resolution is discussed.

Recently, an explicit protocol ${\mathcal{E}}_0$ for faithfully teleporting arbitrary two-qubit states using genuine four-qubit entangled states was presented by us [Phys. Rev. Lett. 96, 060502 (2006)]. Here, we show that ${\mathcal{E}}_0$ with an arbitrary four-qubit mixed-state resource $\Xi$ is equivalent to a generalized depolarizing bichannel with probabilities given by the maximally entangled components of the resource. These are defined in terms of our four-qubit entangled states. We define the generalized singlet fraction $\mathcal{G}\left[\Xi \right]$ and illustrate its physical significance with several examples. We argue that in order to teleport arbitrary two-qubit states with average fidelity better than is classically possible, we have to demand that $\mathcal{G}\left[\Xi \right]>1∕2$. In addition, we conjecture that when $\mathcal{G}\left[\Xi \right]<1∕4$, then no entanglement could be teleported. It is shown that to determine the usefulness of $\Xi$ for ${\mathcal{E}}_0$, it is necessary to analyze $\mathcal{G}\left[\Xi \right]$.

We use robust semidefinite programs and entanglement witnesses to study the distillability of Werner states. We perform exact numerical calculations that show two-undistillability in a region of the state space, which was previously conjectured to be undistillable. We also introduce bases that yield interesting expressions for the distillability witnesses and for a tensor product of Werner states with an arbitrary number of copies.