Quantum optimal control can play a crucial role in realizing a set of universal quantum logic gates with error rates below the threshold required for fault tolerance. Open-loop quantum optimal control relies on accurate modeling of the quantum system under control and does not scale efficiently with system size. These problems can be avoided in closed-loop quantum optimal control, which utilizes feedback from the system to improve control fidelity. In this paper, two gradient-based closed-loop quantum optimal control algorithms, the hybrid quantum-classical approach (HQCA) described by Li et al. [Phys. Rev. Lett. 118, 150503 (2017)] and the finite-difference (FD) method, are experimentally investigated and compared to the open-loop quantum optimal control utilizing the gradient ascent method. We employ a solid-state ensemble of coupled electron-nuclear spins serving as a two-qubit system. Specific single-qubit and two-qubit state preparation gates are optimized using the closed-loop and open-loop methods. The experimental results demonstrate the implemented closed-loop quantum control outperforms the open-loop control in our system. Furthermore, simulations reveal that HQCA is more robust than the FD method to gradient noise which originates from measurement noise in this experimental setting. On the other hand, the FD method is more robust to control field distortions coming from nonideal hardware.

We report absolute optical frequencies of electronic transitions from the $X{}^2\mathrm{\Pi }_{3/2},v^{″}=0,J^{″}=3/2$ rovibronic ground state to the 12 lowest levels of the $A{}^2\mathrm{\Sigma }^{+},v^{\prime }=0$ vibronic state in ${}^{16}\mathrm{OH}$, as well as to the 16 lowest levels of the same vibronic state in ${}^{16}\mathrm{OD}$. The absolute frequencies of these transitions have been determined with a relative uncertainty of a few parts in ${10}^{11}$, representing a $\sim 1000$-fold improvement over previous measurements. To reach this level of precision, an optical frequency comb has been used to transfer the stability of a narrow-linewidth ${\mathrm{I}}_2$-stabilized reference laser onto the 308-nm spectroscopy laser. The comb is also used to compare the optical frequency of the spectroscopy laser to an atomic clock reference, providing absolute accuracy. Measurements have been carried out on OH and OD molecules in a highly collimated molecular beam, reducing possible pressure shifts and minimizing Doppler broadening. Systematic shifts due to retroreflection quality, the Zeeman effect, and the ac Stark effect have been considered during the analysis of the measured spectra; particularly in the case of the OD isotopologue, these effects can result in shifts of the fitted line positions of as much as 300 kHz. The transition frequencies extracted in the analysis were also used to determine spectroscopic constants for the $A{}^2\mathrm{\Sigma }^{+},v^{\prime }=0$ vibronic state. The constants fitted in this work differ significantly from those reported in previous works that measured the $A\text{−}X$ transitions, resulting in typical deviations of the predicted optical transition frequencies of $\sim 150\mathrm{MHz}$, but they generally agree quite well with the constants determined using hyperfine-resolved measurements of splittings within the $A$ state.

Advances in laser spectroscopy of superheavy ($Z>100$) elements enabled determination of the nuclear moments of the heaviest nuclei, which required high-precision atomic calculations of the relevant hyperfine-structure (hfs) constants. Here, we calculated the hfs constants and energy levels for a number of nobelium ($Z=102$) states using a hybrid approach combining linearized coupled-cluster and configuration interaction methods. We also carried out an extensive study of the No energies using the 16-electron configuration interaction method to determine the position of the $5f^{13}7s^{2}6d$ and $5f^{13}7s^{2}7p$ levels with a hole in the $5f$ shell to evaluate their potential effect on the hyperfine-structure calculations of the low-lying $5f^{14}7s6d$ and $5f^{14}7s7p$ levels. We find that unlike the case of Yb, the mixing of the low-lying levels with filled and unfilled $f$ shells is small and does not significantly influence their properties. The resulting hfs constants for the $5f^{14}7s7p{}^1{P}_1^o$ level, combined with laser-spectroscopy measurement, were used to extract nobelium nuclear properties [Raeder et al., Phys. Rev. Lett. 120, 232503 (2018)].

Ultracold atomic gases are an important testing ground for understanding few-body physics. In particular, these systems enable a detailed study of the Efimov effect. We use ultracold ${}^{39}\mathrm{K}$ to investigate the temperature dependence of an Efimov resonance. The shape and position of the observed resonance are analyzed by employing an empirical fit, and universal finite-temperature zero-range theory. Both procedures suggest that the resonance position shifts towards lower absolute scattering lengths when approaching the zero-temperature limit. We extrapolate this shift to obtain an estimate of the three-body parameter at zero temperature. A surprising finding of our study is that the resonance becomes less prominent at lower temperatures, which currently lacks a theoretical description and implies physical effects beyond available models. Finally, we present measurements performed near the Feshbach resonance center and discuss the prospects for observing the second Efimov resonance in ${}^{39}\mathrm{K}$.

Recently, in the tunneling regime of strong-field ionization an unexpected Coulomb field effect has been identified by numerical solution of the time-dependent Schrödinger equation [Phys. Rev. Lett. 117, 243003 (2016)] in photoelectron spectra in the upper energy range of the direct electrons. We investigate the mechanism of the Coulomb effect employing a classical theory with Monte Carlo simulations of trajectories, and a quantum theory based on the generalized eikonal approximation for the continuum electron. The effect is shown to have a classical nature and is due to momentum space bunching of photoelectrons released not far from the peak of the laser field. Moreover, our analysis reveals specific features of the angular distribution of high-energy direct electrons, which can be employed for molecular imaging. For the ${{\mathrm{H}}_2}^{+}$ molecule as an example we show the signatures of the molecule orientation and the molecular structure in the investigated angular distribution.

The measurement of the triple differential cross section in the body frame for double photoionization of a molecule can be made in principle by detecting the ionic fragments and the two photoelectrons in coincidence—but only if the dynamics and geometry of dissociation of the doubly charged molecular ion are known. A classical trajectory study of the nine lowest states of the water dication is presented using high quality ab initio potential-energy surfaces. Sampling from a semiclassical initial distribution of positions and momenta is used to approximate ionization from the Frank-Condon region of the ground vibrational state of neutral ${\mathrm{H}}_2\mathrm{O}$. Excellent agreement in comparison with preliminary experimental momentum imaging measurements of double photoionization of water show that eight dication states can be unambiguously identified in the experiment with the aid of theory. The theoretical trajectory results allow body frame measurements of double photoionization to yield all eight states even though the usual assumption of direct dissociation, the “axial recoil” approximation, breaks down for three of the dication electronic states seen in the experiment.

We demonstrate the use of cold target recoil ion momentum spectroscopy to perform state-selective measurements of the dissociative channels following single-photon double-ionization of ${\mathrm{H}}_2\mathrm{O}$. The two dominant dissociation channels observed lead to two-body (${\mathrm{OH}}^{+}+{\mathrm{H}}^{+}+2e^{-}$) and three-body ($2{\mathrm{H}}^{+}+\mathrm{O}+2e^{-}$) ionic fragmentation channels. In the two-body case we observe the presence of an autoionization process with a double-differential cross section that is similar to the single-photon double-ionization of helium well above threshold. In the three-body case, momentum and energy correlation maps in conjunction with new classical trajectory calculations in the companion theory paper by Z. L. Streeter et al. [Phys. Rev. A 98, 053429 (2018)] lead to the determination of the eight populated dication states and their associated fragmentation geometry. For the latter case, state-specific relative cross sections, median kinetic energy releases, and median angles between asymptotic proton momenta are presented. This benchmark-level experiment demonstrates that, in principle, state-selective fixed-frame triple-differential cross sections can be measured for some dication states of the water molecule.

In parametric-resonance magnetometers (PRMs), optically pumped atoms subject to rf fields allow one to measure the components of a very low magnetic field. Here, instead of using a circularly polarized light for creating atomic orientation, as in previous works, a linearly polarized light is used for creating atomic alignment. A dressed-atom formalism introduced by Polonsky and Cohen-Tannoudji is extended and allows one to map this situation to a simpler Hanle effect on aligned atoms. Analytical expressions for all alignment tensor components and photodetection signals are obtained for both the Hanle magnetometer and PRMs. A two-rf field alignment PRM is shown to display several improvements from its orientation counterpart, providing a secular third axis sensitivity and a lower degradation from the one-axis sensitivity obtained by using a single rf field. These specificities are shown to result from the apparent depolarization of the pumping light acting on the atom dressed by two-rf fields. Experimental measurements showing a good agreement with the theoretical predictions are presented.

This study focuses on the role of negative-ion formation in the decay of core-valence doubly excited water molecules. Combining negative- and positive-ion coincidence measurements with calculated energies of core-valence doubly excited states, we find that ${\mathrm{O}}^{-}$ and ${\mathrm{H}}^{-}$ production is enhanced selectively. In particular, we suggest that ${\mathrm{O}}^{-}$ production is correlated to double occupancy of the antibonding $4a_1$ virtual orbital, while ${\mathrm{H}}^{-}$ appears at electronic states with double occupancy in $2b_2$. We also show that ${\mathrm{H}}^{-}$ and ${\mathrm{O}}^{-}$ can be created as a result of electron recapture close to the O $1s$ ionization potential.

Phase-of-the-phase spectroscopy using two-color collinearly polarized laser pulses has been introduced and experimentally applied to strong-field tunneling ionization by Skruszewicz et al., Phys. Rev. Lett. 115, 043001 (2015) and recently to multiphoton ionization by Almajid , J. Phys. B: At. Mol. Opt. Phys. 50, 194001 (2017). The idea behind phase-of-the-phase spectroscopy is to study in a systematic way the change in the photoelectron yield as a function of the relative phase between the strong fundamental field component (of carrier frequency $\omega$) and a weak, second-color component (e.g., $2\omega$). The observable of interest is the photoelectron-momentum-dependent phase of the change in the electron yield with respect to the relative phase, hence the name “phase of the phase.” In the present paper, phase-of-the-phase spectroscopy is extended to circularly polarized light. With a small, counter-rotating $2\omega$ component, photoelectron spectra have a threefold symmetry in the polarization plane. The same is true for the corresponding phase-of-the-phase spectra. However, a peculiar, very sharp phase flip by $\pi$ occurs at a certain radial momentum of the photoelectron that is sensitive to both laser parameters and the ionization potential. Results from the numerical solution of the time-dependent Schrödinger equation are compared to those from the strong-field approximation. An analytical expression for the momentum at which the phase-of-the-phase flipping occurs is presented.

Optimal control simulation is applied to numerically design nonresonant laser pulses that maximize the degrees of three-dimensional (3D) alignment of $\mathrm{S}{\mathrm{O}}_2$ using the lowest-order induced-dipole interaction. In our trials, combinations of more than two mutually orthogonal, linearly polarized subpulses are always obtained as the optimal solutions. Each subpulse in the optimal pulses impulsively excites the rotational wave packet. The optimal pulses effectively cooperate with the rotational dynamics up to only a few partial revival timings owing to the rotational dephasing that determines the effective control periods. The control mechanisms are interpreted in terms of the time derivatives of the expectation values of the squares of the direction cosines, that of the rotational energy, and the interplay between them. We find a special and important role of the last subpulses as they align the molecular axes using the interaction through the two smallest polarizability components, while the other subpulses excite the rotational wave packet mainly through the largest polarizability component. The control pulses composed of the specified number of subpulses are also numerically optimized by actively utilizing the instantaneous penalty to systematically show the superiority of the use of more than two subpulses over that of two subpulses, the latter of which leads to the saturation of the degree of 3D alignment as a function of total fluence.

We explore the ground-state properties of a few bosons with dipole-dipole interactions in a one-dimensional optical lattice. For comparatively strong interactions, a transition from a Mott-insulator state to a crystal state occurs. Herein, we provide a detailed characterization and a detection protocol for the resulting crystal state. Using the eigenvalues of the reduced one-body density matrix, we define an order parameter that characterizes all the emergent states occurring in the finite-sized ensemble and agrees with the signatures obtained from the analysis of the one- and two-body densities. We further demonstrate that these few-body emergent states can be detected experimentally using the variance of single-shot measurements.

Realization of strong synthetic magnetic fields in driven optical lattices has enabled implementation of topological bands in cold-atom setups. A milestone has been reached by a recent measurement of a finite Chern number based on the dynamics of incoherent bosonic atoms. The measurements of the quantum Hall effect in semiconductors are related to the Chern-number measurement in a cold-atom setup; however, the design and complexity of the two types of measurements are quite different. Motivated by these recent developments, we investigate the dynamics of weakly interacting incoherent bosons in a two-dimensional driven optical lattice exposed to an external force, which provides a direct probe of the Chern number. We consider a realistic driving protocol in the regime of high driving frequency and focus on the role of weak repulsive interactions. We find that interactions lead to the redistribution of atoms over topological bands both through the conversion of interaction energy into kinetic energy during the expansion of the atomic cloud and due to an additional heating. Remarkably, we observe that the moderate atomic repulsion facilitates the measurement by flattening the distribution of atoms in the quasimomentum space. Our results also show that weak interactions can suppress the contribution of some higher-order nontopological terms in favor of the topological part of the effective model.

We consider a system of weakly interacting bosons confined on a planar double ring lattice subjected to two artificial gauge fields. We determine its ground state by solving coupled discrete nonlinear Schrödinger equations at mean-field level. At varying inter-ring tunnel coupling, flux, and interactions, we identify the vortex, Meissner, and biased-ladder phases also predicted for a bosonic linear ladder by a variational ansatz. We also find peculiar features associated to the ring geometry, in particular parity effects in the number of vortices, and the appearance of a single vortex in the Meissner phase. We show that the persistent currents on the rings carry precise information on the various phases. Finally, we propose a way of observing the Meissner and vortex phases via spiral interferogram techniques.

Exact diagonalization expansions of Bose or Fermi gases with contact interactions converge very slowly due to a nonanalytic cusp in the wave function. Here we develop a transcorrelated approach where the cusp is treated exactly and folded into the many-body Hamiltonian with a similarity transformation that removes the leading-order singularity. The resulting transcorrelated Hamiltonian is not Hermitian but can be treated numerically with a standard projection approach. The smoothness of the wave function improves by at least one order and thus the convergence rate for the ground-state energy improves. By numerical investigation of a one-dimensional gas of spin-$\frac{1}{2}$ fermions we find the error in the transcorrelated energy to scale as $M^{-3}$ with a single-particle basis of $M$ plane waves compared to $M^{-1}$ for the expansion of the original Hamiltonian and $M^{-2}$ using conventional lattice renormalization.

We analyze quantum phase transitions in a system of optical lattice bosons coupled to an array of atomic quantum dots. Atomic quantum dots are represented by hard-core bosons of different hyperfine species and therefore can be mapped onto pseudospins 1/2. The system parallels the Bose-Hubbard model with an additional assisted tunneling via coupling to the atomic quantum dots. We calculate the phase diagram of the combined system, numerically within the Gutzwiller ansatz and analytically using the mean-field decoupling approximation. The result of the assisted Bose-Hubbard model is that the Mott-superfluid transition still takes place; however, the Mott lobes strongly depend on the system parameters such as the detuning. One can even reverse the usual hierarchy of the lobes with the first lobe becoming the smallest. The phase transition in the bosonic subsystem is accompanied by a magnetization rotation in the pseudospin subsystem with the tilting angle being an effective order parameter. When direct tunneling is taken into account, the Mott lobes can be made to disappear and the bosonic subsystem becomes superfluid throughout.

The transmission of an interacting Bose-Einstein condensate incident on a repulsive Gaussian barrier is investigated through numerical simulation. The dynamics associated with interatomic interactions are studied across a broad parameter range not previously explored. Effective one-dimensional Gross-Pitaevskii equation (GPE) simulations are compared to classical Boltzmann-Vlasov equation (BVE) simulations in order to isolate purely coherent matter-wave effects. Quantum tunneling is then defined as the portion of the GPE transmission not described by the classical BVE. An exponential dependence of transmission on barrier height is observed in the classical simulation, suggesting that observing such an exponential dependence is not a sufficient condition for quantum tunneling. Furthermore, the transmission is found to be predominately described by classical effects, although interatomic interactions are shown to modify the magnitude of the quantum tunneling. Interactions are also seen to affect the amount of classical transmission, producing transmission in regions where the noninteracting equivalent has none. This theoretical investigation clarifies the contribution quantum tunneling makes to overall transmission in many-particle interacting systems, potentially informing future tunneling experiments with ultracold atoms.

In this paper, we study the effects of laser phase noise on the detection of a weak classical mechanical force on a free particle based upon dissipative optomechanical coupling. We show that for an optimum choice of various parameters, one can realize force sensing below the standard quantum limit even in the presence of laser phase noise. Moreover, we also investigate the effect of mechanical damping and thermal noise on force measurement in the presence of laser phase fluctuations. We show that force sensing strongly depends upon the phase fluctuations associated with the driving laser.

A generic envelope equation is proposed for describing the evolution of scalar pulses in systems with spatiotemporal dispersion and cubic-quintic nonlinearity. Our analysis has application, for instance, in waveguide optics where the physical origin of the dielectric response lies in the ${\chi }^{\left(3\right)}$ and ${\chi }^{\left(5\right)}$ susceptibilities. Exact analytical bright and gray solitons are derived by coordinate transformations and methods of direct integration. Known solitons of conventional pulse theory (based on nonlinear-Schrödinger prescriptions) are shown to emerge asymptotically as subsets of the more general spatiotemporal solutions, and simulations test the stability of the latter through a class of perturbed initial-value problem.

We consider an envelope equation with space-time symmetry for describing scalar waves in systems with spatiotemporal dispersion and a generic saturable nonlinearity. Exact bright and gray solitons are derived by direct integration methods and coordinate transformations, with the results for cubic-quintic systems [see companion article— Phys. Rev. A 98, 053842 (2018)] recovered in the limit of weak saturation. Classic predictions from a nonlinear Schrödinger formulation of the propagation problem are shown to emerge asymptotically as subsets of the more general spatiotemporal solutions. The robustness of the new solitons against perturbations to the local pulse shape is then tested by deploying integral stability criteria, symmetry principles, and numerical analysis.