One of the remarkable features of quantum mechanics is the ability to ensure secrecy. Private states embody this effect, as they are precisely those multipartite quantum states from which two parties can produce a shared secret that cannot under any circumstances be correlated with an external system. Naturally, these play an important role in quantum key distribution (QKD) and quantum information theory. However, a general distillation method has heretofore been missing. Inspired by Koashi’s complementary control scenario [M. Koashi, e-print arXiv:0704.3661 (2007)], we give a new definition of private states in terms of one party’s potential knowledge of two complementary measurements made on the other and use this to construct a general method of private state distillation using quantum error-correcting codes. The procedure achieves the same key rate as recent, more information-theoretic approaches while demonstrating the physical principles underlying privacy of the key. Additionally, the same approach can be used to establish the hashing inequality for entanglement distillation, as well as the direct quantum coding theorem.

We present the construction and detailed analysis of highly optimized self-refocusing pulse shapes for several rotation angles. We characterize the constructed pulses by the coefficients appearing in the Magnus expansion up to second order. This allows a semianalytical analysis of the performance of the constructed shapes in sequences and composite pulses by computing the corresponding leading-order error operators. Higher orders can be analyzed with the numerical technique suggested by us previously. We illustrate the technique by analyzing several composite pulses designed to protect against pulse amplitude errors, and on decoupling sequences for potentially long chains of qubits with on-site and nearest-neighbor couplings.

The photoelectron spectra produced in the photodetachment of ${\mathrm{H}}^{-}$ (treated in the single-active-electron approximation) by strong high-frequency laser pulses with adequately chosen laser parameters in the stabilization regime are theoretically studied for elliptic polarization over an extended parameter range. An oscillating substructure in the above-threshold ionization peaks is observed, which confirms similar findings in the one-dimensional (1D) [K. Toyota et al., Phys. Rev. A 76, 043418 (2007)] and 3D calculations for linear polarization [O. I. Tolstikhin, Phys. Rev. A 77, 032712 (2008)]. The mechanism is an interference between the photoelectron wave packets created in the rising and falling parts of the pulse which is specific to the stabilization regime. We thus conclude that this interference substructure is robust for any polarization and over a wide range of the laser parameters, and hence should be observable experimentally.

We consider a superfluid state in a two-component gas of fermionic atoms with equal densities and unequal masses in the BCS limit. We develop a perturbation theory along the lines proposed by Gorkov and Melik-Barkhudarov and find that for a large difference in the masses of heavy $\left(M\right)$ and light $\left(m\right)$ atoms one has to take into account both the second-order and third-order contributions. The result for the critical temperature and order parameter is then quite different from the prediction of the simple BCS approach. Moreover, the small parameter of the theory turns out to be $(p_F\mid a\mid ∕\hslash )\sqrt{M∕m}⪡1$, where $p_F$ is the Fermi momentum and $a$ the scattering length. Thus, for a large mass ratio $M∕m$ the conventional perturbation theory requires significantly smaller Fermi momenta (densities) or scattering lengths than in the case of $M\sim m$, where the small parameter is $p_F\mid a\mid ∕\hslash ⪡1$. We show that three-body scattering resonances appearing at a large mass ratio due to the presence of three-body bound Efimov states do not influence the result, which in this sense becomes universal.

We examine the resolution of a ghost imaging system for the case in which the entangled photons are nondegenerate in frequency. The signal photon illuminates the object and is detected by a bucket detector. The idler photon is detected by a point detector. We consider the two cases in which the imaging lens is in the same arm as the object and when it is in the other arm. In the first case, the Airy disk is shown to depend on the wavelength of the idler photon; however, because the magnification depends on the two wavelengths, the resolution of a pair of point scatters on the object depends on the wavelength of both photons. In cases in which the position of the object can be controlled, the minimum resolvable distance can be optimized. In the case in which the object is in the far field, the resolution depends only on the signal wavelength. In the second case, the Airy disk depends on the wavelength of both photons but the resolution depends on the signal photon. While the ghost imaging system has flexibility for certain applications, the resolution of the nondegenerate ghost imaging system does not offer improvement over the classical illumination of the object.

Based on a microscopic derivation of the emission spectra of a bulk semiconductor, we arrive at a clear physical interpretation of the noise current operators in macroscopic quantum electrodynamics. This opens the possibility to study medium effects on nonclassical radiation propagating through an absorbing or amplifying semiconductor. As an example, the propagation of an incident squeezed vacuum is analyzed.

We extend our previous work [Phys. Rev. Lett. 100, 183602 (2008)] on the generalization of the Casimir-Lifshitz theory to treat anisotropic magnetodielectric media, focusing on the forces between metals and magnetodielectric metamaterials and on the possibility of inferring magnetic effects by measurements of these forces. We present results for metamaterials including structures with uniaxial and biaxial magnetodielectric anisotropies, as well as for structures with isolated metallic or dielectric properties that we describe in terms of filling factors and a Maxwell Garnett approximation. The elimination or reduction of Casimir “stiction” by appropriate engineering of metallic-based metamaterials, or the indirect detection of magnetic contributions, appear from the examples considered to be very challenging, as small background Drude contributions to the permittivity act to enhance attraction over repulsion, as does magnetic dissipation. In dielectric-based metamaterials the magnetic properties of polaritonic crystals, for instance, appear to be too weak for repulsion to overcome attraction. We also discuss Casimir-Polder experiments, that might provide another possibility for the detection of magnetic effects.

We study the fully entangled fraction of quantum states. An upper bound is obtained for arbitrary dimensional bipartite systems. This bound is shown to be exact for the case of two-qubit systems. An inequality related the fully entangled fraction of two qubits in a three-qubit mixed state has been also presented.

If a quantum channel or process cannot be described by any measure-and-prepare scheme, we may say the channel is in the quantum domain (QD) since it can transmit quantum correlations. The concept of the QD clarifies the role of the quantum channel in quantum-information theory based on the local operation and classical communication (LOCC) paradigm: The quantum channel is useful only if it cannot be simulated by LOCC. We construct a simple scheme to verify that a given physical process or channel is in the QD by using two nonorthogonal states. We also consider its application for experiments such as the transmission or storage of quantum optical coherent states, single-photon polarization states, and squeezed vacuum states.

The dynamics of a cascaded system that consists of two atom-cavity subsystems is studied by using the quantum trajectory method. Considering two atom-cavity subsystems driven by a Raman interaction, analytical solutions are obtained. Subsequently, the entanglement evolution between the two atoms is studied, and it is shown that the entanglement can be stored by switching off the Raman coupling. By monitoring the radiation field, the entanglement between the two atoms can be enhanced.

The process of bound-free pair production of electrons and positrons in combined laser and Coulomb fields is investigated. It is assumed that an ion collides at relativistic speed with an intense x-ray laser beam of linear polarization. The process proceeds nonlinearly due to simultaneous absorption of a few laser photons. The capture of the electron into the ground state and the $L$ shell is considered. The scaling of the total rate, the angular distributions of the emitted positrons, and a comparison to the competing free-free channel are surveyed. Numerical results of pair production rates for parameters for the planned x-ray free-electron lasers at DESY and SLAC are presented. We find that pair production with these laser facilities can become observable in the near future.

It is shown that any Bose-Einstein-condensed fluid in its ground state will exhibit macroscopic single-particle quantum behavior (MSPQB). That is, (1) the many-particle wave function $\Psi ({\mathbf{r}}_1,\dots ,{\mathbf{r}}_n)$ factors into a single-particle product ${\prod }_n\eta \left({\mathbf{r}}_n\right)$; (2) the function $\eta \left(\mathbf{r}\right)$ extends over macroscopic length scales and obeys the usual quantum equations for particle flux in a single-particle system; and (3) $\eta \left(\mathbf{r}\right)$ obeys a nonlinear single-particle Schrödinger equation. The latter equation reduces to the Gross-Pitaevskii equation when interactions are weak and determines the density distribution of the fluid and the time development of this distribution. The arguments used rely only on elementary concepts of probability theory and many-particle wave mechanics and are valid even in strongly interacting fluids such as superfluid ${}^4\mathrm{He}$. It is shown that Bose-Einstein condensation implies that the $N$-particle wave function $\Psi$ is delocalized. That is, if one considers a single-particle coordinate $\mathbf{r}$, then for all values that occur of the other $N-1$ coordinates, $\Psi$ is a nonzero function of $\mathbf{r}$ over a region of space proportional to $V$, where $V$ is the total volume within which the fluid is contained. MSPQB is a consequence of this delocalization and the absence of long-range correlations between particle positions in fluids. The results are accurate provided that only averages over regions of space containing many particles are considered. For averages over volumes of space containing $N_{\Omega }$ particles, inaccuracies due to quantum fluctuations are $\sim 1∕\sqrt{N_{\Omega }}$.

We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the canonical worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and interspecies interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.

We report on light-shift tomography of a cloud of ${}^{87}\mathrm{Rb}$ atoms in a far-detuned optical-dipole trap at $1565\mathrm{nm}$. Our method is based on standard absorption imaging, but takes advantage of the strong light shift of the excited state of the imaging transition, which is due to a quasiresonance of the trapping laser with a higher excited level. We use this method to (i) map the equipotentials of a crossed optical-dipole trap and (ii) study the thermalization of an atomic cloud by following the evolution of the potential energy of atoms during the free-evaporation process.

A formal Hamiltonian is presented that allows quantum logic with quantized control fields beyond the $1∕\overline{n}$ error level, if the field is initially in a (multimode) number state. The key requirement is that the interaction be completely insensitive to the phase of the field. We find, however, that when we try to satisfy this requirement by using a realistic interaction model for trapped ions in phase-insensitive decoherence-free subspaces, the $1∕\overline{n}$ scaling is obtained again. We conjecture that it may not be possible to improve on this scaling by physically realizable radiation-matter interactions.

In this work we consider the dynamical Casimir effect for a massless scalar field—under Dirichlet boundary conditions—between two concentric spherical shells. We obtain a general expression for the average number of particle creation, for an arbitrary law of radial motion of the spherical shells, using two distinct methods: by computing the density operator of the system and by calculating the Bogoliubov coefficients. We apply our general expression to breathing modes: when only one of the shells oscillates and when both shells oscillate in or out of phase. Since our results were obtained in the framework of the perturbation theory, under resonant breathing modes they are restricted to a short-time approximation. We also analyze the number of particle production and compare it with the results for the case of plane geometry.