We have developed an all-optical method for measuring the lifetimes of $nS$ and $nD$ Rydberg states and demonstrate its capabilities with measurements on a dilute cloud of ultracold ${}^{87}\mathrm{Rb}$ atoms in a cryogenic environment. The method is based on the time-resolved observation of resonant light absorption by ground-state atoms and selective transfer of Rydberg atoms into the ground state at varying delay times in order to reconstruct Rydberg decay curves. Our measurements of the ${}^{87}\mathrm{Rb}$ $30S_{1/2}$ state indicate an increase of the lifetime at lowered environment temperatures, as expected due to decreased blackbody radiation. For the $38D_{5/2}$ state with an attractive dipole-dipole interaction, ionization and lifetime reduction due to collisional effects are observed.

Gross-Oliveira-Kohn density-functional theory (GOK-DFT) for ensembles is, in principle, very attractive but has been hard to use in practice. A practical model based on GOK-DFT for the calculation of electronic excitation energies is discussed. The model relies on two modifications of GOK-DFT: use of range separation and use of the slope of the linearly interpolated ensemble energy, rather than orbital energies. The range-separated approach is appealing, as it enables the rigorous formulation of a multideterminant state-averaged DFT method. In the exact theory, the short-range density functional, which complements the long-range wave-function-based ensemble energy contribution, should vary with the ensemble weights even when the density is held fixed. This weight dependence ensures that the range-separated ensemble energy varies linearly with the ensemble weights. When the (weight-independent) ground-state short-range exchange-correlation functional is used in this context, curvature appears, thus leading to an approximate weight-dependent excitation energy. In order to obtain unambiguous approximate excitation energies, we propose to interpolate linearly the ensemble energy between equiensembles. It is shown that such a linear interpolation method (LIM) can be rationalized and that it effectively introduces weight dependence effects. As proof of principle, the LIM has been applied to He, Be, and ${\text{H}}_2$ in both equilibrium and stretched geometries as well as the stretched ${\text{HeH}}^{+}$ molecule. Very promising results have been obtained for both single (including charge transfer) and double excitations with spin-independent short-range local and semilocal functionals. Even at the Kohn-Sham ensemble DFT level, which is recovered when the range-separation parameter is set to 0, LIM performs better than standard time-dependent DFT.

Two-color ionization of atoms with a strong 800-nm fundamental component and a weak 400-nm component with perpendicular polarization gives detailed insight into the ionization dynamics. When the delay between the two colors is varied on a subcycle scale, the slow-electron signal shows an oscillatory structure due to intracycle interference between different ionization times. Using a trajectory-based interference model, we extract the relative strength of the two contributing pathways. Ionization times can be read directly from the delay scan, and the times for the long trajectories agree well with the quantum-orbit model. The fast electrons arise predominantly from long rescattering trajectories.

The differential cross section for electron-impact excitation of helium atoms in the presence of a linearly polarized laser field is calculated. The interaction of the laser field with both the projectile electron and the target atom is treated in a fully nonperturbative way, while the electron-atom interaction is treated within the first Born approximation. We are interested in studying two cases where the photon energy of the laser field is chosen to be far from resonance and when it matches with $2{}^{1}S⟶2{}^{1}P$ and $3{}^{1}S⟶3{}^{1}P$ transition frequencies. The agreement between perturbative and nonperturbative results is good, except close to the resonance where the perturbative cross sections diverge while the nonperturbative ones predict no maximum of the cross sections. Another interesting effect is the presence of an avoided crossing of the Floquet pseudoenergies at resonance.

We propose a scheme for preparing an ensemble of atoms in a maximally entangled $W$ state by exploiting the Rydberg blockade effect. The success of our protocol is indicated by the detection of an ion, which thus serves as a herald for successful entangled-state preparation. The fidelity of the preparation scheme is independent of the number of atoms in the ensemble. Therefore, a small cloud of atoms in a dipole trap randomly loaded from a background gas can be reliably prepared in a maximally entangled state despite atom number fluctuations.

The change in the decay rate of an excited atom that is brought about by extinction and thermal-radiation effects in a nearby dielectric medium is determined from a quantum-mechanical model. The medium is a collection of randomly distributed thermally excited spherical scatterers with absorptive properties. The modification of the decay rate is described by a set of correction functions for which analytical expressions are obtained as sums over contributions from the multipole moments of the scatterers. The results for the modified decay rate as a function of the distance between the excited atom and the dielectric medium show the influence of absorption, scattering and thermal-radiation processes. Some of these processes are found to be mutually counteractive. The changes in the decay rate are compared to those following from an effective-medium theory in which the discrete scatterers are replaced by a continuum.

We undertake a thorough analysis of the thermodynamics of the trajectories followed by a quantum harmonic oscillator coupled to $N$ dissipative baths by using an approach to large-deviation theory inspired by phase-space quantum optics. As an illustrative example, we study the archetypal case of a harmonic oscillator coupled to two thermal baths, allowing for a comparison with the analogous classical result. In the low-temperature limit, we find a significant quantum suppression in the rate of work exchanged between the system and each bath. We further show how the presented method is capable of giving analytical results even for the case of a driven harmonic oscillator. Based on that result, we analyze the laser cooling of the motion of a trapped ion or optomechanical system, illustrating how the emission statistics can be controllably altered by the driving force.

For continuous weak measurements of qubits, we obtain exact expressions for weak values (WVs) from the postselection restricted average of measurement outputs, by using both the quantum-trajectory equation (QTE) and the quantum Bayesian approach. The former is applicable to short-time weak measurement, while the latter can relax the measurement strength to finite. We find that even in the “very” weak limit the result can be essentially different from the one originally proposed by Aharonov, Albert, and Vaidman (AAV), in the sense that our result incorporates nonperturbative correction which could be important when the AAV WV is large. Within the Bayesian framework, we obtain also elegant expressions for finite measurement strength and find that the amplifier's noise in quantum measurement has no effect on the WVs. In particular, we obtain very useful results for homodyne measurement in a circuit-QED system, which allows for measuring the real and imaginary parts of the AAV WV by simply tuning the phase of the local oscillator. This advantage can be exploited as an efficient state-tomography technique.

Considering the evolution of the quantum state of a pair of entangled photons in a turbulent atmosphere and using the quadratic approximation to the Kolmogorov model of turbulence, we provide an analytical solution for the dynamical equation (an infinitesimal propagation equation) that describes this evolution in the plane-wave basis. As such, this solution fully incorporates the effect of multiple scattering, caused by the medium. After being converted into a discrete orbital angular momentum (OAM) basis, this solution retains the effect of coupling between different OAM modes on the twin-photon state for arbitrary propagation distances and arbitrary turbulence strengths. We define a minimal set of parameters that determines the entanglement evolution in the regime of strong scintillation. Furthermore, we show that in the limit of weak scintillation, our solutions reduce to those obtained from the single-phase-screen model.

We have measured the relative probability for the production of ${\mathrm{N}}_2{}^{2+}$ using monochromatized synchrotron radiation in the range of 38 to 400 eV. We find the energy dependence of the ratio ${\mathrm{N}}_2{}^{2+}/{\mathrm{N}}_2{}^{+}$ to be very similar to that of the ${\mathrm{He}}^{2+}/{\mathrm{He}}^{+}$ ratio, which indicates a similarity in the double-photoionization mechanism. This may allow us to predict the relative dication production for other simple molecules, such as ${\mathrm{O}}_2$, without the need to measure an extended photon-energy range. We obtain a threshold for the production of ${\mathrm{N}}_2{}^{2+}$ ions of 42.97(10) eV.

We theoretically analyze quasi-one-dimensional Bose-Einstein condensates under the influence of a harmonic trap and a narrow potential defect that moves through the atomic cloud. Performing simulations on the mean-field level, we explore a robust mechanism in which a single dark soliton is nucleated and immediately pinned by the moving defect, making it possible to drag it to a desired position and release it there. We argue on a perturbative level that a defect potential which is attractive to the atoms is suitable for holding and moving dark solitons. The soliton generation protocol is investigated over a wide range of model parameters and its success is systematically quantified by a suitable fidelity measure, demonstrating its robustness against parameter variations, but also the need for tight focusing of the defect potential. Holding the soliton at a stationary defect for long times may give rise to dynamical instabilities, whose origin we explore within a Bogoliubov–de Gennes linearization analysis. We show that iterating the generation process with multiple defects offers a perspective for initializing multiple soliton dynamics with freely chosen initial conditions.

Confined quantum systems involving $N$ identical interacting fermions are found in many areas of physics, including condensed matter, atomic, nuclear, and chemical physics. In a previous series of papers, a many-body perturbation method that is applicable to both weakly and strongly interacting systems of bosons has been set forth by the author and coworkers. A symmetry-invariant perturbation theory was developed that uses group theory coupled with the dimension of space as the perturbation parameter to obtain an analytic correlated wave function through first order for a system under spherical confinement with a general two-body interaction. In the present paper, we extend this formalism to large systems of fermions, circumventing the numerical demands of applying the Pauli principle by enforcing the Pauli principle on paper. The method does not scale in complexity with $N$ and has minimal numerical cost. We apply the method to a unitary Fermi gas and compare to recent Monte Carlo values.

In this report we study the Vernier effect in coupled laser systems consisting of two cavities. We show that depending on the nature of their coupling, not only can the “supermodes” formed at overlapping resonances of these two cavities have the lowest thresholds as previously found, leading to lasing at these overlapping resonances and a manifestation of the typical Vernier effect, but also they can have increased thresholds and are hence suppressed, which can be viewed as an inverse Vernier effect. The inverse Vernier effect can also lead to an increased free spectrum range and possibly single-mode lasing, which may explain the experimental findings in several previous studies. We illustrate this effect using two coupled micro-ring cavities and a micro-ring cavity coupled to a slab cavity, and we discuss its relation to the existence of exceptional points in coupled lasers.

We show that the role of the Lyapunov exponents can be extended beyond the customary local instability, such as limit cycle behavior, to include its use as an evolutionary predictor of the dynamics of a laser with injected signal (LIS). Numerical studies of LIS reveal that as a function of the input-signal strength the evolution of two nonzero Lyapunov exponents (generally equal) distinctively predicts the evolutionary trend of the fundamental frequency of the laser output signal (an important dynamic characteristic of the LIS) even with the presence of some noise. This globally predictive behavior of the Lyapunov exponents includes also the dynamic behavior of the individual coexisting attractors. Different coexisting attractors of LIS and configurations of Lyapunov exponents for both individual attractors and the global system are reported. Two LIS case studies are considered: (I) a high-gain system with a rich history of nonlinear behavior but not experimentally accessible, and (II) a low-gain system that has complex dynamics and is experimentally accessible for Class B lasers. Universality arguments support the thesis that these different configurations and the extended role of the Lyapunov exponents as an evolutionary predictor of the dynamics will be observed in other nonlinear, dynamic dissipative systems as well.

Nanoparticle-induced modifications of the spectrum of whispering-gallery modes (WGMs) of optical spheroidal resonators are studied theoretically. Combining an ab initio solution of a single-resonator problem with a dipole approximation for the particle, we derive simple analytical expressions for frequencies and widths of the particle-modified resonances, which are valid for resonators with moderate deviations from the spherical shape. The derived expressions are used to analyze spectral properties of the resonator-particle system as functions of the particle's position, the size of the resonators, and the characteristics of WGMs. The obtained results are shown to agree well with available experimental data. It is also demonstrated that the particle-induced spectral effects can be significantly enhanced by careful selection of the resonator's size, refractive index, and other experimental parameters. The results presented in the paper can be useful for applications of WGM resonators in biosensing, cavity QED, optomechanics, and other areas.

We derive a generalized wave-particle duality relation for arbitrary multipath quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a quantifier as the normalized quantum coherence, recently defined in the framework of quantum information theory. To witness the particle nature, we quantify the path distinguishability or the which-path information based on unambiguous quantum state discrimination. Then, the Bohr complementarity principle for multipath quantum interference can be stated as a duality relation between the quantum coherence and the path distinguishability. For two-path interference, the quantum coherence is identical to the interference fringe visibility, and the relation reduces to the well-known complementarity relation. The duality relation continues to hold in the case where mixedness is introduced due to possible decoherence effects.

High-order-harmonic generation (HHG) for the ${{\mathrm{H}}_2}^{+}$ molecule in a 3-fs, 800-nm few-cycle Gaussian laser pulse combined with a static field is investigated by solving the one-dimensional electronic and one-dimensional nuclear time-dependent Schrödinger equation within the non-Born-Oppenheimer approximation. The spatial distribution in HHG is demonstrated and the results present the recombination process of the electron with the two nuclei, respectively. The spatial distribution of the HHG spectra shows that there is little possibility of the recombination of the electron with the nuclei around the origin $z=0$ a.u. and equilibrium internuclear positions $z=\pm 1.3$ a.u. This characteristic is irrelevant to laser parameters and is only attributed to the molecular structure. Furthermore, we investigate the time-dependent electron-nuclear wave packet and ionization probability to further explain the underlying physical mechanism.

Trapping a large number of ${}^6\mathrm{Li}$ atoms in a simplified experimental setup is a long-term pursuit in the studies of degenerate Fermi gases. We experimentally and theoretically demonstrate the enhancement of ${}^6\mathrm{Li}$ trapping efficiency in a three-dimensional magneto-optical trap (3D MOT) by using the multiple-sideband cooling in a two-dimensional magneto-optical trap (2D MOT). In the 2D MOT, we increase the spectral width of the cooling light to 102 MHz by generating six frequency sidebands in order to couple fast atoms. The capture velocity is dramatically increased by employing the multiple-sideband cooling. The number of trapped atoms in the 3D MOT is $6.0\times {10}^8$, which is higher by a factor of 4 than in the case of single-frequency cooling. We have investigated the dependence of atom number on laser detuning, and our experimental result agrees well with the prediction of a simple two-level model. The efficiency of the multiple-sideband cooling for lithium (in contrast to many other alkali-metal atoms) is also confirmed by the analysis of the loss due to fine-structure changing collisions.

We examine the residual current to investigate the conversion efficiency from the few-cycle laser pulse into the terahertz radiation of ${\text{H}}_2{}^{+}$ by solving the time-dependent Schrödinger equation in the non-Born-Oppenheimer approach. It is found that the nuclear motion and high vibrational states will improve the optical-to-terahertz conversion efficiency significantly, while with the increasing of the laser intensity, ionization saturation will suppress the effects of moving nuclei. Moreover, based on the dependence of the residual current on the delay time of the nuclear vibration, we conclude that the terahertz signal may serve as a tool to probe the nuclear dynamics.

We present a theoretical description of the radio-frequency (rf) spectroscopy of fermionic atomic gases, based on the second-order response theory at finite temperature. This approach takes into account the energy resolution due to the envelope of the rf pulse. For a noninteracting final state, the momentum- and energy-resolved rf intensity depends on the fermion spectral function and pulse envelope. The contributions due to interactions in the final state can be classified by means of diagrams. Using this formalism, as well as the local density approximation in two and three dimensions, we study the interplay of inhomogeneities and Hartree energy in forming the line shape of the rf signal. We show that the effects of inhomogeneities can be minimized by taking advantage of interactions in the final state, and we discuss the most relevant final-state effects at low temperature and density, in particular the effect of a finite lifetime.