Open quantum systems can display periodic dynamics at the classical level either due to external periodic modulations or to self-pulsing phenomena typically following a Hopf bifurcation. In both cases, the quantum fluctuations around classical solutions do not reach a quantum-statistical stationary state, which prevents adopting the simple and reliable methods used for stationary quantum systems. Here we put forward a general and efficient method to compute two-time correlations and corresponding spectral densities of time-periodic open quantum systems within the usual linearized (Gaussian) approximation for their dynamics. Using Floquet theory, we show how the quantum Langevin equations for the fluctuations can be efficiently integrated by partitioning the time domain into one-period duration intervals, and relating the properties of each period to the first one. Spectral densities, like squeezing spectra, are computed similarly, now in a two-dimensional temporal domain that is treated as a chessboard with one-period $\times$ one-period cells. This technique avoids cumulative numerical errors as well as efficiently saving computational time. As an illustration of the method, we analyze the quantum fluctuations of a damped parametrically driven oscillator (degenerate parametric oscillator) below threshold and far away from rotating-wave approximation conditions, which is a relevant scenario for modern low-frequency quantum oscillators. Our method reveals that the squeezing properties of such devices are quite robust against the amplitude of the modulation or the low quality of the oscillator, although optimal squeezing can appear for parameters that are far from the ones predicted within the rotating-wave approximation.

We theoretically investigate the prospects for photoassociation (PA) of ${\mathrm{Rb}}_3$, in particular at close range. We provide an overview of accessible states and possible transitions. The major focus is placed on the calculation of equilibrium structures, the survey of spin-orbit effects, and the investigation of transition dipole moments. Furthermore we discuss Franck-Condon overlaps and special aspects of trimers including the (pseudo) Jahn-Teller effect and the resulting topology of adiabatic potential-energy surfaces. With this we identify concrete and suitable PA transitions to potentially produce long-lived trimer bound states. Calculations are performed using the multireference configuration-interaction method together with a large-core effective core potential and a core-polarization potential with a large uncontracted even-tempered basis set.

We show how the time-varying phase or frequency of a chirped strong-field ultrafast laser pulse can be used to control the ionization yield to different ionic states in a polyatomic molecule. The control is based upon a competition between multiphoton resonance and internal conversion. The multiphoton resonance is facilitated by dynamic Stark shifts, while the internal conversion (coupling between electronic states) is due to violation of the Born-Oppenheimer approximation. Our measurements are compared with and interpreted in terms of calculations of the strong-field ionization dynamics, which include multiphoton resonance, dynamic Stark shifts, as well as vibrational dynamics and internal conversion during the ionization process. The measurements and calculations illustrate how the light matter coupling can compete with the coupled motions of electrons and nuclei in strong-field laser-molecule interactions.

We describe a laser spectroscopic study of ytterbium monomethoxide, ${\mathrm{YbOCH}}_3$, a species of interest to searches for time-reversal symmetry violation using laser-cooled molecules. We report measurements of vibrational structure in the $\tilde{X}$ and $\tilde{A}$ states, vibrational branching ratios for several components of the $\tilde{A}$ state, and radiative lifetimes of low-lying electronic states. Ab initio calculations are used to aid the assignment of vibronic emission bands and provide insight into the electronic and vibrational structure. Our results demonstrate that rapid optical cycling is feasible for ${\mathrm{YbOCH}}_3$, opening a path to orders-of-magnitude increased sensitivity in future measurements of $P$- and/or $T$-violating physics.

Optomechanical gradient forces arise from evanescent fields of guided waves in parallel photonic waveguides. When designed to be of an attractive nature, they increase exponentially as the gap between the waveguides decreases. Moreover, the amplitude of the gradient force can be well controlled due to its linear dependence on the input laser power. Here, we propose to exploit the intrinsic nonlinear nature of the optomechanical gradient force to induce a tunable three-wave coupling between the fundamental modes of two doubly clamped nanophotonic beams. For one of the beams having half the width of the other beam, the 1:2 internal resonance between the fundamental modes supports degenerate spontaneous parametric down conversion (SPDC). We theoretically explore the main feature of the dissipative phase diagram of the underlying degenerate parametric oscillator model to show that the critical point of the SPDC occurs at parameters which are well in reach of state-of-the-art experiments.

Spatially resolving two incoherent point sources whose separation is well below the diffraction limit dictated by classical optics has recently been shown possible using techniques that decompose the incoming radiation into orthogonal transverse modes. Such a demultiplexing procedure, however, must be perfectly calibrated to the transverse profile of the incoming light as any misalignment of the modes effectively restores the diffraction limit for small source separations. We study by how much can one mitigate such an effect at the level of measurement which, after being imperfectly demultiplexed due to inevitable misalignment, may still be partially corrected by linearly transforming the relevant dominating transverse modes. We consider two complementary tasks: the estimation of the separation between the two sources and the discrimination between one and two incoherent point sources. We show that, although one cannot fully restore super-resolving powers even when the value of the misalignment is perfectly known, its negative impact on the ultimate sensitivity can be significantly reduced. In the case of estimation we analytically determine the exact relation between the minimal resolvable separation as a function of misalignment whereas for discrimination we analytically determine the relation between misalignment and the probability of error, as well as numerically determine how the latter scales in the limit of long interrogation times.

We investigate theoretically the strong-field regime of light-matter interactions in the topological-insulator class of quantum materials. In particular, we focus on the process of nonperturbative high-order harmonic generation from the paradigmatic three-dimensional topological insulator bismuth selenide (${\mathrm{Bi}}_2{\mathrm{Se}}_3$) subjected to intense midinfrared laser fields. We analyze the contributions from the spin-orbit-coupled bulk states and the topological surface bands separately and reveal a major difference in how their harmonic yields depend on the ellipticity of the laser field. Bulk harmonics show a monotonic decrease in their yield as the ellipticity increases, in a manner reminiscent of high harmonic generation in gaseous media. However, the surface contribution exhibits a highly nontrivial dependence, culminating with a maximum for circularly polarized fields. We attribute the observed anomalous behavior to (i) the enhanced amplitude and the circular pattern of the interband dipole and the Berry connections in the vicinity of the Dirac point and (ii) the influence of the higher-order, hexagonal warping terms in the Hamiltonian, which are responsible for the hexagonal deformation of the energy surface at higher momenta. The latter are associated directly with spin-orbit-coupling parameters. Our results thus establish the sensitivity of strong-field-driven high harmonic emission to the topology of the band structure as well as to the manifestations of spin-orbit interaction.

The correspondence principle suggests that quantum systems grow classical when large. Classical systems cannot violate Bell inequalities. Yet agents given substantial control can violate Bell inequalities proven for large-scale systems. We consider agents who have little control, implementing only general operations suited to macroscopic experimentalists: preparing small-scale entanglement and measuring macroscopic properties while suffering from noise. That experimentalists so restricted can violate a Bell inequality appears unlikely, in light of earlier literature. Yet we prove a Bell inequality that such an agent can violate, even if experimental errors have variances that scale as the system size. A violation implies nonclassicality, given limitations on particles' interactions. A product of singlets violates the inequality; experimental tests are feasible for photons, solid-state systems, atoms, and trapped ions. Consistently with known results, violations of our Bell inequality cannot disprove local hidden-variables theories. By rejecting the disproof goal, we show, one can certify nonclassical correlations under reasonable experimental assumptions.

Rich physics emerges as the result of interplay between discrete and continuous quantum states. A process of reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) reveals a similar phenomenon. In RABBITT, primary XUV driven ionization is aided by secondary IR photon absorption or emission. The latter processes involve transitions between continuous states. We demonstrate that when RABBITT crosses the ionization threshold and proceeds via a discrete bound state, its phase makes a sudden jump which can be related to the phase of the continuous transitions above the threshold. Up to now, this phase remained undetermined experimentally and could only be estimated theoretically. The under-threshold RABBITT provides alternative means of assessing this quantity.

For a large class of variational quantum circuits, we show how arbitrary-order derivatives can be analytically evaluated in terms of simple parameter-shift rules, i.e., by running the same circuit with different shifts of the parameters. As particular cases, we obtain parameter-shift rules for the Hessian of an expectation value and for the metric tensor of a variational state, both of which can be efficiently used to analytically implement second-order optimization algorithms on a quantum computer. We also consider the impact of statistical noise by studying the mean-square error of different derivative estimators. Some of the theoretical techniques for evaluating quantum derivatives are applied to their typical use case: the implementation of quantum optimizers. We find that the performance of different estimators and optimizers is intertwined with the values of different hyperparameters, such as the step size or the number of shots. Our findings are supported by several numerical and hardware experiments, including an experimental estimation of the Hessian of a simple variational circuit and an implementation of the Newton optimizer.

Using differential geometry, I derive a form of the Bayesian Cramér-Rao bound that remains invariant under reparametrization. With the invariant formulation at hand, I find the optimal and naturally invariant bound among the Gill-Levit family of bounds. By assuming that the prior probability density is the square of a wave function, I also express the bounds in terms of functionals that are quadratic with respect to the wave function and its gradient. The problem of finding an unfavorable prior to tighten the bound for minimax estimation is shown, in a special case, to be equivalent to finding the ground state of a Schrödinger equation, with the Fisher information playing the role of the potential. To illustrate the theory, two quantum estimation problems, namely, optomechanical waveform estimation and subdiffraction incoherent optical imaging, are discussed.

We report on improvements extending the capabilities of the atom-by-atom assembler described by Barredo et al. [Science 354, 1021 (2016)] that we use to create fully-loaded target arrays of more than 100 single atoms in optical tweezers, starting from randomly loaded, half-filled initial arrays. We describe four variants of the sorting algorithm that decrease the number of moves needed for assembly and enable the assembly of arbitrary, nonregular target arrays. We demonstrate experimentally the performance of this enhanced assembler for a variety of target arrays.

Quantum annealing has great promise in leveraging quantum mechanics to solve combinatorial optimization problems. However, to realize this promise to its fullest extent we must appropriately leverage the underlying physics. In this spirit, we examine how the well-known tendency of quantum annealers to seek solutions where more quantum fluctuations are allowed can be used to trade off optimality of the solution to a synthetic problem for the ability to have a more flexible solution, where some variables can be changed at little or no cost. We demonstrate this tradeoff experimentally using the reverse annealing feature a D-Wave Systems quantum processing unit for both problems composed of all binary variables, and those containing some higher-than-binary discrete variables. We further demonstrate how local controls on the qubits can be used to control the levels of fluctuations and guide the search. We discuss places where leveraging this tradeoff could be practically important, namely in hybrid algorithms where some penalties cannot be directly implemented on the annealer and provide some proof-of-concept evidence of how these algorithms could work.

We demonstrate that the orbital angular momentum (OAM) flux density of a paraxial light beam can change on propagation in free space. These changes are entirely due to the spatial coherence state of the source, and the effect is analogous to correlation-induced changes in the intensity, spectrum, and polarization of a beam. The use of the source coherence state to control the width, shape, and transverse shifts of the OAM flux density is demonstrated with numerical examples.

We develop the theory of a special type of scattering state in which a set of asymptotic channels is chosen as inputs, and the complementary set is chosen as outputs, and there is zero reflection back into the input channels at specific frequencies. These states define perfectly impedance-matched input wavefronts for arbitrary finite scattering structures in any dimension. We find that an infinite number of such solutions exist at discrete frequencies in the complex $\omega$ (or energy) plane for any choice of the input-output sets under general conditions. Our results apply to linear electromagnetic and acoustic wave scattering and also, in many cases, to quantum scattering. We refer to such states as reflection-zeros ($R$-zeros) when they occur off the real-frequency axis and as reflectionless scattering modes (RSMs) when they occur or are tuned to the real-frequency axis and exist as steady-state harmonic solutions. The specific monochromatic input wavefront necessary is given by the eigenvector of a filtered scattering matrix with eigenvalue zero. RSMs may be realized either by tuning parameters of the scatterer which preserve flux conservation (index tuning) or by adding gain or absorption (gain-loss tuning), which do not. We show that in general only a single continuous system parameter needs to be tuned to create an RSM from an $R$-zero for a given choice of input-output channels for both guided wave and free-space excitation. In addition, a coupled-mode analysis shows that RSMs are the result of a generalized type of critical coupling. A symmetry analysis of $R$-zeros and RSMs implies that RSMs of flux-conserving cavities or structures are bidirectional: the input and output channels can be interchanged and the resulting state will also be an RSM at the same frequency. RSMs of cavities with gain and/or absorption are generically unidirectional, and do not satisfy this interchange symmetry. Non-flux-conserving systems with $\mathcal{P}T$ symmetry have unidirectional $R$-zeros in complex-conjugate pairs, implying that for small enough $\mathcal{T}$ breaking their reflectionless states arise at real frequency, without the need of any parameter tuning. This explains the widely observed existence of unidirectional unit transmission resonances in one-dimensional $\mathcal{P}T$ systems, and their disappearance as a result of spontaneous $\mathcal{P}T$-symmetry breaking. An alternative type of exceptional point is shown to occur at this transition, leading to an observable change in the reflection and/or transmission line shape. Numerical examples of RSMs are given for one-dimensional cavities with and without gain or loss, a one-dimensional $\mathcal{P}T$ cavity, a two-dimensional multiwaveguide junction, and a two-dimensional deformed dielectric cavity in free space. We outline and implement a general technique for solving such problems, which shows promise for designing photonic structures which are perfectly impedance matched for specific inputs, or can perfectly convert inputs from one set of modes to a complementary set.

Wigner-friend scenarios—in which an external agent describes quantum mechanically a laboratory in which a friend is making a measurement—give rise to possible inconsistencies due to the ambiguous character of quantum measurements. In this paper, we investigate Wigner-friend scenarios in which the external agents can probe in a noninvasive manner the dynamics inside the laboratories. We examine probes that can be very weakly coupled to the systems measured by the friends, or to the pointers or environments inside the laboratories. These couplings, known as weak measurements, are asymptotically small and do not change the outcomes obtained by the friends or their probabilities. Within our scheme, we show that the weakly coupled probes indicate to the external agents how to obtain consistent predictions, irrespective of the possible inconsistencies of quantum measurement theory. These noninvasive couplings could be implemented with present-day technologies.

We propose the application of laser cooling to a number of transition-metal atoms, allowing numerous bosonic and fermionic atomic gases to be cooled to ultralow temperatures. The nonzero electron orbital angular momentum of these atoms implies that strongly atom-state-dependent light-atom interactions occur even for light that is far-detuned from atomic transitions. At the same time, many transition-metal atoms have small magnetic dipole moments in their low-energy states, reducing the rate of dipolar-relaxation collisions. Altogether, these features provide compelling opportunities for future ultracold-atom research. Focusing on the case of atomic titanium, we identify the metastable $a{}^5{F}_5$ state as supporting a $J\to J+1$ optical transition with properties similar to the $D_2$ transition of alkali-metal atoms, and suited for laser cooling. The high total angular momentum and electron spin of this state suppresses leakage out of the nearly closed optical transition to a branching ratio estimated below $\sim {10}^{-5}$. Following the pattern exemplified by titanium, we identify optical transitions that are suited for laser cooling of elements in the scandium group (Sc, Y, La), the titanium group (Ti, Zr), the vanadium group (V, Nb), the manganese group (Mn, Tc), and the iron group (Fe, Ru).

Thermodynamic principles are often deceptively simple and yet surprisingly powerful. We show how a simple rule, such as the net flow of energy in and out of a moving atom under a nonequilibrium steady state condition, can expose the shortcomings of many popular theories of quantum friction. Our thermodynamic approach provides a conceptual framework in guiding atom-optical experiments, thereby highlighting the importance of fluctuation-dissipation relations and long-time correlations between subsystems. Our results introduce consistency conditions for (numerical) models of nonequilibrium dynamics of open quantum systems.

Measurements of nuclear spin-dependent parity-violating (NSD-PV) effects provide an excellent opportunity to test nuclear models and to search for physics beyond the Standard Model. Molecules possess closely spaced states with opposite parity which may be easily tuned to degeneracy to greatly enhance the observed parity-violating effects. A high-sensitivity measurement of NSD-PV effects using light triatomic molecules is in preparation [E. B. Norrgard et al., Commun. Phys. 2, 77 (2019)]. Importantly, by comparing these measurements in light nuclei with prior and ongoing measurements in heavier systems, the contribution to NSD-PV from $Z^0$-boson exchange between the electrons and the nuclei may be separated from the contribution of the nuclear anapole moment. Furthermore, light triatomic molecules offer the possibility to search for new particles, such as the postulated $Z^{\prime }$ boson. In this work, we detail a sensitive measurement scheme and present high-accuracy molecular and nuclear calculations needed for interpretation of NSD-PV experiments on triatomic molecules composed of light elements, Be, Mg, N, and C. The ab initio nuclear structure calculations, performed within the no-core shell model provide a reliable prediction of the magnitude of different contributions to the NSD-PV effects in the four nuclei. These results differ significantly from the predictions of the standard single-particle model and highlight the importance of including many-body effects in such calculations. In order to extract the NSD-PV contributions from measurements, a parity-violating interaction parameter $W_{\text{PV}}$, which depends on the molecular structure, needs to be known with a high accuracy. We have calculated these parameters for the triatomic molecules of interest using the relativistic coupled-cluster approach. In order to facilitate the interpretation of future experiments we provide uncertainties on the calculated parameters. A scheme for measurement using laser-cooled polyatomic molecules in a molecular fountain is presented, along with an estimate of the expected sensitivity of such an experiment. This experimental scheme, combined with the presented state-of-the-art calculations, opens exciting prospects for a measurement of the anapole moment and the PV effects due to the electron-nucleon interactions with unprecedented accuracy and for a new path towards detection of signatures of physics beyond the Standard Model.

Gauge potential is known to account for quite a few fundamental physical issues, such as electromagnetic interaction in electrodynamics, the standard model in particle physics, and even topological phenomena in condensed matter physics. Therefore engineering the so-called artifical gauge potential in controllable experimental platforms has been an attractive topic that may expedite the research on these issues. In this paper, we propose to periodically modulate the frequency of the superconducting flux qubit via two-tone drives, which can be further used to engineer the artificial gauge potential. As an example, we show that the fermionic ladder model penetrated with effective magnetic flux can be constructed by superconducting flux qubits using such two-tone-drive-engineered artificial gauge potential. In this superconducting quantum circuit system, the single-particle ground state can range from vortex phase to the Meissner phase due to the competition between the interleg coupling strength and the effective magnetic flux. We also present the method to experimentally measure the chiral currents by the single-particle Rabi oscillations between adjacent qubits. In contrast to previous methods of generating artificial gauge potential, our proposal does not need the aid of auxiliary couplers and in principle remains valid only if the qubit circuit maintains enough anharmonicity. The fermionic ladder model with effective magnetic flux can also be interpreted as one-dimensional spin-orbit-coupled model, which thus lays a foundation towards the realization of the quantum spin Hall effect.