Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the $6p$, $7s$, $7p$, $8s$, $8p$, and $6d$ states and the dynamic dipole polarizabilities of the $6p$ and $7s$ states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the $7s_{1/2}$, $7p_{1/2}$, $8p_{1/2}$, and $8p_{3/2}$ states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the $6p_{1/2}$–$7s$ and $6p_{3/2}$–$7s$ transitions in the range of 488–1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the $7s_{1/2}$–$7p_{1/2}$ and $7s_{1/2}$–$7p_{3/2}$ transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the $6p_{1/2}$–$7p_{1/2}$ transition, are also evaluated and compared with available theoretical and experimental values.

Different from the high-order harmonic generation (HHG) from gases, we find that the yield of HHG from solids exhibits unexpected modulations as a function of the driving laser intensity and wavelength. Its mechanism can be unraveled by the interference between currents inside the solids induced by two adjacent Zener tunneling events. Our simulations agree well with the experimental measurements of HHG from ZnSe and solid Ar. We also find that the dephasing time plays a key role in this subcycle interference and can turn it on or off by controlling the overlap between the channels. It provides an avenue to optimize the ultrafast electron dynamics and HHG emission processes in solids, which will be useful for the compact ultrafast EUV light sources. We also propose an experimental scheme by using ultrashort lasers to explore this interference in other solid materials.

In this paper we consider a recent experiment [Phys. Rev. A 95, 053638 (2017)] in which an antiferromagnetic spin-1 condensate of ${}^{23}\mathrm{Na}$ atoms was quenched from the easy-axis polar phase into the easy-plane polar phase. We simulate the phase-transition dynamics by using a classical field method with noisy initial conditions and find good agreement with the experimental observations. We analyze the late-time dynamics in terms of phase ordering by using the nematic order parameter that we have developed in earlier work [Phys. Rev. A 96, 013602 (2017)]. We show that these experiments are able to explore the early stages of universal phase ordering where the domains grow diffusively.

We investigate numerically light propagation in a single spiral waveguide formed in a nonlinear dielectric medium for a low spatial frequency of the waveguide rotation. We present a general procedure for finding solitonic solutions in spiral waveguiding structures, as well as the variational approach to calculate soliton parameters analytically. Solitons supported by the spiral waveguide perform robust stable rotational oscillatory motion, with the period predicted by their static characteristics, without any signatures of wave radiation or soliton decay over many rotation periods and diffraction lengths.

Systems of atoms coupled to a single or a few waveguide modes provide a test-bed for physically and practically interesting interference effects. We consider the dynamics of a pair of atoms, approximated as two-level quantum emitters, coupled to a linear guided mode. In particular, we analyze the evolution of an initial state in which both atoms are excited, which is expected to decay into an asymptotic two-photon state. We investigate the lifetime of the initial configuration and the properties of the asymptotic photon correlations, and analyze the probability that the two photons are emitted in the same or in opposite directions. We find that the ratio $R$ between parallel and antiparallel emission probabilities is maximal when the interatomic distance is an odd multiple of a quarter wavelength of the emitted light. In such a case, $R=3$ in the small-coupling regime.

We examine angular distribution of the probability of correlated fluorescence photon emission from a linear chain of identical equidistant two-level atoms. We selectively excite one of the atoms by a resonant laser field. The atoms are coupled to each other via the dipole-dipole interaction and collective spontaneous emission. Our attention is focused on the simultaneous observation of correlated pairs of photons. It is found that the interference between the emitting atoms can result in a highly directional emission of photon pairs. These pairs of photons exhibit strong correlations and their emission is highly concentrated into specific directions. We demonstrate the crucial role of the selective coherent excitation in such a geometrical configuration. Shifting the driving field from an atom located at one end of the chain to the other causes the radiation pattern to flip to the opposite half of the detection plane. Furthermore, we find that atomic systems in which only an atom situated at a particular position within the linear chain is driven by a laser field can radiate correlated twin photons in directions along which the radiation of single photons is significantly reduced. Alternatively, superbunching in the emitted photon statistics preferentially occurs in directions of negligible or vanishing single-photon emission. The effect of superbunching strengthens as more emitters are added to the chain. Depending on the number of atoms and the position of the driven atom within the chain, the strongly correlated pairs of photons can be emitted into few well-defined directions.

Spin-exchange collisions in hot vapors are generally regarded as a decoherence mechanism. In contrast, we show that linear and nonlinear spin-exchange coupling can lead to the generation of atomic coherence in a Bell-Bloom magnetometer. In particular, we theoretically and experimentally demonstrate that nonlinear spin-exchange coupling, acting in an analogous way to a wave-mixing mechanism, can create additional modes of coherent excitation which inherit the magnetic properties of the natural Larmor coherence. The generated coherences further couple via linear spin-exchange interaction, leading to an increase of the natural coherence lifetime of the system. Notably, the measurements are performed in a low-density caesium vapor and for nonzero magnetic field, outside the standard conditions for collisional coherence transfer. The strategies discussed are important for the development of spin-exchange coupling into a resource for an improved measurement platform based on room-temperature alkali-metal vapors.

The isotope effect and the $g-u$ symmetry in the HD predissociation have been studied by detecting the $\mathrm{H}\left(2s\right)$, $\mathrm{H}\left(2p\right)$, $\mathrm{D}\left(2s\right)$, and $\mathrm{D}\left(2p\right)$ fragments. For transitions to the $3p\pi D{}^1{\mathrm{\Pi }}_u^{+}\left(\upsilon =4\right)$, $4p\pi D^{\prime }{}^1{\mathrm{\Pi }}_u^{+}\left(\upsilon =1\right)$, and $4p\sigma B^{\prime \prime }{}^1{\mathrm{\Sigma }}_u^{+}\left(\upsilon =2\right)$ states of HD, the branching ratios of the four dissociation channels, $\mathrm{H}\left(2s\right)+\mathrm{D}\left(1s\right)$, $\mathrm{H}\left(2p\right)+\mathrm{D}\left(1s\right)$, $\mathrm{D}\left(2s\right)+\mathrm{H}\left(1s\right)$, and $\mathrm{D}\left(2p\right)+\mathrm{H}\left(1s\right)$, were measured. Strong asymmetric distributions are found between the $\mathrm{H}\left(2s\right)+\mathrm{D}\left(1s\right)$ and $\mathrm{D}\left(2s\right)+\mathrm{H}\left(1s\right)$, and between the $\mathrm{H}\left(2p\right)+\mathrm{D}\left(1s\right)$ and $\mathrm{D}\left(2p\right)+\mathrm{H}\left(1s\right)$ channels. The results indicate the existence of $g-u$ symmetry breaking as well as strong nonadiabatic couplings near the HD dissociation limits. However, the angular anisotropy parameters are found to be the same for the $\mathrm{H}(2s/2p)$ and $\mathrm{D}(2s/2p)$ fragments. In addition, the observed Beutler-Fano profiles in the $\mathrm{H}(2s/2p)$- and $\mathrm{D}(2s/2p)$-atom action spectra show no dependence on the H and D isotopes. This implies that the angular distribution of the fragments and the Beutler-Fano profiles are determined chiefly by the Franck-Condon transitions and are not affected by the $g-u$-state mixing.

For a molecule, the two-center interference and the molecular scattering phase of the electron are important for almost all the processes that may occur in a laser field. In this study, we investigate their effects in the transfer of linear photon momentum to the ionized electron by absorbing a single photon. The time-dependent Schrödinger equation of ${{\text{H}}_2}^{+}$ is numerically solved in the multipolar gauge in which the electric quadrupole term and the magnetic dipole term are explicitly expressed. This allows us to separate the contributions of the two terms in the momentum transfer. For different configurations of the molecular and the laser orientation, the transferred momentum to the electron is evaluated at different internuclear distances with various photon energies and two-center interferences are identified in the whole region. At small electron energies and small internuclear distances, we find significant deviations from the prediction of the classical double-slit model due to the strong mediation of the Coulomb potential. Finally, even for a large internuclear distance, our results show that a varying molecular scattering phase is important at all electron energies, which is beyond the simple prediction of the linear combination of the atomical orbitals.

We provide an in-depth analysis of high-order above-threshold ionization of atoms and molecules by strong laser pulses, using three different theoretical approaches beyond the electric dipole approximation: (i) the numerical solution of the time-dependent Schrödinger equation, (ii) the classical three-step model, and (iii) the quantum-orbit model. In the classical and quantum-orbit models, we include an accurate description of the rescattering step by target-specific differential scattering cross sections. The considerable forward shift of the photoelectron momentum distributions along the laser propagation direction can be understood in terms of the nondipole electron motion after rescattering. An explanation of the additionally observed forward-backward asymmetry of the signal strength requires the accurate modeling of the rescattering step and the electron dynamics before the rescattering event. For the ${\mathrm{H}}_2{}^{+}$ molecular ion, we compare the cases of parallel and perpendicular alignment of the molecular axis and we show that the interference pattern and its modification due to the nondipole effects are orientation dependent. Compared to atoms, the nondipole effects in molecular high-order above-threshold ionization appear more pronounced and amenable to experimental observation.

We study theoretically the behavior of laser-cooled calcium monofluoride (CaF) molecules in an optical molasses and magneto-optical trap (MOT), and compare our results to recent experiments. We use multilevel optical Bloch equations to estimate the force and the diffusion constant, followed by a Fokker-Planck-Kramers equation to calculate the time evolution of the velocity distribution. The calculations are done in three dimensions, and we include all the relevant energy levels of the molecule and all the relevant frequency components of the light. Similar to simpler model systems, the velocity-dependent force curve exhibits Doppler and polarization-gradient forces of opposite signs. We show that the temperature of the MOT is governed mainly by the balance of these two forces. Our calculated MOT temperatures and photon scattering rates are in broad agreement with those measured experimentally over a wide range of parameters. In a blue-detuned molasses, the temperature is determined by the balance of polarization-gradient cooling, and heating due to momentum diffusion, with no significant contribution from Doppler heating. In the molasses, we calculate a damping rate similar to the measured one, and steady-state temperatures that have the same dependence on laser intensity and applied magnetic field as measured experimentally, but are consistently a few times smaller than measured. We attribute the higher temperatures in the experiments to fluctuations of the dipole force which are not captured by our model. We show that the photon scattering rate is strongly influenced by the presence of dark states in the system, but that the scattering rate does not go to zero even for stationary molecules because of the transient nature of the dark states.

Multiphoton entangled states play a crucial role in quantum information applications such as secure quantum communication, scalable computation, and high-precision quantum metrology. Quantum memory for entangled states is a key component of quantum repeaters, which are indispensable in realizing quantum communications. Storing a single photon or an entangled photon has been realized through different protocols. However, there has been no report demonstrating whether or not a multiphoton state can be stored in any physical system. Here, we report on the experimental storage of a two-photon NOON state in a cold-atomic ensemble. Quantum interference measured before and after storage clearly shows that the properties of the two-photon NOON state are preserved during storage. Our experiment completes a step towards storing a multiphoton entangled state.

We find that the measurement sensitivity of an optical integrating gyroscope is fundamentally limited due to ponderomotive action of the light leading to the standard quantum limit of the rotation angle detection. The uncorrelated quantum fluctuations of power of clockwise and counterclockwise electromagnetic waves result in optical power-dependent uncertainty of the angular gyroscope position. We also show that, on the other hand, a quantum backaction evading measurement of the angular momentum of a gyroscope becomes feasible if the proper measurement strategy is selected. The angle is perturbed in this case. This observation hints at the fundamental inequivalence of integrating and rate gyroscopes.

High-dimensional entanglement is a valuable resource for quantum communication, and photon pairs entangled in orbital angular momentum (OAM) are commonly used for encoding high-dimensional quantum states. However, methods for the preparation of maximally entangled states of arbitrary dimensionality are still lacking, and currently used approaches essentially rely on filtering and entanglement concentration. Here, we experimentally realize a method for the generation of high-dimensional maximally entangled OAM states of photon pairs which does not require any of these procedures. Moreover, the prepared state is restricted to the subspace of the specified dimensionality, thus requiring minimal spatial postselection.

We establish a general connection between entropic uncertainty relations, Einstein-Podolsky-Rosen steering, and joint measurability. Specifically, we construct steering inequalities from any entropic uncertainty relation, given that the latter satisfies two natural properties. We obtain steering inequalities based on Rényi entropies. These turn out to be tight in many scenarios using max- and min-entropies. Considering steering tests with two noisy measurements, our inequalities exactly recover the noise threshold for steerability. This is the case for any pair of qubit two-outcome measurements as well as for pairs of mutually unbiased bases in any dimension. This shows that easy-to-evaluate quantities, such as entropy, can optimally witness steering, despite the fact that they are coarse-grained representations of the underlying statistics.

By considering the spin connection, we deduce the effective equation for a spin-1/2 particle confined to a curved surface with the nonrelativistic limit and in the thin-layer quantization formalism. We obtain a pseudo-magnetic-field and an effective spin-orbit interaction generated by the spin connection. Geometrically, the pseudo-magnetic field is proportional to the Gaussian curvature and the effective spin-orbit interaction is determined by the Weingarten curvature tensor. In particular, we find that the pseudo-magnetic-field and the effective spin-orbit interaction can be employed to separate the electrons with different spin orientations. All these results are demonstrated in two examples: a straight cylindrical surface and a bent one.

Maximally entangled photon pairs with a spatial degree of freedom is a potential way for realizing high-capacity quantum computing and communication. However, methods to generate such entangled states with high quality, high brightness, and good controllability are needed. Here, a scheme is experimentally demonstrated that generates spatially maximally entangled photon pairs with an orbital angular momentum degree of freedom via spontaneous parametric down-conversion in a nonlinear crystal. Compared with existing methods using postselection, the technique can directly modulate the spatial spectrum of down-converted photon pairs by engineering the input pump beam. In addition, the relative phase between spatially entangled photon pairs can be easily manipulated by preparing the relative phase of input pump states.

Using fixed-node diffusion quantum Monte Carlo (DMC) simulation we investigate the structural properties and energetics of the linear and cyclic carbon clusters ${\mathrm{C}}_n$ for $n\le 10$. We calculate the binding energy, the electron correlation energy, the dissociation energy, and the second difference in energy. We also present an analysis of the structural properties of the clusters. It is found that the bond lengths, binding energies, and dissociation energies obtained from the DMC calculations are in excellent agreement with the available experimental results. The electron-correlation contribution to the binding energy indicates that in the case of the linear isomers, the clusters of odd-number size are relatively more favored than their neighbors of even-number size, whereas for the cyclic isomers, we do not observe the oscillation pattern. In the range of cluster size under investigation, we find that the electron-correlation impact in the binding energy of the cyclic clusters is larger than that of the corresponding linear ones, varying from $30\%$ to $40\%$ of the binding energy values. The electron correlation is also essential to the stability of the clusters enhancing by up to $52\%$ their dissociation energy. A comparative analysis of the dissociation energy and second difference in energy indicates that the linear isomers ${\mathrm{C}}_3$ and ${\mathrm{C}}_5$ are the most stable ones.

A classical approach based on hyperspherical coordinates is used to derive a first-principles formulation of the the ion-neutral-neutral three-body recombination rate, ${\mathrm{A}}^{+}$ + A + A $\to$ ${{\mathrm{A}}_2}^{+}$ + A, in terms of the mass of the atom and its polarizability. The robustness and predictive power of our approach have been checked in comparison with experimental data of rare gas three-body recombination as well as previous theoretical frameworks, which need one or two atom-dependent fitting parameters. Thus, our approach is general and applicable to any ion-atom-atom system.

Characterizing and controlling matter driven far from equilibrium represents a major challenge for science and technology. Here, we develop a theory for the optical absorption of electronic materials driven far from equilibrium by resonant and nonresonant lasers. In it, the interaction between matter and the driving light is treated exactly through a Floquet analysis, while the effects of the probing light are captured to first order in perturbation theory. The resulting equations are reminiscent to those for equilibrium absorption but with the Floquet modes playing the role of the pristine eigenstates. The formalism is employed to characterize the optical properties of a model nanoscale semiconductor dressed by nonresonant light of intermediate intensity (nonperturbative, but nonionizing). As shown, nonresonant light can reversibly turn this transparent semiconductor into a broadband absorber and open strong absorption and stimulated emission bands at very low frequencies ($\sim \mathrm{meV}$). Further, the absorption spectra of the driven material exhibit periodic features energetically spaced by the photon energy of the driving light that reflect the periodic structure of the Floquet bands. These developments offer a platform to understand and predict the emergent optical properties of materials dressed by the electric field of light, and catalyze the design of laser-driven materials with desired optical properties.