We propose a method for straightforward characterization of the temporal shape of femtosecond pulses in the extreme-ultraviolet and soft x-ray spectral region. The approach is based on the presence of a significant linear frequency chirp in the pulse. This allows us to establish an homothetic relation between the pulse spectrum and its temporal profile. The theoretical approach is reminiscent of the one employed by Fraunhofer for describing far-field diffraction. As an application, we consider the case of a seeded free-electron laser (FEL). The theory is successfully benchmarked with numerical simulations and with experimental data collected on the FERMI@Elettra FEL. The proposed method provides FEL users with an online, shot-to-shot spectrotemporal diagnostic for time-resolved experiments.

Refractive index enhancement accompanied by vanishing absorption in a four-level atomic system interacting with two control and two probe fields in a regime of four-wave mixing (FWM) has been predicted and studied in the present work. We analyzed the maximal index enhancement in the four-level FWM system and gave index estimates for a real atomic gas of ${}^{40}$K, taking into account its multilevel structure and collisional and Doppler broadenings at large atomic densities. We also discussed how vanishing absorption with no nearby amplification can be realized in a two species system, consisting of a four-level FWM and a two-level system, where the latter provides additional absorption for one of the probe fields. We numerically estimated the index change in a system composed of ${}^{40}$K and ${}^{39}$K gases.

Statistical mechanics of two coupled vector fields is studied in the tight-binding model that describes propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. The energy and power conservation laws enable the formulation of the equilibrium properties of the polarization state in terms of the Gibbs measure with positive temperature. The transition line $T=\infty$ is established beyond which the discrete vector solitons are created. Also in the limit of the large nonlinearity an analytical expression for the distribution of Stokes parameters is obtained, which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity. The evolution of the system to the final equilibrium state is shown to pass through the intermediate stage when the energy exchange between the waveguides is still negligible. The distribution of the Stokes parameters in this regime has a complex multimodal structure strongly dependent on the nonlinear coupling coefficients and the initial conditions.

An ideal phase-preserving linear amplifier is a deterministic device that adds to an input signal the minimal amount of noise consistent with the constraints imposed by quantum mechanics. A noiseless linear amplifier takes an input coherent state to an amplified coherent state, but only works part of the time. Such a device is actually better than noiseless, since the output has less noise than the amplified noise of the input coherent state; for this reason we refer to such devices as immaculate. Here we bound the working probabilities of probabilistic and approximate immaculate amplifiers and construct theoretical models that achieve some of these bounds. Our chief conclusions are the following: (i) The working probability of any phase-insensitive immaculate amplifier is very small in the phase-plane region where the device works with high fidelity; (ii) phase-sensitive immaculate amplifiers that work only on coherent states sparsely distributed on a phase-plane circle centered at the origin can have a reasonably high working probability.

In contrast to the free-space evolution of an atom governed by a multimode interaction with the surrounding electromagnetic vacuum, the evolution of a cavity-QED system can be characterized by just three parameters: (i) atom-cavity coupling strength $g$, (ii) cavity relaxation rate $\kappa$, and (iii) atomic decay rate into the noncavity modes $\gamma$. In the case of an atom inserted into a planar resonator with an input beam coupled from the outside, it has been shown by Koshino [Phys. Rev. A 73, 053814 (2006)] that these three parameters are determined not only by the atom and cavity characteristics, but also by the spatial distribution of the input pulse. By an ab initio treatment, we generalize the framework of Koshino and determine the cavity-QED parameters of a coupled system of atom, planar (leaky) resonator, and input single-photon pulse as functions of the lateral profile of the pulse and the length of resonator. We confirm that the atomic decay rate can be suppressed by tailoring appropriately the lateral profile of the pulse. Such an active suppression of atomic decay opens an attractive route towards an efficient quantum memory for long-term storage of an atomic qubit inside a planar resonator.

The collective nature of light interactions with atomic and nuclear ensembles yields the fascinating phenomena of superradiance and radiation trapping. We study the interaction of $\gamma$ rays with a coherently vibrating periodic array of two-level nuclei. Such nuclear motion can be generated, e.g., in ionic crystals illuminated by a strong driving optical laser field. We find that deflection of the incident $\gamma$ beam into the Bragg angle can be switched on and off by nuclear vibrations on a superradiant time scale determined by the collective nuclear frequency ${\Omega }_a$, which is of the order of terahertz. Namely, if the incident $\gamma$ wave is detuned from the nuclear transition by frequency $\Delta \gg {\Omega }_a$ it passes through the static nuclear array. However, if the nuclei vibrate with frequency $\Delta$ then parametric resonance can yield energy transfer into the Bragg deflected beam on the superradiant time scale, which can be used for fast control of $\gamma$ rays.

We present a scheme to strongly enhance the readout sensitivity of the squared displacement of a mobile scatterer placed in a Fabry-Pérot cavity. We investigate the largely unexplored regime of cavity electrodynamics in which a highly reflective element positioned between the end mirrors of a symmetric Fabry-Pérot resonator strongly modifies the cavity response function, such that two longitudinal modes with different spatial parity are brought close to frequency degeneracy and interfere in the cavity output field. In the case of a movable middle reflector we show that the interference in this generic “optical coalescence” phenomenon gives rise to an enhanced frequency shift of the peaks of the cavity transmission that can be exploited in optomechanics.

We study cooperative single-photon spontaneous emission from three multilevel atoms with one of them being excited for different atomic configurations in optical vector theory. The dynamic evolution is solved by finding the eigenvalues of a 3 × 3 matrix, and then the relevant decay rates and Lamb shifts are obtained analytically. It is shown that the symmetry of atomic configuration has a big influence on the super-radiance of the system. To obtain strong super-radiance requires not only the distances among the three atoms to be much shorter than the wavelength, but also to have symmetrical distribution. We also calculate the emission spectra and find that it normally has three peaks, but it has two peaks under the equilateral-triangle configuration.

We develop a classification of perfectly transmitting resonances occurring in effectively one-dimensional optical media which are decomposable into locally reflection symmetric parts. The local symmetries of the medium are shown to yield piecewise translation-invariant quantities, which are used to distinguish resonances with arbitrary field profile from resonances following the medium symmetries. Focusing on light scattering in aperiodic multilayer structures, we demonstrate this classification for representative setups, providing insight into the origin of perfect transmission. We further show how local symmetries can be utilized for the design of optical devices with perfect transmission at prescribed energies. Providing a link between resonant scattering and local symmetries of the underlying medium, the proposed approach may contribute to the understanding of optical response in complex systems.

It is known that quantum discord might experience a sudden transition in its dynamics when calculated for certain Bell-diagonal states (BDS) that are in interaction with their surroundings. We examine this phenomenon, known as the sudden change of quantum discord, considering the case of two qubits independently interacting with dephasing reservoirs. We first demonstrate that, for a class of initial states which can be chosen arbitrarily close to BDS, the transition is in fact not sudden, although it might numerically appear so if not studied carefully. Then, we provide an extension of this discussion covering the $\mathsf{X}$-shaped density matrices. Our findings suggest that the transition of quantum discord might be sudden only for an highly idealized zero-measure subset of states within the set of all possible initial conditions of two qubits.

It has been shown already that when the harmonic trap is opened (or closed) as a function of time while keeping the adiabatic parameter $\mu =[d\omega \left(t\right)/dt]/{\omega }^2\left(t\right)$ fixed, a sharp transition from an oscillatory to a monotonic exponential dynamics occurs at $\mu =2$ [Uzdin, Dalla Torre, Kosloff, and Moiseyev, Phys. Rev. A 88, 022505 (2013)]. Here we show that by using time-dependent linear coordinate transformation the time-dependent Schrödinger equation with Hermitian time-dependent Hamiltonian is transformed into a time-dependent Schrödinger equation with a time-independent harmonic oscillator with the dimensionless frequency of $\sqrt{1-{(\mu /2)}^2}$. At $\mu =2$ a transition to a non-Hermitian Hamiltonian is obtained as the potential well is transformed to a parabolic potential barrier. While in a harmonic trap noninteracting particles have classical periodic motions, they are pushed apart exponentially in time as the potential well is suddenly transformed into a parabolic potential barrier in the new variable representation.

We derive a mean-field model that is based on a two-component Pauli-like equation and incorporates quantum, spin, and relativistic effects up to second order in $1/c$. Using a Lagrangian approach, we obtain the self-consistent charge and current densities that act as sources in the Maxwell equations. A physical interpretation is provided for the second-order corrections to the sources. The Maxwell equations are also expanded to the same order. The resulting self-consistent model constitutes a suitable semirelativistic approximation to the full Dirac-Maxwell equations.

In the Bell scenario, any nonlocal correlation shared between two spatially separated parties can be modeled deterministically either by allowing communications between the two parties or by restricting their free will in choosing the measurement settings. Recently, the Bell scenario has been generalized into a “semiquantum” scenario where external quantum inputs are provided to the parties. We show that in the semiquantum scenario, entangled states produce correlations whose deterministic explanation is possible only if measurement independence is reduced. Thus in simulating quantum correlation the semiquantum scenario reveals a qualitative distinction between signaling and measurement dependence which is absent in the Bell scenario. We further show that such distinction is not observed in the “steering-game” scenario, a special case of the semiquantum scenario.

We investigate some basic scenarios in which a given set of bipartite quantum states may consistently arise as the set of reduced states of a global $N$-partite quantum state. Intuitively, we say that the multipartite state “joins” the underlying correlations. Determining whether, for a given set of states and a given joining structure, a compatible $N$-partite quantum state exists is known as the quantum marginal problem. We restrict to bipartite reduced states that belong to the paradigmatic classes of Werner and isotropic states in $d$ dimensions and focus on two specific versions of the quantum marginal problem which we find to be tractable. The first is Alice-Bob, Alice-Charlie joining, with both pairs being in a Werner or isotropic state. The second is $m$-$n$ sharability of a Werner state across $N$ subsystems, which may be seen as a variant of the $N$-representability problem to the case where subsystems are partitioned into two groupings of $m$ and $n$ parties, respectively. By exploiting the symmetry properties that each class of states enjoys, we determine necessary and sufficient conditions for three-party joinability and 1-$n$ sharability for arbitrary $d$. Our results explicitly show that although entanglement is required for sharing limitations to emerge, correlations beyond entanglement generally suffice to restrict joinability, and not all unentangled states necessarily obey the same limitations. The relationship between joinability and quantum cloning as well as implications for the joinability of arbitrary bipartite states are discussed.

Photon subtraction (PS), due to its feasibility in physical implementation, has been widely utilized in Gaussian entanglement distillation. However, in this paper, we will show that photon addition (PA) can be employed to provide an additional enhancement in both the quality of distilled entanglement and the success probability if the input state is a weak two-mode squeezed vacuum state. Moreover, compared with biside PS, the distillation probability gains a $O\left(\frac{1}{{\lambda }^2}\right)$ improvement, which increases rapidly when $\lambda \ll 1$. Our PA-based scheme is obtained first by single-photon injection and later by vacuum state projection. The performance of PA in the presence of both an approximated single photon and amplitude-damping noise has been analyzed. Our result sheds more light on the indispensable non-Gaussian ingredients in Gaussian-state distillation and could be of great use in developing more efficient distillation schemes. Finally, the sensitivity of the PA scheme to inefficient photon detection has also been investigated.

Recent ultrafast spectroscopy experiments have demonstrated the entanglement of chromophores in photosynthetic light harvesting. Here we apply the cumulant parts of reduced density matrices (RDMs) to measure the statistical dependence and entanglement between electronic quantum domains in light harvesting. Because the cumulant RDMs are invariant to one-electron unitary transformations, they provide a measure of electron correlation and entanglement that is independent of the orbital basis set. Specifically, we apply the cumulant to a three-chromophore subsystem of the Fenna-Matthews-Olson complex, which has been shown to exhibit similar entanglement as the full system. Time-dependent Frobenius norms of the cumulant $p$-RDMs for $2\le p\le 6$ reveal correlation and entanglement in groupings of $p$ chromophores. The results show that the entanglement of pairs of chromophores is significantly more important than the entanglement in higher groupings of the chromophores. Data from the model are generally consistent with recent findings from ultrafast spectroscopy. Beyond their application to light harvesting, the Frobenius norms of the cumulant RDMs provide a useful measure of statistical dependence, correlation, and entanglement between electronic quantum domains with applications to molecules and materials.

Laser pump-probe schemes are explored numerically from a molecular time-dependent Schrödinger equation for monitoring attosecond electron motion by high-order-harmonic generation (HHG) from a coherent superposition of electronic states. Varying the time delay between the probe and pump pulse on an attosecond time scale alters the HHG signal, leading to universal interference patterns. By using an extended three-step recollision model, we show that various regular interference patterns in the HHG spectra, including continuous harmonic frequency redshifts as a function of pump-probe delay, are related to interference between specific pairs of short or long quantum orbits. For small excited-state population (regime A), interferences are controlled by electron-tunneling times, whereas for equal populations (regime B), recollision time control dominates thus allowing for control of the HHG process by the pump-probe delay time and by electron-state populations. We show that each specific pattern is closely related to the interference between pairs of specific (short or long) quantum orbits originating from a specific electron bound state. One can generate a specific pattern by varying the populations in the coherent superposition, the laser intensity, wavelength, and ionization potential of the electronic states.

We compute spin diffusion in a dilute Fermi gas at arbitrary temperature, polarization, and strong interaction in the normal phase using kinetic theory. While the longitudinal spin diffusivity $D_{\parallel }$ depends weakly on polarization and diverges for small temperatures, the transverse spin diffusivity $D_{\perp }$ has a strong polarization dependence and approaches a finite value for $T\to 0$ in the Fermi liquid phase. For a 3D unitary Fermi gas at infinite scattering length, the diffusivities reach a minimum near the quantum limit of diffusion $\hslash /m$ in the quantum degenerate regime and are strongly suppressed by medium scattering, and we discuss the importance of the spin-rotation effect. In two dimensions, $D_{\perp }$ attains a minimum at strong coupling $-1\lesssim \ln \left(k_F{a}_{2D}\right)\lesssim 1$ and reaches $D_{\perp }\sim 0.2...0.3\hslash /m$ at large polarization. These values are consistent with recent measurements of two-dimensional ultracold atomic gases in the strong coupling regime.