We investigate the electromagnetic Casimir interactions of an object contained within an otherwise empty, perfectly conducting spherical shell. For a small object we present analytical calculations of the force, which is directed away from the center of the cavity, and the torque, which tends to align the object opposite to the preferred alignment outside the cavity. For a perfectly conducting sphere as the interior object, we compute the corrections to the proximity force approximation (PFA) numerically. In both cases the results for the interior configuration match smoothly onto those for the corresponding exterior configuration.

We report on a means to generate tunable ultrashort optical pulses. We demonstrate that dispersive waves generated by solitons within the small-core features of a photonic crystal fiber cladding can be used to obtain femtosecond pulses tunable over an octave-wide spectral range. The generation process is highly efficient and occurs at the relatively low laser powers available from a simple Ti:sapphire laser oscillator. The described phenomenon is general and will play an important role in other systems where solitons are known to exist.

Because of the fundamental importance of Bell’s theorem, a loophole-free demonstration of a violation of local realism (LR) is highly desirable. Here, we study violations of LR involving photon pairs. We quantify the experimental evidence against LR by using measures of statistical strength related to the Kullback-Leibler (KL) divergence, as suggested by van Dam et al. [W. van Dam, R. D. Gill, and P. D. Grunwald, IEEE Trans. Inf. Theory. 51, 2812 (2005)]. Specifically, we analyze a test of LR with entangled states created from two independent polarized photons passing through a polarizing beam splitter. We numerically study the detection efficiency required to achieve a specified statistical strength for the rejection of LR depending on whether photon counters or detectors are used. Based on our results, we find that a test of LR free of the detection loophole requires photon counters with efficiencies of at least $89.71\%$, or photon detectors with efficiencies of at least $91.11\%$. For comparison, we also perform this analysis with ideal unbalanced Bell states, which are known to allow rejection of LR with detector efficiencies above $2/3$.

We propose a scheme for an exact efficient transformation of a tensor product state of many identically prepared qubits into a state of a logarithmically small number of qubits. Using a quadratic number of elementary quantum gates we transform $N$ identically prepared qubits into a state, which is nontrivial only on the first $\lceil \log {}_2(N+1)\rceil$ qubits. This procedure might be useful for quantum memories, as only a small portion of the original qubits has to be stored. Another possible application is in communicating a direction encoded in a set of quantum states, as the compressed state provides a high-effective method for such an encoding.

The nature of the explicit dependence on the particle number $N$ and on the spin number $N$${}_s$ of the Lieb definition for the energy density functional is examined both in spin-independent and in spin-polarized density functional theory. It is pointed out that the nonuniqueness of the external magnetic field $B(\mathrm{r⃑})$ corresponding to a given pair of ground-state density $n(\mathrm{r⃑})$ and spin density $s(\mathrm{r⃑})$ in spin-polarized density functional theory implies the nonexistence of the total derivative of the SDFT Lieb functional $F_{N,N_s}^L[n,s]$ with respect to $N$${}_s$. By giving a suitable extension of $F_N^L[n]$ and $F_{N,N_s}^L[n,s]$ for $N\ne \int n(\mathrm{r⃑})d\mathrm{r⃑}$ and $N_s\ne \int s(\mathrm{r⃑})d\mathrm{r⃑}$, it is then shown that their derivatives with respect to $N$ and $N$${}_s$ are equal to the derivatives, with respect to $N$ and $N$${}_s$, of the total energies $E[N,v]$ and $E[N,N_s,v,B]$ minus the external-field energy components, respectively.

Using the $B$ ${}^3{\Pi }_u^{+}$ state of neutral ${\mathrm{I}}_2$ as an intermediate state, we populate an excited electronic state, designated as ($2,0$), of ${\mathrm{I}}_2^{\hspace{0.5em}2+}\hspace{0.5em}$in its bound region of internuclear separation with short laser pulses. Trapping of the molecules in the ($2,0$) state is deduced from the disappearance of the ($2,0$) dissociation signal when populated at large internuclear separation, and wavelength-dependent results rule out electron localization as an alternative explanation for this disappearance. The wavelength dependence also firmly establishes the $B$ state as the intermediate state. Moreover, simulation results are consistent with the experiments, which confirm the previously measured ($2,0$) potential curve. The ($2,0$) state correlates to the ${\mathrm{I}}^{2+}+{\mathrm{I}}^{0+}$ dissociation limit and has played an important role in strong field physics. It is also the lowest lying truly bound (not metastable) state of the dication. In addition, the potential curve of the ${\mathrm{I}}_2^{\hspace{0.5em}3+}$ ground-state manifold is measured. Finally, calculations show a general picture of the wavelength dependence for trapping molecules in potential wells using intermediate states.

A scheme based on (i) upcoming brilliant x-ray free-electron laser (FEL) sources, (ii) innovative energy and angular-dispersive large-area electron imagers, and (iii) the well-known photoelectron holography is elaborated that provides time-dependent three-dimensional structure determination of small to medium-sized molecules with Ångström spatial and femtosecond time resolution. Inducing molecular dynamics, wave-packet motion, dissociation, passage through conical intersections, or isomerization by a pump pulse this motion is visualized by the x-ray FEL probe pulse launching keV photoelectrons within a few femtoseconds from specific and well-defined sites, deep core levels of individual atoms, inside the molecule. On their way out, the photoelectrons are diffracted generating a hologram on the detector that encodes the molecular structure at the instant of photoionization, thus providing “femtosecond snapshot images of the molecule from within.” Detailed calculations in various approximations of increasing sophistication are presented and three-dimensional retrieval of the spatial structure of the molecule with Ångström spatial resolution is demonstrated. Due to the large photoabsorption cross sections the method extends x-ray-diffraction-based time-dependent structure investigations envisioned at FEL’s to new classes of samples that are not accessible by any other method. Among them are dilute samples in the gas phase such as aligned, oriented, or conformer-selected molecules, ultracold ensembles and/or molecular or cluster objects containing mainly light atoms that do not scatter x rays efficiently.

We calculate the emission times of the radiation in high-order harmonic generation using the Gabor transform of numerical data obtained from solving the time-dependent Schrödinger equation in one, two, and three dimensions. Both atomic and molecular systems, including nuclear motion, are investigated. Lewenstein model calculations are used to gauge the performance of the Gabor method. The resulting emission times are compared against the classical simple man’s model as well as against the more accurate quantum orbit model based on complex trajectories. The influence of the range of the binding potential (long or short) on the level of agreement is assessed. Our analysis reveals that the short-trajectory harmonics are emitted slightly earlier than predicted by the quantum orbit model. This partially explains recent experimental observations for atoms and molecules. Furthermore, we observe a distinct signature of two-center interference in the emission times for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$.

Resonant spontaneous bremsstrahlung by an electron scattered by a nucleus in the field of a pulsed light wave is theoretically investigated. The approximation is examined when the pulse width is considerably greater than the characteristic time of wave oscillations. The electron interaction with the Coulomb potential of a nucleus is considered in the Born approximation. An analytic expression for the resonant differential cross section of the investigated process was obtained for the range of moderately strong fields. The bremsstrahlung cross section contains a resonant peak. The resonant peak’s altitude and width are defined by the external pulsed wave properties. The resonant cross section is studied within the ranges of nonrelativistic, relativistic, and ultrarelativistic electron energies. It is demonstrated that the resonant cross section of spontaneous bremsstrahlung may be several orders of magnitude greater than the corresponding cross section in the absence of an external field. Results obtained may be experimentally verified, for example, by the scientific facilities at the SLAC National Accelerator Laboratory.

In a Stark decelerator, polar molecules are slowed down and focused by an inhomogeneous electric field which switches between two configurations. For the decelerator to work, it is essential that the molecules follow the changing electric field adiabatically. When the decelerator switches from one configuration to the other, the electric field changes in magnitude and direction, and this can cause molecules to change state. In places where the field is weak, the rotation of the electric field vector during the switch may be too rapid for the molecules to maintain their orientation relative to the field. Molecules that are at these places when the field switches may be lost from the decelerator as they are transferred into states that are not focused. We calculate the probability of nonadiabatic transitions as a function of position in the periodic decelerator structure and find that for the decelerated group of molecules the loss is typically small, while for the un-decelerated group of molecules the loss can be very high. This loss can be eliminated using a bias field to ensure that the electric field magnitude is always large enough. We demonstrate our findings by comparing the results of experiments and simulations for the Stark deceleration of LiH and CaF molecules. We present a simple method for calculating the transition probabilities which can easily be applied to other molecules of interest.

Turbulent scaling phenomena are studied in an ultracold Bose gas away from thermal equilibrium. Fixed points of the dynamical evolution are characterized in terms of universal scaling exponents of correlation functions. The scaling behavior is determined analytically in the framework of quantum field theory, using a nonperturbative approximation of the two-particle irreducible effective action. While perturbative Kolmogorov scaling is recovered at higher energies, scaling solutions with anomalously large exponents arise in the infrared regime of the turbulence spectrum. The extraordinary enhancement in the momentum dependence of long-range correlations could be experimentally accessible in dilute ultracold atomic gases. Such experiments have the potential to provide insight into dynamical phenomena directly relevant also in other present-day focus areas like heavy-ion collisions and early-universe cosmology.

We consider diffusion of a cold Fermi gas in the presence of a random optical speckle potential. The evolution of the initial atomic cloud in space and time is discussed. Analytical and numerical results are presented in various regimes. Diffusion of a Bose-Einstein condensate is also briefly discussed and similarity with the Fermi gas case is pointed out.

We study Stokes and anti-Stokes processes in cavity optomechanics in the regime of strong coupling. The Stokes and anti-Stokes signals exhibit prominently the normal-mode splitting. We report gain for the Stokes signal. We also report lifetime splitting when the pump power is less than the critical power for normal-mode splitting. The nonlinear Stokes processes provide a useful method for studying the strong-coupling regime of cavity optomechanics. We also investigate the correlations between the Stokes and the anti-Stokes photons produced spontaneously by the optomechanical system. At zero temperature, our nanomechanical system leads to the correlations between the spontaneously generated photons exhibiting photon antibunching and those violating the Cauchy-Schwartz inequality.

This article presents a unified kinetic formulation of partially coherent nonlinear optical waves propagating in a noninstantaneous response Kerr medium. We derive a kinetic equation that combines the weak Langmuir turbulence kinetic equation and a Vlasov-like equation within a general framework: It describes the evolution of the spectrum of a random field that exhibits a quasistationary statistics in the presence of a noninstantaneous nonlinear response. The kinetic equation sheds new light on the dynamics of partially coherent nonlinear waves and allows for a qualitative interpretation of the interplay between the noninstantaneous nonlinearity and the nonstationary statistics of the incoherent field. It is shown that the incoherent modulational instability of a random nonlinear wave can be suppressed by the noninstantaneous nonlinear response. Moreover, incoherent modulational instability can prevent the generation of spectral incoherent solitons.

We show that a deterministic value and measurement of the Purcell factor in a semiconductor microcavity can be obtained by using spontaneous Raman scattering as an internal source. In this case the emitter characteristics are entirely determined by the cavity design and do not depend on uncontrolled random factors, as it is usually the case when quantum dot emitters are used. We derive a theoretical expression for the Purcell factor of the cavity in the particular case of Raman scattering, in very good agreement with the experimental measurement.

We study the general problem of matter-laser interaction within the framework of nonrelativistic quantum electrodynamics, with particular emphasis on strong laser field effects. Consequently, we formulate a well-defined approximation leading in a straightforward manner toward the conventional semiclassical mode of description. Namely, we arrive naturally to two coupled equations of motion: (i) the Schrödinger equation which governs the quantum dynamics of an atomic system driven by classically described radiation field (composed of an incoming laser pulse plus radiation emitted from the atom), and (ii) the classical Maxwell wave equation which describes the emission of radiation from the mentioned atomic source. Employing the formalism of adiabatic Floquet theory, we derive a simple criterion of validity of the just described semiclassical approach. It shows that the semiclassical treatment is justified in most situations. On the other hand, it turns out that the semiclassical approximation breaks down completely in certain special but realistic cases, regardless of the fact that the incoming laser pulse contains a huge number of photons. Under such special circumstances, we anticipate new effects arising due to the quantized nature of the radiation field, to be observable, for example, in harmonic generation spectra. Our considerations are illustrated more explicitly using a simple model of a two-level atom strongly driven by a laser. The quantum dynamics of this model problem is resolved within the framework of quantum electrodynamics while adopting well-defined and physically justifiable approximations. As an outcome, analytic formulas are found serving as a quantitative criterion of (non)applicability of the semiclassical approach and demonstrating the breakdown of semiclassical theory under well-defined conditions. An illustrative numerical calculation is provided.

We propose an efficient method for controlled generation of field squeezing with cold atomic clouds trapped close to a superconducting transmission line resonator. It is shown that, based on the coherent strong magnetic coupling between the collective atomic spins and microwave fields in the transmission line resonator, two-mode or single-mode field squeezed states can be generated through coherent control on the dynamics of the system. The degree of squeezing and preparing time can be directly controlled through tuning the external classical fields. This protocol may offer a promising platform for implementing scalable on-chip quantum information processing with continuous variables.

A recent Brief Report [Phys. Rev. A 79, 035801 (2009)] investigates two figures of merit for heralded photon sources based on spontaneous parametric down-conversion with a continuous pump, namely, the time-averaged temporal coherence between the signal and idler beams and the time-averaged conditioned second-order degree of coherence for photons in the heralded arm. However, contrary to what is claimed, no one-arm second-order effect is actually measured.

We evaluate one-loop effects for QED${}_{4+1}$ compactified to ${\mathbf{R}}^4\times S^1$ in a nontrivial vacuum for the gauge field such that a nonvanishing magnetic flux is encircled along the extra dimension. We obtain the vacuum polarization tensor and evaluate the exact parity-breaking term, presenting the results from the point of view of the effective ($3+1$)-dimensional theory.