We report a three-dimensional numerical implementation of the multiconfiguration time-dependent Hartree-Fock method based on a multiresolution Cartesian grid, with no need to assume any symmetry of molecular structure. We successfully compute high-harmonic generation of ${\mathrm{H}}_2$ and ${\mathrm{H}}_2\mathrm{O}$. The present implementation will open a way to the first-principles theoretical study of intense-field- and attosecond-pulse-induced ultrafast phenomena in general molecules.

The promise of innovative applications has triggered the development of many modern technologies capable of exploiting quantum effects. But in addition to future applications, such quantum technologies have already provided us with the possibility of accessing quantum-mechanical scenarios that seemed unreachable just a few decades ago. With this spirit, in this work we show that modern optomechanical setups are mature enough to implement one of the most elusive models in the field of open system dynamics: degenerate parametric oscillation. Introduced in the eighties and motivated by its alleged implementability in nonlinear optical resonators, it rapidly became a paradigm for the study of dissipative phase transitions whose corresponding spontaneously broken symmetry is discrete. However, it was found that the intrinsic multimode nature of optical cavities makes it impossible to experimentally study the model all the way through its phase transition. In contrast, here we show that this long-awaited model can be implemented in the motion of a mechanical object dispersively coupled to the light contained in a cavity, when the latter is properly driven with multichromatic laser light. We focus on membranes as the mechanical element, showing that the main signatures of the degenerate parametric oscillation model can be studied in state-of-the-art setups, thus opening the possibility of analyzing spontaneous symmetry breaking and enhanced metrology in one of the cleanest dissipative phase transitions. In addition, the ideas put forward in this work would allow for the dissipative preparation of squeezed mechanical states.

We investigate, in the case of the $2P\text{−}1S$ transition in atomic hydrogen, the behavior of the spontaneously emitted electromagnetic field in space-time. We focus on Glauber's wave function for the emitted photon, a quantity which we find is nonzero outside the light cone at all times after the start of the emission. We identify the uncertainty on the position of the decaying electron as a source of departure from causality in the naive sense of the term. We carry out a detailed study of the emitted electric field in the mid- and far-field regions, through analytical and numerical computations as well as asymptotic arguments.

A theoretical investigation on the influence of birefringence in the modulational instability (MI) spectra of an oppositely directed coupler (ODC) with a negative index material (NIM) channel is presented. We study the effect of birefringence on MI in linear and circular birefringent ODCs for both normal and anomalous dispersion regimes. It is found that besides the instability band due to nonlinear positive index material (PIM) and negative index material (NIM) channels, new symmetric instability regions are observed as a result of birefringent effects. Also defocusing nonlinearity suppresses the NIM band in the normal dispersion regime, but in the anomalous dispersion regime the defocusing nonlinearity enhances the gain of the NIM band. In contrast to the case of linear birefringence, in terms of MI gain from circular birefringence, only two birefringent bands dominate: the inherently PIM and NIM bands. This preponderance is attributed to the fact that the cross-phase modulation effect for the case of circular birefringence is stronger, thus allowing a better coupling between the beams, which results in the enhancement of the gain. Therefore, the manipulation of MI and solitons in an ODC is better performed when the birefringence is circular rather than linear. Here we report how to generate and manipulate MI and solitons in birefringent ODCs with a particular emphasis on a NIM channel.

Quantum steering can be detected via the violation of steering inequalities, which provide sufficient conditions for the steerability of quantum states. Here we discuss the converse problem, namely, ensuring that an entangled state is unsteerable and hence Bell local. We present a simple criterion, applicable to any two-qubit state, that guarantees that the state admits a local hidden state model for arbitrary projective measurements. Specifically, we construct local hidden state models for a large class of entangled states, which thus cannot violate any steering or Bell inequality. In turn, this leads to sufficient conditions for a state to be only one-way steerable and provides the simplest possible example of one-way steering. Finally, by exploiting the connection between steering and measurement incompatibility, we give a sufficient criterion for a continuous set of qubit measurements to be jointly measurable.

We propose a universal language to assess macroscopic quantumness in terms of coherence, with a set of conditions that should be satisfied by any measure of macroscopic coherence. We link the framework to the resource theory of asymmetry. We show that the quantum Fisher information gives a good measure of macroscopic coherence, enabling a rigorous justification of a previously proposed measure of macroscopicity. This picture lets us draw connections between different measures of macroscopicity and evaluate them; we show that another widely studied measure fails one of our criteria.

The Leggett-Garg (LG) inequalities were proposed in order to assess whether sets of pairs of sequential measurements on a single quantum system can be consistent with an underlying notion of macrorealism. Here, the LG inequalities are explored using a simple quasiprobability linear in the projection operators to describe the properties of the system at two times. We show that this quasiprobability is measurable, has the same correlation function as the usual two-time measurement probability (for the bivalent variables considered here) and has the key property that the probabilities for the later time are independent of whether an earlier measurement was made, a generalization of the no-signaling in time condition of Kofler and Brukner. We argue that this quasiprobability, appropriately measured, provides a noninvasive measure of macrorealism per se at the two-time level. This measure, when combined with the LG inequalities, provides a characterization of macrorealism more detailed than that provided by the LG inequalities alone. When the quasiprobability is non-negative, the LG system has a natural parallel with the Einstein-Podolsky-Rosen-Bohm system and Fine's theorem. A simple spin model illustrating key features of the approach is exhibited.

We derive a Markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion. Our equation provides a unifying picture of the consequences of recoil and indistinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics, and applies equally well to distinguishable and indistinguishable atoms. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, and we find closed-form formulas for a number of relevant states (Gaussian states, Fock states, and thermal states). In particular, we show that dipole-dipole interactions and cooperative photon emission can be modulated through the external state of motion.

We analyze a scheme for storage of entanglement quantified by the quantum Fisher information in the two-axis countertwisting model. A characteristic feature of the two-axis countertwisting Hamiltonian is the existence of the four stable center and two unstable saddle fixed points in the mean-field phase portrait. The entangled state is generated dynamically from an initial spin-coherent state located around an unstable saddle fixed point. At an optimal moment of time the state is shifted to a position around the stable center fixed points by a single rotation, where its dynamics and properties are approximately frozen. We also discuss evolution with noise. In some cases the effect of noise turns out to be relatively weak, which is explained by parity conservation.

The effects of endohedral confinement on the correlation energy of Be, Mg, and Ca atoms have been investigated using modified Hartree-Fock and multiconfiguration Hartree-Fock methods where the endohedral system $(A@{\text{C}}_{60})$ is approximated as an atom enclosed in an attractive spherically symmetric potential well of inner radius $r\sim 5.8$ a.u. and thickness of $\mathrm{\Delta }\sim 1.89$ a.u., and correlation energies are studied as a function of the depth of the confining potential ($0\le U_0\le 1$ a.u.) to give some idea as to how the correlation energy behaves in different endohedral environments. In general, we have found that as a function of well depth, starting from the free atom, valence electrons diffuse outward in the presence of the confining potential, which causes the electrons to be further apart, thereby decreasing the correlation energy; however, with further increase of well depth, the valence electrons become trapped in the confining well and, as a result of their being closer together, the correlation energy increases.

We present tables for the bound-state energies for atomic hydrogen. The tabulated energies include the hyperfine structure and thus this work extends the work of Mohr et al. [P. J. Mohr et al., Rev. Mod. Phys. 84, 1527 (2012)], which excludes the hyperfine structure. The tabulation includes corrections of the hyperfine structure due to the anomalous moment of the electron, due to the finite mass of the proton, and due to off-diagonal matrix elements of the hyperfine Hamiltonian. These corrections are treated incorrectly in most other works. Simple formulas valid for all quantum numbers are presented for the hyperfine corrections. The tabulated energies have uncertainties of less than 1 kHz for all states. This accuracy is possible because of the recent precision measurement [R. Pohl et al., Nature (London) 466, 213 (2010)] of the proton radius. The effect of this radius on the energy levels is also tabulated and the energies are compared to precision measurements of atomic hydrogen energy intervals.

Absolute measurements of charge-exchange cross sections of ${\mathrm{H}}^{+},{\mathrm{H}}_2^{+},{\mathrm{H}}_3^{+},{\mathrm{He}}^{+}$, and ${\mathrm{He}}_2^{+}$ ions in CO and ${\mathrm{CO}}_2$ have been made for energies below 1000 eV, an equivalent of the energy of ionized particles at typical solar-wind conditions. An attenuation method for the case of complex ions of a molecule, taking into account the influence on the ion beam composition of the processes of disintegration of the primary ions into secondary ones with different charge-exchange cross sections, is described. Also the secondary effects, like three-body collisions and re-ionization processes that could emerge at higher pressures of the gas layer, are discussed. Dependence of the cross sections on the number of atomic centers in the projectile have been explained on the basis of the energy defect of the reactions and asymmetric near-resonant charge-exchange process between the ion and target molecule including the Doppler broadening in the interaction of the monoenergetic ion beam and target molecules having an isotropic Maxwellian velocity distribution corresponding to room temperature. Using the semiempirical approach based on the parametrized numerical coupled-channel two-state calculations, we have extrapolated the cross sections to a broader range of velocities.

Threshold phenomena (or channel-closing effects) are analyzed in high-order harmonic generation (HHG) by atoms in a two-color laser field with orthogonal linearly polarized components of a fundamental field and its second harmonic. We show that the threshold behavior of HHG rates for the case of a weak second harmonic component is sensitive to the parity of a closing multiphoton ionization channel and the spatial symmetry of the initial bound state of the target atom, while for the case of comparable intensities of both components, suppression of threshold phenomena is observed as the relative phase between the components of a two-color field varies. A quantum orbit analysis as well as phenomenological considerations in terms of Baz' theory of threshold phenomena [Zh. Eksp. Teor. Fiz. 33, 923 (1957)] are presented in order to describe and explain the major features of threshold phenomena in HHG by a two-color field.

We have conducted laser photodetachment spectroscopy near the detachment threshold of the electron affinity of ${\mathrm{S}}_2$ in a 1.8-T field. The ions are prepared by dissociative electron attachment to carbonyl sulfide. The experiment is conducted in a Penning ion trap and with a narrow-band, tunable, Ti:sapphire laser. A hybrid model for photodetachment in an ion trap is fit to the data using the appropriate Franck-Condon factors. The observations reveal detachment from and to the first few vibrational levels of the anion and the neutral molecule, respectively. Evaporative cooling of the anion ensemble condenses the thermal distribution to the lowest initial vibrational states. The subsequent detachment spectroscopy yields results consistent with a vibrationally cooled anion population.

We show that a composite spin-½ Kondo system can be formed by coupling a superconducting quantum interference device (SQUID) to the internal hyperfine states of a trapped ultracold atomic Fermi gas. Here, the SQUID, or flux qubit, acts as an effective magnetic impurity that induces spin-flip scattering near the Fermi energies of the trapped gas. Although the ultracold gas and SQUID are at vastly different temperatures, the formation of a strongly correlated Kondo state between the two systems is found when the gas is cooled below the Kondo temperature. We find that the Kondo temperature of this hybrid system is within current experimental limits. Furthermore, the momentum distribution of the trapped fermions is calculated, which clearly shows an experimental signature of the Kondo screening length. In addition to probing Kondo physics, the controllability of this system can be used to systematically explore the relaxation and equilibration of a strongly correlated system that has been initially prepared in a selected nonequilibrium state.

We investigate competition between two phase transitions of the second kind induced by the self-attractive nonlinearity, viz., self-trapping of the leaky modes, and spontaneous symmetry breaking (SSB) of both fully trapped and leaky states. We use a one-dimensional mean-field model, which combines the cubic nonlinearity and a double-well-potential (DWP) structure with an elevated floor, which supports leaky modes (quasi-bound states) in the linear limit. The setting can be implemented in nonlinear optics and Bose–Einstein condensates. The order in which the SSB and self-trapping transitions take place with the growth of the nonlinearity strength depends on the height of the central barrier of the DWP: the SSB happens first if the barrier is relatively high, while self-trapping comes first if the barrier is lower. The SSB of the leaky modes is characterized by specific asymmetry of their radiation tails, which, in addition, feature a resonant dependence on the relation between the total size of the system and radiation wavelength. As a result of the SSB, the instability of symmetric modes initiates spontaneous Josephson oscillations. Collisions of freely moving solitons with the DWP structure admit trapping of an incident soliton into a state of persistent shuttle motion, due to emission of radiation. The study is carried out numerically, and basic results are explained by means of analytical considerations.

We investigate the optical-response properties of a levitated optomechanical cavity coupled to a higher order excited atomic medium. The cavity field driven through the atom-field interaction is responsible for trapping a dielectric nanosphere, whose steady-state position is biased by the Coulomb force between the nanosphere and the cavity wall. We show that the phenomena of optomechanically induced transparency (OMIT) and amplification can be generated from the output probe field in the presence of an effective optomechanical coupling between the nanosphere and the cavity field. Further, the width of the transparency window increases with increasing strength of the effective optomechanical coupling, which is controlled easily by varying the Coulomb interaction and the radius of the nanosphere. In particular, when the higher order excitation of the atomic medium is included, a large driving of the atomic ensemble but a relatively small atom-field detuning can be applied to help observe the OMIT behavior in the hybrid system.

A mechanism for the synchronization of driven colloidal rotors via optical coupling torques is presented and analyzed. Following our recent experiments [Brzobohatý et al., Opt. Express 23, 7273 (2015)], we consider a counterpropagating optical beam trap that carries spin angular momentum, but no net linear momentum, operating in an aqueous solvent. The angular momentum carried by the beams causes the continuous low-Reynolds-number rotation of spheroidal colloids. Due to multiple scattering, the optical torques experienced by these particles depend on their relative orientations, while the effect of hydrodynamic interaction is negligible. This results in frequency pulling, which causes weakly dissimilar spheroids to synchronize their rotation rates and lock their relative phases. The effect is qualitatively captured by a coupled dipole model and quantitatively reproduced by $T$-matrix calculations. For pairs of rotors, the relative torque $\mathrm{\Delta }\tau$ is shown to vary with relative phase $\mathrm{\Delta }\varphi$ according to $\mathrm{\Delta }\tau \approx Asin(2\mathrm{\Delta }\varphi +\delta )+B$ for constants $A,B,\delta$, so the resulting motion is governed by the well-known Adler equation. We show that this behavior can be preserved for larger numbers of particles. The application of these phenomena to the inertial motion of particles in vacuum could provide a route to the sympathetic cooling of mesoscopic particles.

We demonstrate that four-wave mixing processes in high-quality nonlinear resonators can lead to Rabi-like oscillations in photon occupation numbers and second-order correlation functions, being a characteristic feature of the presence of entangled photon pairs in the optical signal. In the case of a system driven by a continuous coherent pump, the oscillations occur in the transient regime. We show that driving the system with pulsed coherent pumping would generate strongly antibunched photon states.

We study the cross-Kerr (CK) effect on an optomechanical system driven by two-tone fields. We show that in the presence of the CK effect, a bistable behavior of the mean photon number in the cavity becomes more robust against the fluctuations of the frequency detuning between the cavity mode and the control field. The bistability can also be turned into a tristability within the experimentally accessible range of the system parameters. Also, we find that the symmetric profile of the optomechanically induced transparency is broken and the zero-absorption point is shifted in the presence of the CK effect. This shift can be used to measure the strength of the CK effect and the asymmetric absorption profiles can be employed to engineer a high quality factor of the cavity.