The tunneling reaction ${\mathrm{H}}_2+{\mathrm{D}}^{-}\to \mathrm{HD}+{\mathrm{H}}^{-}$ was studied in a recent experimental work at low temperatures (10, 19, and 23 K) by Endres et al. [Phys. Rev. A 95, 022706 (2017)]. An upper limit of the rate coefficient was found to be about ${10}^{-18}{\mathrm{cm}}^3$/s. In the present study, reaction probabilities are determined using the ABC program developed by Skouteris et al. [Comput. Phys. Commun. 133, 128 (2000)]. The probabilities for ortho-${\mathrm{H}}_2$ and para-${\mathrm{H}}_2$ in their ground rovibrational states are obtained numerically at collision energies above 50 meV with the total angular momentum $J=0$–15 and extrapolated below 50 meV using a WKB approach. Thermally averaged rate coefficients for ortho- and para-${\mathrm{H}}_2$ are obtained; the largest one, for ortho-${\mathrm{H}}_2$, is about $3.1\times {10}^{-20}{\mathrm{cm}}^3$/s, which agrees with the experimental results.

Strong-field ionization (SFI) of the homonuclear noble gas dimer ${\mathrm{Xe}}_2$ is investigated and compared with SFI of the Xe atom and of the ArXe heteronuclear dimer by using ultrashort Ti:sapphire laser pulses and photoelectron momentum spectroscopy. The large separation of the two nuclei of the dimer allows the study of two-equivalent-center interference effects on the photoelectron momentum distribution. Comparing the experimental results with a new model calculation, which is based on the strong-field approximation, actually reveals the influence of interference. Moreover, the comparison indicates that the presence of closely spaced gerade and ungerade electronic state pairs of the ${{\mathrm{Xe}}_2}^{+}$ ion at the ${\mathrm{Xe}}_2$ ionization threshold, which are strongly dipole coupled, affects the photoelectron momentum distribution.

The attractive two-site Bose-Hubbard model is studied within the framework of the analytical solution obtained by the application of the quantum inverse scattering method. The structure of the ground and excited states is analyzed in terms of solutions of Bethe equations, and an approximate solution for the Bethe roots is given. This yields approximate formulas for the ground-state energy and for the first excited-state energy. The obtained formulas work with remarkable precision for a wide range of parameters of the model, and are confirmed numerically. An expansion of the Bethe state vectors into a Fock space is also provided for evaluation of expectation values, although this does not have accuracy similar to that of the energies.

Considerable theoretical and experimental efforts have been devoted to the quench dynamics, in particular, the dynamical quantum phase transition (DQPT) and the steady-state transition. These developments have motivated us to study the quench dynamics of the topological systems, from which we find the connection between these two transitions, that is, the DQPT, accompanied by a nonanalytic behavior as a function of time, always merges into a steady-state transition signaled by the nonanalyticity of observables in the steady limit. As the characteristic time of the DQPT diverges, it exhibits universal scaling behavior, which is related to the scaling behavior at the corresponding steady-state transition.

We address an experimental scheme to analyze the optical bistability and the entanglement of two movable mirrors coupled to a two-mode laser inside a doubly resonant cavity. With this aim we investigate the master equations of the atom-cavity subsystem in conjunction with the quantum Langevin equations that describe the interaction of the mirror cavity. The parametric amplification-type coupling induced by the two-photon coherence on the optical bistability of the intracavity mean photon numbers is found and investigated. Under this condition, the optical intensities exhibit bistability for all large values of cavity laser detuning. We also provide numerical evidence for the generation of strong entanglement between the movable mirrors and show that it is robust against environmental thermalization.

We study photoelectron holography in strong bicircular two-color laser fields by solving the time-dependent Schrödinger equation (TDSE) and a semiclassical rescattering model with implementing interference effect. The holographic patterns observed in the TDSE are well recaptured by the semiclassical rescattering model. Four types of photoelectron holographic interferences between the forward scattered and nonscattered trajectories are predicted by the semiclassical rescattering model in the bicircular two-color laser field. We find that those holographic patterns are spatially separated from each other in the electron momentum distribution. We further show that the dependence of the initial transverse momentum at the tunnel exit on the ionization time for the rescattering electron is recorded by the holographic patterns.

We propose and analyze an electrostatic-optical nanoscale trap for cold diatomic polar molecules. The main ingredient of our proposal is a square array of ferroelectric nanorods with alternating polarization. We show that, in contrast to electrostatic traps using the linear Stark effect, a quadratic Stark potential supports long-lived trapped states. The molecules are kept at a fixed height from the nanorods by a standing-wave optical dipole trap. For the molecules and materials considered, we find nanotraps with trap frequency up to 1 MHz, ground-state width $\sim 20\mathrm{nm}$ with lattice periodicity of $\sim 200\mathrm{nm}$. Analyzing the loss mechanisms due to nonadiabaticity, surface-induced radiative transitions, and laser-induced transitions, we show the existence of trapped states with lifetime $\sim 1\mathrm{s}$, competitive with current traps created via optical mechanisms. As an application we extend our discussion to a one-dimensional (1D) array of nanotraps to simulate a long-range spin Hamiltonian in our structure.

The coupling of atomic arrays and one-dimensional subwavelength waveguides gives rise to interesting photon transport properties, such as recent experimental demonstrations of large Bragg reflection, and paves the way for a variety of potential applications in the field of quantum nonlinear optics. Here, we present a theoretical analysis for the process of single-photon scattering in this configuration using a full microscopic approach. Based on this formalism, we analyze the spectral dependencies for different scattering channels from either ordered or disordered arrays. The developed approach is entirely applicable for a single-photon scattering from a quasi-one-dimensional array of multilevel atoms with degenerate ground-state energy structure. Our approach provides an important framework for including not only Rayleigh but also Raman channels in the microscopic description of the cooperative scattering process.

When two identical (coherent) beams are injected at a semi-infinite non-Hermitian medium from left and right, we show that both reflection $(r_L,r_R)$ and transmission $(t_L,t_R)$ amplitudes are nonreciprocal. In a parametric domain, there exists spectral singularity (SS) at a real energy $E=E_{*}=k_{*}^2$ and the determinant of the time-reversed two port scattering matrix, i.e., $|det\left(S(-k)\right)|=|t_L(-k)t_R(-k)-r_L(-k)r_R(-k)|$, vanishes sharply at $k=k_{*}$, displaying the phenomenon of coherent perfect absorption (CPA). In the complementary parametric domain, the potential becomes either left or right reflectionless at $E=E_z$. We rule out the existence of invisibility despite $r_R\left(E_i\right)=0$ and $t_R\left(E_i\right)=1$ but $T\left(E_i\right)\ne 1$, in this avenue. We present two simple exactly solvable models where expressions for $E_{*}$, $E_z$, $E_i$, and parametric conditions on the potential have been obtained in explicit and simple forms. Earlier, the phenomena of SS and CPA have been found to occur only in the scattering complex potentials which are spatially localized (vanish asymptotically) and have $t_L=t_R$.

We introduce an entanglement-depth criterion optimized for planar quantum-squeezed (PQS) states. It is connected with the sensitivity of such states for estimating a phase generated by rotations about an axis orthogonal to its polarization. We compare numerically our criterion with the well-known extreme spin-squeezing condition of Sørensen and Mølmer [Phys. Rev. Lett. 86, 4431 (2001)] and show that our condition detects a higher depth of entanglement when both planar spin variances are squeezed below the standard quantum limit. We employ our theory to monitor the entanglement dynamics in a PQS state produced via quantum nondemolition measurements using data from a recent experiment [Phys. Rev. Lett. 118, 233603 (2017)].

Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-$k$-SAT problems, use $k$-local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved $n$-body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

We propose and investigate a method of error detection and noise correction for bosonic linear networks using a method of unitary averaging. The proposed error averaging does not rely on ancillary photons or control and feedforward correction circuits, remaining entirely passive in its operation. We construct a general mathematical framework for this technique and then give a series of proof of principle examples including numerical analysis. Two methods for the construction of averaging are then compared to determine the most effective manner of implementation and probe the related error thresholds. Finally we discuss some of the potential uses of this scheme.

We report measurements of the scalar and tensor static polarizabilities of the ${}^{115}\mathrm{In}7p_{1/2}$ and $7p_{3/2}$ excited states using two-step diode laser spectroscopy in an atomic beam. These scalar polarizabilities are one to two orders of magnitude larger than for lower-lying indium states due to the close proximity of the $7p$ and $6d$ states. For the scalar polarizabilities, we find values (in atomic units) of $1.811\left(4\right)\times {10}^5{a}_0^3$ and $2.876\left(6\right)\times {10}^5{a}_0^3$ for the $7p_{1/2}$ and $7p_{3/2}$ states, respectively. We determine the tensor polarizability component of the $7p_{3/2}$ state to be $-1.43\left(18\right)\times {10}^4{a}_0^3$. These measurements set high-precision benchmarks of the transition properties for highly excited states in trivalent atomic systems. We also present ab initio calculations of these quantities and other In polarizabilities using two high-precision relativistic methods to make a global comparison of the accuracies of the two approaches. The precision of the experiment is sufficient to differentiate between the two theoretical methods as well as to allow precise determination of the indium $7p\text{−}6d$ matrix elements. The results obtained in this paper are applicable to other heavier and more complicated systems, and provide much needed guidance for the development of even more precise theoretical approaches.

The theory is developed for one- and two-atom interactions when the atom has a Rydberg electron attached to a hyperfine-split core state. This situation is relevant for some of the rare-earth and alkaline-earth atoms that have been proposed for experiments on Rydberg-Rydberg interactions. For the rare-earth atoms, the core electrons can have a very substantial total angular momentum $J$ and a nonzero nuclear spin $I$. In the alkaline-earth atoms there is a single ($s$) core electron whose spin can couple to a nonzero nuclear spin for odd isotopes. The resulting hyperfine splitting of the core state can lead to substantial mixing between the Rydberg series attached to different thresholds. Compared to the unperturbed Rydberg series of the alkali-metal atoms, the series perturbations and near degeneracies from the different parity states could lead to qualitatively different behavior for single-atom Rydberg properties (polarizability, Zeeman mixing and splitting, etc.) as well as Rydberg-Rydberg interactions ($C_5$ and $C_6$ matrices).

We explore theoretically the generation and all-optical control of optical frequency combs (OFCs) in photon transmission based on a combination of single-atom-cavity quantum electrodynamics (CQED) and electromagnetically induced transparency (EIT). Here an external control field is used to form the cavity dark mode of the CQED system. When the strengths of the applied EIT control field are appropriately tuned, enhanced comb generation can be achieved. We discuss the properties of the dark mode and clearly show that the formation of the dark mode enables the efficient generation of OFCs. In our approach, the comb spacing is determined by the beating frequency between the driving pump and seed lasers. Our demonstrated theory may pave the way towards all-optical coherent control of OFCs using a CQED architecture.

We investigate the quantum annealing of the ferromagnetic $p$-spin model in a dissipative environment ($p=5$ and $p=7$). This model, in the large-$p$ limit, codifies Grover's algorithm for searching in an unsorted database [L. K. Grover, Proceedings of the 28th Annual ACM Symposium on Theory of Computing (ACM, New York, 1996), pp. 212–219]. The dissipative environment is described by a phonon bath in thermal equilibrium at finite temperature. The dynamics is studied in the framework of a Lindblad master equation for the reduced density matrix describing only the spins. Exploiting the symmetries of our model Hamiltonian, we can describe many spins and extrapolate expected trends for large $N$ and $p$. While at weak system-bath coupling the dissipative environment has detrimental effects on the annealing results, we show that in the intermediate-coupling regime, the phonon bath seems to speed up the annealing at low temperatures. This improvement in the performance is likely not due to thermal fluctuation but rather arises from a correlated spin-bath state and persists even at zero temperature. This result may pave the way to a new scenario in which, by appropriately engineering the system-bath coupling, one may optimize quantum annealing performances below either the purely quantum or the classical limit.