Hypothesis testing is a fundamental issue in statistical inference and has been a crucial element in the development of information sciences. The Chernoff bound gives the minimal Bayesian error probability when discriminating two hypotheses given a large number of observations. Recently the combined work of Audenaert et al. [Phys. Rev. Lett. 98, 160501 (2007)] and Nussbaum and Szkola [e-print arXiv:quant-ph/0607216] has proved the quantum analog of this bound, which applies when the hypotheses correspond to two quantum states. Based on this quantum Chernoff bound, we define a physically meaningful distinguishability measure and its corresponding metric in the space of states; the latter is shown to coincide with the Wigner-Yanase metric. Along the same lines, we define a second, more easily implementable, distinguishability measure based on the error probability of discrimination when the same local measurement is performed on every copy. We study some general properties of these measures, including the probability distribution of density matrices, defined via the volume element induced by the metric. It is shown that the Bures and the local-measurement based metrics are always proportional. Finally, we illustrate their use in the paradigmatic cases of qubits and Gaussian infinite-dimensional states.

A scheme for fine tuning of quantum operations to improve their performance is proposed. A quantum system in $\Lambda$ configuration with two-photon Raman transitions is considered without adiabatic elimination of the excited (intermediate) state. Conditional dynamics of the system is studied with focus on improving fidelity of quantum operations. In particular, the $\pi$ pulse and $\pi ∕2$ pulse quantum operations are considered. The dressed states for the atom-field system, with an atom driven on one transition by a classical field and on the other by a quantum cavity field, are found. A discrete set of detunings is given for which high fidelity of desired states is achieved. Analytical solutions for the quantum state amplitudes are found in the first order perturbation theory with respect to the cavity damping rate $\kappa$ and the spontaneous emission rate $\gamma$. Numerical solutions for higher values of $\kappa$ and $\gamma$ indicate a stabilizing role of spontaneous emission in the $\pi$ and $\pi ∕2$ pulse quantum operations. The idea can also be applied for excitation pulses of different shapes.

Based on quantitative complementarity relations (QCRs), we analyze the multipartite correlations in four-qubit cluster-class states. It is proven analytically that the average multipartite correlation $E_{ms}$ is entanglement monotone. Moreover, it is also shown that the mixed three-tangle is a correlation measure compatible with the QCRs in this kind of quantum state. More arrestingly, with the aid of the QCRs, a set of hierarchy entanglement measures is obtained rigorously in the present system.

We demonstrate pulsed operation of a bidirectionally pumped polarization Sagnac interferometric down-conversion source and its generation of narrow-band, high-visibility polarization-entangled photons. Driven by a narrow-band, mode-locked pump at 390.35 nm, the phase-stable Sagnac source with a type-II phase-matched periodically poled ${\text{KTiOPO}}_4$ crystal is capable of producing 0.01 entangled pair per pulse in a 0.15-nm bandwidth centered at 780.7 nm with 1 mW of average pump power at a repetition rate of 31.1 MHz. We have achieved a mean photon-pair generation rate of as high as 0.7 pair per pulse, at which multipair events dominate and significantly reduce the two-photon quantum-interference visibility. For low generation probability $\alpha$, the reduced visibility $V=1-\alpha$ is independent of the throughput efficiency and of the polarization analysis basis, which can be utilized to yield an accurate estimate of the generation rate $\alpha$. At low $\alpha$ we have characterized the source entanglement quality in three different ways: average quantum-interference visibility of 99%, the Clauser-Horne-Shimony-Holt $S$ parameter of $2.739\pm 0.119$, and quantum state tomography with 98.85% singlet-state fidelity. The narrow-band pulsed Sagnac source of entangled photons is suitable for use in quantum information processing applications such as free-space quantum key distribution.

The coherent control of a small quantum system is considered. For a two-level system coupled to an arbitrary bath we consider a pulse of finite duration. We derive the leading and the next-leading order corrections to the evolution operator due to the noncommutation of the pulse and the bath Hamiltonian. The conditions are computed that make the leading corrections vanish. The pulse shapes optimized in this way are given for $\pi$ and $\frac{\pi }{2}$ pulses.

We have used an optical frequency comb referenced to coordinated universal time (UTC) to perform spectroscopic measurements of the $D_1$ transition in laser-cooled ${}^{85}\text{R}\text{b}$ and ${}^{87}\text{R}\text{b}$. Our measurements of the optical frequencies have uncertainties of 28 kHz for ${}^{85}\text{R}\text{b}$ and 79 kHz for ${}^{87}\text{R}\text{b}$. These measurements were used to calculate the magnetic dipole constant $A\left({{}^{2}P}_{1/2}\right)$ for ${}^{85}\text{R}\text{b}$ and ${}^{87}\text{R}\text{b}$ with similar ranges of uncertainty. Previously, $A\left({{}^{2}P}_{1/2}\right)$ for these isotopes was determined with a stated 7–15 kHz uncertainty level; however, there is a large discrepancy, 140 kHz for ${}^{85}\text{R}\text{b}$ and 2.2 MHz for ${}^{87}\text{R}\text{b}$, between the two apparently most precise measurements. Our transition frequency measurements, which avoid saturated absorption spectroscopy and transfer resonator systematics, help resolve this disagreement.

Möller and Plesset in early work demonstrated quantitatively the high quality of the Hartree-Fock ground-state electron density ${\rho }_{\text{HF}}\left(\mathbf{r}\right)$. Therefore, Cordero, March, and Alonso recently proposed, for atoms, a fine-tuning of ${\rho }_{\text{HF}}\left(\mathbf{r}\right)$ to satisfy both the known asymptotic behavior of the density far from the nucleus, as well as the Kato cusp condition at the nuclei. Here we extend the diagonal density $\rho \left(\mathbf{r}\right)$ proposed by Cordero et al. to an off-diagonal idempotent one-particle density matrix. The orthonormal orbitals used in this construction are then to be found from the solution of generalized Hartree-Fock equations. We report calculations on the Be isoelectronic series of atomic ions with $Z$ from ${\text{Li}}^{-}$ to ${\text{Ca}}^{16+}$.

Population trapping occurs when a particular quantum-state superposition is immune to action by a specific interaction, such as the well-known dark state in a three-state $\Lambda$ system. We here show that in a three-state loop linkage, a Hilbert-space Householder reflection breaks the loop and presents the linkage as a single chain. With certain conditions on the interaction parameters, this chain can break into a simple two-state system and an additional spectator state. Alternatively, a two-photon resonance condition in this Householder-basis chain can be enforced, which heralds the existence of another spectator state. These spectator states generalize the usual dark state to include contributions from all three bare basis states and disclose hidden population trapping effects and hence hidden constants of motion. Insofar as a spectator state simplifies the overall dynamics, its existence facilitates the derivation of analytic solutions and the design of recipes for quantum-state engineering in the loop system. Moreover, it is shown that a suitable sequence of Householder transformations can cast an arbitrary $N$-dimensional Hermitian Hamiltonian in a tridiagonal form. The implication is that a general $N$-state system, with arbitrary linkage patterns where each state connects to any other state, can be reduced to an equivalent chainwise-connected system, with nearest-neighbor interactions only, with ensuing possibilities for discovering hidden multidimensional spectator states and constants of motion.

We present the results of a variational calculation of the frequencies of the low-lying Landau two-fluid hydrodynamic modes in a trapped Fermi superfluid gas at unitarity. Landau’s two-fluid hydrodynamics is expected to be the correct theory of Fermi superfluids at finite temperatures close to unitarity, where strong interactions give rise to collisional hydrodynamics. Two-fluid hydrodynamics predicts the existence of in-phase modes in which the superfluid and normal fluid components oscillate together, as well as out-of-phase modes where the two components move against each other. We prove that, at unitarity, the dipole and breathing in-phase modes are locally isentropic. Their frequencies are independent of temperature and are the same above and below the superfluid transition, a feature due as much to the harmonic trapping potential as to the thermodynamic properties at unitarity. The out-of-phase modes, in contrast, are strongly dependent on temperature and hence can be used to test the thermodynamic properties and superfluid density of a Fermi gas at unitarity. We give numerical results for the frequencies of these modes as function of temperature in an isotropic trap at unitarity.

We have theoretically analyzed nonclassical paired photons generated spontaneously from a four-level inverted-Y atomic system. We discuss the feasibility of biphoton generation due to different pumping arrangements. Two types of correlated photon pair emissions have been carefully examined: dressed cascade and dressed double-$\Lambda$ emissions. In the dressed cascade two-photon emission, the coincidence counting rate may exhibit a damped Rabi oscillation, in contrast with a simple exponential decay feature in the literatures. In the dressed double-$\Lambda$ configuration, we show that not only is the temporal correlation of entangled Stokes–anti-Stokes photons in agreement with discussions presented by Wen et al. [Phys. Rev. A 76, 013825 (2007)], but also the oscillation period may be manipulated by altering either the control Rabi frequency or the dressing Rabi frequency or both. All the observed damped Rabi oscillations in the two-photon coincidences result from the destructive interference among the possible four-wave mixing processes occurring in the atom-field interaction system. This feature of the two-photon amplitude is governed by the convolution between the phase matching and third-order nonlinear susceptibility. The methodology adopted here can be applied to other atomic-level configurations and provides a useful tool to study the spectroscopy of the system. The generated narrow-band photon pairs may have potential applications in long-distance quantum communication and quantum information processing.

We present generic outcomes of collisions between stable solitons with intrinsic vorticity $S=1$ or $S=2$ in the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity, for the axially symmetric configuration. An essential ingredient of the complex Ginzburg-Landau equation is an effective transverse diffusivity (which is known in models of laser cavities), as vortex solitons cannot be stable without it. For the sake of comparison, results are also included for fundamental three-dimensional solitons, with $S=0$. Depending on the collision momentum, $\chi$, three generic outcomes are identified: merger of the solitons into a single one, at small $\chi$; quasielastic interaction, at large $\chi$; and creation of an extra soliton, in an intermediate region. In addition to the final outcomes, we also highlight noteworthy features of the transient dynamics.

I present a simple theoretical interpretation of an anomalous magneto-optical effect at the domain boundary. This effect was discovered by Schäfer and Hubert [Phys. Status Solidi A 118, 271 (1990)] but was not supported by a clear physical explanation. From a familiar dielectric law, I derive the boundary magneto-optical effect concurrently with the bulk magneto-optical effect, i.e., the Faraday-Kerr effect. This boundary effect originates in the boundary charge density and is identified as the Schäfer-Hubert effect, based on a comparison of my theory and experimental results. Furthermore, I demonstrate that the Schäfer-Hubert effect predominates over the Faraday-Kerr effect and will be observed in the near field of a system with small-scale domains.

We consider the radiative trapping and cooling of a partially reflecting mirror suspended inside an optical cavity, generalizing the case of a perfectly reflecting mirror previously considered [M. Bhattacharya and P. Meystre, Phys. Rev. Lett. 99, 073601 (2007)]. This configuration was recently used in an experiment to cool a nanometers-thick dielectric membrane [J. D. Thompson et al., e-print arXiv:0707.1724v2]. The self-consistent cavity field modes of this system depend strongly on the position of the middle mirror, leading to important qualitative differences in the radiation pressure effects: in one case, the situation is similar to that of a perfectly reflecting middle mirror, with only minor quantitative modifications. In addition, we also identify a range of mirror positions for which the radiation-mirror-coupling becomes purely dispersive and the back-action effects that usually lead to cooling are absent, although the mirror can still be optically trapped. The existence of these two regimes leads us to propose a bichromatic scheme that optimizes the cooling and trapping of partially reflective mirrors.

All previously published nonrelativistic and scalar relativistic electronic structure calculations of platinum hexafluoride predict a paramagnetic distorted octahedral molecule with a triplet ground state. The four-component spin-free method also predicts a distorted octahedral molecule with longest axial Pt-F bond due to the Jahn-Teller effect. However, four-component Dirac molecular Hartree-Fock and density-functional theory (DFT) and the two-component zeroth-order regular approach (ZORA) including spin-orbit interaction calculations predict a diamagnetic octahedral molecule with a closed-shell ground state, which is in accordance with the observation of the ${}^{\text{19}}\text{F}$ and ${}^{\text{195}}\text{P}\text{t}$ high-resolution nuclear magnetic resonance spectra and its undisturbed ir and Raman spectra of ${\text{PtF}}_6$. The excitation energies involving the $d\text{−}d$ transitions are well calculated by performing time-dependent DFT calculations using the two-component ZORA method. Thus, its octahedral molecular structure with a closed-shell ground state is stabilized by the effect of a spin-orbit interaction.

We experimentally demonstrate that broad, tunable bandwidth of an optical ring cavity can be achieved by making use of the negative dispersion of the Kerr nonlinear refractive index in the three-level electromagnetically-induced transparency medium. For a given cavity field intensity, the white-light cavity condition can always be satisfied by choosing the appropriate coupling beam parameters. This white-light cavity scheme can be used effectively to achieve large buildup intensity in the signal-recycling cavity with a broad bandwidth in future advanced gravitational wave detectors.

Using the stabilizer formalism we construct the minimal code into a $D$-dimensional Hilbert space (qudit) to protect a qubit against phase damping. The effectiveness of this code is then studied by means of input-output fidelity.

We discuss aspects of the convex-roof extension of multipartite entanglement measures, that is, $\mathrm{SL}(2,\mathbb{C})$ invariant tangles. We highlight two key concepts that contain valuable information about the tangle of a density matrix: the zero polytope is a convex set of density matrices with vanishing tangle whereas the convex characteristic curve readily provides a nontrivial lower bound for the convex roof and serves as a tool for constructing the convex roof outside the zero polytope. Both concepts are derived from the tangle for superpositions of the eigenstates of the density matrix. We illustrate their application by considering examples of density matrices for two-qubit and three-qubit states of rank 2, thereby pointing out both the power and the limitations of the concepts.

The vibrations of a chain of trapped ions can be considered, under suitable experimental conditions, as an ensemble of interacting phonons, whose quantum dynamics is governed by a Bose-Hubbard Hamiltonian. In this work we study the quantum phases which appear in this system, and show that thermodynamical properties, such as critical parameters and critical exponents, can be measured in experiments with a limited number of ions. In addition to that, interacting phonons in trapped ions offer us the possibility to access regimes which are difficult to study with ultracold bosons in optical lattices, such as models with attractive or site-dependent phonon-phonon interactions.

We present a temperature-dependent Hartree-Fock-Bogoliubov-Popov theory to analyze the properties of the equilibrium states of an homogeneous mixture of bosonic atoms in two different hyperfine states and in the presence of an internal Josephson coupling. In our calculation we show that the bistable structure of the equilibrium states at zero temperature changes when we increase the temperature of the system. We investigate two mechanisms of the disappearance of bistability. In one, near the collapse of one of the equilibrium states, the acoustical branch becomes unstable and the gap of the optical branch goes to zero. In the other, there is no divergent behavior of the system and bistability disappears at a temperature in which the two equilibrium states merge at a zero-population fraction imbalance. When we further increase the temperature, this state remains as a unique equilibrium configuration.