We consider decay of a quasiparticle in a nearly-one-dimensional quasicondensate of trapped atoms, where virtual excitations of transverse modes break down one-dimensionality and integrability, giving rise to effective three-body elastic collisions. We calculate the matrix element for the process that involves one incoming quasiparticle and three outgoing quasiparticles. Scattering that involves low-frequency modes with high thermal population results in a diffusive dynamics of a bunch of quasiparticles created in the system.

We study the phase transitions in a one-dimensional Bose-Einstein condensate on a ring whose atomic scattering length is modulated periodically along the ring. By using a modified Bogoliubov method to treat such a nonlinear lattice in the mean-field approximation, we find that the phase transitions are of different orders when the modulation period is 2 and greater than 2. We further perform a full quantum mechanical treatment based on the time-evolving block decimation algorithm which confirms the mean-field results and reveals interesting quantum behavior of the system. Our studies yield important knowledge of competing mechanisms behind the phase transitions and the quantum nature of this system.

A method is proposed to generate and study the dynamics of spatial light solitons in a birefringent medium with quadratic nonlinearity. Although no analytical expression for propagating solitons has been obtained, our numerical simulations show the existence of stable localized spatial solitons in the frequency forbidden band gap of the medium. The dynamics of these objects is quite rich and manifests for instance elastic reflections, or inelastic collisions where two solitons merge and propagate as a single solitary wave. We derive the dynamics of the slowly varying envelopes of the three fields (second harmonic pump and two-component signal) and study this new system theoretically. We show that it does present a threshold for nonlinear supratransmission that can be calculated from a series expansion approach with a very high accuracy. Specific physical implications of our theoretical predictions are illustrated on LiGaTe${}_2$ (LGT) crystals. Once irradiated by a cw laser beam of $10\hspace{0.5em}\mu$m wavelength, at an incidence beyond the extinction angle, such crystals will transmit light, in the form of spatial solitons generated in the nonlinear regime above the nonlinear supratransmission threshold.

We have found several families of vortex soliton solutions in two-dimensional discrete dissipative systems governed by the cubic-quintic complex Ginzburg-Landau equation. There are symmetric and asymmetric solutions, and some of them have simultaneously two different topological charges for two different closed loops encircling, i.e., centered at, the singularity. Their regions of existence and stability are determined. Additionally, we have analyzed the relationship between dissipation and stability for a number of solutions, finding that dissipation favors the stability of the vortex soliton solutions.

It is shown that thermal energy from a heat source can be converted to useful work in the form of maser-laser light by using a combination of a Stern-Gerlach device and stimulated emissions of excited particles in a maser-laser cavity. We analyze the populations of atoms or quantum dots exiting the cavity, the photon statistics, and the internal entropy as a function of atomic transit time, using the quantum theory of masers and lasers. The power of the laser light is estimated to be sufficiently high for device applications. The thermodynamics of the heat converter is analyzed as a heat engine operating between two reservoirs of different temperature but is generalized to include the change of internal quantum states. The von Neumann entropies for the internal degree are obtained. The sum of the internal and external entropies increases after each cycle and the second law is not violated, even if the photon entropy due to finite photon number distribution is not included. An expression for efficiency relating to the Carnot efficiency is obtained. We resolve the subtle paradox on the reduction of the internal entropy with regards to the path separation after the Stern-Gerlach device.

We present a semiclassical model for plasmon-enhanced high-order harmonic generation (HHG) in the vicinity of metal nanostructures. We show that, besides the field enhancement, both the inhomogeneity of the enhanced local fields and electron absorption by the metal surface play an important role in the HHG process and lead to the generation of even harmonics and a significantly increased cutoff. For the examples of silver-coated nanocones and bowtie antennas, we predict that the required intensity reduces by up to three orders of magnitude due to plasmonic field enhancement. The study of the enhanced high-order harmonic generation is connected with a finite-element simulation of the electric field enhancement due to the excitation of the plasmonic modes.

The ac Stark effect is a well-known, well-established effect associated with the displacement of the atomic energy levels in the presence of an electromagnetic (e.m.) field. As the origin of the e.m. field is irrelevant, a self-induced ac Stark effect should be present in a laser. However, not only has this effect never been reported but it is not included in any laser model. Here, we show that a self-induced ac Stark shift does exist in the theoretical description of a two-level laser, provided that the reduced equations are derived not from the rotating-wave approximation, but from the full density matrix formulation. Interesting fundamental consequences are discussed and quantitative estimates of the self-induced frequency shift resulting from the laser field’s ac Stark shift are obtained for a variety of lasers. We find that the effect is generally small but (at least in some cases) measurable and that the transfer of laser amplitude noise into frequency noise may play a role in future, ultrahigh-precision metrological applications.

The paper of Hsieh, Luo, and Brun (HLB) [Phys. Rev. A 78, 042306 (2008)] contains several issues with the capacity theorem presented there, one of which is the suggestion that a sender and receiver can achieve entanglement-assisted classical capacity without any entanglement at all, and another of which is a violation of the Holevo bound. There is also an issue with the converse proof of the capacity theorem. In this comment, I point out these issues and provide revisions of the capacity theorem and the converse proof.

The possibility of making precise predictions for the Casimir force is essential for the theoretical interpretation of current precision experiments on the thermal Casimir effect with metallic plates, especially for submicron separations. For this purpose it is necessary to estimate very accurately the dielectric function of a conductor along the imaginary frequency axis. This task is complicated in the case of ohmic conductors because optical data do not usually extend to sufficiently low frequencies to permit an accurate evaluation of the standard Kramers-Kronig integral used to compute $\epsilon (i\xi )$. By making important improvements to the results of a previous paper by the author, it is shown that this difficulty can be resolved by considering suitable weighted dispersion relations, which strongly suppress the contribution of low frequencies. The weighted dispersion formulas presented in this paper permit us to estimate accurately the dielectric function of ohmic conductors for imaginary frequencies, on the basis of optical data extending from the IR to the UV, with no need for uncontrolled data extrapolations toward zero frequency that are necessary with standard Kramers-Kronig relations. Applications to several sets of data for gold films are presented to demonstrate the viability of the dispersion formulas presented in this paper.

Ontological theories of quantum mechanics provide a realistic description of single systems by means of well-defined quantities conditioning the measurement outcomes. In order to be complete, they should also fulfill the minimal condition of macroscopic realism. Under the assumption of outcome determinism and for Hilbert space dimension greater than 2, they were all proved to be contextual for projective measurements. In recent years a generalized concept of noncontextuality was introduced that applies also to the case of outcome indeterminism and unsharp measurements. It was pointed out that the Beltrametti-Bugajski model is an example of measurement noncontextual indeterminist theory. Here we provide a simple proof that this model is the only one with such a feature for projective measurements and Hilbert space dimension greater than 2. In other words, there is no extension of quantum theory providing more accurate predictions of outcomes and simultaneously preserving the minimal labeling of events through projective operators. As a corollary, noncontextuality for projective measurements implies noncontextuality for unsharp measurements. By noting that the condition of macroscopic realism requires an extension of quantum theory, unless a breaking of unitarity is invoked, we arrive at the conclusion that the only way to solve the measurement problem in the framework of an ontological theory is by relaxing the hypothesis of measurement noncontextuality in its generalized sense.

We use the “modes of the universe” approach to study a cavity-mediated two-photon logical gate recently proposed by Koshino, Ishizaka, and Nakamura. We clarify the relationship between the more commonly used input-output formalism and that of Koshino et al. and show that some elements of this gate had been anticipated by other authors. We conclude that their proposed gate can work both in the good and bad cavity limits, provided only that the pulses are long enough. Our formalism allows us to estimate analytically the size of the various error terms and to follow the spectral evolution of the field+cavity system in the course of the interaction.

We introduce a connection between entanglement induced by interaction and geometric phases acquired by a composite quantum spin system. We begin by analyzing the evaluation of cyclic (Aharonov-Anandan) and noncyclic (Mukunda-Simon) geometric phases for general spin chains evolving in the presence of time-independent magnetic fields. Then, by considering Heisenberg chains, we show that the interaction geometric phase, namely, the total geometric phase with subtraction of free spin contributions, is directly related to the global (Meyer-Wallach) entanglement exhibited by an initially separable state during its evolution in Hilbert space. This is analytically shown for $N=2$ spins and numerically illustrated for larger chains. This relationship promotes the interaction geometric phase to an indicator of global entanglement in the system, which may constitute a useful tool for quantum tasks based on entanglement as a resource to their performance.

We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semilocal Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term “CV graph state” currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the “closest” CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CV one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.

Bound information, a cryptographic classical analog of bound entanglement, is defined as classical secret correlations from which no secret key can be extracted. Its existence was conjectured and shown in a multipartite case. In this work, we provide an example of bound information in a four-partite scenario. Later, using this example, we prove that bound information can be superactivated and moreover unlockable in a finite-copy scenario. We also show that bound entangled states (bound information) can be used to distribute multipartite pure-state entanglements (secret keys).

We generalize the quantal density-functional theory (QDFT) of electrons in the presence of an external electrostatic field $\mathcal{E}(\mathbf{r})=-\nabla v(\mathbf{r})$ to include an external magnetostatic field $\mathbf{B}(\mathbf{r})=\nabla \times \mathbf{A}(\mathbf{r})$, where $\{v(\mathbf{r}),\mathbf{A}(\mathbf{r})\}$ are the respective scalar and vector potentials. The generalized QDFT, valid for nondegenerate ground and excited states, is the mapping from the interacting system of electrons to a model of noninteracting fermions with the same density $\rho (\mathbf{r})$ and physical current density $\mathbf{j}(\mathbf{r})$, and from which the total energy can be obtained. The properties $\{\rho (\mathbf{r}),\mathbf{j}(\mathbf{r})\}$ constitute the basic quantum-mechanical variables because, as proved previously, for a nondegenerate ground state they uniquely determine the potentials $\{v(\mathbf{r}),\mathbf{A}(\mathbf{r})\}$. The mapping to the noninteracting system is arbitrary in that the model fermions may be either in their ground or excited state. The theory is explicated by application to a ground state of the exactly solvable (two-dimensional) Hooke’s atom in a magnetic field, with the mapping being to a model system also in its ground state. The majority of properties of the model are obtained in closed analytical or semianalytical form. A comparison with the corresponding mapping from a ground state of the (three-dimensional) Hooke’s atom in the absence of a magnetic field is also made.

The dynamics of an interface in a two-component Bose-Einstein condensate driven by a spatially uniform time-dependent force is studied. Starting from the Gross-Pitaevskii Lagrangian, the dispersion relation for linear waves and instabilities at the interface is derived by means of a variational approach. A number of diverse dynamical effects for different types of driving force is demonstrated, which includes the Rayleigh-Taylor instability for a constant force, the Richtmyer-Meshkov instability for a pulse force, dynamic stabilization of the Rayleigh-Taylor instability and onset of the parametric instability for an oscillating force. Gaussian Markovian and non-Markovian stochastic forces are also considered. It is found that the Markovian stochastic force does not produce any average effect on the dynamics of the interface, while the non-Markovian force leads to exponential perturbation growth.

It is shown numerically that Bose-Einstein condensates in optical lattices may be localized as self-induced waveguides and that these waveguides may take complex forms, including bends and X junctions. The waveguides are found to support continuous condensate flow, even around multiple right-angle bends. It is demonstrated that pulsed matter-wave transport may also occur along single-site waveguides in the form of solitons and that these solitons may propagate around bends and collide without change of shape or dependence on phase. A scheme based on single-site addressability techniques and the Kibble-Zurek mechanism is proposed for observing these effects.

This paper concerns the theoretical, numerical, and experimental study of the second-harmonic-generation (SHG) process under conditions of phase and group-velocity mismatch and aims to demonstrate the dimensionality transition of the SHG process caused by the change of the fundamental wave diameter. We show that SHG from a narrow fundamental beam leads to the spontaneous self-phase-matching process with, in addition, the appearance of angular dispersion for the off-axis frequency components generated. The angular dispersion sustains the formation of the short X pulse in the second harmonic (SH) and is recognized as three-dimensional (3D) dynamics. On the contrary, the large-diameter fundamental beam reduces the number of the degrees of freedom, does not allow the generation of the angular dispersion, and maintains the so-called one-dimensional (1D) SHG dynamics, where the self-phase-matching appears just for axial components and is accompanied by the shrinking of the SH temporal bandwidth, and sustains a long SH pulse formation. The transition from long SH pulse generation typical of the 1D dynamics to the short 3D X pulse is illustrated numerically and experimentally by changing the conditions from the self-defocusing to the self-focusing regime by simply tuning the phase mismatch. The numerical and experimental verification of the analytical results are also presented.

An optical realization of the tunneling dynamics of two interacting bosons in a double-well potential, based on light transport in a four-core microstructured fiber, is proposed. The optical setting enables one to visualize, in a purely classical system, the entire crossover from Rabi oscillations to correlated pair tunneling and to tunneling of a fragmented pair in the fermionization limit.

The Faddeev random-phase approximation is a Green’s function technique that makes use of Faddeev equations to couple the motion of a single electron to the two-particle–one-hole and two-hole–one-particle excitations. This method goes beyond the frequently used third-order algebraic diagrammatic construction method: all diagrams involving the exchange of phonons in the particle-hole and particle-particle channel are retained, but the phonons are now described at the level of the random-phase approximation, which includes ground-state correlations, rather than at the Tamm-Dancoff approximation level, where ground-state correlations are excluded. Previously applied to atoms, this paper presents results for small molecules at equilibrium geometry.