We investigate theoretically amplification of a high-order harmonic pulse in an active medium of x-ray laser. Using a model based on Maxwell-Bloch equations, which are modified to incorporate time-dependent gain and statistical character of spontaneous emission, the time-dependent nature of the interaction including coherent process is studied. The temporal shape of the output pulse is found to consist of three components: amplified spontaneous emission, coherent transient phase, and coherent decay. Based on this analysis, energy extraction and duration of the output pulse are discussed. The expectation regarding the properties such as radiation polarization, coherence, and divergence is also considered.

By using a powerful reductive perturbation technique, or a multiscale analysis, a generic Kadomtsev-Petviashvili evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in quadratic nonlinear media beyond the slowly varying envelope approximation is put forward. Direct numerical simulations show the formation, from adequately chosen few-cycle input pulses, of both stable line solitons (in the case of a quadratic medium with normal dispersion) and of stable lumps (for a quadratic medium with anomalous dispersion). Besides, a typical example of the decay of the perturbed unstable line soliton into stable lumps for a quadratic nonlinear medium with anomalous dispersion is also given.

We investigate cancellation of spatial aberrations induced by an object placed in a quantum coincidence interferometer with type-II parametric down conversion as a light source. We analyze in detail the physical mechanism by which the cancellation occurs and show that the aberration cancels only when the object resides in one particular plane within the apparatus. In addition, we show that for a special case of the apparatus it is possible to produce simultaneous cancellation of both even-order and odd-order aberrations in this plane.

Cavity solitons (CSs) are localized structures appearing as single intensity peaks in the homogeneous background of the field emitted by a nonlinear (micro) resonator driven by a coherent field (holding beam). By introducing a phase gradient in the holding beam, it is possible to induce CS drift. This motion is strongly influenced by the presence of defects in the device structure. We analyze numerically two situations that appeared in the experiments. In the first one, a structure is self-generated on the defect and a regular sequence of moving CS originates from it. We investigate the properties of this “tap” of CS as a function of the defect characteristics and of the parameters values. The second situation corresponds to the interaction between a moving CS and a defect, which plays a fundamental role in CS applications such as the delay line or the shift register.

Parametric down-conversion (PDC) is a technique of ubiquitous experimental significance in the production of nonclassical, photon-number-correlated twin beams. Standard theory of PDC as a two-mode squeezing process predicts and homodyne measurements observe a thermal photon number distribution per beam. Recent experiments have obtained conflicting distributions. In this article, we explain the observation by an a priori theoretical model solely based on directly accessible physical quantities. We compare our predictions with experimental data and find excellent agreement.

Inspired by the optical experimental scheme [Phys. Rev. Lett. 86, 369 (2001)], we propose and implement a NMR experiment to observe an Abelian geometric phase shift arising from the cyclic evolution of U(2)-invariant states. Such a phase shift geometrically refers to the Bargmann invariant in a four-dimensional SU(3)/U(2) parameter space, while the usual geometric phases arise in the evolution of U(1)-invariant states and is related to solid angles in a two-dimensional $\text{SU}\left(2\right)/\text{U}\left(1\right)\approx S^2$ parameter space (or Poincaré sphere). We present the experiment in a four-level system and investigate its topological invariance for different circuits. This may provide a realistic candidate to design complex geometric quantum circuits for future quantum computers.

The lifetime of the $7s6d$ ${{}^{1}D}_2$ state of atomic radium is determined to be $385\left(45\right)\mu \text{s}$ using cold ${}^{226}\text{R}\text{a}$ atoms prepared in a magneto-optical trap. The ${{}^{1}D}_2$ state is populated from the decay of the ${{}^{1}P}_1$ state which is excited by a pulse of 483 nm light. The decay of the ${{}^{1}D}_2$ state is observed by detecting delayed fluorescence at 714 nm from the last step in the decay sequence ${{}^{1}P}_1\text{−}{{}^{1}D}_2\text{−}{{}^{3}P}_1\text{−}{{}^{1}S}_0$. The measured lifetime is compared to a number of theoretical calculations. An improved value of the $7s7p$ ${{}^{1}P}_1$ level of $20715.598\left(6\right){\text{cm}}^{-1}$ is obtained.

Exchange interaction strongly influences the long-range behavior of localized electron orbitals and quantum tunneling amplitudes. In the Hartree-Fock approximation the exchange produces a power-law decay instead of the usual exponential decrease at large distances. To show that this effect is real (i.e., not a result of the approximation) we consider a simple model where different effects may be accurately analyzed. Applications include huge enhancement of inner electron ionization by a static electric field or laser field considered by Amusia (e-print arxiv:0904.4395).

On the basis of macroscopic quantum electrodynamics, a theory of Casimir forces in the presence of linearly amplifying bodies is presented which provides a consistent framework for studying the effect of, e.g., amplifying left-handed metamaterials on dispersion forces. It is shown that the force can be given in terms of the classical Green tensor and that it can be decomposed into a resonant component associated with emission processes and an off-resonant Lifshitz-type component. We explicitly demonstrate that our theory extends additive approaches beyond the dilute-gas limit.

We consider the problem of obtaining the entanglement witnesses for a given quantum system. We present a method to convert this problem to a standard convex optimization problem by defining a feasible region. Then we develop a generic two-step algorithm for this problem which can be applied to the entanglement detection of $N$-partite quantum system. This permits an organized construction of nonlinear and linear entanglement witnesses for a given quantum system. To demonstrate the capability of this approach, we apply our results to several three-qubit systems which in some cases lead to necessary and sufficient conditions for separability.

Quantum communication places stringent requirements on single-photon sources. Here we report a theoretical study of the cavity Purcell enhancement of two diamond point defects, the nickel-nitrogen (NE8) and silicon-vacancy (SiV) centers, for high-performance, near on-demand single-photon generation. By coupling the centers strongly to high-finesse optical photonic-band-gap cavities with modest quality factor $Q=O\left({10}^4\right)$ and small mode volume $V=O\left({\lambda }^3\right)$, these system can deliver picosecond single-photon pulses at their zero-phonon lines with probabilities of 0.954 (NE8) and 0.812 (SiV) under a realistic optical excitation scheme. The undesirable blinking effect due to transitions via metastable states can also be suppressed with $O\left({10}^{-4}\right)$ blinking probability. We analyze the application of these enhanced centers, including the previously studied cavity-enhanced nitrogen-vacancy (NV) center, to long-distance Bennett-Brassard 1984 protocol quantum key distribution (QKD) in fiber-based, open-air terrestrial and satellite-ground setups. In this comparative study, we show that they can deliver performance comparable with decoy state implementation with weak coherent sources, and are most suitable for open-air communication.

We prove a connection between Schmidt rank and weight of quadratic forms. This provides a new tool for the classification of graph states based on entanglement. Our main tool arises from a reformulation of previously known results concerning the weight of quadratic forms in terms of graph states properties. As a byproduct, we obtain a straightforward characterization of the weight of functions associated with pivot-minor of bipartite graphs.

The creation and detection of atomic polarization is examined theoretically through the study of basic optical-pumping mechanisms and absorption and fluorescence measurements and the dependence of these processes on the size of ground- and excited-state hyperfine splittings is determined. The consequences of this dependence are studied in more detail for the case of nonlinear magneto-optical rotation in the Faraday geometry (an effect requiring the creation and detection of rank-two polarization in the ground state) with alkali-metal atoms. Analytic formulas for the optical rotation signal under various experimental conditions are presented.

We study the behavior of an ultracold atomic gas of bosons in a bichromatic lattice, where the weaker lattice is used as a source of disorder. We numerically solve a discretized mean-field equation, which generalizes the one-dimensional Aubry-Andrè model for particles in a quasiperiodic potential by including the interaction between atoms. We compare the results for commensurate and incommensurate lattices. We investigate the role of the initial shape of the wave packet as well as the interplay between two competing effects of the interaction, namely, self-trapping and delocalization. Our calculations show that, if the condensate initially occupies a single lattice site, the dynamics of the interacting gas is dominated by self-trapping in a wide range of parameters even for weak interaction. Conversely, if the diffusion starts from a Gaussian wave packet, self-trapping is significantly suppressed and the destruction of localization by interaction is more easily observable.

We study the dynamics and thermalization of strongly correlated fermions in finite one-dimensional lattices after a quantum quench. Our calculations are performed using exact diagonalization. We focus on one- and two-body observables such as the momentum distribution function $\left[n\left(k\right)\right]$ and the density-density structure factor $\left[N\left(k\right)\right]$, respectively, and study the effects of approaching an integrable point. We show that while the relaxation dynamics and thermalization of $N\left(k\right)$ for fermions is very similar to the one of hardcore bosons, the behavior of $n\left(k\right)$ is distinctively different. The latter observable exhibits a slower relaxation dynamics in fermionic systems. We identify the origin of this behavior, which is related to the off-diagonal matrix elements of $n\left(k\right)$ in the basis of the eigenstates of the Hamiltonian. More generally, we find that thermalization occurs far away from integrability and that it breaks down as one approaches the integrable point.

The sensitivity of electron tunneling to the phase of an ionizing light field is shown to manifest itself in detectable features in the spectral and temporal evolution of intense few-cycle light pulses in an ionizing medium. An ultrafast buildup of electron density in the regime of tunneling ionization gives rise to a modulation of a few-cycle field wave form and enhances the short-wavelength part of its spectrum. In a low-pressure gas, the signatures of electron tunneling in the evolution of few-cycle pulses can be isolated from the effects related to atomic nonlinear susceptibilities, giving an access to attosecond electron tunneling dynamics.

We present a theory of the quantum vacuum radiation that is generated by a fast modulation of the vacuum Rabi frequency of a single two-level system strongly coupled to a single cavity mode. The dissipative dynamics of the Jaynes-Cummings model in the presence of antirotating-wave terms is described by a generalized master equation including non-Markovian terms. Peculiar spectral properties and significant extracavity quantum vacuum radiation output are predicted for state-of-the-art circuit cavity quantum electrodynamics systems with superconducting qubits.

We introduce quantum spin models whose ground states allow for sizable entanglement between distant spins. We discuss how spin models with global end-to-end entanglement realize quantum teleportation channels with optimal compromise between scalability and resilience to thermal decoherence and can be implemented straightforwardly in suitably engineered arrays of coupled optical cavities.

In this paper, we present progress on the study of the symmetric extension criterion for separability. First, we show that a perturbation of order $O\left(1/N\right)$ is sufficient and, in general, necessary to destroy the entanglement of any state admitting an $N$ Bose-symmetric extension. On the other hand, the minimum amount of local noise necessary to induce separability on states arising from $N$ Bose-symmetric extensions with positive partial transpose (PPT) decreases at least as fast as $O\left(1/N^2\right)$. From these results, we derive upper bounds on the time and space complexity of the weak membership problem of separability when attacked via algorithms that search for PPT-symmetric extensions. Finally, we show how to estimate the error we incur when we approximate the set of separable states by the set of (PPT) $N$-extendable quantum states in order to compute the maximum average fidelity in pure state estimation problems, the maximal output purity of quantum channels, and the geometric measure of entanglement.