We report on the photoassociation (PA) spectroscopy of cold ${}^{171}\mathrm{Yb}$ atoms in a one-dimensional optical lattice. The PA spectral lines correlating to the ${}^{1}S_0+{}^{3}P_1$ $(f=1/2)$ state are observed experimentally. High accuracy and narrow atom-loss spectra are measured ranging up to about 1.2 GHz red detuning with respect to the atomic resonance. The main systematic frequency shifts of the PA transitions are determined with total uncertainties less than 100 kHz, which is more accurate than previous similar experimental results. We determine the initial scattering state of the PA spectra by comparing the spectra with polarized and unpolarized atomic samples. By comparatively analyzing theoretical results calculated based on an adiabatic molecular potential with experimental data, the excited molecular potentials corresponding to the spectral lines are clarified. The precision measurement of the narrow PA spectra plays an important role in exploring atomic interactions and lays the groundwork for the study of cold ytterbium molecules.

Scrambling of quantum information is an important feature at the root of randomization and benchmarking protocols, the onset of quantum chaos, and black-hole physics. Unscrambling this information is possible given perfect knowledge of the scrambler [arXiv:1710.03363]. We show that one can retrieve the scrambled information even without any previous knowledge of the scrambler, by a learning algorithm that allows the building of an efficient decoder. Remarkably, the decoder is classical in the sense that it can be efficiently represented on a classical computer as a Clifford operator. It is striking that a classical decoder can retrieve with fidelity one all the information scrambled by a random unitary that cannot be efficiently simulated on a classical computer, as long as there is no full-fledged quantum chaos. This result shows that one can learn the salient properties of quantum unitaries in a classical form and sheds a new light on the meaning of quantum chaos. Furthermore, we obtain results concerning the algebraic structure of $t$-doped Clifford circuits, i.e., Clifford circuits containing $t$ non-Clifford gates, their gate complexity, and learnability that are of independent interest. In particular, we show that a $t$-doped Clifford circuit $U_t$ can be decomposed into two Clifford circuits $U_0,U_0^{\prime }$ that sandwich a local unitary operator $u_t$, i.e., $U_t=U_0{u}_t{U}_0^{\prime }$. The local unitary operator $u_t$ contains $t$ non-Clifford gates and acts nontrivially on at most $t$ qubits. As simple corollaries, the gate complexity of the $t$-doped Clifford circuit $U_t$ is $O(n^2+t^3)$, and it admits a efficient process tomography using $poly(n,2^t)$ resources.

The persistent separability of certain quantum states, known as symmetric absolutely separable (SAS), under symmetry-preserving global unitary transformations is of key significance in the context of quantum resources for bosonic systems. In this paper, we develop criteria for detecting SAS states of any number of qubits. Our approach is based on the Glauber-Sudarshan $P$ representation for finite-dimensional quantum systems. We introduce three families of SAS witnesses, one linear and two nonlinear in the eigenvalues of the state, formulated respectively as an algebraic inequality or a quadratic optimization problem. These witnesses are capable of identifying more SAS states than previously known counterparts. We also explore the geometric properties of the subsets of SAS states detected by our witnesses, shedding light on their distinctions.

The braiding operations of quantum states have attracted substantial attention due to their great potential for realizing topological quantum computations. In this paper, we show that a threefold-degenerate eigensubspace can be obtained in a four-level Hamiltonian which is the minimal physical system. Braiding operations are proposed to apply to dressed states in the subspace. The topology of the braiding diagram can be characterized through physical methods once the sequential braiding pulses are adopted. We establish an equivalent relationship function between the permutation group and the output states where different output states correspond to different values of the function. The topological transition of the braiding happens when two operations overlap, which is detectable through the measurement of the function. Combined with the phase variation method, we can analyze the wringing pattern of the braiding. Therefore, the experimentally feasible system provides a platform to investigate braiding dynamics, the SU(3) physics, and the qutrit gates.

We address metrological problems where the parameter of interest is encoded in the internal degree of freedom of a discrete-time quantum walker, and provide evidence that coin dimensionality is a potential resource to enhance precision. In particular, we consider estimation problems where the coin parameter governs rotations around a given axis and show that the corresponding quantum Fisher information (QFI) may increase with the dimension of the coin. We determine the optimal initial state of the walker to maximize the QFI and discuss whether, and to what extent, precision enhancement may be achieved by measuring only the position of the walker. Finally, we consider Grover-like encoding of the parameter and compare results with those obtained from rotation encoding.

Nonadiabatic geometric quantum computation (NGQC) has emerged as an excellent proposal for achieving fast and robust quantum control against control errors. However, previous NGQC protocols could not be strongly resilient against the noise from decay of bare states in a realistic system, which can be equivalently described by a non-Hermitian Hamiltonian. Here we show how to perform NGQC in non-Hermitian quantum systems. By utilizing a geometric phase generated by nonunitary evolution of the system, a universal set of geometric gates can be realized with a high fidelity. Moreover, we demonstrate that the nonadiabatic process does not lead to the loss of fidelity from decay.

We present a comprehensive theoretical study of the ionization potentials of the $M\mathrm{F}$ $(M=\mathrm{Ca}, \mathrm{Sr}, \mathrm{and} \mathrm{Ba})$ molecules using the state-of-the-art relativistic coupled-cluster approach with single, double, and perturbative triple excitations [CCSD(T)]. We have further corrected our results for higher-order excitations (up to full triples) and the QED self-energy and vacuum-polarization contributions. We have performed an extensive investigation of the effect of the various computational parameters on the calculated ionization potentials, which allowed us to assign realistic uncertainties to our predictions. For CaF and BaF, where precise experimental measurements are available, our predictions are in excellent agreement with the measured values. In the case of SrF, we provide a theoretical prediction of the ionization potential that deviates from the available experimental measurements, motivating further experimental investigations.

We present an improved action for renormalizable effective field theories (EFTs) of systems near the two-body unitarity limit. The ordering of EFT interactions is constrained, but not entirely fixed, by the renormalization group. The remaining freedom can be used to improve the theory's convergence, to simplify its applications, and to connect it to phenomenological models. We exemplify the method on a contact theory applied to systems of up to five ${}^4\mathrm{He}$ atoms. We solve the EFT at leading order including a subleading interaction that accounts for part of the two-body effective range. We show that the effects of such fake range can be compensated in perturbation theory at next-to-leading order, as long as the fake range is smaller or comparable to the experimental effective range. These results open the possibility of using similar improved actions for other many-body systems.

A systematic investigation of dielectronic satellite lines in hydrogenlike ions with $Z$ values ranging from 9 to 92 is carried out, with a focus on the effects of the Breit interaction and the generalized Breit interaction on their linear polarization. We present a detailed analysis of the polarization behaviors and resonance strengths of the satellite lines, facilitating the spectral analysis under the electron-beam ion-trap measurement conditions. Emphasizing the second-step radiative decay process in dielectronic recombination of hydrogenlike ${\mathrm{Ti}}^{21+}$, ${\mathrm{Kr}}^{35+}$, ${\mathrm{Mo}}^{41+}$, and ${\mathrm{U}}^{91+}$ ions, the alignment parameters of the singly excited states are determined by using both the deorientation factor formalism and density-matrix theory. These calculations indicate a promising opportunity for understanding the effect of the Breit interaction as well as differentiating the formalism of the deorientation factor and the density-matrix theory for the calculations of dielectronic satellite lines.

Bound states in the continuum (BICs) are resonances with infinite lifetimes, even though they are embedded in the continuous spectrum of free space. Merging multiple BICs can be a promising approach to further improve the $Q$ factors of nearby states over a broad wave-vector range. Previous studies have shown that merging BICs can only appear for specific parameter values of a structure; thus, it is commonly believed that they do not have stability. Here, we analytically study the existence and stability of merging BICs in parameter space, including material and geometric parameters. Specifically, we derive the conditions for the existence of merging-BICs in a system with a periodic plasmonic chain and demonstrate that merging BICs can stably exist when the other parameters are varied. Furthermore, in the momentum-geometric-material space, a BIC surface can be obtained analytically without performing a tedious numerical search of diverging $Q$ factors in a multiple parameter space. Based on this surface, BICs at the Γ point that merge in the momentum space can also merge again in the parameter space by changing the material parameters. The merging BIC with improved $Q$ factor not only covers a broad wave-vector range but also spans a wide geometric parameter space when compared with the original BIC. Our findings provide a different perspective in the investigation of ultrahigh $Q$ factors that substantially enhance light-matter interaction and improve the performance of photonic devices.

Recently, a solid-state-like high-harmonic generation (HHG) mechanism has been proposed from rotationally periodic molecules. Based on the quasi-energy band model, we investigate the HHG of ring-type polyynic cyclo[18]carbon (${\mathrm{C}}_{18}$) by further considering its bond length difference ($R_{\mathrm{diff}}$) between the short and long C-C bonds. For $R_{\mathrm{diff}}$ values ranging from 0.06 to $0.12\AA$ with a linearly polarized laser, the seventh harmonic intensity of polyynic ${\mathrm{C}}_{18}$ exhibits the most significant structural sensitivity compared to the third and fifth harmonics. Transition energy level distribution, paired with time-frequency analysis and transition dipole moment behavior, indicate that the seventh harmonic arises from pure interband processes. Conversely, the HHG properties driven by two consecutive circularly polarized laser pulses at each considered laser intensity combination remain unaffected by changing these $R_{\mathrm{diff}}$ values. This characteristic allows polyynic ${\mathrm{C}}_{18}$ to be utilized for designing a variety of logic gate operations based on its harmonic ellipticity in ultrafast strong laser fields.

We propose a scheme to analyze the generation and detection of optical vortices via spontaneous emission spectra. We consider a five-level M-type atomic system that interacts with two structured coherent light sources and the vacuum radiation field. The photon emitted via spontaneous decay carries information about the orbital angular momentum (OAM) of the newly generated structured light. It is found that by varying the OAM of the driving fields, one can obtain various unique structured light fields via the interference of the two spontaneous decay channels. This research provides deep insights into how the manipulation of OAM of the driving fields coupled with multilevel atomic systems can enable control over the azimuthal aspects of the spontaneous emission. Considering the rich applications of structured light ranging from optical storage to optical communication, our proposal might be useful in quantum information processing techniques.

In a recent article [Nat. Commun. 13, 2 (2022)], we devised a method of constructing the Lorentz-covariant Bohmian trajectories of single photons via weak measurements of the photon's momentum and energy. However, whether such a framework can consistently describe multiparticle interactions remains to be seen. Here we present a nontrivial generalization of our framework to describe the relativistic Bohmian trajectories of two interacting photons (this interaction arising from the symmetrization of the two-particle wave function) exhibiting nonclassical interference due to their indistinguishability. We begin by deriving the average velocity fields of the indistinguishable photons using a conditional weak measurement protocol, with detectors that are agnostic to the identity of the respective photons. We demonstrate a direct correspondence between the operationally derived trajectories and those obtained using a position- and time-symmetrized multiparticle Klein-Gordon wave function, whose dynamics are manifestly Lorentz covariant. We propose a space-time metric that depends nonlocally on the positions of both particles as a curvature-based interpretation of the resulting trajectories. Contrary to prior expectations, our results demonstrate a consistent trajectory-based interpretation of relativistic multiparticle dynamics in quantum theory.

Pawłowski and Winter's hyperbit theory, proposed in 2012, presented itself as an alternative to quantum theory, suggesting novel ways of redefining entanglement and classical communication paradigms. This research undertakes a meticulous reevaluation of hyperbit theory, uncovering significant operational constraints that question its equivalence with quantum mechanics. Crucially, the supposition that hyperbit theory and quantum theory are equivalent relies on the receiver having unattainable additional knowledge about the sender's laboratory, indicating that the work by Pawłowski and Winter is incorrect. This study accentuates the constraints of hyperbits in information processing and sheds light on the superiority of quantum communication, thereby advancing the investigation at the intersection of classical and quantum communication.

A set of orthogonal multipartite quantum states are called (distinguishability-based) genuinely nonlocal if they are locally indistinguishable across any bipartition of the subsystems. In this work, we consider the problem of constructing small genuinely nonlocal sets consisting of generalized Greenberger-Horne-Zeilinger (GHZ) states in multipartite systems. For system ${\left({\mathbb{C}}^2\right)}^{\otimes N}$ where $N$ is large, using the language of group theory, we show that a tiny proportion $\mathrm{\Theta }(1/\sqrt{2^N})$ of the states among the $N$-qubit GHZ basis suffice to exhibit genuine nonlocality. Similar arguments also hold for the canonical generalized GHZ bases in systems ${\left({\mathbb{C}}^d\right)}^{\otimes N}$, wherever $d$ is even and $N$ is large. What is more, moving to the condition that any fixed $N$ is given, we show that $d+1$ genuinely nonlocal generalized GHZ states exist in ${\left({\mathbb{C}}^d\right)}^{\otimes N}$, provided the local dimension $d$ is sufficiently large. As an additional merit, within and beyond an asymptotic sense, the latter result also indicates some evident limitations of the “trivial othogonality-preserving local measurements” (TOPLM) technique that has been utilized frequently for detecting genuine nonlocality.

Decoherence-protected spins associated with nitrogen-vacancy color centers in diamond possess remarkably long coherence time, which makes them one of the most promising and robust quantum registers. The current demand is to explore practical rapid control strategies for preparing and manipulating such registers. Our work provides all-microwave control strategies optimized using multiple optimization methods to significantly reduce the processing time by $80\%$ with a set of smooth near-zero-end-point control fields that are shown to be experimentally realizable. Furthermore, we optimize and analyze the robustness of these strategies under frequency and amplitude imperfections of the control fields, during which process we use only 16 samples to give a fair estimation of the robustness map with 2500 pixels. Overall, we provide a ready-to-implement recipe to facilitate high-performance information processing via a decoherence-protected quantum register for future quantum technology applications.

Recent developments in qudit-based quantum computing, in particular with trapped ions, open interesting possibilities for scaling quantum processors without increasing the number of physical information carriers. Here, we propose a method for compiling quantum circuits in the case, where qubits are embedded into qudits of experimentally relevant dimensionalities, $d=3,...,8$, for the trapped-ion platform. In particular, we demonstrate how single-qubit, two-qubit, and multiqubit gates can be realized using single-qudit operations and the $\text{M}ø\text{lmer-S}ø\text{rensen}$ (MS) gate as a basic two-particle operation. We expect that our findings are directly applicable to the current generation of trapped-ion-based qudit processors.

We consider nonadiabatic coupling in the “trilobite”-like long-range Rydberg molecules created by perturbing degenerate high-$\ell$ Rydberg states with a ground-state atom. Due to the flexibility granted by the high Rydberg level density, the avoided crossings between relevant potential energy curves can become extremely narrow, leading to highly singular nonadiabatic coupling. We find that the gap between the trilobite potential curve and neighboring “butterfly” or “dragonfly” potential curves can even vanish, as in a conical intersection, if the gap closes at an internuclear distance which matches a node of the $s$-wave radial wave function. This is an unanticipated outcome of Kato's theorem.

Negative ions are unique quantum systems where electron correlation plays a decisive role in determining their properties. The lack of optically allowed transitions prevents traditional optical spectroscopy and the electron affinity is, therefore, for most elements, the only atomic quantity that can be determined with high accuracy. In this work, we present a high-precision experimental determination of the electron affinity of cesium. A collinear laser-ion beam apparatus was used to investigate the partial photodetachment cross section for the cesium anion, leaving the neutral atom in the $6p {}^2{\mathit{P}}_{3/2}$ excited state. A resonance ionization scheme was used to obtain final-state selectivity, which enabled the investigation of a sharp onset of the cross section associated with a Wigner $s$-wave threshold behavior. The electron affinity was determined to be $0.4715983\left(38\right)\mathrm{eV}$.

Computing dynamical properties of strongly interacting quantum many-body systems poses a major challenge to theoretical approaches. Usually, one has to resort to numerical analytic continuation of results on imaginary frequencies, which is a mathematically ill-defined procedure. Here we present an efficient method to compute the spectral functions of the two-component Fermi gas near the strongly interacting unitary limit directly in real frequencies. To this end, we combine the Keldysh path integral that is defined in real time with the self-consistent $T$-matrix approximation. The latter is known to predict thermodynamic and transport properties in good agreement with experimental observations in ultracold atoms. We validate our method by comparison with thermodynamic quantities obtained from imaginary-time calculations and by transforming our real-time propagators to imaginary time. By comparison with state-of-the-art numerical analytic continuation of the imaginary-time results, we show that our real-time results give qualitative improvements for dynamical quantities. Moreover, we show that no significant pseudogap regime exists in the self-consistent $T$-matrix approximation above the critical temperature $T_c$, an issue that has been under significant debate. We close by pointing out the versatile nature of our method as it can be extended to other systems, like the spin- or mass-imbalanced Fermi gas, other Bose-Fermi models, two-dimensional systems, and systems out of equilibrium.