We argue that although the experiment of Remez et al. [Phys. Rev. Lett. 123, 060401 (2019)] is interesting, and its conclusions may well be correct, the observed lack of dependence of the measured angular distributions on the electron's transverse coherence length could have been expected for the parameters chosen. This is because for Smith-Purcell radiation it is the coherence length of a virtual photon ${\sigma }_{\perp }^{\left(\gamma \right)}\approx \beta \gamma \lambda \lesssim \lambda$ that plays a role of the radiation formation width and not the entire electron's coherence length that can well be orders of magnitude larger than the former. This is a common feature for all the radiation processes in which a photon is emitted not directly by the electron packet, which can be delocalized in space, but rather by a much better localized atom or a conduction electron on a surface. Therefore, in our opinion the results of Remez et al. cannot rule out the alternative hypothesis of the delocalized charge. The question, mainly addressed in the Comment by Karnieli et al., of whether the measurements were performed in the wave zone or not is interesting but somewhat secondary. We emphasize that the measured azimuthal distributions are unusually wide and there exists a family of classical effects that could also have resulted in the measured distributions. Such alternative classical hypotheses include: (i) effects of the beam sizes, of its angular divergence, of the temporal coherence of the radiation process, which is also related to how the wave zone is defined, and (ii) influence of the grating shape and of its material—the effects that are known to be of crucial importance for Smith-Purcell radiation from nonrelativistic electrons. Finally, we propose to repeat the experiment and to measure diffraction radiation from a thin metallic semiplane (or a strip) in which case the aforementioned classical effects play a much smaller role.

Temperature is a deceptively simple concept that still raises deep questions at the forefront of quantum physics research. The observation of thermalization in completely isolated quantum systems, such as cold-atom quantum simulators, implies that a temperature can be assigned even to individual, pure quantum states. Here, we propose a scheme to measure the temperature of such pure states through quantum interference. Our proposal involves interferometry of an auxiliary qubit probe, which is prepared in a superposition state and subsequently decoheres due to weak coupling with a closed, thermalized many-body system. Using only a few basic assumptions about chaotic quantum systems, namely, the eigenstate thermalization hypothesis and the emergence of hydrodynamics at long times, we show that the qubit undergoes pure exponential decoherence at a rate that depends on the temperature of its surroundings. We verify our predictions by numerical experiments on a quantum spin chain that thermalizes after absorbing energy from a periodic drive. Our Letter provides a general method to measure the temperature of isolated, strongly interacting systems under minimal assumptions.

The study of recurrences and revivals in quantum systems has attracted a great deal of interest because of its importance in the control of quantum systems and its potential use in developing new technologies. In this paper, we introduce a protocol to induce full-state revivals in a huge class of quantum walks on a $d$-dimensional lattice governed by a $c$-dimensional coin system. The protocol requires two repeated interventions in the coin degree of freedom. We also present a characterization of the walks that admit such a protocol. Moreover, we modify the quantity known as the Pólya number, typically used in the study of recurrences in classical random walks and quantum walks, to create a witness of the first revival of the walk.

Generating Greenberger-Horne-Zeilinger (GHZ) states of solid-state spins is of great significance for quantum metrology and quantum error correction. We propose here an efficient scheme for generating high fidelity GHZ states in a solid-state setup where multiple silicon-vacancy (SiV) centers are embedded in a quasi-one-dimensional acoustic diamond waveguide. The lattice distortion gives rise to a strong strain coupling between the orbital degree of freedom of SiV centers and the continuum phonon modes. Due to the permutation symmetry, we can take advantage of the decoherence-free subspace to avoid dissipation. Under the quantum Zeno regime, two control fields are used to achieve a ladderlike coupling structure in decoherence-free subspace along with an off-resonant two-photon Raman transition process. We calculate the pulse sequences for $N=4$ and at the same time analyze the effect of different collective decay rates. Moreover, we consider the disorder in the imperfect position of SiV centers and the inhomogeneous strain coupling. This paper may provide a feasible protocol for the generation of GHZ states in a solid-state system.

Device-independent certification schemes have gained a lot of interest lately, not only for their applications in quantum information tasks, but also their implications towards foundations of quantum theory. The strongest form of device-independent certification, known as self-testing, often requires for a Bell inequality to be maximally violated by specific quantum states and measurements. In this work, using the techniques developed recently [S. Sarkar et al., npj Quantum Inf. 7, 151 (2021)], we provide a self-testing scheme for the multipartite Greenberger-Horne-Zeilinger states of arbitrary local dimension that does not rely on self-testing results for qubit states and that exploits the minimal number of two measurements per party. This makes our results interesting as far as practical implementation of device-independent certification methods is concerned. Our self-testing statement relies on maximal violation of a Bell inequality proposed recently [R. Augusiak et al., New J. Phys. 21, 113001 (2019)].

We investigate the energy dynamics of noncrystallized (melted) ions, confined in a Paul trap. The nonperiodic Coulomb interaction experienced by melted ions forms a medium for nonconservative energy transfer from the radio-frequency (rf) field to the ions, a process known as rf heating. We study rf heating by analyzing numerical simulations of noncrystallized ion motion in Paul trap potentials, in which the energy of the ions' secular motion changes at discrete intervals, corresponding to ion-ion collisions. The analysis of these collisions is used as a basis to derive a simplified model of rf heating energy dynamics, from which we conclude that the rf heating rate is predominantly dependent on the rf field strength. We confirm the predictability of the model experimentally: Two trapped ${}^{40}\mathrm{Ca}^{+}$ ions are deterministically driven to melt, and their fluorescence rate is used to infer the ions' energy. Under these experimental conditions, we investigate which Doppler cooling parameters are required for efficient recrystallization, and compare our results to simulations.

We study the emergence of finite-temperature topological phase transitions of the Berezinskii-Kosterlitz-Thouless type and the collective mode spectrum of two-dimensional Fermi gases in the presence of attractive $s$-wave interactions, spin-orbit coupling, and Zeeman fields. We show that neglecting the spin-dependent phase shift on the fermionic wave function misses an important point. Including this spin-dependent shift, we derive the effective low-energy and long-wavelength quantum action for independent (unlocked) phase fluctuations in the U(1) (charge) and SU(2) (spin) sectors and show that at least two phase transitions occur because charge and spin degrees of freedom are coupled due to the presence of spin-orbit and Zeeman fields. Furthermore, we demonstrate that vortex and antivortex excitations are characterized by two topological quantum numbers, corresponding to the quantized circulation of charge and spin velocities. Finally, we show that there are two collective modes in the superfluid phase at low temperatures which arise due to the coupling between sound and transverse-spin waves.

A Poincaré sphere representation of electromagnetic spectral two-point spatial coherence was recently introduced for fully polarized light beams. In this work, we employ the singular-value decomposition of the cross-spectral density matrix and establish a rigorous interpretation for the formalism in the context of partial polarization. At a single point, the construction reduces to the traditional polarization Poincaré sphere, which therefore can be regarded as a limiting case of the coherence sphere. The formalism is illustrated with paraxial blackbody radiation and Gaussian Schell-model beams. We expect our results will find use in understanding the coherence-polarization state of optical beams in situations dealing with random light.

For the optimal success probability under minimum-error discrimination between $r\ge 2$ arbitrary quantum states prepared with any a priori probabilities, we find new general analytical lower and upper bounds and specify the relations between these new general bounds and the known general bounds, lower and upper. We also present the example where the values of the new general lower and upper bounds on the optimal success probability are tighter than the values of most of the general analytical bounds known in the literature. The new upper bound on the optimal success probability explicitly generalizes to $r>2$ the form of the Helstrom bound. For $r=2$, each of our new bounds, lower and upper, reduces to the Helstrom bound.

Recently, a protocol called quantum-gravity-induced entanglement of masses (QGEM) that aims to test the quantum nature of gravity using the entanglement of two qubits was proposed. The entanglement can arise only if the force between the two spatially superposed masses is occurring via the exchange of a mediating virtual graviton. In this paper we examine a possible improvement of the QGEM setup by introducing a third mass with an embedded qubit so that there are now three qubits to witness the gravitationally generated entanglement. We compare the entanglement generation for different experimental setups with two and three qubits and find that a three-qubit setup where the superpositions are parallel to each other leads to the highest rate of entanglement generation within $\tau =5\mathrm{s}$. We show that the three-qubit setup is more resilient to the higher rate of decoherence. The entanglement can be detected experimentally for the two-qubit setup if the decoherence rate $\gamma$ is $\gamma <0.11\mathrm{Hz}$ compared to $\gamma <0.16\mathrm{Hz}$ for the three-qubit setup. However, the introduction of an extra qubit means that more measurements are required to characterize entanglement in an experiment. We conduct experimental simulations and estimate that the three-qubit setup would allow detecting the entanglement in the QGEM protocol at a $99.9\%$ certainty with $O\left({10}^4\right)–O\left({10}^5\right)$ measurements when $\gamma \in [0.1,0.15]\mathrm{Hz}$. Furthermore, we find that the number of needed measurements can be reduced to $O\left({10}^3\right)–O\left({10}^5\right)$ if the measurement schedule is optimized using joint Pauli basis measurements. For $\gamma >0.06\mathrm{Hz}$ the three-qubit setup is favorable compared to the two-qubit setup in terms of the minimum number of measurements needed to characterize the entanglement. Thus, the proposed setup here provides a promising avenue for implementing the QGEM experiment.

We calculate analytically the entanglement and Rényi entropies, the negativity, and the mutual information together with all the density and many-particle correlation functions for free bosons on a lattice in the ground state, for both homogeneous and inhomogeneous systems. We show that all those quantities can be derived from a multinomial form of the reduced density matrix in the configuration space whose diagonal elements dictate the statistics of the particle distribution, while the off-diagonal coherence terms control the quantum fluctuations. We provide by this analysis a unified approach based on a reduced density matrix technique useful to calculate both the entanglement properties and an infinite number of correlation functions.

We consider a continuous-variable (CV) quantum key distribution (QKD) protocol over free-space channels, which is simpler and more robust than typical CV QKD protocols. It uses a bright laser, squeezed and modulated in the amplitude quadrature, and self-homodyne detection. We consider a scenario, where the line of sight is classically monitored to detect active eavesdroppers, so that we can assume a passive eavesdropper. Under this assumption, we analyze security of the QKD protocol in the composable finite-size regime. Proper modulation of the squeezed laser to the shot-noise level can completely eliminate information leakage to the eavesdropper and also eliminate the turbulence-induced noise of the channel in the amplitude quadrature. Under these conditions, estimation of the eavesdropper's information is no longer required. The protocol is extremely robust to modulation noise and highly loss-tolerant, which makes it a promising candidate for satellite-based continuous-variable quantum communication.

We present two protocols for constructing quantum processor nodes in randomly doped rare-earth-ion crystals and analyze their properties. By varying the doping concentration and the accessible laser tunability, the processor nodes can contain anywhere from only a few tens to almost 1000 qubits. Furthermore, the average number of qubits each qubit can interact with, denoted by the connectivity, can be partly tailored to lie between just a few and roughly 100. We also study how a limited tunability of the laser affects the results and conclude that a tuning range of 100 GHz limits the results to roughly 100 qubits with around 50 connections per qubit on average. In order to construct an even larger processor, the vision is that several of these quantum processor nodes should be connected to each other in a multinode architecture via, e.g., optical interfaces or flying qubits in the form of light. Our results are encouraging for establishing the rare-earth-ion-based systems as a quantum computing platform with strong potential and can serve to focus the efforts within the field.

The recent measurement of the generalized oscillator strengths (GOSs) for $\tilde{A}{}^{1}B_1$ and $\tilde{B}{}^{1}A_1$ of ${\mathrm{H}}_2\mathrm{O}$ exhibits the apparent deviations from the first Born approximation calculations in the large squared momentum transfer region [W. Q. Xu et al., Phys. Rev. A 103, 032808 (2021)]. Here a simplified theoretical model was proposed to calculate the GOSs of the two excitations at large momentum transfer within the second Born approximation. The accord of the experimental GOSs and the theoretical ones is improved, but the differences still exist. In addition, the GOSs and the integral cross sections for the higher excitations of ${\mathrm{H}}_2\mathrm{O}$ in 9.85–12.15 eV are presented, which could be used to complete the database of electron-impact excitation cross sections of ${\mathrm{H}}_2\mathrm{O}$ and be beneficial for modeling interaction processes between electrons and ${\mathrm{H}}_2\mathrm{O}$ in the earth's atmosphere, plasmas, radiation physics, biology, etc.

Extreme ultraviolet (EUV) optical transitions of lanthanide highly charged ions have been studied. The $\left[\mathrm{Ni}\right]4s^{2}4p–\left[\mathrm{Ni}\right]4s^{2}4d$ and $\left[\mathrm{Ni}\right]4s^{2}4p–\left[\mathrm{Ni}\right]4s4p^2$ transition lines of galliumlike lanthanide elements have been spectroscopically measured in large helical device (LHD) plasma and electron-beam ion trap (EBIT) plasma. The wavelengths for Eu ions agreed within $0.03\%$ between the LHD and EBIT measurements. Due to the enhancement of spin-orbit interactions along with the increase of atomic number $Z$ in $4p$ atomic orbitals, energy splitting between $4p_{1/2}$ and $4p_{3/2}$ orbitals increases significantly from lanthanum to lutetium, causing the crossing of $Z$-dependent wavelength curves. The spectral line positions and strengths are theoretically calculated by means of the multiconfiguration Dirac-Fock method. The mixing of the $\left[\mathrm{Ni}\right]4s^{2}4d$ and $\left[\mathrm{Ni}\right]4s4p^2$ configurations leads to an avoided crossing in the apparent wavelength curves. The configuration mixing makes both the $\left[\mathrm{Ni}\right]4s^{2}4p–\left[\mathrm{Ni}\right]4s^{2}4d$ and $\left[\mathrm{Ni}\right]4s^{2}4p–\left[\mathrm{Ni}\right]4s4p^2$ lines well visible in the EUV spectra near the level crossing point. The levels are found to cross between $Z=62$ and 63.

The multiphonon quantum dynamics in laser-pumped cavity optomechanical samples containing a vibrating mirror is investigated. Especially, we focus on dispersive interaction regimes where the externally applied coherent field frequency detuning from the optical resonator frequency is not equal to the mirror's oscillating frequency or to its multiples. As a result, for moderately strong couplings among the involved subsystems, the quantum dynamics of this complex system is described by multiphonon absorption or emission processes, respectively. Particularly, we demonstrate efficient ways to monitor the phonon quantum dynamics via photon detection. The possibility to extract the relevant sample parameters, for instance, the coupling strength between the mechanical mirror and the electromagnetic field, is also discussed.

Bound states in the continuum (BICs), both the symmetry-protected and accidental ones, can be realized in the band of antisymmetric mode in a nanoparticle chain as long as the particles radiate exactly out of phase pairwisely. However, for the symmetric mode, BICs cannot form in this way. Here, we show that accidental BICs can be generated from the symmetric mode, as exemplified by a toroidal dipole mode-induced BIC in a trimerized system. This type of BIC is fully studied by an eigenmode analysis as well as multipole decomposition. It is also demonstrated that the BICs correspond to certain phase singularity of the system, indicating the robust existence of the BICs ensured by their topological nature. The combination of BICs and toroidal dipole resonance may find applications in lasing and subwavelength waveguiding.

Optical amplification in a disordered system leads to modification of the localization properties and the relative fluctuations of transport parameters. Here, we study the effect of gain on the localization properties and transport parameters of Anderson-localized modes at critical disorder in a one-dimensional periodic-on-average random amplifying system. We experimentally measured the inverse participation ratio (IPR) and localization length $\xi$ to quantify the localization behavior. At high disorder, IPR and ${\xi }^{-1}$ exhibit a linear relationship, as expected from theoretical studies. However, it shows an anomalous behavior below a critical disorder and transitions into a near-quadratic relationship at weak disorder. We further study the mesoscopic conductance $g^{\prime }$ and statistical distributions of modal and integrated intensities to quantify the transport. The intensity distributions show power-law tails whose exponents show atypical gain dependence across the critical disorder. Motivated by the experimental results, we performed numerical studies using a model based on transfer matrices and laser rate equations which endorses our experimental observations.

The recoil of atoms in dense ensembles during light-matter interactions is studied using quantized vibrational states for the atomic motion. The recoil resulting from the forces due to the near-field collective dipole interactions and far-field laser and decay interactions are explored. The contributions to the recoil and the dependence on the trap frequency of the different terms of the Hamiltonian and Lindbladian are studied. These calculations are compared with previous results using the impulse model in the slow-oscillation approximation. Calculations in highly subradiant systems show enhanced recoil indicating that recoil effects cannot be ignored in such cases.

Due to strong photon-phonon interaction, coupled microcavities have provided a fruitful platform for chaos investigation. In particular, the parity-time symmetric microcavities pair has attracted unprecedented attention since the exceptional point (EP) in the non-Hermitian system offers more intriguing and abundant dynamics. Motivated by achieving a robust EP, a novel exceptional surface (ES) notion is proposed in the coupled microcavities. However, the chaotic dynamics on the ES remain yet unexplored. This study explores the chaos generation on the ES. We discover that the ES could dramatically decrease the threshold of chaos generation by >50% compared to the eigenvalues escaping from the ES. Unlike conventional chaotic dynamics, chaotic signals on the ES possess a surprising globally flattened, but locally chirped spectrum. Such an advantage provides an additional degree of freedom to implement chaotic applications on the physical layer. In addition, a coupling phase-induced chaos is found, which demonstrates an accumulated chaos generation beyond the conventional wisdom. More importantly, such an arrangement enables chaotic signals to achieve the temporal Vernier and harmonic Vernier effects, expanding the scope of chaos. This study of chaos generation on the ES further stimulates applications in compact chaotic devices and potentially facilitates fundamental chaotic dynamics research.