We have completed a measurement of the $\left(6s^{2}6p^2\right){}^{3}P_0\to {}^{3}P_2$ 939 nm electric quadrupole ($E2$) transition amplitude in atomic lead. Using a Faraday rotation spectroscopy technique and a sensitive polarimeter, we have measured this very weak $E2$ transition, and determined its amplitude to be $\langle {}^{3}P_2\left|\right|Q\left|\right|{}^{3}P_0\rangle =8.91\left(9\right)$ a.u. We also present an ab initio theoretical calculation of this matrix element, determining its value to be 8.86(5) a.u., which is in excellent agreement with the experimental result. We heat a quartz vapor cell containing ${}^{208}\mathrm{Pb}$ to between 800 and $940{}^{\circ }\mathrm{C}$, apply a $\sim 10\mathrm{G}$ longitudinal magnetic field, and use polarization modulation and lock-in detection to measure optical rotation amplitudes of order 1 mrad with noise near $1\mu \mathrm{rad}$. We compare the Faraday rotation amplitude of the $E2$ transition to that of the ${}^{3}P_0-{}^{3}P_1$ 1279 nm magnetic dipole ($M1$) transition under identical sample conditions.

We report time-correlated measurements of the lifetimes of the $7p{}^2{P}_{3/2}$ and $7p{}^2{P}_{1/2}$ states of atomic cesium. The results of these measurements are ${\tau }_{3/2}=137.54\left(16\right)$ ns and ${\tau }_{1/2}=165.21\left(19\right)$ ns. We use these lifetimes, together with other previously determined electric dipole matrix elements of ${}^{133}\mathrm{Cs}$, to determine the matrix elements $\langle 5d{}^2{D}_{5/2}\parallel r\parallel 7p{}^2{P}_{3/2}\rangle , \langle 5d{}^2{D}_{3/2}\parallel r\parallel 7p{}^2{P}_{3/2}\rangle$, and $\langle 5d{}^2{D}_{3/2}\parallel r\parallel 7p{}^2{P}_{1/2}\rangle$. These matrix elements are in good agreement with, but of higher precision than, calculated values of these same matrix elements.

Single ionization by electron impact of the ${\mathrm{Fe}}^{3+}$ ion is investigated using the Dirac-Fock-Slater approximation for the levels of the ground and first-excited $3d^{4}4s$ configuration. Contributions from direct ionization (DI) and excitation-autoionization (EA) processes are taken into account. The scaled distorted-wave (DW) cross sections for DI and excitation by electron impact are used to analyze the experimental data. The study demonstrates the importance of correlation effects for the EA process. Good agreement with experimental data reveals that currently available DW cross sections and, therefore, the corresponding Maxwellian rate coefficients for electron-impact ionization process in ${\mathrm{Fe}}^{3+}$ are overestimated and their usage may lead to wrong predictions for charge state distribution in plasma.

We propose a scheme which can produce desired nonadiabatic passages for the stimulated Raman transition in three-level systems. The state transfer in the protocol is realized by following the evolution of the dynamical basis itself and no additional coupling field is required. We also investigate the interplay between the present nonadiabatic passages and the shortcut to adiabaticity. By incorporating the latter technology, we show that alternative passages with less occupancy of the intermediate level could be designed.

We present a mixed quantum-classical approach to strong-field ionization—a semiclassical two-step model with quantum input. In this model the initial conditions for classical trajectories that simulate an electron wave packet after ionization are determined by the exact quantum dynamics. As a result, the model allows to overcome deficiencies of standard semiclassical approaches in describing the ionization step. The comparison with the exact numerical solution of the time-dependent Schrödinger equation shows that for ionization of a one-dimensional atom the model yields quantitative agreement with the quantum result. This applies both to the width of the photoelectron momentum distribution and to the interference structure.

Classical nonlinear waves exhibit a phenomenon of condensation that results from the natural irreversible process of thermalization toward the Rayleigh-Jeans equilibrium spectrum. Wave condensation originates in the divergence of the thermodynamic equilibrium Rayleigh-Jeans distribution, which is responsible for the macroscopic population of the fundamental mode of the system. Several recent experiments revealed a remarkable phenomenon of spatial organization of an optical beam that propagates through a graded-index multimode optical fiber (MMF), a phenomenon termed beam self-cleaning. Our aim in this article is to provide some physical insight into the mechanism underlying optical beam self-cleaning through the analysis of wave condensation in the presence of structural disorder inherent to MMFs. We consider experiments of beam self-cleaning where long pulses are injected and populate many modes of a 10–20 m MMF, for which the dominant contribution of disorder originates from polarization random fluctuations (weak disorder). On the basis of the wave turbulence theory, we derive nonequilibrium kinetic equations describing the random waves in a regime where disorder dominates nonlinear effects. The theory reveals that the presence of a conservative weak disorder introduces an effective dissipation in the system, which is shown to inhibit wave condensation in the usual continuous wave turbulence approach. On the other hand, the experiments of beam cleaning are described by a discrete wave turbulence approach, where the effective dissipation induced by disorder modifies the regularization of wave resonances, which leads to an acceleration of condensation that can explain the effect of beam self-cleaning. By considering different models of weak disorder in MMFs, we show that a model where the modes experience a partially correlated noise is sufficient to accelerate the thermalization, whereas a fully mode-correlated noise does not lead to a dissipation-induced acceleration of condensation. The simulations are in quantitative agreement with the theory, and evidence an effect of beam cleaning even in a regime of moderate weak disorder. At the leading order linear regime, random mode coupling among degenerate modes (strong disorder) can enforce thermalization and condensation. The analysis also reveals that the effect of beam cleaning is characterized by a partial repolarization as a natural consequence of the condensation process. In addition, the discrete wave turbulence approach explains why optical beam self-cleaning has not been observed in step-index multimode fibers.

The development of new optical technology plays a key role in the essential evolution of optical science. In this article, we experimentally demonstrate an optical technology that enables the arbitrary manipulation of amplitudes and phases of highly discrete spectra. This optical technology is simple and practically useful: we may only place a few fundamental optical elements on an optical axis and control their thicknesses precisely. As a typical application, we show generation of a train of ultrashort pulses in the time domain, with a pulse duration close to 1 fs and a repetition rate exceeding 100 THz.

This paper provides, first, a succinct theoretical derivation of Bose-Einstein condensation in a grand-canonical ideal photon gas elaborating on previous results [Müller, Ann. Phys. 184, 219 (1988); Physica A (Amsterdam, Neth.) 139, 165 (1986)] additionally including new results on the condensate function and, second, applies this framework to consistently explain experimental findings on Bose-Einstein condensation of photons in an optical microcavity [Klaers, Schmitt, Vewinger, and Weitz, Nature 468, 545 (2010)]. A grand-canonical photon gas is realized by a steady state of a photon flux deviating from a canonical thermodynamic Planck equilibrium. The theoretical approach presented here invites to significantly widen the experimental framework for Bose-Einstein condensation of photons including three-dimensional photon resonators and thermalization mechanisms different from a dye medium in the cavity.

To observe a vibrational instability in a molecule or Raman lasing, the molecules should be placed in a resonator and illuminated by a laser. Both these phenomena are self-oscillations of either photons in a resonator or nuclei in molecules. We show that, thanks to the coupling of the forced oscillations of electrons in a molecule with its nucleus vibrations, these two effects are manifestations of the same phenomenon. When the ratio of damping rates of the molecule and the resonator is large, the number of coherent photons is also large, causing Raman lasing. In this case, the number of quanta of the coherent molecular vibrations is negligible. In the opposite case, the number of coherent vibration quanta is large, causing vibrational instability. This leads to the nonlinear response in Raman scattering, which was recently observed in a surface-enhanced Raman spectroscopy (SERS) experiment [A. Lombardi et al., Phys. Rev. X 8, 011016 (2018)].

Interference of two beams produced at separate biphoton sources was first observed more than two decades ago. The phenomenon, often called “induced coherence without induced emission,” has recently gained attention after its applications to imaging, spectroscopy, and measuring biphoton correlations have been discovered. The sources used in the corresponding experiments are nonlinear crystals pumped by laser light. The use of a laser pump makes the occurrence of induced (stimulated) emission unavoidable, and the effect of stimulated emission can be observed in the joint detection rate of the two beams. This fact raises the question whether the stimulated emission also plays a role in inducing the coherence. Here we investigate a case in which the crystals are pumped with a single-photon Fock state. We find that coherence is induced even though the possibility of stimulated emission is now fully ruled out. Furthermore, the joint detection rate of the two beams becomes ideally zero. Our results rule out any classical or semiclassical explanation of the phenomenon and also suggest that it is, in principle, possible to perform similar experiments with fermions, for which stimulated emission is strictly forbidden.

Vectorial nonlinear optics refers to the investigation of optical processes whose nonlinear polarization (NP) undergoes spin-orbit-coupling (SOC) interactions where, in general, the driving light field or the new field generated by the interaction contains the SOC property. To contribute to fundamental knowledge in this domain, we examine the type-II second-harmonic generation (SHG) induced by vectorial laser modes. First, we provide a general theory to analyze the vectorial SHG process. Second, by using two typical vector modes as examples, we show how the SOC of the pump field dictates nonlinear interaction. Finally, we corroborate our theoretical predictions through experiments to confirm the crucial role of the SOC in nonlinear interactions. These results enhance our fundamental understanding of SOC-mediated nonlinear optics and lay the foundation for further fundamental studies as well as possible applications.

Establishing end-to-end quantum connections requires quantified link characteristics, and operations need to coordinate decision making between nodes across a network. We introduce the RuleSet-based communication protocol for supporting quantum operations over distant nodes to minimize classical packet transmissions for guaranteeing synchronicity. RuleSets are distributed to nodes along a path at connection setup time, and hold lists of operations that need to be performed in real time. We simulate the RuleSet-based quantum link bootstrapping protocol, which consists of recurrent purifications and link-level tomography, to quantify the quantum link fidelity and its throughput. Our Markov-chain Monte Carlo simulation includes various error sources, such as the memory error, gate error, and channel error, modeled on currently available hardware. We found that when two quantum nodes, each with 100 memory qubits capable of emitting photons ideally to the optical fiber, are physically connected with a 10-km MeetInTheMiddle link, the Recurrent Single selection–Single error purification (RSs-Sp) protocol is capable of bringing up the fidelity from an average input $F_r=0.675$ to around $F_r=0.865$ with a generation rate of 1106 Bell pairs per second, as determined by simulated tomography. The system gets noisier with longer channels, in which case errors may develop faster than the purification gain. In such a situation, a stronger purification method, such as the double selection-based purification, shows an advantage for improving the fidelity. The knowledge acquired from bootstrapping can later be distributed to nodes within the same network, and used for other purposes such as route selection.

We predict the recoil-induced molecular dissociation in hard-x-ray photoionization. The recoil effect is caused by electronic and photon momentum exchange with the molecule. We show the strong role of relativistic effects for the studied molecular fragmentation. The recoil-induced fragmentation of the molecule is caused by elongation of the bond due to the vibrational recoil effect and because of the centrifugal force caused by the rotational recoil. The calculations of the x-ray photoelectron spectra of the ${\mathrm{H}}_2$ and NO molecules show that the predicted effects can be observed in high-energy synchrotrons like SOLEIL, SPring-8, PETRA, and XFEL SACLA. The relativistic effect enhances the recoil momentum transfer and makes it strongly sensitive to the direction of ejection of the fast photoelectron with respect to the photon momentum.

The tunneling and multiphoton ionization of a weakly bound level in an intense laser field of an arbitrary polarization and a constant uniform magnetic field, under the condition when the frequency $\omega$ of a laser field coincides with the cyclotron frequency ${\omega }_H$, are discussed in the quasistationary quasienergy state (QQES) formalism framework. The integral equation is derived for the complex quasienergy of the photoelectron, on the basis of the exact solution of the Schrödinger equation for an electron moving in an arbitrary electromagnetic wave and a constant magnetic field, obtained in Rylyuk [Phys. Rev. A 93, 053404 (2016)]. Simple analytical expressions for ionization rates in the tunneling and the multiphoton regimes by using the saddle-point method are derived and discussed. Using the “imaginary-time” method, the extremal subbarrier trajectory, the barrier width, and the emission angle of photoelectrons are considered. We theoretically demonstrate that when the frequency of a left polarized laser field coincides with the cyclotron frequency, the constant magnetic field does not stabilize the bound level, which leads to an enhancement of the ionization rate as compared to when the magnetic field is absent.

An out-of-phase soliton distribution of the wave field is found for a multicore fiber (MCF) from an even number of cores located in a ring. Its stability is proved with respect both to small wave-field perturbations, including azimuthal ones, and to small deformations of the MCF structure. As an example of using this soliton distribution, the problem of laser pulse compression in an active MCF is studied. The optimal fiber parameters, the minimum duration of the output pulse, and the compression length are found, and they are in good agreement with the results of numerical simulation. In order to achieve high energies in the output laser pulse, the requirements for MCF deformations are determined.

We propose a method for measuring parity violation in neutral atoms. It is an adaptation of a seminal work by Fortson [Phys. Rev. Lett. 70, 2383 (1993)], proposing a scheme for a single trapped ion. In our version, a large sample of neutral atoms should be localized in an optical lattice overlapping a grid of detection sites, all tailored as the single site in Fortson's work. The methodology is of general applicability, but as an example, we estimate the achievable signal in an experiment probing a nuclear spin independent parity violation on the line $6s{}^{2}S_{1/2}-5d{}^{2}D_{3/2}$ in ${}^{133}\mathrm{Cs}$. The projected result is based on realistic parameters and ab initio calculations of transition amplitudes, using the relativistic coupled-cluster method. The final result is a predicted spectroscopic signature, evidencing parity violation, of the order of 1 Hz, for a sample of ${10}^8$ atoms. We show that a total interrogation time of 30 000 s should, together with existing theoretical data, suffice for achieving a precision in the determination of the weak charge of Cs of the order of 0.1%—a sensitivity surpassing previously reported determinations by at least a factor of 5.

In theories of communication, it is usually presumed that the involved parties perform actions in a fixed causal order. However, practical and fundamental reasons can induce uncertainties in the causal order. Here we show that a maximal uncertainty in the causal order forbids asymptotic quantum communication, while still enabling the noisy transfer of classical information. Therefore causal order, like shared entanglement, is an additional resource for communication. The result is formulated within an asymptotic setting for processes with no fixed causal order, which sets a basis for a quantum information theory in general quantum causal structures.

In this work, we carry out experimental measurements and theoretical calculations of the branching fractions for the $4P_{3/2}$ state of ${}^{40}\mathrm{Ca}^{+}$. The measurements are based on counting photon numbers emitted from hundreds of ions trapped in a linear Paul trap, as their being affected by lasers. The calculations are performed using the relativistic coupled-cluster method at different approximations. The measured values for the decays of the $4P_{3/2}$ state into the $4S_{1/2}$, $3D_{5/2}$, and $3D_{3/2}$ states are, respectively, 0.9350(4), 0.0587(4), and 0.0063(2), which agree well with our recommended theoretical values 0.9344(13), 0.0590(12), and 0.0066(1). Our measured values are also consistent with the experimental values of Gerritsma et al. [R. Gerritsma, G. Kirchmair, F. Zähringer, J. Benhelm, R. Blatt, and C. F. Roos, Eur. Phys. J. D 50, 13 (2008)] using a completely different method. Furthermore, we also calculate the branching fractions of the $4P_{1/2}$ state using the same method, and compare to the available experimental and theoretical data.

We investigate the use of microwave radiation to produce a repulsive shield between pairs of ultracold polar molecules and prevent collisional losses that occur when molecular pairs reach short range. We carry out coupled-channels calculations on $\mathrm{RbCs}+\mathrm{RbCs}$ and $\mathrm{CaF}+\mathrm{CaF}$ collisions in microwave fields. We show that effective shielding requires predominantly circular polarization but can still be achieved with elliptical polarization that is around 90% circular.

We have investigated collective breathing modes of a unitary Fermi gas in deformed harmonic traps. The ground state is studied by the superfluid local density approximation (SLDA) and small-amplitude collective modes are studied by the iterative quasiparticle random phase approximation (QRPA). The results illustrate the evolutions of collective modes of a small system in traps from spherical to elongated or pancake-shaped deformations. For small spherical systems, the influences of different SLDA parameters are significant, and, in particular, a large pairing strength can shift up the oscillation frequency of collective modes. The transition currents from QRPA show that the compressional flow patterns are nontrivial and dependent on the deformation. Finally, the finite-size effects are demonstrated to be reasonable when progressing towards larger systems. The hydrodynamical results of collective frequencies can be reproduced by SLDA-QRPA with reduced pairing strengths. Our studies indicate that experiments on small and medium systems are valuable for understanding effective interactions in systems with varying sizes and trap deformations.