We study the dynamics of a two-level atom interacting with a Lorentzian structured reservoir considering initial system-environment correlations. It is shown that under strong system-reservoir coupling the dynamics of purity can determine whether there are initial correlations between the system and the environment. Moreover, we investigate the interaction of two two-level atoms with the same reservoir. In this case, we show that, besides determining if there are initial system-environment correlations, the dynamics of the purity of the atomic system allows the identification of the distinct correlated initial states. In addition, the dynamics of quantum and classical correlations is analyzed.

We revisit the problem of discriminating orthogonal quantum states within the local-quantum-operation-and-classical-communication (LOCC) paradigm. Our particular focus is on the asymptotic situation where the parties have infinite resources and the protocol may become arbitrarily long. Our main result is a necessary condition for perfect asymptotic LOCC discrimination. As an application, we prove that for complete product bases, unlimited resources are of no advantage. On the other hand, we identify an example for which it still remains undecided whether unlimited resources are superior.

It is shown that the electron-electron mutual Coulomb repulsion energy-density functional $V_{ee}^{\gamma }\left[\rho \right]$ satisfies the equation $V_{ee}^{\gamma }\left[{\rho }_N^1\right]-V_{ee}^{\gamma }\left[{\rho }_{N-1}^{\gamma }\right]=\int d^{3}r\frac{\delta V_{ee}^{\gamma }\left[{\rho }_N^1\right]}{\delta {\rho }_N^1\left(\mathbf{r}\right)}[{\rho }_N^1\left(\mathbf{r}\right)-{\rho }_{N-1}^{\gamma }\left(\mathbf{r}\right)],$where ${\rho }_N^1\left(\mathbf{r}\right)$ and ${\rho }_{N-1}^{\gamma }\left(\mathbf{r}\right)$ are $N$-electron and $(N-1)$-electron densities determined from the same adiabatic scaled external potential of the $N$-electron system at coupling strength $\gamma .$

Cross-section data for electron scattering from biologically relevant molecules are important for the modeling of energy deposition in living tissue. Relative elastic differential cross sections have been measured for cytosine and thymine using the crossed-beam method. These measurements have been performed for six discrete electron energies between 60 and 500 eV and for detection angles between 15° and 130°. Calculations have been performed via the screen-corrected additivity rule method and are in good agreement with the present experiment.

We consider bound-free electron-positron pair production in extreme relativistic collisions of a highly charged nucleus and a molecule. We show that, in such collisions, pronounced interference effects can arise in the emission pattern of the created positrons that are caused by the coherent interaction of the lepton field with the nuclei of the molecule.

The question whether a spin-imbalanced Fermi gas can accommodate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state has been the subject of intense study. This state, in which Cooper pairs obtain a nonzero momentum, has hitherto eluded experimental observation. Recently, we demonstrated that the FFLO state can be stabilized in a 3D Fermi gas, by adding a 1D periodic potential. Until now it was assumed that the FFLO wave vector always lies parallel to this periodic potential (FFLO-P). In this contribution we show that, surprisingly, the FFLO wave vector can also lie skewed with respect to the potential (FFLO-S). Starting from the partition sum, the saddle-point free energy of the system is derived within the path-integral formalism. Minimizing this free energy allows us to study the different competing ground states of the system. To qualitatively understand the underlying pairing mechanism, we visualize the Fermi surfaces of the spin-up and spin-down particles. From this visualization, we find that tilting the FFLO wave vector with respect to the direction of the periodic potential can result in a larger overlap between the pairing bands of both spin species. This skewed FFLO state can provide an additional experimental signature for observing FFLO superfluidity in a 3D Fermi gas.

We theoretically investigate a scheme for atom interferometry that surpasses the standard quantum limit. A four-wave mixing scheme similar to the recent experiment performed by Pertot et al. [Phys. Rev. Lett. 104, 200402 (2010)] is used to generate subshotnoise correlations between two modes. These two modes are then interfered with the remaining two modes in such a way as to surpass the standard quantum limit, whilst utilizing all of the available atoms. Our scheme can be viewed as using two correlated interferometers. That is, the signal from each interferometer when looked at individually is classical, but there are correlations between the two interferometers that allow for the standard quantum limit to be surpassed.

We consider the statistics of time-integrated energy fluctuations of a driven bosonic single-mode resonator, as measured by a quantum nondemolition (QND) detector, using the standard Keldysh prescription to define higher moments. We find that, due to an effective cascading of fluctuations, these statistics are surprisingly nonclassical: the low-temperature, quantum probability distribution is not equivalent to the high-temperature classical distribution evaluated at some effective temperature. Moreover, for a sufficiently large drive detuning and low temperatures, the Keldysh-ordered quasiprobability distribution characterizing these fluctuations fails to be positive-definite; this is similar to the full counting statistics of charge in superconducting systems. We argue that this indicates a kind of nonclassical behavior akin to that tested by Leggett-Garg inequalities.

Spontaneous emission by an excited fermionic atom can be suppressed due to the Pauli exclusion principle if the relevant final states after the decay are already occupied by identical atoms in the ground state. Here we discuss a setup where a single atom is prepared in the first excited state on a single site of an optical lattice under conditions of very tight trapping. We investigate these phenomena in the context of two experimental realizations: (1) with alkali-metal atoms, where the decay rate of the excited state is large, and (2) with alkaline-earth-metal-like atoms, where the decay rate from metastable states can be tuned in experiments. This phenomenon has potential applications towards reservoir engineering and dissipative many-body state preparation in an optical lattice.

Recently, waveguide lattices with nonuniform tunneling amplitudes have been explored due to their myriad tunable properties, many of which arise from the extended nature of their eigenstates in the absence of disorder. Here, we investigate the dynamics, localization, and parity- and time-reversal-symmetry ($\mathcal{P}\mathcal{T}$-symmetry) breaking in lattices that support only localized eigenstates in the disorder-free limit. We propose three families of tunneling profiles that lead to qualitatively different single-particle time evolution and show that the effects of weak disorder contain signatures of the localized or extended nature of clean-lattice eigenstates. We show that, in lattices with localized eigenstates, the signatures of $\mathcal{P}\mathcal{T}$-symmetry breaking are acutely sensitive to the initial form of the wave packet. Our results suggest that waveguide lattices with localized eigenstates will exhibit a wide array of phenomena that are absent in traditional systems.

We give a concrete experimental scheme for engineering the insulator-superfluid transition of light in a one-dimensional (1D) array of coupled superconducting stripline resonators. In our proposed architecture, the on-site interaction and the photon-hopping rate can be tuned independently by adjusting the transition frequencies of the charge qubits inside the resonators and at the resonator junctions, respectively, which permits us to systematically study the quantum phase transition of light in a complete parameter space. By combining the techniques of photon-number-dependent qubit transition and fast readout of the qubit state using a separate low-$Q$ resonator mode, the statistical property of the excitations in each resonator can be obtained with a high efficiency. An analysis of the various decoherence sources and disorders shows that our scheme can serve as a guide to upcoming experiments involving a small number of coupled resonators.

Recent work [J. A. Dunningham, V. Palge, and V. Vedral, Phys. Rev. A 80, 044302 (2009)] has shown how single-particle entangled states are transformed when boosted in relativistic frames for certain restricted geometries. Here we extend that work to consider completely general inertial boosts. We then apply our single-particle results to multiparticle entanglements by focusing on Cooper pairs of electrons. We show that a standard Cooper pair state consisting of a spin-singlet acquires spin-triplet components in a relativistically boosted inertial frame, regardless of the geometry. We also show that, if we start with a spin-triplet pair, two out of the three triplet states acquire a singlet component, the size of which depends on the geometry. This transformation between the different singlet and triplet superconducting pairs may lead to a better understanding of unconventional superconductivity.

Mutually coupled modes of a pair of active LRC circuits, one with amplification and another with an equivalent amount of attenuation, provide an experimental realization of a wide class of systems where gain and loss mechanisms break the Hermiticity while preserving parity-time $\mathcal{PT}$ symmetry. For a value ${\gamma }_{\mathcal{PT}}$ of the gain and loss strength parameter the eigenfrequencies undergo a spontaneous phase transition from real to complex values, while the normal modes coalesce, acquiring a definite chirality. The consequences of the phase transition in the spatiotemporal energy evolution are also presented.

The preparation of arbitrary $N$-particle Dicke states in a one-dimensional $N$-qubit chain with nearest-neighbor $XXZ$ interaction is investigated. We show by perturbation approach that each of the $N+1$ Dicke states can be approximately created as the nondegenerate ground state of the system when suitable external magnetic field and inter-qubit coupling are applied. In some small $N$ situations, the perturbative results agree very well with the exact solutions. We further demonstrate by numerical methods that the proposed ground-state preparation of the Dicke states is robust against the finite temperature in the $N=4$ case. We also discuss the feasibility of our scheme in several physical systems including semiconductor quantum dots and an optical lattice.

In bipartite quantum systems of dimension $3\times 3$, entangled states that are positive under partial transposition (PPT) can be constructed with the use of unextendible product bases (UPBs). As discussed in a previous publication, all the lowest rank entangled PPT states of this system seem to be equivalent, under $\mathrm{SL}\otimes \mathrm{SL}$ transformations, to states that are constructed in this way. Here we consider a possible generalization of the UPB constuction to low-rank entangled PPT states in higher dimensions. The idea is to give up the condition of orthogonality of the product vectors, while keeping the relation between the density matrix and the projection on the subspace defined by the UPB. We examine first this generalization for the $3\times 3$ system where numerical studies indicate that one-parameter families of such generalized states can be found. Similar numerical searches in higher dimensional systems show the presence of extremal PPT states of similar form. Based on these results we suggest that the UPB construction of the lowest rank entangled states in the $3\times 3$ system can be generalized to higher dimensions, with the use of nonorthogonal UPBs.

We consider a general anisotropic spin-orbit coupling and analyze the phase diagrams of both balanced and imbalanced Fermi gases for the entire BCS-BEC evolution. In the first part, we use the self-consistent mean-field theory at zero temperature, and show that the topological structure of the ground-state phase diagrams is quite robust against the effects of anisotropy. In the second part, we go beyond the mean-field description, and investigate the effects of Gaussian fluctuations near the critical temperature. This allows us to derive the time-dependent Ginzburg-Landau theory, from which we extract the effective mass of the Cooper pairs and their critical condensation temperature in the molecular BEC limit.

Interactions of ultracold atoms with Rashba spin-orbit coupling, currently being studied with simulated (artificial) gauge fields, have nontrivial ultraviolet and infrared behavior. Examining the ultrastructure of the Bethe-Salpeter equation, we show that the linear ultraviolet divergence in the bare interaction can be renormalized as usual in terms of low-energy scattering lengths, and that for both bosons and fermions ultraviolet logarithmic divergences are absent. Calculating the leading order effective interaction with full dependence on the spin-orbit coupling strength and the center-of-mass momentum of the colliding pair, we elucidate the relation between mean-field interactions and physical three-dimensional scattering lengths. As a consequence of infrared logarithmic divergences in the two-particle propagator, the effective interaction vanishes as the center-of-mass momentum approaches zero.

We analyze the evolution of an electromagnetic field inside a double cavity when the difference in length between the two cavities is changed, e.g., by translating the common mirror. We find that this allows photons to be moved deterministically from one cavity to the other. We are able to obtain the conditions for adiabatic transfer by first mapping the Maxwell wave equation for the electric field onto a Schrödinger-like wave equation and then using the Landau-Zener result for the transition probability at an avoided crossing. Our analysis reveals that this mapping only rigorously holds when the two cavities are weakly coupled (i.e., in the regime of a highly reflective common mirror) and that, generally speaking, care is required when attempting a Hamiltonian description of cavity electrodynamics with time-dependent boundary conditions.

The propagation of a bulk optical solitary wave in a rectangular cell filled with a nematic liquid crystal—a nematicon—is mathematically modelled. In order to overcome the Freédricksz threshold the cell walls are rubbed to pretilt the nematic. A modulation theory, based on a Lagrangian formulation, is developed for the $(2+1)$-dimensional propagation of the solitary wave beam down the cell. This modulation theory is based on two different formulations of the director distribution. The relative advantages and disadvantages of these two methods are discussed. A previously unexplored method based on images is found to possess significant advantages. Excellent agreement with full numerical solutions of the nematicon equations is found for both methods. Finally, the implications of the results obtained for some widely used approximations to the nematicon equations are discussed, particularly their use in comparisons with experimental results.

We derive simple practical procedures revealing the quantum behavior of angular momentum variables by the violation of classical upper bounds on the statistics. Data analysis is minimum and definite conclusions are obtained without evaluation of moments, or any other more sophisticated procedures. These nonclassical tests are very general and independent of other typical quantum signatures of nonclassical behavior such as sub-Poissonian statistics, squeezing, or oscillatory statistics, being insensitive to the nonclassical behavior displayed by other variables.