Ultracold Fermi atoms confined in optical lattices coupled to quantized modes of an optical cavity are an ideal scenario to engineer quantum simulators in the strongly interacting regime. The system has both short-range and cavity-induced long-range interactions. We propose such a scheme to investigate the coexistence of superfluid pairing, density order, and quantum domains having antiferromagnetic or density order in the Hubbard model in a high-finesse optical cavity at $T=0$. We demonstrate that those phases can be accessed by properly tuning the linear polarizer of an external pump beam via the cavity back-action effect, while modulating the system doping. This allows one to emulate the typical scenarios of analog strongly correlated electronic systems.

We consider a type of light-dressing effect in molecules which is due to laser-induced deformation of molecules. We derive general formulas which describe the change of the equilibrium bond lengths, bending angles, and vibration frequencies for a polyatomic molecule. Up to the second-order terms in the field strength, the normal coordinates of the molecule are not changed. Explicit expressions for the change of the geometric parameters and vibration frequencies are found for a nonlinear triatomic molecule of the $A_{2}B$ type. These results are applied to calculation of the tunnel-ionization rates for ${\mathrm{H}}_2\mathrm{O}$, ${\mathrm{H}}_2{\mathrm{O}}^{+}$, and ${\mathrm{SO}}_2$ molecules, both in ac and dc fields. The main influence of the laser-induced deformation on the tunnel ionization is due to the changes in Franck-Condon factors, which are determined by overlap of the nuclei wave function of the molecule and its residual ion. In a laser field with an intensity of $\sim {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, the contribution of the laser-dressing effect to the ionization rate is within 5% for ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{H}}_2{\mathrm{O}}^{+}$, while accounting for this effect changes the ionization rate of the ${\mathrm{SO}}_2$ molecule by up to 20 times depending on the molecule's orientation with respect to the electric-field vector. Such a large difference is due to the electronic structures of these molecules.

Photoassociation of ultracold atoms with pulsed laser light is shown to lead to alignment of the product molecules along the excitation laser polarization axis. We theoretically investigate pulsed two-photon photoassociation of ${}^{87}\mathrm{Rb}$ atoms into a specific weakly bound level of the $a{}^3{\mathrm{\Sigma }}_u^{+}$ metastable electronic state and find both stationary and time-dependent field-free alignment. Although a transform-limited pulse yields significant alignment, a frequency-chirped pulse dramatically enhances the ultracold molecular formation rate at the cost of a slight decrease in the alignment. Employing multiple pulses synchronized with the vibrational and rotational periods leads to coherent enhancement of both population and alignment of the target state. Inclusion of the rotational degree of freedom in the model gives rise to processes with multiple quantum paths, which lead to quantum effects such as interference and coherence revivals.

We consider a three-component Fermi gas that has SU(3) symmetry and is confined to two dimensions (2D). For realistic cold atomic gas experiments, we show that the phase diagram of the quasi-2D system can be characterized using two 2D scattering parameters: the scattering length and the effective range. Unlike the case in three dimensions (3D), we argue that three-body bound states (trimers) in the quasi-2D system can be stable against three-body losses. Using a low-density expansion coupled with a variational approach, we investigate the fate of such trimers in the many-body system as the attractive interactions are decreased (or, conversely, as the density of particles is increased). We find that remnants of trimers can persist in the form of strong three-body correlations in the weak-coupling (high-density) limit.

The lowest Landau level (LLL) equation emerges as an accurate approximation for a class of dynamical regimes of Bose-Einstein condensates (BEC) in two-dimensional isotropic harmonic traps in the limit of weak interactions. Building on recent developments in the field of spatially confined extended Hamiltonian systems, we find a fully nonlinear solution of this equation representing periodically modulated precession of a single vortex. Motions of this type have been previously seen in numerical simulations and experiments at moderately weak coupling. Our paper provides a controlled analytic prediction for trajectories of a single vortex, suggests new targets for experiments, and opens up the prospect of finding analytic multivortex solutions.

We investigate the magnetic properties of a repulsive fermionic $\mathrm{SU}\left(3\right)$ Hubbard model on the Lieb lattice from weak to strong interaction by means of the mean-field approximation. To validate the method we employed, we first discuss the $\mathrm{SU}(2$) Hubbard model at the mean-field level, and find that our results are consistent with known rigorous theorems. We then extend the calculation to the case of $\mathrm{SU}\left(3\right)$ symmetry. We find that, at $4/9$ filling, the $\mathrm{SU}\left(3\right)$ symmetry spontaneously breaks into the $\mathrm{SU}\left(2\right)\times \mathrm{U}\left(1\right)$ symmetry in the ground state, leading to a staggered ferromagnetic state for any repulsive $U$ at zero temperature. We then investigate the stability of the ferromagnetic state by relaxing the filling away from $4/9$, and conclude that the ferromagnetic state is sensitive but robust to fillings, as it can persist within a certain filling regime. We also apply the mean-field approximation to finite temperature to calculate the critical temperature and the critical entropy of the ferromagnetic state. As the resulting critical entropy per particle is significantly greater than what can be realized in experiments, we expect some quasi-long-range-ordered features of such a ferromagnetic state can be realized and observed with fermionic alkaline-earth-metal(-like) atoms loaded into optical lattices.

We present a theoretical study of lasing action when plasmonic metallic structures that show lattice plasmon resonances are embedded in a gain medium. Our model combines classical electrodynamics for arrays of gold nanoparticles with a four-level quantum Liouville model of the laser dye photophysics. A numerical solution was implemented using finite-difference time-domain calculations coupled with a finite-difference solution to the Liouville equation. A particular focus of this work is the influence of dephasing in the quantum dynamics on the emission intensity at the threshold for lasing. We find that dephasing in the quantum system leads to reduced lasing emission, but with little effect on the long-term population inversion. Both electronic and vibrational dephasing is considered, but only electronic dephasing is significant, with the fully dephased result appearing for dephasing times comparable to plasmon dephasing ($\sim 10$ fs) while fully coherent results involve $>100$ ps dephasing times as determined by the rate of stimulated emission. There are factor-of-2 differences between the Maxwell-Liouville results (greater emission intensities and narrower widths) compared to the corresponding results of rate-equation models of the dye states, which indicates the importance of using the Maxwell-Liouville approach in modeling these systems. We also examine rate-equation models with and without constraints arising from the Pauli exclusion principle, and we find relatively small effects.

Dissipative entanglement-generation protocols embrace environmental interactions to generate long-lived entangled states. In this paper, we report on the antibunching dynamics for a pair of actively driven quantum emitters coupled to a shared dissipative plasmonic reservoir. We find that antibunching is a universal signature for entangled states generated by dissipative means and examine its use as an entanglement diagnostic. We discuss the experimental validation of plasmonically mediated entanglement generation by Hanbury Brown-Twiss interferometry with picosecond timing resolution determined by an effective two-qubit Rabi frequency, and we analyze the robustness of entanglement generation with respect to perturbations in local detunings, couplings, and driving fields.

Classical imaging works by scattering photons from an object to be imaged, and achieves resolution scaling as $1/\sqrt{t}$, with $t$ the imaging time. By contrast, the laws of quantum mechanics allow one to utilize quantum coherence to obtain imaging resolution that can scale as quickly as $1/t$ – the so-called “Heisenberg limit.” However, ambiguities in the obtained signal often preclude taking full advantage of this quantum enhancement, while imaging techniques designed to be unambiguous often lose this optimal Heisenberg scaling. Here we demonstrate an imaging technique which combines unambiguous detection of the target with Heisenberg scaling of the resolution. We also demonstrate a binary search algorithm which can efficiently locate a coherent target using the technique, resolving a target trapped ion to within 0.3% of the $1/e^2$ diameter of the excitation beam.

It is proposed to observe the $\mathcal{P},\mathcal{T}$-odd Faraday effect, i.e., the rotation of the polarization plane of the light propagating through a medium in the presence of an electric field in intracavity absorption spectroscopy experiments. The $\mathcal{P},\mathcal{T}$-odd Faraday effect may be caused by $\mathcal{C}\mathcal{P}$ violation within the standard model. For this purpose the vapors of heavy atoms such as Tl, Pb, and Bi are most suitable. Estimates based on the achievements of modern intracavity absorption spectroscopy demonstrate that the observation of the $\mathcal{P},\mathcal{T}$-odd Faraday effect may compete with the observation of the $\mathcal{P},\mathcal{T}$-odd electron spin rotation in an external electric field which now provides the most stringent bounds for the $\mathcal{P},\mathcal{T}$-odd effects in atomic physics.

The universal programmable discriminator is a device for discrimination between unknown quantum states. It has two kinds of registers: the program register and the data register. The states that are stored in registers are all unknown. It is assured that the data state is identical with one of the program states with the certain probability. The aim is to optimally identify the state stored in the data register with one of the program states that it is done by discriminating between unknown states of the combined system contains program and data registers. We design an optimal universal unambiguous programmable discriminator that has $N$ qubit systems in the program register, to unambiguously identify the qubit state of data with one of $N$ program qubit states. All unknown qubit states are pure and $N_D$ copies of the data state are available. We determine the optimal positive-operator valued measure (POVM) elements in two different ways. First, we find optimal POVMs that maximize the average of the overall success probability of discrimination between $N$ unknown pure states of the combined system. In another way, the problem of discrimination between $N$ unknown pure states of the combined system is reduced to discrimination between $N$ known average mixed states. It is shown that theses two different ways lead to the same results. We show that at least $N-1$ copies of the data state are necessary for discriminating between $N$ unknown states of the combined system.

We study the behavior of autoionizing states of the hydrogen molecule subject to screened Coulomb interactions using an ab initio Feshbach configuration interaction method. Special attention is given to the algorithms developed for the evaluation of (i) screened molecular orbitals expressed in terms of one-center expansions using B-spline polynomial basis functions and (ii) screened two-electron integrals between configurations expressed in terms of such molecular orbitals, by solving the screened Poisson equation. As an illustration of the method we focus on the lowest Feshbach resonance of the ${\mathcal{Q}}_1{}^1{\mathrm{\Sigma }}_g^{+}$ series of doubly excited states of ${\mathrm{H}}_2$, which lies between the first ${\mathrm{H}}_2{}^{+}$ ($1s{\sigma }_g$) and the second ${\mathrm{H}}_2{}^{+}$ ($2p{\sigma }_u$) ionization thresholds. We show that Coulomb screening in the electron-proton interaction and between electrons may significantly alter the resonance position and autoionizing decay as a function of internuclear distance. In general, screening increases the resonance lifetime. However, when electron-proton screening dominates over electron-electron screening, we find that the ${\mathcal{Q}}_1$ resonance acquires a pronounced shape-resonance character at internuclear distances where the resonance approaches the lower ionization threshold, thus leading to a pronounced decrease of its lifetime.

We analyze the time-dependent nonlinear response of helium atom to a strong laser pulse in form of the induced nonlinear electric susceptibility. Our theoretical predictions are based on ab initio solutions of the time-dependent Schrödinger equation obtained using a numerical basis state method and the short-time Fourier transform. The results qualitatively reproduce features seen in recent experimental data. In particular, we observe deviations from the adiabatic (field-following) response in the electric susceptibility at high intensities. According to our analysis a shift of the peak towards the front of the pulse and changes in the concavity of the slope in the trailing edge of the pulse can be related to the population of continuum states and bound excited states with high angular quantum number during the interaction of the atom with the laser pulse.

We present a scheme for tomographic imaging of asymmetric molecular orbital based on high-order harmonic generation with a two-color orthogonally polarized multicycle laser field. With the two-dimensional manipulation of the electron trajectories, the electrons can recollide with the target molecule from two noncollinear directions, and then the dipole moment generated from the single direction can be obtained to reconstructed the asymmetric molecular orbital. The recollision is independent from the molecular structure and the angular dependence of the ionization rate in the external field. For this reason, this scheme can avoid the negative effects arising from the modification of the angle-dependent ionization rate induced by Stark shift and be applied to various molecules.

The angular dependence of photoemission time delay for the inner $n{d}_{3/2}$ and $n{d}_{5/2}$ subshells of free and confined Xe is studied in the dipole relativistic random phase approximation. A finite spherical annular well potential is used to model the confinement due to fullerene $C_{60}$ cage. Near cancellations in a variety of the dipole amplitudes, Cooper-like minima, are found. The effects of confinement on the angular dependence, primarily confinement resonances, are demonstrated and detailed.

We study the decoherence dynamics of dipole-coupled two-level quantum systems in Ramsey-type experiments. We focus on large networks of two-level systems, confined to two spatial dimensions and with positional disorder giving rise to disordered dipolar couplings. This setting is relevant for modeling the decoherence dynamics of the rotational excitations of polar molecules confined to deep optical lattices, where disorder arises from the random filling of lattice sites with occupation probability $p$. We show that the decoherence dynamics exhibits a phase transition at a critical filling $p_c\simeq 0.15$. For $p<p_c$ the dynamics is disorder dominated and the Ramsey interference signal decays on a time scale $T_2\propto p^{-3/2}$. For $p>p_c$ the dipolar interactions dominate the disorder, and the system behaves as a collective spin-ordered phase, representing synchronization of the two-level systems and persistent Ramsey oscillations with divergent $T_2$ for large systems. For a finite number of two-level systems $N$, the spin-ordered phase at $p>p_c$ undergoes a crossover to a collective spin-squeezed state on a time scale ${\tau }_{\mathrm{sq}}\propto \sqrt{N}$. We develop a self-consistent mean-field theory that is capable of capturing the synchronization transition at $p_c$, and provide an intuitive theoretical picture that describes the phase transition in the long-time dynamics. We also show that the decoherence dynamics appear to be ergodic in the vicinity of $p_c$, the long-time behavior being well described by the predictions of equilibrium thermodynamics. The results are supported by the results of exact diagonalization studies of small systems.

We investigate the ground-state properties and the collective modes of a two-dimensional two-component Rydberg-dressed Fermi liquid in the dipole-blockade regime. We find instability of the homogeneous system toward phase-separated and density ordered phases, using the Hartree-Fock and random-phase approximations, respectively. The spectral weight of collective density oscillations in the homogenous phase also signals the emergence of density-wave instability. We examine the effect of exchange hole on the density-wave instability and on the collective-mode dispersion using the Hubbard local-field factor.

We study the collective dynamics of accelerated atoms interacting with a massless field via an Unruh-deWitt–type interaction. We first derive a general Hamiltonian describing such a system and then, employing a Markovian master equation, we study the corresponding collective dynamics. In particular, we observe that the emergence of entanglement between two-level atoms is linked to the building up of coherences between them and to superradiant emission. In addition, we show that the derived Hamiltonian can be experimentally implemented by employing impurities in Bose-Einstein condensates.

We study vortex patterns in a prototype nonlinear optical system: counterpropagating laser beams in a photorefractive crystal, with or without the background photonic lattice. The vortices are effectively planar and have two “flavors” because there are two opposite directions of beam propagation. In a certain parameter range, the vortices form stable equilibrium configurations which we study using the methods of statistical field theory and generalize the Berezinsky-Kosterlitz-Thouless transition of the $\mathit{XY}$ model to the “two-flavor” case. In addition to the familiar conductor and insulator phases, we also have the perfect conductor (vortex proliferation in both beams or “flavors”) and the frustrated insulator (energy costs of vortex proliferation and vortex annihilation balance each other). In the presence of disorder in the background lattice, a phase appears which shows long-range correlations and absence of long-range order, thus being analogous to glasses. An important benefit of this approach is that qualitative behavior of patterns can be known without intensive numerical work over large areas of the parameter space. The observed phases are analogous to those in magnetic systems, and make (classical) photorefractive optics a fruitful testing ground for (quantum) condensed matter systems. As an example, we map our system to a doped $\text{O}\left(3\right)$ antiferromagnet with ${\mathbb{Z}}_2$ defects, which has the same structure of the phase diagram.