We report observations of the dynamics of electromagnetically induced transparency (EIT) in a $\Lambda$ system when the ground states are Stark shifted. Interactions of this type exhibit large optical nonlinearities called Kerr nonlinearities, and have numerous applications. The EIT Kerr nonlinearity is relatively slow, which is a limiting factor that may make many potential applications impossible. Using rubidium atoms, we observe the dynamics of the EIT Kerr nonlinearity using a Mach-Zehnder interferometer to measure phase modulation of the EIT fields resulting from a pulsed signal beam Stark shifting the ground state energy levels. The rise times and transients agree well with theory.

The detailed nature of the correlated first-order density matrix for the model atoms in the title for arbitrary interparticle interaction $u\left(r_{12}\right)$ is studied. One representation with contracted information is first explored by constructing the momentum density $\rho \left(\mathbf{p}\right)$ in terms of the wave function of the relative motion, say ${\Psi }_R\left(r_{12}\right)$, which naturally depends on the choice of $u\left(r_{12}\right)$. For $u\left(r_{12}\right)=e^2∕r_{12}$, the so-called Hookean atom, and for the inverse square law $u\left(r_{12}\right)=\lambda ∕r_{12}^2$, plots are presented of the above density $\rho \left(\mathbf{p}\right)$ in momentum space. The correlated kinetic energy is recovered from averaging $p^2∕2m$, $m$ denoting the electron mass, with respect to $\rho \left(\mathbf{p}\right)$. The second method developed is in coordinate space and expands the density matrix $\gamma ({\mathbf{r}}_1,{\mathbf{r}}_2)$ in Legendre polynomials, using relative coordinate ${\mathbf{r}}_1-{\mathbf{r}}_2$, center-of-mass coordinate $({\mathbf{r}}_1+{\mathbf{r}}_2)∕2$ and the angle, $\theta$ say, between these two vectors. For the Moshinsky atom in which $u\left(r_{12}\right)=\frac{1}{2}k{r}_{12}^2$ only the $s$ term $(l=0)$ contributes to the Legendre polynomial expansion. The specific example we present of the inverse square law model is shown to be characterized by the low-order terms $(s+d)$ of the Legendre expansion. The Wigner function is finally calculated analytically for both Moshinsky and inverse square law models.

Differential cross sections for elastic electron scattering in xenon have been measured at the energies of 5, 7.9, and $10\mathrm{eV}$ over the scattering angle range from $30°$ to $180°$. For the measurements in the backward-angle scattering range the magnetic angle-changing technique has been employed. The differential cross sections obtained have been integrated to yield the elastic integral and momentum transfer cross sections. A detailed comparison of the present differential and integral cross sections is made with the existing experimental data and the results of various theoretical calculations. This comparison indicates that the theoretical results achieve a better overall agreement with the experimental cross sections in the backward scattering region than for the case of argon.

In contrast to the long-wavelength regime, x-ray nonlinear optical processes are characterized in general by sequential single-photon single-electron interactions. Despite this fact, the sequential absorption of multiple x-ray photons depends on the statistical properties of the radiation field. Treating the x rays generated by a self-amplified spontaneous emission free-electron laser as fully chaotic, a quantum-mechanical analysis of inner-shell two-photon absorption is performed. It is demonstrated that double-core-hole formation via x-ray two-photon absorption is enhanced by chaotic photon statistics. Numerical calculations using rate equations illustrate the impact of field chaoticity on x-ray nonlinear ionization of helium and neon for photon energies near $1\mathrm{keV}$. In the case of neon, processes are discussed that involve up to seven photons. Assuming an x-ray coherence time of $2.6\mathrm{fs}$, double-core-hole formation in neon is found to be statistically enhanced by about 30% at an intensity of ${10}^{16}\mathrm{W}∕{\mathrm{cm}}^2$.

In the framework of the state-specific expansion approach, we have solved nonperturbatively the time-dependent Schrödinger equation for systems involving the time-dependent excitation of nonstationary states by hypershort one or two electromagnetic pulses. The related problems concern the quantitative determination of the consequences of strong electron correlation in excited atomic states of the discrete or of the continuous spectrum. As prototypical applications we chose the time-resolved coherent excitation and decay of the $2s$-hole $1s^{2}2s2p^{6}3s^{2}3p{}^{1,3}P^0$ Auger states of aluminum, where dominant channels representing one- as well as two-electron continua are taken into account, and the preparation of nonstationary states and the subsequent electron correlation beats in Al and in ${\mathrm{N}}^{3+}$. Calculations for the problem of coherent inner-hole ionization and Auger decay in Al account for the effect of interference coming from the presence of the channel of direct two-electron ionization. The result is that for the ${\mathrm{Al}}^{+}{}^{1}P^0$ channel the Auger electron distribution is asymmetric. On the contrary, for the ${\mathrm{Al}}^{+}{}^{3}P^0$ channel the contribution of the direct two-electron ionization is weak and the corresponding Auger distribution is essentially symmetric. The intensities used were weak, so as to avoid shifts and to render high order processes beyond those in resonance or near-resonance essentially negligible. As a result, the transition probabilities are very small, a result that ought to guide experimental work. For example, for intensity $8.75\times {10}^{11}\mathrm{W}∕{\mathrm{cm}}^2$ the percentage of initial state population that ionizes is 0.02%. In spite of the overall reasonable approximations and size reductions, for the Al problem the system of coupled integrodifferential equations that had to be solved contains more than 300,000 basis wave functions.

We consider the generation of single photons on demand by pumping an emitter which is enclosed within a spherical distributed dielectric resonator, and then letting it emit spontaneously. The three-dimensional confinement in space of the electromagnetic field gives rise to deep dips and high peaks in the spectral profile of the density of states. The dips can be made use of to store the excitation energy and the peaks to narrow the time window during which a photon is emitted. The feasibility of the proposed scheme is discussed.

We present a multimode treatment of the optical parametric oscillator, which is valid for both pulsed and continuous-wave pump fields. The two-time correlation functions of the output field are derived, and we apply the theory to analyze a scheme for heralded production of nonclassical field states that may be subsequently stored in an atomic quantum memory.

We report an experimental discovery of deviations from the known regularities in collisional excitation transfer processes for metal atoms. The collisional excitation transfer with excited screened energy levels of thulium and dysprosium atoms is studied. The selecting role of the screening 6s shell in collisional excitation transfer is shown.

It has been shown that whispering gallery modes can be used to obtain a combination of modal and geometrical quasi-phase-matching in second-harmonic generation. This could be achieved in isotropic, nonferroelectric, strongly dispersive and highly nonlinear materials such as III-V semiconductors. Unfortunately the poor overlap between the second-harmonic field and second order nonlinear polarization limits the conversion efficiency. In this paper we show that by engineering the refractive index it is possible to increase field overlap and to enhance effective second order nonlinear polarization of semiconductor microdisks.

We consider the influence of the inclusion of interatomic interactions on the $\delta$-kicked accelerator model. Our analysis concerns in particular quantum accelerator modes, namely quantum ballistic transport near quantal resonances. The atomic interaction is modeled by a Gross-Pitaevskii cubic nonlinearity, and we address both attractive (focusing) and repulsive (defocusing) cases. The most remarkable effect is enhancement or damping of the accelerator modes, depending on the sign of the nonlinear parameter. We provide arguments showing that the effect persists beyond mean-field description, and lies within the experimentally accessible parameter range.

By utilizing a fiber-based indistinguishable photon-pair source in the $1.55\mu \mathrm{m}$ telecommunications band [J. Chen et al., Opt. Lett. 31, 2798 (2006)], we present the first, to the best of our knowledge, deterministic quantum splitter based on the principle of time-reversed Hong-Ou-Mandel quantum interference. The deterministically separated identical photons’ indistinguishability is then verified by using a conventional Hong-Ou-Mandel quantum interference, which exhibits a near-unity dip visibility of $94\pm 1\%$, making this quantum splitter useful for various quantum information processing applications.

We study control of electron-nuclear spin dynamics at magnetic field strengths where the Larmor frequency of the nucleus is comparable to the hyperfine coupling strength. The quantization axis for the nuclear spin differs from the static $B_0$ field direction and depends on the state of the electron spin. The quantization axis can be switched by flipping the state of electron spin, allowing for universal control of nuclear spin states. We show that by performing a sequence of flips (each followed by a suitable delay), we can perform any desired rotation of the nuclear spin, which can also be conditioned on the state of the electron spin. These operations, combined with electron spin rotations, can be used to synthesize any unitary transformation of the coupled electron-nuclear spin system. We discuss how these methods can be used for design of experiments for transfer of polarization from the electron to the nuclear spins.

On the premises that total correlations in a bipartite quantum state are measured by the quantum mutual information, and that separation of total correlations into quantum and classical parts satisfies an intuitive dominance relation, we examine to what extent various entropic entanglement measures, such as the distillable entanglement, the relative entropy entanglement, the squashed entanglement, the entanglement cost, and the entanglement of formation, can be regarded as consistent measures of quantum correlations. We illustrate that the entanglement of formation often overestimates quantum correlations and thus is too big to be a genuine measure of quantum correlations. This indicates that the entanglement of formation does not quantify the quantum correlations intrinsic to a quantum state, but rather characterizes the pure entanglement needed to build the quantum state via local operations and classical communication. Furthermore, it has the consequence that, if the additive conjecture for the entanglement of formation is true (as is widely believed), then the entanglement cost, which is an operationally defined measure of entanglement with significant physical meaning, cannot be a consistent measure of quantum correlations in the sense that it may exceed total correlations. Alternatively, if the entanglement cost is dominated by total correlations, as our intuition suggests, then we can immediately disprove the additive conjecture. Both scenarios have their counterintuitive and appealing aspects, and a natural challenge arising in this context is to prove or disprove that the entanglement cost is dominated by the quantum mutual information.

Bit commitment protocols whose security is based on the laws of quantum mechanics alone are generally held to be impossible. We give a strengthened and explicit proof of this result. We extend its scope to a much larger variety of protocols, which may have an arbitrary number of rounds, in which both classical and quantum information is exchanged, and which may include aborts and resets. Moreover, we do not consider the receiver to be bound to a fixed “honest” strategy, so that “anonymous state protocols,” which were recently suggested as a possible way to beat the known no-go results, are also covered. We show that any concealing protocol allows the sender to find a cheating strategy, which is universal in the sense that it works against any strategy of the receiver. Moreover, if the concealing property holds only approximately, the cheat goes undetected with a high probability, which we explicitly estimate. The proof uses an explicit formalization of general two-party protocols, which is applicable to more general situations, and an estimate about the continuity of the Stinespring dilation of a general quantum channel. The result also provides a natural characterization of protocols that fall outside the standard setting of unlimited available technology and thus may allow secure bit commitment. We present such a protocol whose security, perhaps surprisingly, relies on decoherence in the receiver’s laboratory.

We investigate the possibility of distinguishing a set of mutually orthogonal multipartite quantum states by local operations and classical communication (LOCC). We connect this problem with generators of SU($\mathit{N}$) and present a condition that is necessary for a set of orthogonal states to be locally distinguishable. We show that even in multipartite cases there exists a systematic way to check whether the presented condition is satisfied for a given set of orthogonal states. Based on the proposed checking method, we find that LOCC cannot distinguish three mutually orthogonal states in which two of them are Greenberger-Horne-Zeilinger-like states.

The ionization dynamics of $\mathrm{H}_2{}^{+}$ in an intense xuv laser pulse is studied beyond the dipole approximation in fields of linear and circular polarization. Our theoretical work shows distinct signatures of new ionization mechanisms and subsequent dynamics. Both low- and high-energy electrons emerge from the interaction to yield a characteristic and universal multilobe structure in the angular distributions which is uniquely linked to the initial molecular orientation. Each lobe is associated with its own characteristic electron dynamics. The emission spectra reveal processes that can be associated with single-center scattering, but show also clear evidence of two-center interference dynamics that can be explained by a simple two-center interference-diffraction model capturing the symmetry differences between $1{\sigma }_g$ and $1{\sigma }_u$ initial states.

The present investigation is concerned with the study of pulsed second-harmonic generation under conditions of phase and group velocity mismatch, and generally low conversion efficiencies and pump intensities. In positive-index, nonmetallic materials, we generally find qualitative agreement with previous reports regarding the presence of a double-peaked second harmonic signal, which comprises a pulse that walks off and propagates at the nominal group velocity one expects at the second-harmonic frequency, and a second pulse that is “captured” and propagates under the pump pulse. We find that the origin of the double-peaked structure resides in a phase-locking mechanism that characterizes not only second-harmonic generation, but also ${\chi }^{\left(3\right)}$ processes and third-harmonic generation. The phase-locking mechanism that we describe occurs for arbitrarily small pump intensities, and so it is not a soliton effect, which usually relies on a threshold mechanism, although multicolor solitons display similar phase locking characteristics. Thus, in second harmonic generation a phase-matched component is always generated, even under conditions of material phase mismatch: This component is anomalous, because the material does not allow energy exchange between the pump and the second-harmonic beam. On the other hand, if the material is phase matched, phase locking and phase matching are indistinguishable, and the conversion process becomes efficient. We also report a similar phase-locking phenomenon in negative index materials. A spectral analysis of the pump and the generated signals reveals that the phase-locking phenomenon causes the forward moving, phase-locked second-harmonic pulse to experience the same negative index as the pump pulse, even though the index of refraction at the second-harmonic frequency is positive. Our analysis further shows that the reflected second-harmonic pulse generated at the interface and the forward-moving, phase-locked pulse appear to be part of the same pulse initially generated at the surface, part of which is immediately back-reflected, while the rest becomes trapped and dragged along by the pump pulse. These pulses thus constitute twin pulses generated at the interface, having the same negative wave vector, but propagating in opposite directions. Almost any break of the longitudinal symmetry, even an exceedingly small ${\chi }^{\left(2\right)}$ discontinuity, releases the trapped pulse which then propagates in the backward direction. These dynamics are indicative of very rich and intricate interactions that characterize ultrashort pulse propagation phenomena.

We investigate the possibility to perform quantum nondemolition measurements of the collective alignment of an atomic ensemble in the case of a $F\ge 1$ spin. We compare the case of purely vectorial and purely tensorial Hamiltonians and show how to achieve conditional squeezing or entanglement of atomic alignment components.

We present a concrete picture of spoof surface plasmons (SSPs) combined with cavity resonance to clarify the basic mechanism underlying extraordinary light transmission through metal films with subwavelength slits or holes. This picture may indicate a general mechanism of metallic nanostructure optics: When light is incident on a nonplanar conducting surface, the free electrons cannot move homogeneously in response to the incident electric field, i.e., their movement can be impeded at the rough parts, forming inhomogeneous charge distributions. The oscillating charges and dipoles then emit photons (similar to Thomson scattering of x rays by oscillating electrons), and the interference between the photons may give rise to anomalous transmission, reflection, or scattering.

In a recent paper [Z. J. Zhang and Z. X. Man, Phys. Rev. A 72, 022303 (2005)], a multiparty quantum secret sharing protocol based on entanglement swapping was presented. However, as we show, this protocol is insecure in the sense that an unauthorized agent group can recover the secret from the dealer. Hence we propose an improved version of this protocol which can stand against this kind of attack.