We investigate theoretically the limits of single-photon storage in a single $\mathrm{\Lambda }$-type atom, specifically the trade-off between storage efficiency and storage speed. We show that a control field can accelerate the storage process without degrading efficiency too much. However, the storage speed is ultimately limited by the total decay rate of the excited state involved. For a single-photon pulse propagating in a regular one-dimensional waveguide, the storage efficiency has an upper limit of $50\%$. Perfect single-photon storage can be achieved by using a chiral waveguide or the Sagnac interferometry. By comparing the storage efficiencies of Fock-state and coherent-state pulses, we reveal the influence of quantum statistics of light on photon storage at the single-photon level.

Measurement incompatibility stipulates the existence of quantum measurements that cannot be carried out simultaneously on single systems. We show that the set of input-output probabilities obtained from $d$-dimensional classical systems assisted with shared randomness is the same as the set obtained from $d$-dimensional quantum strategies restricted to compatible measurements with shared randomness in any communication scenario. Thus, measurement incompatibility is necessary for quantum advantage in communication, and any quantum advantage (with or without shared randomness) in communication acts as a witness to the incompatibility of the measurements at the receiver's end in a semi-device-independent way. We introduce a class of communication tasks—a general version of random access codes—to witness incompatibility of an arbitrary number of quantum measurements with arbitrary outcomes acting on $d$-dimensional systems and provide generic upper bounds on the success metric of these tasks for compatible measurements. We identify all sets of three incompatible rank-one projective qubit measurements that random access codes can witness. Finally, we present the generic relationship between different sets of probability distributions—classical, quantum with or without shared randomness, and quantum restricted to compatible measurements with or without shared randomness—produced in communication scenarios.

Entanglement is an important quantum resource to achieve high-sensitivity quantum metrology. However, the rapid decoherence of quantum entangled states, due to the unavoidable environmental noise, results in practically the unwanted sharp drop of the measurement sensitivity. To overcome such a difficulty, here we propose a spin-oscillator hybrid quantum interferometer to achieve the desirable precise estimation of the parameter encoded in the vibrations of the oscillator. Differing from the conventional two-mode quantum interferometers input by the two-mode NOON state or entangled coherent states, whose achievable sensitivities are strongly limited by the decoherence of the entangled vibrational states, we demonstrate that the present interferometer, input by a spin-dependent two-mode entangled state, possesses a manifest advantage; i.e., the measurement sensitivity of the estimated parameter is not influenced by the decoherence from the spin-oscillator entanglement. This is because, by applying a spin-oscillator disentangled operation, the information of the estimated parameter encoded originally in the vibrational degrees can be effectively transferred into the spin degree and then can be sensitively estimated by the precise spin-state population measurements. As consequence, the proposed hybrid quantum interferometer possesses manifest robustness against the particle losses of the vibrational modes. Interestingly, the achieved phase measurement sensitivity can still surpass the standard quantum limit obviously, even if a relatively large number of particle loss occurs in one of the two modes. The potential application of the proposed spin-oscillator hybrid quantum interferometer is also discussed.

The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability. In this paper, we present a quantum algorithm that simulates the linearized Vlasov equation with and without collisions, in the one-dimensional electrostatic limit. Rather than solving this equation in its native spatial and velocity phase space, we adopt an efficient representation in the dual space yielded by a Fourier-Hermite expansion. For a given simulation time, the Fourier-Hermite representation is exponentially more compact, thus yielding a classical algorithm that can match the performance of a previously proposed quantum algorithm for this problem. This representation results in a system of linear ordinary differential equations (ODEs) which can be solved with well-developed quantum algorithms: a Hamiltonian simulation in the collisionless case, and quantum ODE solvers in the collisional case. In particular, we demonstrate that a quadratic speedup in system size is attainable.

Simulations of coupled electronic and nuclear dynamics in molecules can be quite challenging due to the involved interplay of the many degrees of freedom. Because a full quantum treatment of both electrons and nuclei is computationally very demanding, it is generally restricted to model systems or rather small molecules and short timescales. Mixed quantum-classical dynamics methods such as Tully's fewest switches surface hopping (FSSH) can be used to overcome this limitation. However, FSSH is known to poorly describe electronic coherences and decoherence phenomena. Here, we present an approach that combines FSSH with ring-polymer molecular dynamics (RPMD) in a specific way that aims to alleviate the coherence problem. Termed the ring-polymer-surface-hopping–density-matrix approach, this method uses an electronic density-matrix formulation to calculate surface hopping rates. This incorporates decoherence effects into FSSH in a natural way by taking into account the spatial spreading of the ring polymer that mimics the width of a nuclear wave packet in each RPMD trajectory. By applying our method to Tully's one-dimensional model system, we demonstrate that this method captures a crucial decoherence mechanism that is missing in FSSH. Furthermore, our method turns out to be superior at describing electronic coherences compared with earlier attempts at combining RPMD and FSSH.

The 1389-nm laser is used as a repumping laser in the ${}^{171}\mathrm{Yb}$ optical lattice clock, which corresponds to the $6s6p{}^3{P}_0\to 5d6s{}^3{D}_1$ transitions. To our knowledge, there is no report on the absolute frequencies for this repumping transition yet. We excite the hyperfine structure transitions with a 1389-nm scannable laser, which is stabilized on an absolute frequency-stabilized optical frequency comb, and obtain the transition spectra. The minimum spectral linewidth is around 705 kHz, which is approximately 1.5 times greater than the natural linewidth of 484 kHz. Based on evaluating the systematic frequency shifts precisely and referencing the frequency measurement results on the secondary representation of the International System of Units second, we are the first to report the direct measurement of the absolute frequencies for $6s6p{}^3{P}_0$ ($F\hspace{0.17em}=1/2$)$\to 5d6s{}^3{D}_1$ ($F\hspace{0.17em}=1/2$, $3/2$) transitions are 215 875 $746.15\pm {\left(0.21\right)}_{\mathrm{stat}}\pm {\left(0.06\right)}_{\mathrm{sys}}$ MHz and 215 872 $697.14\pm {\left(0.11\right)}_{\mathrm{stat}}\pm {\left(0.06\right)}_{\mathrm{sys}}$ MHz, respectively. In addition, the hyperfine splitting and magnetic dipole coefficient $A$ of the $5d6s{}^3{D}_1$ state is determined as 3049.01(26) MHz and $\text{–}2032.67$(17) MHz, which is more accurate than the previous measurements by an order of magnitude.

We present a design for an atom chip trap that uses the time-orbiting-potential technique. The design offers several advantages compared with other chip-trap methods. It uses a simple crossed-wire pattern on the chip, along with a rotating bias field. The trap is naturally close to spherically symmetric, and it can be modified to be exactly symmetric in quadratic order of the coordinates. Loading from a magneto-optical trap is facilitated because the trap can be positioned an arbitrary distance from the chip. The fields can be modified to provide a gradient for support against gravity, and the three-dimensional trap can be adiabatically transformed into a two-dimensional guide.

We propose a scheme to realize frequency conversion of photons, using a hybrid system with a qubit coupled to both a resonator cavity and an optomechanical cavity. In this system, a high-energy photon can be converted into a low-energy photon plus a phonon and vice versa; the qubit works as an intermediate medium with its states unchanged. Moreover, the process can be exquisitely tuned by changing the frequency of the qubit or the resonator mode, providing additional control for the conversion. We further analyze the system dynamics and demonstrate two Rabi oscillation behaviors with dissipations. With the state-of-the-art techniques in cavity quantum electrodynamics and optomechanical systems, our proposal would be implemented and an efficient and controllable quantum light source can be achieved.

We study topological variations of polarization singularity lines in the electric field of electromagnetic radiation reflected from a parabolic mirror irradiated by elliptically polarized Gaussian and Laguerre-Gaussian beams and two types of Poincaré beams. Torus knots and links of the singular lines of polarization appear as a result of their tight focusing in the reflected radiation. Variation of the polarization ellipticity degree of the Gaussian and Laguerre-Gaussian beams and the parameters defining the polarization distribution of the Poincaré beams causes transformation of the singular lines located near the focal point of the mirror, which is accompanied by a variety of decouplings and reconnections. The total linking number of the singular lines of different types predominantly remains constant upon these reconnections.

We propose a framework for the quantum geometry of expectation values over arbitrary sets of operators and establish a link between this geometry and the eigenstates of Hamiltonian families generated by these operators. We show that the boundary of expectation value space corresponds to the ground state, which presents a natural bound that generalizes Heisenberg's uncertainty principle. To demonstrate the versatility of our framework, we present several practical applications, including providing a stronger nonlinear quantum bound that violates the Bell inequality and an explicit construction of the density functional. Our approach provides an alternative time-independent quantum formulation that transforms the linear problem in a high-dimensional Hilbert space into a nonlinear algebro-geometric problem in a low dimension, enabling us to gain new insights into quantum systems.

Indefinite causal order is a key feature involved in the study of quantum higher-order transformations. Recently, intense research has been focused on possible advantages related to the lack of definite causal order of quantum processes. Quite often the quantum switch is claimed to provide advantages in information-theoretic and thermodynamic tasks. We address here the question of whether indefinite causal order is a resource for quantum thermodynamics. Inspired by previous results in the literature, we show that indefinite causal order is not necessary for the reported increase in free energy and ergotropy. More specifically, we show that a simple causally ordered process, which replaces the system's state with a new one before the final measurement, outperforms the quantum switch in all thermodynamic tasks considered so far. We further show that a similar advantage can also be achieved without completely discarding system if we allow for non-Markovian interactions between the system and an environment. We extend the analysis to more extreme examples of indefinite causal order, showing that they do not provide an advantage either. Finally, we discuss a possible way to study the advantages that may arise from indefinite causal order in a general scenario.

Exceptional point and spectral singularity are two types of singularity that are unique to non-Hermitian systems. Here, we report the high-order spectral singularity as a high-order pole of the scattering matrix for a non-Hermitian scattering system, and the high-order spectral singularity is a unification of the exceptional point and spectral singularity. At the high-order spectral singularity, the scattering coefficients have high-order divergence and the scattering system stimulates high-order lasing. The wave emission intensity is polynomially enhanced, and the order of the growth in the polynomial intensity linearly scales with the order of the spectral singularity. Furthermore, the coherent input controls and alters the order of the spectral singularity. Our findings provide profound insights into the fundamentals and applications of high-order spectral singularities.

Bosonic codes provide an alternative option for quantum error correction. An important category of bosonic codes called the Gottesman-Kitaev-Preskill (GKP) code has aroused much interest recently. Theoretically, the error correction ability of the GKP code is limited since it can only correct small shift errors in position and momentum quadratures. A natural approach to promote the GKP error correction for large-scale, fault-tolerant quantum computation is concatenating encoded GKP states with a stabilizer code. The performance of the XZZX surface-GKP code, i.e., the single-mode GKP code concatenated with the XZZX surface code is investigated in this paper under two different noise models. Firstly, in the code-capacity noise model, the asymmetric rectangular GKP code with parameter $\lambda$ is introduced. Using the minimum weight perfect matching decoder combined with the continuous-variable GKP information, the optimal threshold of the XZZX-surface GKP code reaches $\sigma \approx 0.67$ when $\lambda =2.1$, compared with the threshold $\sigma \approx 0.60$ of the standard surface-GKP code. Secondly, we analyze the shift errors of two-qubit gates in the actual implementation and build the full circuit-level noise model. By setting the appropriate bias parameters, the logical error rate is reduced by several times in some cases. These results indicate the XZZX surface-GKP codes are more suitable for asymmetric concatenation under the general noise models. We also estimate the overhead of the XZZX-surface GKP code which uses about 291 GKP states with the noise parameter 18.5 dB ($\kappa /g\approx 0.71\%$) to encode a logical qubit with the error rate $2.53\times {10}^{-7}$, compared with the qubit-based surface code using 3041 qubits to achieve almost the same logical error rate.

Quantifying entanglement for quantum states whose density matrices are unknown is a difficult task, but also becomes more and more necessary because of the fast development of quantum engineering. Machine learning provides practical solutions to this fundamental problem, where one has to train a proper machine learning model to predict entanglement measures of unknown quantum states based on experimentally measurable data, say, moments of density matrices or correlation data produced by local measurements. In this paper, we compare the performance of these two different machine learning approaches systematically. Particularly, we first show that the approach based on moments enjoys a remarkable advantage over that based on correlation data, though the cost of measuring moments is much higher. Next, since correlation data is much easier to obtain experimentally, we try to better its performance by proposing a hybrid quantum-classical machine learning framework for this problem, where the key is to train optimal local measurements, or even optimal tensor products of single-qubit observables, to generate more informative correlation data. Our numerical simulations show that the new hybrid framework brings us comparable performance with the approach based on moments to quantify entanglement, and furthermore, it turns out that the new hybrid framework has a nice noise-resistant capability when handling realistic correlation data.

A frequent starting point of quantum computation platforms is the two-state quantum system, i.e., the qubit. However, in the context of integer optimization problems, relevant to scheduling optimization and operations research, it is often more resource-efficient to employ quantum systems with more than two basis states, so-called qudits. Here, we discuss the quantum approximate optimization algorithm (QAOA) for qudit systems. We illustrate how the QAOA can be used to formulate a variety of integer optimization problems such as graph coloring problems or electric vehicle charging optimization. In addition, we comment on the implementation of constraints and describe three methods to include these in a quantum circuit of a QAOA by penalty contributions to the cost Hamiltonian, conditional gates using ancilla qubits, and a dynamical decoupling strategy. Finally, as a showcase of qudit-based QAOA, we present numerical results for a charging optimization problem mapped onto a maximum-$k$-graph-coloring problem. Our work illustrates the flexibility of qudit systems to solve integer optimization problems.

The spectral emission of hot ${\mathrm{C}}_{60}$ has been experimentally shown to be broad and continuous, in apparent contradiction with the discrete and narrow absorption spectrum associated with the high symmetry of buckminsterfullerene. In the present work we computationally model the emission spectrum of isolated carbon clusters, assuming a broad distribution of isomers that are likely populated under the experimental conditions. The contributions of individual structures to the global spectrum correspond to the relaxation via recurrent fluorescence and vibrational emission, electronic and vibrational structures being described by a simple but efficient density-functional-based tight-binding scheme. The model predicts a blackbody-like emission spectrum that is naturally broad and correctly accounts for the experimental measurements, except for a maximum that is quantitatively shifted with respect to Wien's displacement law. To quantify such differences, we introduce an emissivity parameter $\varepsilon$ as the ratio between the spectral emittance and the corresponding exact blackbody spectrum; $\varepsilon$ is numerically found to scale as ${\left(\lambda T\right)}^{-2}$ at leading order with increasing temperature $T$ and for wavelengths $\lambda >350$ nm, and we provide a theoretical justification for this behavior. Our results are discussed in the light of the astrophysical detection of interstellar fullerenes, as well as in combustion environments where carbon clusters are relevant in the context of nascent soot particle formation.

We have discovered that 5 keV bursts of $5\times 10{}^7$ positrons with an initial longitudinal spin polarization of $(28.8\pm 0.7)\%$, when implanted into a thin Ni(100) crystal, are emitted with 20% efficiency at thermal energies from its surface with $(30.9\pm 0.5)\%$ polarization. We conclude that the positron spin polarization is preserved while interacting with the Ni, despite the 0.61 T average transverse magnetization of the Ni at room temperature. The resulting polarized beam has been focused to a 0.025-mm mean-diameter spot when accelerated to 5 keV and will be uniquely suited for experiments on a neutral spin aligned $e^{+}-e^{-}$ plasma, spin- and angle-resolved positronium emission spectroscopy, and critical for producing a triplet positronium Bose-Einstein condensate.