Calculations of the magnetic hyperfine structure rely on the input of nuclear properties—nuclear magnetic moments and nuclear magnetization distributions—as well as quantum electrodynamic radiative corrections for high-accuracy evaluation in heavy atoms. The uncertainties associated with assumed values of these properties limit the accuracy of hyperfine calculations. For example, for the heavy alkali-metal atoms Cs and Fr, these uncertainties may amount collectively to almost 1% or 2%, respectively. In this paper, we propose a method for removing the dependence of hyperfine structure calculations on assumed values of nuclear magnetic moments and nuclear magnetization distributions by determining these effects empirically from measurements of the hyperfine structure for high states. The method is valid for $s$, $p_{1/2}$, and $p_{3/2}$ states of alkali-metal atoms and alkali-metal-like ions. We have shown that for $s$ states, the dependence on QED effects may also be removed to high accuracy. The ability to probe the electronic wave functions, through hyperfine comparisons, with significantly increased accuracy is important for the analysis of atomic parity violation measurements, and it may enable the accuracy of atomic parity violation calculations to be improved. More broadly, it paves the way for further development of high-precision atomic many-body methods.

Chemical reactions between ions and molecular radicals are important in both terrestrial and extraterrestrial environments. However, due to the challenge of creating dense, pure samples of both species, very few studies have been performed in the laboratory. We present the first measurement of a state-controlled reaction between a radical and an ion, where the ${\mathrm{Ca}}^{+}$ cation and the NO radical molecule combine to form ${\mathrm{CaO}}^{+}$ and a nitrogen atom. The charge transfer between ${\mathrm{Ca}}^{+}$ and NO is simultaneously observed. We utilize a linear Paul ion trap coupled to a time-of-flight mass spectrometer to make direct, simultaneous measurements of multiple ionic product channels. We demonstrate control over the reaction rates by tuning of the excited-state population of the laser cooled ${}^{40}\mathrm{Ca}^{+}$. This control, coupled with a sensitive detection technique, enables precise measurement of the rate constants and branching ratios for this reaction.

We have experimentally investigated a catalysis effect in the resonant energy transfer between ultracold ${}^{85}\mathrm{Rb}$ Rydberg atoms. We studied the time dependence of the process, $34p+34p\to 34s+35s$, and observed an enhancement of $34s$ state population when $34d$ state atoms are added. We have also performed numerical model simulations, which are in qualitative agreement with experiment and indicate that the enhancement arises from a redistribution of $p$-state atoms due to the presence of the $d$-state atoms.

We examine theoretically how dipole-dipole interactions arising from multiple photon scattering lead to a modified distribution of ground-state populations in a driven, ordered one-dimensional array of multilevel atoms. Specifically, we devise a level configuration in which a ground-state population accumulated solely due to dipole-dipole interactions can be up to 20% in regimes accessible to current experiments with neutral atom arrays. For much larger systems, the steady state can consist of an equal distribution of population across the ground-state manifold. Our results illustrate how dipole-dipole interactions can be accentuated through interference, and regulated by the geometry of ordered atom arrays. More generally, control techniques for multilevel atoms that can be degraded by multiple scattering, such as optical pumping, will benefit from an improved understanding and control of dipole-dipole interactions available in ordered arrays.

In our investigation into the effects of the degree of polarization in modulation of partially polarized light, we assume general settings of the interferometry of partially polarized light waves and perform theoretical analysis of the geometric phases: the Uhlmann phase and the interferometric phase. We introduce the relative Uhlmann phase determined by the Uhlmann holonomies of interfering beams and show that the interferometric phase generalized to the case of nonunitary evolution can, similar to the Uhlmann phase, be cast into the holonomy defined form. By using the technique based on a two-arm Mach-Zehnder interferometer, two different dynamical regimes of light modulation are experimentally studied: (a) modulation of the input light by the rotating quarter-wave plate (QWP), and (b) modulation of the testing beam by a birefringent plate with electrically controlled anisotropy represented by the deformed-helix ferroelectric liquid-crystal (DHFLC) cell. In the setup with the rotating QWP, the interferometric phase is found to be equal to the relative Uhlmann phase. Experimental and theoretical results being in excellent agreement show both that this phase is an oscillating function of the QWP angle and increases with the degree of polarization. For modulation by the DHFLC cell, the data derived from our electro-optic measurements are fitted using the theory of the orientational Kerr effect in FLCs. This theory in combination with the results of fitting is used to evaluate electric field dependencies of the interferometric and the Uhlmann phases.

In non-Hermitian coupled-resonator networks, the eigenvectors of degenerate eigenmodes may become parallel due to the singularity at so-called exceptional points (EP). To exploit the extraordinary parametric sensitivity at EPs, an important problem is, given an arbitrary set of resonators, how to generate a desired EP by properly coupling them together. This paper provides the solution for the case of three resonators. We show that all physically admissible EPs can be realized with either weakly coupled linear networks or strongly coupled circular networks, and the latter type of EPs has not been reported in the literature. Each admissible EP eigenvalue is associated with two and only two resonator-network realizations, and the formulas for calculating the required coupling constants are provided. The characteristics of these EPs are illustrated by the sharp change of transmission spectra near them, which verifies the enhanced sensitivity induced by the singularity of EPs. The obtained results lay a basis for designing EP structures towards broader applications.

Given the increasing use of shortcuts to adiabaticity (STA) to optimize the power and efficiency of quantum heat engines, it becomes a relevant question if there are any theoretical limits to their application. We argue that quantum fluctuations in the control device which implements the shortcut deflect the system from the adiabatic path. This not only induces transitions to unwanted final states but also changes the system energy, so that using the STA has a definite cost in terms of conventional work definitions. This may be the ultimate cost of an adiabatic shortcut, in the sense that it is present even for a frictionless, zero-temperature driving. We estimate the effect, to lowest nontrivial order in the derivatives of the time-dependent frequency, on a parametric harmonic oscillator, thus providing a consistency condition for the validity of the classical approximation.

We discuss some fundamental properties of discrete system-time history states. Such states arise for a quantum reference clock of finite dimension and lead to a unitary evolution of system states when satisfying a static discrete Wheeler-DeWitt-type equation. We consider the general case where system-clock pairs can interact, analyzing first their different representations and showing there is always a special clock basis for which the evolution for a given initial state can be described by a constant Hamiltonian $H$. It is also shown, however, that when the evolution operators form a complete orthogonal set, the history state is maximally entangled for any initial state, as opposed to the case of a constant $H$, and can be generated through a simple double-clock setting. We then examine the quadratic system-time entanglement entropy, providing an analytic evaluation and showing it satisfies strict upper and lower bounds determined by the energy spread and the geodesic evolution connecting the initial and final states. We finally show that the unitary operator that generates the history state can itself be considered as an operator history state, whose quadratic entanglement entropy determines its entangling power. Simple measurements on the clock enable one to efficiently determine overlaps between system states and also evolution operators at any two times.

Classical control noise is ubiquitous in qubit devices, making its accurate spectral characterization essential for designing optimized error suppression strategies at the physical level. Here, we focus on multiplicative Gaussian amplitude control noise on a driven qubit sensor and show that sensing protocols using optimally band-limited Slepian modulation offer substantial benefit in realistic scenarios. Special emphasis is given to laying out the theoretical framework necessary for extending nonparametric multitaper spectral estimation to the quantum setting by highlighting key points of contact and differences with respect to the classical formulation. In particular, we introduce and analyze two approaches (adaptive vs single setting) to quantum multitaper estimation, and show how they provide a practical means to both identify fine spectral features not otherwise detectable by existing protocols and to obtain reliable prior estimates for use in subsequent parametric estimation, including high-resolution Bayesian techniques. We quantitatively characterize the performance of both single- and multitaper Slepian estimation protocols by numerically reconstructing representative spectral densities, and demonstrate their advantage over dynamical-decoupling noise spectroscopy approaches in reducing bias from spectral leakage as well as in compensating for aliasing effects while maintaining a desired sampling resolution.

The impact of power loss on fiber-optic solitons and soliton compounds has regained interest recently, as coding schemes employing inverse scattering eigenvalues are being discussed. Loss lifts the integrability of the underlying nonlinear Schrödinger equation and has usually been treated by perturbation analysis. Our approach uses localized loss of arbitrary strength. We investigate two-soliton compounds including the $N=2$ soliton and show that loss causes severe qualitative modifications of the eigenvalue spectrum. Peculiar features include power redistribution between solitons so that one of them is actually enhanced by loss and conversion of solitons at rest into a pair with outward velocities. Earlier reports of such features are put into context. We argue that frequency splitting of soliton pairs requires a mechanism that renders the spectrum double-lobed (or multiply lobed) and that the bifurcation is defined by a balance between dispersive and nonlinear forces. Implications for eigenvalue-based communication formats are pointed out.

Traditional forms of quantum uncertainty relations are invariably based on the standard deviation. This can be understood in the historical context of simultaneous development of quantum theory and mathematical statistics. Here we present alternative forms of uncertainty relations, in both state-dependent and state-independent forms for a general set of deviation measures, with special emphasis on the mean deviation. We illustrate the robustness of this formulation in situations where the standard-deviation-based uncertainty relation is inapplicable. We apply the mean-deviation-based uncertainty relation to detect Einstein-Podolsky-Rosen violation in a lossy scenario for a higher-inefficiency threshold than that allowed by the standard-deviation-based approach. We demonstrate that the mean-deviation-based uncertainty relation can perform equally well as the standard-deviation-based uncertainty relation as the nonlinear witness for entanglement detection.

Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors as well as high-speed realization. Several schemes of its implementation have been put forward based on various physical systems, each of which has some particular merits. In this paper, we put forward an alternative scheme of nonadiabatic holonomic quantum computation, in which a universal set of quantum gates is realized based on Rydberg superatoms. A Rydberg superatom is a mesoscopic atomic ensemble that allows for only a single Rydberg excitation shared by many atoms within a blockade radius and can be used to generate the collective states to encode the qubits. In our scheme, the qubit is encoded into two collective ground states of Rydberg superatoms and the interaction between two long-range Rydberg superatoms is mediated by a microwave cavity with the aid of two additional collective Rydberg states. Different from the previous schemes, which are based on the systems in the microscope scale, the present scheme is based on atomic ensembles in the mesoscopic scale. Besides the common merits of nonadiabatic holonomic quantum computation such as the robustness and the speediness, the Rydberg-superatom-based scheme has the following particular merits: the long coherence time of Rydberg states and the operability of the mesoscopic systems.

We study the impact of finite-size effects on the security of thermal one-way quantum cryptography. Our approach considers coherent and/or squeezed states at the preparation stage, on the top of which the sender adds trusted thermal noise. We compute the key rate incorporating finite-size effects, and we obtain the security threshold at different frequencies. As expected, finite-size effects deteriorate the performance of thermal quantum cryptography. Our analysis is useful to quantify the impact of this degradation on relevant parameters like tolerable attenuation and transmission frequencies at which one can achieve security.

Multiparameter estimation, which aims to simultaneously determine multiple parameters in the same measurement procedure, attracts extensive interest in measurement science and technologies. Here, we propose a multimode many-body quantum interferometry for simultaneously estimating linear and quadratic Zeeman coefficients via an ensemble of spinor atoms. Different from the scheme with individual atoms, by using a $N$-atom multimode Greenberger-Horne-Zeilinger state, the measurement precisions of the two parameters can simultaneously attain the Heisenberg scaling, and they respectively depend on the hyperfine spin number $F$ in the forms of $\mathrm{\Delta }p\propto 1/\left(FN\right)$ and $\mathrm{\Delta }q\propto 1/\left(F^{2}N\right)$. Moreover, the simultaneous estimation can provide better precision than the individual estimation. Further, by taking a three-mode interferometry with Bose-condensed spin-1 atoms for an example, we show how to perform the simultaneous estimation of $p$ and $q$. Our scheme provides a novel paradigm for implementing multiparameter estimation with multimode quantum-correlated states.

Light propagating in a nondispersive medium is accompanied by a mass density wave (MDW) of atoms set in motion by the optical force of the field itself [Phys. Rev. A 95, 063850 (2017)]. This recent result is in strong contrast with the approximation of fixed atoms, which assumes that atoms are fixed to their equilibrium positions when light propagates in a medium and which is deeply rooted in the conventional electrodynamics of continuous media. In many photonic materials, the atoms carry the majority of the total momentum of light and their motion also gives rise to net transfer of medium mass with a light pulse. In this work we use optoelastic continuum dynamics combining the optical force field, elasticity theory, and Newtonian mechanics to analyze the angular momentum carried by the MDW. Our calculations are based on classical physics, but by dividing the numerically calculated angular momenta of Laguerre-Gaussian (LG) pulses with the photon number, we can also study the single-quantum values. We show that accounting for the MDW in the analysis of the angular momentum gives for the field's share of the total angular momentum of light a quantized value that is generally a fraction of $\hslash$. In contrast, the total angular momentum of the mass-polariton (MP) quasiparticle, which is a coupled state of the field and the MDW, and also the elementary quantum of light in a medium, is an integer multiple of $\hslash$. Thus, the angular momentum of the MP has coupled field and medium components, which cannot be separately experimentally measured. This discovery is related to the previous observation that a bare photon including only the field part cannot propagate in a medium. The same coupling is found for orbital and spin angular momentum components. The physical picture of the angular momentum of light emerging from our theory is fundamentally more general than earlier theoretical models, in which the total angular momentum of light is assumed to be carried by the electromagnetic field only or by an electronic polariton state, which also involves dipolar electronic oscillations. These models cannot describe the MDW shift of atoms associated with light. We simulate the MDW of LG pulses in silicon and present a schematic experimental setup for measuring the contribution of the atomic MDW to the total angular momentum of light.

The question of how long a particle takes to pass through a potential barrier is still a controversial topic in quantum mechanics. One of the main theoretical problems in obtaining estimates for measurable times is the fact that several previously defined time operators, which remained within the borders of standard quantum mechanics, present some kind of pathology. Recently, a time operator acting on an additional Hilbert space has been shown to support both Hermiticity and canonical relation with an energy observable. The theory is built in a framework that treats space and time as symmetrically as possible, in the nonrelativistic regime. In this work, we use this formalism to derive a closed analytical expression for the traversal time of a quantum particle impinging on a rectangular potential barrier. To do this, first we discuss the meaning of the expectation values in the additional Hilbert space and, then, we apply it to traversal times. We test our formalism in the specific experimental scenario of a realization by Ranfagni et al. [A. Ranfagni et al., Appl. Phys. Lett. 58, 774 (1991)]. The proposed approach displays a better performance in comparison with the Büttiker-Landauer and the phase-time approximations.

Near-term quantum hardware promises to achieve quantum supremacy. From a quantum dynamical point of view, however, it is not unambiguously clear whether fundamental peculiarities of quantum physics permit any arbitrary speedups in real time. We show that an only recently unveiled property of the quantum Fisher information has profound implications for the rate of possible quantum information processing. To this end, we analyze an exemplary and pedagogical example for a quantum computer consisting of a computational qubit and a quantum memory. We find that frequent interaction between memory and device exhibit the quantum Zeno effect. In a second part, we show that the Zeno effect can be prevented by carefully designing the correlations and interaction between single elements of the quantum memory.

We propose a classical-quantum hybrid algorithm for machine learning on near-term quantum processors, which we call quantum circuit learning. A quantum circuit driven by our framework learns a given task by tuning parameters implemented on it. The iterative optimization of the parameters allows us to circumvent the high-depth circuit. Theoretical investigation shows that a quantum circuit can approximate nonlinear functions, which is further confirmed by numerical simulations. Hybridizing a low-depth quantum circuit and a classical computer for machine learning, the proposed framework paves the way toward applications of near-term quantum devices for quantum machine learning.

A famously hard graph problem with a broad range of applications is computing the number of perfect matchings, that is, the number of unique and complete pairings of the vertices of a graph. We propose a method to estimate the number of perfect matchings of undirected graphs based on the relation between Gaussian boson sampling and graph theory. The probability of measuring zero or one photons in each output mode is directly related to the hafnian of the adjacency matrix, and thus to the number of perfect matchings of a graph. We present encodings of the adjacency matrix of a graph into a Gaussian state and show strategies to boost the sampling success probability for the studied graphs. With our method, a Gaussian boson sampling device can be used to estimate the number of perfect matchings significantly faster and with lower-energy consumption compared to a classical computer.

We propose a scheme for preparation of entangled coherent states for the motion of an ion in a two-dimensional anisotropic trap. In the scheme, the ion is driven by four laser beams along different directions in the ion trap plane, resulting in carrier excitation and couplings between the internal and external degrees of freedom. When the total quantum number of the vibrational modes initially has a definite parity, the competition between the unitary dynamics and spontaneous emission will force the system to evolve to a steady state, where the vibrational modes are in a two-mode cat state. We show that the method can be extended to realization of entangled coherent states for three vibrational modes of an ion in a three-dimensional anisotropic trap.