Differential cross sections for elastic electron scattering from gaseous water are reported. The measurements are obtained using the relative flow method with He as the standard gas and a thin collimating aperture source of gas instead of a conventional needle source. Differential cross sections were measured at incident energies of 1, 2, 4, 6, 8, 10, 15, 20, 30, 50, and $100\mathrm{eV}$ for scattering angles ranging from 5° to 130° and integrated over angles to obtain integral cross sections. Corresponding calculations of the differential cross section are carried out using the Schwinger multichannel method, employing extensive basis sets and considering polarization and dipole-scattering effects. Whereas excellent qualitative agreement with past measurements of differential cross sections is observed, our measurements are found to be consistently in significant quantitative disagreement with these measurements. The present calculations, on the other hand, generally agree in magnitude with previous results.

Consider $N$ bosons in a finite box $\Lambda ={[0,L]}^3\subset {\mathbb{R}}^3$ interacting via a two-body non-negative soft potential $V=\lambda \tilde{V}$ with $\tilde{V}$ fixed and $\lambda >0$ small. We will take the limit $L,N\to \infty$ by keeping the density $\varrho =N∕L^3$ fixed and small. We construct a variational state, which gives an upper bound on the ground-state energy per particle $\epsilon$, $\epsilon ⩽4\pi \varrho a[1+(128∕15\sqrt{\pi }){\left(\varrho a^3\right)}^{1∕2}{S}_{\lambda }]+O\left({\varrho }^2\mid \ln \varrho \mid \right)$, as $\varrho \to 0$, with a constant satisfying $1⩽S_{\lambda }⩽1+C\lambda$. Here $a$ is the scattering length of $V$ and thus depends on $\lambda$. In comparison, the prediction by Lee and Yang [Phys. Rev. 105, 1119 (1957)] and Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957)] asserts that $S_{\lambda }=1$ independent of $\lambda$.

We study the dynamical behavior of dissipative solitons in an optical cavity filled with a Kerr medium when a localized beam is applied on top of the homogeneous pump. In particular, we report on the excitability regime that cavity solitons exhibit which is an emergent property since the system is not locally excitable. The resulting scenario differs in an important way from the case of a purely homogeneous pump and now two different excitable regimes, both class I, are shown. The whole scenario is presented and discussed, showing that it is organized by three codimension-2 points. Moreover, the localized beam can be used to control important features, such as the excitable threshold, improving the possibilities for the experimental observation of this phenomenon.

We theoretically and numerically study the effect of backscattering on rotating ring lasers by employing the Maxwell-Bloch equations. We show that frequency shifts due to the Sagnac effect incorporating the effect of backscattering can be observed without lock-in phenomenon, if the strength of backscattering originating in the bumps of the refractive index is larger than a certain value. It is also shown that the experimental results corresponding to the theoretical ones can actually be obtained by using a semiconductor fiber-optic ring laser gyroscope.

We theoretically study and compare the light-induced Fréedericksz transition and above-threshold reorientation in pure and dye-doped nematic liquid crystals embedded into periodic dielectric structures. The presence of optical defect modes is found to significantly alter the effective influence of dyes as compared to the standard case of liquid crystal films without periodic structure, which is due to the overall resonant absorption of the dye-doped liquid crystal layer. Both statics and dynamics are discussed. In particular, it is found that optical response time can be up to several orders of magnitude faster with pure liquid crystals than with dye-doped ones. Thermal effects caused by absorption of dyes are also investigated to gauge whether it may induce nematic-to-isotropic phase transition.

In view of recent papers on two-photon double ionization of helium, pertaining to a perceived anomaly in the behavior of the sequential process and its influence on the direct process, as well as the dependence of both on the laser pulse duration, we show that upon the proper formulation, the sequential is well defined and free of divergence, and that the dependence on pulse duration is considerably more intricate. We also argue that the apparent sharp rise of the cross section for the direct process, around $54.4\mathrm{eV}$, is due to the unintended inclusion of the sequential process, which in any case is not properly describable in terms of a single cross section.

Using a simple two-channel model, we show that the nuclear kinetic energy spectra for dissociation of $\mathrm{H}_2{}^{+}$ and $\mathrm{D}_2{}^{+}$ induced by an intense, femtosecond laser pulse can be made to match nearly quantitatively. This is accomplished with laser pulses of length $\tau$ for $\mathrm{H}_2{}^{+}$ and $\tau \sqrt{2}$ for $\mathrm{D}_2{}^{+}$ that are otherwise identical. The resemblance is best for short pulses and improves for long pulses when the averages necessary for comparison with experiment are included.

We compare the vibrational coherence induced by “$R$-dependent ionization,” also known as Lochfrass, and bond softening in strong laser fields through numerical simulations. We calculate the pulse-width and intensity dependence of the vibrational amplitude and average internuclear separation at different temperatures. We also present experimental results on the intensity dependence of the vibrational motion induced in the ground electronic state of ${\mathrm{I}}_2$, which agree with the calculations for Lochfrass. Finally, we compare trajectories of vibrational coherence from a thermal ensemble and a single state as a function of intensity in a phase diagram for the two schemes. We conclude that hot molecules produce stronger vibrational motion when excited by Lochfrass compared to bond softening and that Lochfrass can lead to vibrational cooling.

We study superradiant Rayleigh scattering from a Bose-Einstein condensate (BEC) in a parameter regime where pump depletion and the exchange of photons between the end-fire modes are important. Through experiments and simulations, we show that collective atom-light coupling leads to the self-organized formation of dynamic Bragg gratings within the sample. These gratings lead to an efficient backscattering of pump photons and optical resonator structures within the BEC.

We use a quantum nondemolition measurement to probe the collective pseudospin of an atomic ensemble in a high-finesse optical cavity. We analyze the backaction antisqueezing produced by the measurement process to show that our protocol could create conditional spin squeezing in the atomic ensemble.

We discuss the limits of the photon wave function (PWF) formalism, which is experiencing a revival these days as a result of new practical applications in photonics and quantum optics. We build a Dirac-like equation for the PWF written in a manifestly covariant form and show that, in the presence of charged matter fields, it reproduces the standard formulation of (classical) electrodynamics. This shows that attempts to construct a full quantum theory of interacting photons (mutually or interacting with matter) based on the so-called photon wave function approach can lead only to results already described by standard quantum electrodynamics (QED). The PWF formalism can then be used only to provide an easier description of some particular situations—for example, the propagation of free photons or photons propagating in a medium as described in Bialynicki-Birula [in Progress in Optics, edited by E. Wolf (Elsevier, Amsterdam, 1996), pp. 245–294] especially when the photon number remains fixed in time but not to replace QED in toto.

It is of high interest, in the context of adiabatic quantum computation, to better understand the complex dynamics of a quantum system subject to a time-dependent Hamiltonian, when driven across a quantum phase transition. We present here such a study in the Lipkin-Meshkov-Glick (LMG) model with one variable parameter. We first display numerical results on the dynamical evolution across the LMG quantum phase transition, which clearly shows a pronounced effect of the spectral avoided level crossings. We then derive a phenomenological (classical) transition model, which already shows some closeness to the numerical results. Finally, we show how a simplified quantum transition model can be built which strongly improve the classical approach, and shed light on the physical processes involved in the whole LMG quantum evolution. From our results, we argue that the commonly used description in term of Landau-Zener transitions is not appropriate for our model.

We introduce a perturbative approach to solving the time-dependent Schrödinger equation, named adiabatic perturbation theory (APT), whose zeroth-order term is the quantum adiabatic approximation. The small parameter in the power series expansion of the time-dependent wave function is the inverse of the time it takes to drive the system’s Hamiltonian from the initial to its final form. We review other standard perturbative and nonperturbative ways of going beyond the adiabatic approximation, extending and finding exact relations among them, and also compare the efficiency of those methods against the APT. Most importantly, we determine APT corrections to the Berry phase by use of the Aharonov-Anandan geometric phase. We then solve several time-dependent problems, allowing us to illustrate that the APT is the only perturbative method that gives the right corrections to the adiabatic approximation. Finally, we propose an experiment to measure the APT corrections to the Berry phase and show, for a particular spin-$1∕2$ problem, that to first order in APT the geometric phase should be two and a half times the (adiabatic) Berry phase.

Multiple ionization of ${\mathrm{C}}_{60}$ by ${\mathrm{Si}}^{q+}$ ions $(q=1–3)$ has been studied at incident energies of 0.5, 0.8, 2.0, and $6.0\mathrm{MeV}$ covering a velocity range of $v=0.85–2.93$ in atomic units. Fragment ions and secondary electrons were measured in coincidence with charge-selected outgoing projectile ions, enabling us to determine the charge state of prefragmented parent ions $\mathrm{C}_{60}{}^{r+}$. Charge state $\left(r\right)$ distributions correlated with the smallest fragment ions of $\mathrm{C}_m{}^{+}(m⩽3)$ were found to vary rather strongly depending on $v$ and $q$, whereas the $r$ distributions were less sensitive for medium sized ions of $m⩾4$. These results reflect fairly well the difference of the amount of inelastic energy deposition estimated from the local density approximation. Experimental $r$ distributions correlated with specific fragment ions $\mathrm{C}_m{}^{+}(m⩽5)$ were reproduced almost perfectly by our statistical energy deposition model. From our model calculations we also obtained the most probable values of the ionization energy associated with the production of individual fragment ions.

The irradiation of atoms by a strong, quasicontinuous IR laser field of frequency $\omega$ results in the emission of odd harmonics of $\omega$ (“IR harmonics”), by high-harmonic generation. It has been recently shown [A. Fleischer and N. Moiseyev, Phys. Rev. A 77, 010102(R) (2008)] that the addition of a weak XUV field of harmonic frequency $q\omega$ to the IR driver field leads to the appearance of a new set of higher-order harmonics (“XUV harmonics”) $q\pm 2K$ ($q,K$ integers) which were absent in the spectra in the presence of the IR field alone. Here we generalize these results by studying the generation of XUV harmonics upon the addition of an arbitrary high-frequency XUV field $\tilde{q}\omega$, with frequency not necessarily a harmonic of $\omega$, and amplitude ${\epsilon }_{\tilde{q}}^{\mathit{in}}$, which might be large. We have found that as the intensity of the XUV field increases, higher sets of XUV harmonics $\tilde{q}\pm 2K,2\tilde{q}\pm (2K-1),3\tilde{q}\pm 2K,\dots$. gradually appear, where each XUV harmonics set $n_{\tilde{q}}\tilde{q}\pm [2K-1+\mathrm{mod}(n_{\tilde{q}},2)]$ $(n_{\tilde{q}}=1,2,3,\dots )$ is ${\left(\frac{{\epsilon }_{\tilde{q}}^{\mathit{in}}}{{\tilde{q}}^2{\omega }^2}\right)}^{2n_{\tilde{q}}}$ times weaker than the set of IR harmonics. The mechanism responsible for the appearance of the XUV harmonics is analyzed analytically using a generalization of the semiclassical recollision (three-step) model of high-harmonic generation (HHG). It is shown that the emitted HHG radiation field can be written as a series of terms, with the zeroth-order term representing the three-step recollision mechanism in its most familiar context [P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993)] and giving rise to IR harmonics in the spectra. The higher-order terms, which are responsible for the appearance of the new sets of XUV harmonics in the spectra, are shown to originate from the polarization (ac-Stark oscillations) which is induced by the XUV field on the returning electronic wave packet in the recollision process. The XUV harmonics are formed by the same electron trajectories which form the IR harmonics and have the same emission times as the IR harmonics. Due to the small quiver amplitude of the ac-Stark oscillation, they are, however, much weaker than the IR harmonics. Nevertheless, this mechanism allows an extension of the cutoff in the harmonic generation spectra without the necessity of increasing the IR field intensity, as is verified numerically by a quantum-mechanical simulation of a Xe atom irradiated by a combination of IR and XUV classical fields.

We determine the energy density $\xi (3∕5)n{\epsilon }_F$ and the gradient correction $\lambda {\hslash }^2{(\mathbf{\nabla }n)}^2∕\left(8mn\right)$ of the extended Thomas-Fermi (ETF) density functional, where $n$ is the number density and ${\epsilon }_F$ is the Fermi energy, for a trapped two-component Fermi gas with infinite scattering length (unitary Fermi gas) on the basis of recent diffusion Monte Carlo (DMC) calculations [Phys. Rev. Lett. 99, 233201 (2007)]. In particular we find that $\xi =0.455$ and $\lambda =0.13$ give the best fit of the DMC data with an even number $N$ of particles. We also study the odd-even splitting $\gamma N^{1∕9}\hslash \omega$ of the ground-state energy for the unitary gas in a harmonic trap of frequency $\omega$ determining the constant $\gamma$. Finally we investigate the effect of the gradient term in the time-dependent ETF model by introducing generalized Galilei-invariant hydrodynamics equations.

We propose a general quantum theory of optical phase and instantaneous frequency in the time domain for slowly varying optical signals. Guided by classical estimation theory, we design homodyne phase-locked loops that enable quantum-limited measurements of temporal phase and instantaneous frequency. Standard and Heisenberg quantum limits to such measurements are then derived. For optical sensing applications, we propose multipass and Fabry-Pérot position and velocity sensors that take advantage of the signal-to-noise-ratio enhancement effect of wide-band angle modulation without requiring nonclassical light. We also generalize our theory to three spatial dimensions for nonrelativistic bosons and define a Hermitian fluid velocity operator, which provides a theoretical underpinning to the current-algebra approach of quantum hydrodynamics.

We discuss bandwidth enhancement of a cavity without reducing its maximum intensity buildup in a regime where the light propagation dynamics is crucial. The enhancement relies on a frequency-dependent phase compensation via negative dispersion provided by a coherently prepared atomic medium in the cavity. We analyze the spatiotemporal dynamics in such a white-light cavity with a full simulation of the field propagation. We find that the probe field dispersion is in addition changed by a coherent field which is generated within the medium via four-wave mixing. Counterintuitively, this in-medium dynamics leads to a further enhancement of the cavity bandwidth.

Two comparison theorems are established for discrete eigenvalues of the Klein-Gordon equation with an attractive central vector potential in $d⩾1$ dimensions. (I) If ${\psi }_1$ and ${\psi }_2$ are node-free ground states corresponding to positive energies $E_1⩾0$ and $E_2⩾0$, and $V_1\left(r\right)⩽V_2\left(r\right)⩽0$, then it follows that $E_1⩽E_2$. (II) If $V(r,a)$ depends on a parameter $a∊(a_1,a_2)$, $V(r,a)⩽0$, and $E\left(a\right)$ is any positive eigenvalue, then $\partial V∕\partial a⩾0\Rightarrow E^{\prime }\left(a\right)⩾0$ and $\partial V∕\partial a⩽0\Rightarrow E^{\prime }\left(a\right)⩽0$.

The relationship between efficient quantum gate synthesis and control theory has been a topic of recent interest in the quantum computing literature. Motivated by this work, we describe how the dynamic programming technique from optimal control may be used in principle to determine gate complexity and for the optimal synthesis of quantum circuits. We illustrate the dynamic programming methodology using a simple example on the Lie group SU(2).