In collisional thermometry, a system in contact with the thermal bath is probed by a stream of ancillas. Coherences and collective measurements were shown to improve the Fisher information in some parameter regimes, for a stream of independent and identically prepared (i.i.d.) ancillas in some specific states [Seah et al., Phys. Rev. Lett. 123, 180602 (2019)]. Here we refine the analysis of this metrological advantage by optimizing over the possible input ancilla states, also for block-i.i.d. states of block size $b=2$. For both an indirect measurement interaction and a coherent energy exchange channel, we show when the thermal Cramér-Rao bound can be beaten, and when a collective measurement of $N>1$ ancilla may return advantages over single-copy measurements.

Precision measurements of the ${\mathrm{Lu}}^{+}{}^{3}D_1$ and ${}^{3}D_2$ quadrupole moments have been carried out giving $\mathrm{\Theta }\left({}^{3}D_1\right)=0.63862\left(74\right)e{a}_0^2$ and $\mathrm{\Theta }\left({}^{3}D_2\right)=0.8602\left(14\right)e{a}_0^2$, respectively. The measurements utilize the differential shift between ions in a multi-ion crystal so that effects of external field gradients do not contribute, leaving only the well-defined Coulomb interaction. At this level of precision, hyperfine-mediated corrections will likely be important.

We have performed kinematically complete experiments on single-electron capture in slow ${\mathrm{He}}^{2+}$-Ar collisions. Besides the pure capture to the ${\mathrm{He}}^{+}(n=2)$ level, capture into the deep ${\mathrm{He}}^{+}(n=1)$ state with simultaneous excitation of another target electron is also observed. In contrast to the pure capture, the total cross section for this two-electron transition decreases with increasing collision energy, and its angular-differential cross section exhibits a much slighter slope. We take these observations as evidence for electron capture mediated by electron-electron interactions.

We study the electronic and hyperfine structures of ${}^{24}\mathrm{MgH}$ molecule, which are of crucial importance for the laser cooling of the molecule. The accurate spectroscopic constants and hyperfine levels are presented for $X{}^2\mathrm{\Sigma }^{+}$ and $A{}^2\mathrm{\Pi }$ symmetries. The theoretical results are in good agreement with the experimental data. We then provide a scheme for the laser-driven cycling transitions of $A{}^2\mathrm{\Pi }_{1/2}\leftarrow X{}^2\mathrm{\Sigma }_{1/2}$. In addition, we calculate the hyperfine branching ratios for the rate of decay from $|A{}^2\mathrm{\Pi }_{1/2},J^{\prime }=1/2,+\rangle$ to $|X{}^2\mathrm{\Sigma }_{1/2},N=1,-\rangle$ transition. We also provide a sideband modulation scheme to the pumping lasers to match all four hyperfine levels of the $X{}^2\mathrm{\Sigma }_{1/2}$ ($v=0$, $N=1$). Finally, we calculate the Zeeman shift of the ($X{}^2\mathrm{\Sigma }_{1/2}$, $v=0$, $N=1$) ground state, and the typical hyperfine structure magnetic $g$ factor $g_F$ and mixed $g$ factors $g_F^{\mathrm{eff}}$ are also calculated. Our study is expected to be useful for the laser-cooling ${}^{24}\mathrm{MgH}$ molecule and the interpretation of astronomical spectra involving MgH molecule.

We demonstrate detection of NaRb Feshbach molecules at high magnetic field by combining molecular photodissociation and absorption imaging of the photofragments. The photodissociation process is carried out via a spectroscopically selected hyperfine Zeeman level correlated with the Na ($3P_{3/2}$) $+$ Rb ($5S_{1/2}$) asymptote which, following spontaneous emission and optical pumping, leads to ground-state atoms in a single level with near unity probability. Subsequent to the dissociation, the number of molecules is obtained by detecting the resultant ${}^{23}\mathrm{Na}$ and ${}^{87}\mathrm{Rb}$ atoms. We have also studied the heating effect caused by the photodissociation process and optimized the detection protocol for extracting the temperature of the molecular cloud. This method enables the $insitu$ detection of fast timescale collision dynamics between NaRb Feshbach molecules and will be a valuable capability in studying few-body physics involving molecules.

Structural chirality can induce counterintuitive optical forces due to inherent symmetry properties. While optical forces on a single chiral particle in the Rayleigh regime have been well studied, optical forces in coupled chiral particles remain less explored. By using full-wave numerical simulations and an analytical method of source representation, we investigated the optical forces induced by a plane wave on two chiral particles coupling with each other via the evanescent near fields. We found that the induced electric and magnetic dipoles of the chiral particles have complicated couplings that give rise to dark and bright modes. The interaction force between the particles can be either attractive or repulsive, and its magnitude can be significantly enhanced by the resonance modes. The attractive force is much stronger if two particles are of opposite handedness compared with the case of the same handedness. The electric dipole force and the magnetic dipole force have the same sign for two particles with the same handedness, while they are of different signs for two particles with opposite handedness. The results can lead to a better understanding of chirality-induced optical forces with potential applications in optical manipulations and chiral light-matter interactions.

Benefiting from the tunability of their phase delay and gain, we show the possibility of realizing level attraction, parity-time ($\mathcal{PT}$)-, and anti-$\mathcal{PT}$-symmetric photonic structures with indirectly coupled active and passive microresonators mediated by drop-filter waveguides. We find that level attraction originates from two mechanisms, i.e., exceptional point and resonance, and it may emerge not only for dissipative coupling but also coherent coupling and hybrid coupling after considering the gain and loss of microresonators, which confirms the universality of level attraction in the coupled photonic system. On the other hand, the transition from $\mathcal{PT}$ to anti-$\mathcal{PT}$ symmetry or vice versa may be realizable by tuning their phase delay and gain; thus the indirectly coupled microresonators may provide an excellent platform for exhibiting the unique features of $\mathcal{PT}$ and anti-$\mathcal{PT}$ symmetry. Furthermore, we also reveal the intrinsic relationship of the line shape and phase behavior of the reflection spectrum with $\mathcal{PT}$ symmetry, anti-$\mathcal{PT}$ symmetry, and level attraction.

Schrödinger-cat states are useful for many applications, ranging from quantum-information processing to high-precision measurements. In this paper we propose a method for creating such cat states, based on photon-assisted Landau-Zener-Stückelberg interferometry in a hybrid system consisting of a qubit coupled to a photon cavity. We show that by initializing the qubit in one of its basis states, performing three consecutive sweeps of the qubit energy splitting across the 1-photon resonance, and finally projecting the qubit to the same basis state, the parity of the photon field can be purified to very high degree; when the initial photon state is a coherent state, the final state will then be very close to a Schrödinger-cat state. We present numerical simulations that confirm that our protocol could work with high fidelity ($\sim 0.99$) for coherent states of reasonable size (${\left|\alpha \right|}^2\sim 10$). Furthermore, we suggest that our protocol can also be used to transfer quantum information between the qubit and a superposition of orthogonal cat states in the cavity.

Identification of complicated quantum environments lies in the core of quantum engineering, which systematically constructs an environment model with the aim of accurate control of quantum systems. In this paper, we present an inverse-system method to identify damping rate functions, which describe non-Markovian environments in time-convolution-less master equations. To access information on the environment, we couple a finite-level quantum system to the environment and measure time traces of local observables of the system. By using sufficient measurement results, an algorithm is designed, which can simultaneously estimate multiple damping rate functions for different dissipative channels. Further, we show that identifiability for the damping rate functions corresponds to the invertibility of the system and a necessary condition for identifiability is also given. The effectiveness of our method is shown in examples of an atom and three-spin-chain non-Markovian systems.

We study the quantum capacity of a continuous-variable dephasing channel, which is a notable example of a non-Gaussian quantum channel. We prove that a single-letter formula applies. The optimal input state is found to be diagonal in the Fock basis and with a distribution that is a discrete version of a Gaussian. We discuss how its mean and variance are related to the dephasing rate and input energy. We then show that by increasing the input energy, the capacity saturates to a finite value. We also show that it decays exponentially for large values of dephasing rates.

We study the exact open system dynamics of one- and two-qubit gates during a measurement-based quantum computation considering non-Markovian environments. We obtain analytical solutions for the average gate fidelities and analyze them for amplitude damping and phase damping channels. We show, for both channels, that the average fidelity is identical for the $X$ gate and $Z$ gate and very similar for the $\pi /4$ gate when considering the amplitude damping channel. Also, we show that fast application of the projective measurements does not necessarily imply high gate fidelity nor does slow application necessarily imply low gate fidelity. Indeed, for highly non-Markovian environments, it is of utmost importance to know the best time to perform the measurements, since a huge variation in the gate fidelity may occur given this scenario. Furthermore, we show that whereas for amplitude damping the knowledge of the dissipative map is sufficient to determine the best measurement times, i.e., the best times at which measures are taken, the same is not necessarily true for phase damping. For the latter, the time of the set of measures becomes crucial since a phase error in one qubit can fix the phase error that takes place in another. Finally, we show that these peculiar results disappear if all qubits are subjected to Markovian processes.

Generation of electron vortices in photodetachment of ${\mathrm{H}}^{-}$ by circularly polarized laser pulses is analyzed by means of strong-field approximation and by numerically solving the time-dependent Schrödinger equation. A very good agreement is shown for the magnitude and the phase of the probability amplitude of photodetachment from both approaches. We demonstrate that spiral-like patterns in the probability amplitude of detachment, observed for a pair of counter-rotating circularly polarized laser pulses, cannot be associated with nonvanishing topological charge vortices. The latter can be generated, on the other hand, by a circularly polarized laser pulse or a sequence of such pulses with corotating polarizations. Such interpretation of our results follows from the hydrodynamical formulation of quantum mechanics and its generalization to arbitrary parametric spaces.

We study the effect of intercomponent interactions on the dynamical properties of quantum walkers. We consider the simplest situation of two indistinguishable noninteracting walkers on a tilted optical lattice interacting with a walker from a different component. The mediated effect of the third particle is then analyzed in the backdrop of various controlling parameters. The interaction-induced two-particle correlations are shown to be nontrivially affected by the particle statistics, choice of initial states, and tilt configurations of the lattice. Our analysis thus offers an overall picture and serves as a starting point of a study of interacting multicomponent quantum walkers.

Although Heisenberg's uncertainty principle is represented by a rigorously proven relation about intrinsic uncertainties in quantum states, Heisenberg's error-disturbance relation (EDR) has been commonly believed to be another aspect of the principle. Based on the recent development of universally valid reformulations of Heisenberg's EDR, we study the error and disturbance of Stern-Gerlach measurements of a spin-1/2 particle. We determine the range of the possible values of the error and disturbance for arbitrary Stern-Gerlach apparatuses with the orbital degree prepared in an arbitrary Gaussian state. We show that their error-disturbance region is close to the theoretical optimal and actually violates Heisenberg's EDR in a broad range of experimental parameters. We also show the existence of orbital states in which the error is minimized by the screen at a finite distance from the magnet, in contrast to the standard assumption.

We show that one-body entanglement, which is a measure of the deviation of a pure fermionic state from a Slater determinant (SD) and is determined by the mixedness of the single-particle density matrix (SPDM), can be considered as a quantum resource. The associated theory has SDs and their convex hull as free states, and number conserving fermion linear optics operations (FLO), which include one-body unitary transformations and measurements of the occupancy of single-particle modes, as the basic free operations. We first provide a bipartitelike formulation of one-body entanglement, based on a Schmidt-like decomposition of a pure $N$-fermion state, from which the SPDM [together with the $(N-1)$-body density matrix] can be derived. It is then proved that under FLO operations the initial and postmeasurement SPDMs always satisfy a majorization relation, which ensures that these operations cannot increase, on average, the one-body entanglement. It is finally shown that this resource is consistent with a model of fermionic quantum computation which requires correlations beyond antisymmetrization. More general free measurements and the relation with mode entanglement are also discussed.

Surface codes are a promising method of quantum error correction and the basis of many proposed quantum computation implementations. However, their efficient decoding is still not fully explored. Recently, approaches based on machine learning techniques have been proposed by Torlai and Melko [Phys. Rev. Lett. 119, 030501 (2017)] as well as Varsamopoulos et al. [Quantum Sci. Technol. 3, 015004 (2017)]. In these approaches, a so-called high-level decoder is used to post-correct an underlying decoder by correcting logical errors. A significant problem is that these methods require large amounts of training data even for relatively small code distances. The above-mentioned methods were tested on the rotated surface code which encodes one logical qubit. Here, we show that they are viable even for the toric surface code which encodes two logical qubits. Furthermore, we explain how symmetries of the toric code can be exploited to reduce the amount of training data that is required to obtain good decoding results. Finally, we compare different underlying decoders and show that the accuracy of high-level decoding noticeably depends on the quality of the underlying decoder in the realistic case of imperfect training.

Bell nonlocality is a cornerstone of quantum theory with applications in information processing ranging from cryptography to distributed computing and game theory. Indeed, it is known that Bell's theorem can be formally linked to Bayesian games, allowing the use of nonlocal correlations to advise players and thereby achieve new points of equilibrium that are unavailable classically. Here we generalize this link, proving the connection between multistage games of incomplete information with Bell scenarios involving the communication of measurement outcomes between the parties. We apply the general framework for a few cases of interest and analyze the equilibrium reached by quantum nonlocal correlations.

We propose a scheme that generalizes the loss scaling properties of twin-field or phase-matching quantum key distribution (QKD) related to a channel of transmission ${\eta }_{\mathrm{total}}$ from $\sqrt{{\eta }_{\mathrm{total}}}$ to $\sqrt[2n]{{\eta }_{\mathrm{total}}}$ by employing $n-1$ memory stations with spin qubits and $n$ beam-splitter stations including optical detectors. Our scheme's resource states are similar to the coherent-state-based light-matter entangled states of a previous hybrid quantum repeater, but unlike the latter our scheme avoids the necessity of employing $2n-1$ memory stations and writing the transmitted optical states into the matter memory qubits. The full scaling advantage of this memory-assisted phase-matching QKD (MA-PM QKD) is obtainable with threshold detectors in a scenario with only channel loss. We mainly focus on the obtainable secret-key rates per channel use for up to $n=4$ including memory dephasing and for $n=2$ (i.e., $\sqrt[4]{{\eta }_{\mathrm{total}}}$-MA-PM QKD assisted by a single memory station) for error models including dark counts, memory dephasing and depolarization, and phase mismatch. By combining the twin-field concept of interfering phase-sensitive optical states with that of storing quantum states up to a cutoff memory time, distances well beyond 700 km with rates well above ${\eta }_{\mathrm{total}}$ can be reached for realistic, high-quality quantum memories (up to 1-s coherence time) and modest detector efficiencies. Similarly, the standard single-node quantum repeater, scaling as $\sqrt{{\eta }_{\mathrm{total}}}$, can be beaten when approaching perfect detectors and exceeding spin coherence times of 5 s; beating ideal twin-field QKD requires 1 s. As for further experimental simplifications, our treatment includes the notion of weak nonlinearities for the light-matter states, a discussion on the possibility of replacing the threshold by homodyne detectors, and a comparison between sequential and parallel entanglement distributions.

We experimentally and theoretically show that the electron energy spectra strongly depend on the relative helicity in highly intense, circularly polarized two-color laser fields, which is an unexpected finding. The employed counter-rotating two-color (CRTC) fields and the corotating two-color (CoRTC) fields are both a superposition of circularly polarized laser pulses at a central wavelength of 390 and 780 nm (intensity ratio $I_{390}/I_{780}\approx 250)$. For the CRTC field, the measured electron energy spectrum is dominated by peaks that are spaced by 3.18 eV (corresponds to the photon energy of light at a wavelength of 390 nm). For the CoRTC field, we observe additional energy peaks (sidebands). Using our semiclassical, trajectory-based models, we conclude that the sideband intensity is modulated by a subcycle interference, which sensitively depends on the relative helicity in circularly polarized two-color fields.