We present a scheme which transforms a one-input qubit to $M$ identical copies with optimal fidelity via free dynamical evolution of spin star networks. We demonstrate that the Heisenberg $XXZ$ coupling can meet the challenge. The initial state of the copying machine and the parameters of the spin Hamiltonian are discussed in detail. Furthermore we have proposed a feasible method to prepare the initial state of the copying machine.

We have calculated the atomic electric dipole moments (EDMs) $d$ of ${}^3\mathrm{He}$ and ${}^{171}\mathrm{Yb}$ induced by their respective nuclear Schiff moments $S$. Our results are $d\left({}^3\mathrm{He}\right)=8.3\times {10}^{-5}$ and $d\left({}^{171}\mathrm{Yb}\right)=-1.9$ in units of ${10}^{-17}(S∕e{\mathrm{fm}}^3)e\mathrm{cm}$. By considering the nuclear Schiff moments induced by the parity- and time-reversal violating nucleon-nucleon interaction, we find $d\left({}^{171}\mathrm{Yb}\right)\sim 0.6d\left({}^{199}\mathrm{Hg}\right)$. For ${}^3\mathrm{He}$ the nuclear EDM coupled with the hyperfine interaction gives a larger atomic EDM than the Schiff moment. The result for ${}^3\mathrm{He}$ is required for a neutron EDM experiment that is under development, where ${}^3\mathrm{He}$ is used as a comagnetometer. We find that the EDM for ${}^3\mathrm{He}$ is orders of magnitude smaller than the neutron EDM. The result for ${}^{171}\mathrm{Yb}$ is needed for the planning and interpretation of experiments that have been proposed to measure the EDM of this atom.

Complementarity is usually considered as a phenomenon of microscopic systems. In this paper, we report an experimental observation of complementarity in correlated double-slit interference with a pseudothermal light source. The thermal light beam is divided into test and reference beams which are correlated with each other. The double slit is set in the test arm, and an interference pattern can be observed in the intensity correlation between the two arms. The experimental results show that the disappearance of the interference fringe depends on whether which-path information is gained through the reference arm. The experiment therefore shows complementarity occurring in the macroscopic domain.

We construct a large class of quantum $d\otimes d$ states which are positive under partial transposition (so called PPT states). The construction is based on certain direct sum decomposition of the total Hilbert space displaying characteristic circular structure—that is why we call them circulant states. It turns out that partial transposition maps any such decomposition into another one and hence both original density matrix and its partially transposed partner share similar cyclic properties. This class contains many well-known examples of PPT states from the literature and gives rise to a huge family of completely new states.

The “released-phase” diffusion quantum Monte Carlo method is used to calculate the ground-state energies of atoms with nuclear charges from $Z=2,3,4,\dots ,26$ for magnetic field strengths relevant for neutron stars. The feature of our study is the use of adiabatic approximation wave functions as guiding wave functions to initialize the quantum Monte Carlo procedure. Our calculations are motivated by the discovery of broad features in the thermal spectra of isolated neutron stars, which may be due to heavy atoms. Our results confirm previous results for nuclear charge numbers up to 10, and are the most accurate ones available in the literature to date for $Z>10$.

A recent experimental study of the photodetachment of negative fluorine ions by a strong, circularly polarized laser field has been used as a test case for comparison of different gauges in a strong-field theory. Earlier studies concluded that the length gauge was the more suitable theory, but it was necessary to view the experimental peak intensity as a fitting parameter, and this had to be altered to 145% of the measured peak intensity. That amount of variation is not possible. There were two independent experimental measurements of the peak intensity: one direct and the other through a measurement of the momentum distribution of the photodetached electron. These two measurements give the same result for the peak intensity, and so the 45% increase required to have a fit to the length gauge is not an acceptable theoretical explanation for the experimental results. In contrast, the velocity gauge calculation provides a good match to the spectrum peak with no alteration necessary for the measured peak intensity. The theoretical spectrum is somewhat narrower than the measured spectrum, but that is consistent with the fact that the intensity parameters are not quite large enough to ensure detailed accuracy of the strong-field approximation.

We propose and analyze a scheme for measuring the quadrature statistics of an atom laser beam using extant optical homodyning and Raman atom laser techniques. Reversal of the normal Raman atom laser outcoupling scheme is used to map the quantum statistics of an incoupled atomic beam to an optical probe beam. A multimode model of the spatial propagation dynamics shows that the Raman incoupler gives a clear signal of de Broglie wave quadrature squeezing for both pulsed and continuous inputs. Finally, we show that experimental realizations of the scheme may be tested with existing methods via intensity correlation measurements.

We examine the collective quantum dynamics of photons and atoms driven by Raman transitions inside a low-$Q$ cavity. At short times, we show that most of the Stokes photons can be captured by a single time-varying field mode. We determine an approximate analytical form of the mode function and construct a single-mode effective Hamiltonian. The model allows us to address the structure of the photon-atom state explicitly. In particular, we indicate that photons and atoms exhibit a form of photon-atom squeezing during the initial stage of the evolution.

In this Brief Report we show the relation between three-qubit entanglement invariants and two-qubit concurrence with the help of projective measurements. How to use these invariants to represent the entanglement property of three-qubit pure states is also investigated.

The degree of entanglement between two spins may change due to interaction. Regarding this, we find that a wrong result in a recent work by Ge and Wadati [Phys. Rev. A 72, 052101 (2005)] would breach the basic principle.

An analysis is presented that shows specific features of three-photon coincidences from a synchrotron radiation source and points out that these features are measurable at presently operated, advanced hard-x-ray facilities. Analogies with three-pion correlations of high-energy physics are considered, leading to the conclusion that triple coincidences of x rays can be measured more accurately than the three-pion coincidences.

We propose a generalized structure of Bell inequalities for arbitrary $d$-dimensional bipartite systems, which includes the existing two types of Bell inequalities introduced by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)] and Son et al. [Phys. Rev. Lett. 96, 060406 (2006)]. We analyze Bell inequalities in terms of correlation functions and joint probabilities, and show that the coefficients of correlation functions and those of joint probabilities are in Fourier transform relations. We finally show that the coefficients in the generalized structure determine the characteristics of quantum violation and tightness.

A so-called quasientanglement measure was obtained [J. Zhang et al., Phys. Rev. A 73, 022319 (2006)] by extending Jaeger’s Minkowskian norm entanglement measure to general multipartite mixed states. The obtained quasientanglement measure has good properties, but it is still left open whether it is nonincreasing under general local operations and classical communications (LOCC). We show that the obtained quasientanglement measure is indeed nonincreasing on average under LOCC at least for two-qubit states. Thus, it is a good candidate for the two-qubit entanglement monotone. Further, it is shown that this entanglement measure is less than the concurrence for a large class of mixed entangled states.

There exists a great gap between one-time pad with perfect secrecy and conventional mathematical encryption. The Yuen 2000 (Y00) protocol or $\alpha \eta$ scheme may provide a protocol which covers from the conventional security to the ultimate one, depending on implementations. This paper presents the complexity-theoretic security analysis on some models of the Y00 protocol with nonlinear pseudo-random-number-generator and quantum noise diffusion mapping (QDM). Algebraic attacks and fast correlation attacks are applied with a model of the Y00 protocol with nonlinear filtering like the Toyocrypt stream cipher as the running key generator, and it is shown that these attacks in principle do not work on such models even when the mapping between running key and quantum state signal is fixed. In addition, a security property of the Y00 protocol with QDM is clarified. Consequently, we show that the Y00 protocol has a potential which cannot be realized by conventional cryptography and that it goes beyond mathematical encryption with physical encryption.

We consider cigar-shaped Fermi superfluid in the Bose-Einstein condensation (BEC)-BCS crossover. Using the polytropic form of equation of state, we derive low energy multibranch bosonic excitations and the corresponding density fluctuations in three different regimes along the crossover, namely weak-coupling BCS, unitarity, and molecular BEC regimes. Bragg spectroscopy can be used to probe the multibranch nature of the low-energy bosonic excitations by measuring the dynamic structure factor. Therefore we calculate the dynamic structure factor in those three different regimes. In Bragg spectroscopy, an actual observable is momentum imparted to the superfluid due to the Bragg potential. We also present results of the momentum imparted to the superfluid due to the Bragg pulses.

We propose the implementation of a strongly driven one-atom laser, based on the off-resonant interaction of a three-level atom in $\Lambda$ configuration with a single cavity mode and three laser fields. We show that the system can be described equivalently by a two-level atom resonantly coupled to the cavity and driven by a strong effective coherent field. The effective dynamics can be solved exactly, including a thermal field bath, allowing an analytical description of field statistics and entanglement properties. We also show the possible generation of quantum superposition (Schrödinger cat) states for the whole atom-field system and for the field alone after atomic measurement. We propose a way to monitor the system decoherence by measuring atomic populations. Finally, we confirm the validity of our model through numerical solutions.

We derive the form of the cross-Kerr interaction in a four-level atomic system in an N configuration. We use time-independent perturbation theory to calculate the eigenenergies and eigenstates of the Schrödinger equation for the system. The system is considered as a perturbation of a Raman-resonant three-level $\lambda$ scheme for which exact solutions are known. We show that within the strong control field limit the cross-Kerr interaction can arise between two weak probe fields. The strength of this nonlinear coupling is several orders of magnitude larger than that achievable using optical fibres.

In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)], we used a universal physical picture to optimize and demonstrate equivalence between a wide range of techniques for storage and retrieval of photon wave packets in $\Lambda$-type atomic media in free space, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo-based techniques. In the present paper, we perform the same analysis for the cavity model. In particular, we show that the retrieval efficiency is equal to $C∕(1+C)$ independent of the retrieval technique, where $C$ is the cooperativity parameter. We also derive the optimal strategy for storage and, in particular, demonstrate that at any detuning one can store, with the optimal efficiency of $C∕(1+C)$, any smooth input mode satisfying $TC\gamma ⪢1$ and a certain class of resonant input modes satisfying $TC\gamma \sim 1$, where $T$ is the duration of the input mode and $2\gamma$ is the transition linewidth. In the two subsequent papers of the series, we present the full analysis of the free-space model and discuss the effects of inhomogeneous broadening on photon storage.

In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)], we presented a universal physical picture for describing a wide range of techniques for storage and retrieval of photon wave packets in $\Lambda$-type atomic media in free space, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo based techniques. This universal picture produced an optimal control strategy for photon storage and retrieval applicable to all approaches and yielded identical maximum efficiencies for all of them. In the present paper, we present the full details of this analysis as well some of its extensions, including the discussion of the effects of non-degeneracy of the two lower levels of the $\Lambda$ system. The analysis in the present paper is based on the intuition obtained from the study of photon storage in the cavity model in the preceding paper [Gorshkov et al., previous paper, Phys. Rev. A. 76, 033804 (2007)].

In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)] and in the two preceding papers [Gorshkov et al., this issue, Phys. Rev. A 76, 033804 (2006); 76, 033805 (2006)], we used a universal physical picture to optimize and demonstrate equivalence between a wide range of techniques for storage and retrieval of photon wave packets in homogeneously broadened $\Lambda$-type atomic media, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo-based techniques. In the present paper, we generalize this treatment to include inhomogeneous broadening. In particular, we consider the case of Doppler-broadened atoms and assume that there is a negligible difference between the Doppler shifts of the two optical transitions. In this situation, we show that, at high enough optical depth, all atoms contribute coherently to the storage process as if the medium were homogeneously broadened. We also discuss the effects of inhomogeneous broadening in solid state samples. In this context, we discuss the advantages and limitations of reversing the inhomogeneous broadening during the storage time, as well as suggest a way for achieving high efficiencies with a nonreversible inhomogeneous profile.