The tight connection between mass and energy unveiled by special relativity, summarized by the iconic formula $E=m{c}^2$, has revolutionized our understanding of nature and even shaped our political world over the past century through its military application. It is certainly one of the most exhaustively tested and well-known equations of modern science. Although we have become used to its most obvious implication—mass-energy equivalence —it is surprising that one of its subtle—yet, inevitable—consequences is still a matter of confusion: the so-called hidden momentum. Often considered as a peculiar feature of specific systems or as an artifact to avoid paradoxical situations, here we present a relativistic “paradox” which exposes the true nature and ubiquity of hidden momentum. We also show that hidden momentum can be forced to reveal itself through observable effects, hopefully putting an end to decades of controversy about its reality.

The well-known Robertson-Schrödinger uncertainty relations miss an irreducible lower bound. This is widely attributed to the lower bound's state dependence. Therefore, Abbott et al. introduced a general approach to derive tight state-independent uncertainty relations for qubit measurements [Mathematics 4, 8 (2016)]. The relations are expressed in two measures of uncertainty, which are standard deviation and entropy, both functions of the expectation value. Here, we present a neutron polarimetric test of the tight state-independent preparation uncertainty relations for orthogonal, as well as nonorthogonal, Pauli spin observables. The final results, obtained with pure and mixed spin states, reproduce the theoretical predictions clearly for arbitrary initial states of variable degree of polarization.

We demonstrate an application of a liquid-metal ion source for collinear laser spectroscopy in proof-of-principle measurements on naturally abundant ${\mathrm{In}}^{+}$. The superior beam quality, i.e., the actively stabilized current and energy of a beam with very low transverse emittance, allowed us to perform precision spectroscopy on the $5s^2{}^1{S}_0\to 5s5p{}^3{P}_1$ intercombination transition in ${}^{115}\mathrm{In}^{+}$, which is, to our knowledge, the slowest transition measured with collinear fluorescence laser spectroscopy so far. By applying collinear and anticollinear spectroscopy, we improved the center-of-gravity frequency ${\nu }_{\mathrm{cg}}=1299617759.3\left(1.2\right)\mathrm{MHz}$ and the hyperfine constants $A=6957.19\left(28\right)\mathrm{MHz}$ and $B=-443.7\left(2.4\right)\mathrm{MHz}$ by more than one order of magnitude. A similar accuracy was reached for ${}^{113}\mathrm{In}^{+}$ in combination with the literature data, and the isotope shift between both naturally abundant isotopes was deduced to $\nu {(}^{113}\mathrm{In})-\nu {(}^{115}\mathrm{In})=696.3\left(3.1\right)\mathrm{MHz}$. Nuclear alignment induced by optical pumping in a preparation section of the ion beam line was demonstrated as a pump-and-probe approach to provide sharp features on top of the Doppler-broadened resonance profile.

Anisotropic distributions of the Lyman-${\alpha }_1$ transition of the down-charged $\mathrm{X}{\mathrm{e}}^{53+*}$ ions are observed in fast $\mathrm{X}{\mathrm{e}}^{54+}$ with Kr and Xe collisions, in which the electron is transferred by the nonradiative electron capture mechanism. At the energy of 95 MeV/u, the alignment parameter of the projectile $2p_{3/2}$ state, ${\mathcal{A}}_{20}$, is determined to be −0.35 ± 0.02 for both targets. While the projectile energy is 146 MeV/u, the parameter for the Kr and Xe target is −0.28 ± 0.02 and −0.29 ± 0.04, respectively. The present results demonstrate that the electron capture to the $m_j=\pm 1/2$ magnetic substates is about two times more probable than to the $m_j=\pm 3/2$ ones.

The mean path-length invariance property is a very important property of scattering media illuminated by an isotropic and homogeneous radiation. Here, we investigate the case of inhomogeneous media with refractive-index mismatch between the external environment and also among their subdomains. The invariance property remains valid by the introduction of a correction, dependent on the refractive index, of the mean path-length value. It is a consequence of the stationary solution of the radiative transfer equation in a medium subjected to an isotropic and homogeneous radiance. The theoretical results are in agreement with the reported results for numerical simulations for both the three-dimensional and the two-dimensional media.

We characterize via the second-order correlation function the quantum correlations in the transmitted light in a two-cascaded-cavities system side-coupled to a common waveguide via bidirectional propagation. Adopting a full quantum master equation and standard input-output theory, we calculate the zero-time-delay second-order correlation function and identify clearly distinguished parameter regimes with the photon bunching and antibunching. Our numerical results clearly show that strong photon antibunching can be achieved in the cascaded double-cavity system without the need for extra modal-overlap-based coupling between the two cavities. Remarkably, this strong photon antibunching appears in the weak-coupling regime of cavity quantum electrodynamics. The photon antibunching properties can be manipulated by adjusting the propagation phase. In addition, we discuss the influences of the emitter-to-cavity coupling strength and the waveguide-to-cavity coupling rate on the photon antibunching. Also, the experimental feasibility of our proposal with the current photonic crystal technique is analyzed. This study offers an alternative way to generate the strongly antibunched photons, which may have applications in on-chip quantum information processing.

We study the $2p$ core hole states of the ${{\mathrm{SiH}}^{+}}_{(n=1,2,3)}$ silicon hydride cations. The $L$-edge photoelectron spectra for these species are computed thanks to a nonperturbative effective Hamiltonian model. Furthermore, we investigate the signature on the photoelectron spectra of the relative sign and strength of the spin-orbit and molecular-field splittings. We show that, in the silicon hydride cations, the absolute values of these two contributions are of comparable magnitude but their relative signs may differ, leading to substantially different photoelectron spectra. We show that the valence shell occupation in the ground state of the systems controls the sign of the molecular-field splitting. The electronic relaxation and correlation effects on the spectra are also examined.

Supersolidity—a coexistence of superfluidity and crystalline or amorphous density variations—has been vividly debated ever since its conjecture. While the initial focus was on helium-4, recent experiments uncovered supersolidity in ultracold dipolar quantum gases. Here we propose a self-bound supersolid phase in a binary mixture of Bose gases with short-range interactions, making use of the nontrivial properties of spin-orbit coupling. We find that a first-order phase transition from a self-bound supersolid stripe phase to a zero-minimum droplet state of the Bose gas occurs as a function of the Rabi coupling strength. These phases are characterized using the momentum distribution, the transverse spin polarization, and the superfluid fraction. The critical point of the transition is estimated in an analytical framework. The predicted density-modulated supersolid stripe and zero-minimum droplet phase should be experimentally observable in a binary mixture of ${}^{39}\mathrm{K}$ with spin-orbit coupling.

Shell-shaped hollow Bose-Einstein condensates (BECs) exhibit behavior distinct from their filled counterparts and have recently attracted attention due to their potential realization in microgravity settings. Here we study distinct features of these hollow structures stemming from vortex physics and the presence of rotation. We focus on a vortex-antivortex pair as the simplest configuration allowed by the constraints on superfluid flow imposed by the closed-surface topology. In the two-dimensional limit of an infinitesimally thin shell BEC, we characterize the long-range attraction between the vortex-antivortex pair and find the critical rotation speed that stabilizes the pair against energetically relaxing towards self-annihilation. In the three-dimensional case, we contrast the bounds on vortex stability with those in the two-dimensional limit and the filled sphere BEC, and evaluate the critical rotation speed as a function of shell thickness. We thus demonstrate that analyzing vortex stabilization provides a nondestructive means of characterizing a hollow sphere BEC and distinguishing it from its filled counterpart.

We show that the standard method of introducing the quantum description of the electromagnetic field—by canonical field quantization—is not the only one. We have chosen here the relativistic quantum mechanics of the photon as the starting point. The treatment of photons as elementary particles merges smoothly with the description in terms of the quantized electromagnetic field but it also reveals some essential differences. The most striking result is the appearance of various measures of fidelity for quantum states of photons. These measures are used to characterize the localization of photons.

Strong quantum nonlocality was introduced recently as a stronger manifestation of nonlocality in multipartite systems through the notion of local irreducibility in all bipartitions. Known existing results for sets of strongly nonlocal orthogonal states are limited to product states. In this paper, based on the Rubik's cube, we give a construction of such sets consisting of entangled states in $d\otimes d\otimes d$ for all $d\ge 3$. Consequently, we answer an open problem given by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)], that is, orthogonal entangled bases that are strongly nonlocal do exist. Furthermore, we propose two entanglement-assisted protocols for local discrimination of our results. Each protocol consumes less entanglement resources than the teleportation-based protocol on average. Our results exhibit the phenomenon of strong quantum nonlocality with entanglement.

Ultradilute quantum droplets are an intriguing new state of matter, in which the attractive mean-field force can be balanced by the repulsive force from quantum fluctuations to avoid collapse. Here, we present a microscopic theory of ultradilute quantum droplets in three-, one-, and two-dimensional two-component Bose-Bose mixtures by generalizing the conventional Bogoliubov theory to include the bosonic pairing arising from the interspecies attraction. Our pairing theory is fully equivalent to a variational approach and hence gives an upper bound for the energy of quantum droplets. In three dimensions, we predict the existence of a strongly interacting Bose droplet at the crossover from Bose-Einstein condensates (BECs) to BCS superfluids and map out the bosonic BEC-BCS crossover phase diagram. In one dimension, we find that the energy of the one-dimensional Bose droplet calculated by the pairing theory is in excellent agreement with the latest diffusion Monte Carlo simulation [L. Parisi et al., Phys. Rev. Lett. 122, 105302 (2019)] for nearly all the interaction strengths at which quantum droplets exist. In two dimensions, we show that Bose droplets disappear and may turn into a solitonlike many-body bound state, when the interspecies attraction exceeds a critical value. Below the threshold, the pairing theory predicts more or less the same results as the Bogoliubov theory derived by D. S. Petrov and G. E. Astrakharchik [Phys. Rev. Lett. 117, 100401 (2016)]. The predicted energies from both theories are higher than the diffusion Monte Carlo results due to the weak interspecies attraction and the increasingly important role played by the beyond-Bogoliubov-approximation effect in two dimensions. Our pairing theory provides an ideal starting point to understand interesting ground-state properties of quantum droplets in various dimensions, including their shape and collective oscillations.

An ultradilute quantum droplet is a self-bound liquidlike state recently observed in ultracold Bose-Einstein condensates. In most previous theoretical studies, it is described by a phenomenological low-energy effective theory, termed as the extended Gross-Pitaevskii equation. Here, we microscopically derive the Gross-Pitaevskii equation for the condensate and also for a pairing field in an inhomogeneous quantum droplet realized by Bose-Bose mixtures with attractive interspecies interaction. We show that the inclusion of the pairing field is essential, in order to have a consistent description of the droplet state. We clarify that the extended Gross-Pitaevskii equation used earlier should be understood as the equation of motion for the pairing field, rather than the condensate. The fluctuations of the pairing field give rise to low-energy collective excitations of the droplet. We also present the Bogoliubov equations for gapless phonon modes and gapped modes due to pairing in real space, which characterizes single-particle-like excitations of the droplet. The equations of motion derived in this work for the condensate and the pairing field serve as an ideal starting point to understand the structure and collective excitations of nonuniform ultradilute quantum droplets in ongoing cold-atom experiments.

We derive an exact description of the nonequilibrium dynamics at finite temperature for the anyonic Tonks-Girardeau gas, extending the results of Atas et al. [Phys. Rev. A 95, 043622 (2017)] to the case of arbitrary statistics. The one-particle reduced density matrix is expressed as the Fredholm minor of an integral operator, with the kernel being the one-particle Green's function of free fermions at finite temperature and the statistics parameter determining the constant in front of the integral operator. We show that the numerical evaluation of this representation using Nyström's method significantly outperforms the other approaches present in the literature when there are no analytical expressions for the overlaps of the wave functions. We illustrate the distinctive features and novel phenomena present in the dynamics of anyonic systems in two experimentally relevant scenarios: the quantum Newton's cradle setting and the breathing oscillations initiated by a sudden change of the trap frequency.

The weak-value (WV) measurement proposed by Aharonov, Albert, and Vaidman (AAV) has attracted a great deal of interest in connection with quantum metrology. In this paper, we extend the analysis beyond the AAV limit and obtain a few main results. (i) We obtain a nonperturbative result for the signal-to-noise ratio (SNR). In contrast to the AAV prediction, we find that the SNR asymptotically gets worse when the AAV WV $A_w$ becomes large, i.e., in the case $g|A_w{|}^2\gg 1$, where $g$ is the measurement strength. (ii) With the increase of $g$ (but also small), we find that the SNR is comparable to the result under the AAV limit, while both can reach—actually the former can slightly exceed—the SNR of the standard measurement. However, with a further increase of $g$, the WV technique will become less efficient than the standard measurement, despite the fact that the postselection probability is increased. (iii) We find that the Fisher information can characterize the estimate precision qualitatively well as the SNR, yet the difference will become more prominent with the increase of $g$. (iv) We carry out analytic expressions of the SNR in the presence of technical noises and illustrate the particular advantage of the imaginary WV measurement. The nonperturbative result of the SNR manifests a favorable range of the noise strength and allows an optimal determination.

An experimental study on spatial coherence of electron trajectory-resolved higher-order harmonic generation (HHG) in an argon-filled gas cell (length ∼15 mm) using single-color (λ ∼ 800 nm) and two-color laser pulses (λ ∼ 800 nm + 400 nm) is performed. The contribution of both a long and short electron trajectory is observed in HHG using single-color laser pulse, whereas a dominant contribution of short trajectory is observed in HHG using two-color laser pulses. The spatial coherence of trajectory-resolved higher-order harmonics is investigated using a double slit experiment. The fringe visibility is higher (∼0.7) at low gas cell pressure, for both short and long trajectory harmonics. At higher gas pressure ($\ge 50$ mbar), the fringe visibility of short trajectory harmonics (∼0.7) is significantly higher than the long trajectory harmonics (∼0.3–0.4). In the case of two-color laser pulses, the fringe visibility (∼0.75) is found to be further higher than the single-color short trajectory harmonics and is nearly independent of gas pressure (∼10–100 mbar). A theoretical model is used to explain the observed result and the intensity dependent dipole coefficient for short and long trajectory is estimated, which is in good agreement with the other reported results. The study provides an easy tool to study and control the role of different electron trajectories responsible for higher-order harmonic generation and also the spatial coherence property of higher-order harmonics generated from gas cell.

We present a scheme leading to ground-state cooling of the fundamental out-of-plane (flexural) mode of a suspended graphene sheet. Our proposal exploits the coupling between a driven Rydberg atom and the graphene resonator, which is enabled by vacuum forces. Thanks to the large atomic polarizability of the Rydberg states, the Casimir-Polder force is several orders of magnitude larger than the corresponding force achieved for atoms in the ground state. By tuning the distance between the atom and the graphene membrane, we show that resolved sideband cooling is possible, bringing the occupation number of the fundamental flexural mode down to its quantum limit. Our findings are expected to motivate physical applications of graphene at extremely low temperatures.

The structural phase transition (SPT) occurring in trapped-ion systems is a typical many-body physics, and the SPT induced by the thermal effect represents a special thermodynamic phenomenon between traditional thermodynamics and quantum thermodynamics. We explore this thermal-effect-induced SPT by embedding trapped ${}^{40}\mathrm{Ca}^{+}$ ion crystals in an optical lattice, in which the ion crystals are confined by a surface-electrode trap and laser-cooled down to a temperature of several millikelvins. The considered thermal effect, leading to a temperature variation of tens of microkelvins in the SPT, comes completely from the optical lattice, which is independent of the laser irradiation regarding cooling of the ion crystals. In comparison with previous work [J. Li et al., Phys. Rev. A 99, 063402 (2019)], the present investigation helps to further clarify the effect of thermal fluctuation and further explore the positive role of the fluctuation in thermodynamics at the atomic level, even for potentially practical applications.

Superfluid-insulator transitions in a one-dimensional mixture of two-color fermions and scalar bosons are studied within the framework of the Bose-Fermi-Hubbard model. Zero-temperature phase diagrams are constructed for repulsive intraspecies interactions and attractive or repulsive interspecies couplings. In addition to the trivial Mott insulator phases, we report the emergence of nontrivial insulator phases that depend on the sign of the boson-fermion interaction. These nontrivial insulator phases satisfy the conditions ${\rho }_B\pm {\rho }_F=n$ and ${\rho }_B\pm \frac{1}{2}{\rho }_F=n$, with the plus (minus) sign for repulsive (attractive) interactions and $n$ an integer. Far from fermionic half filling, the boson-fermion interaction drives a gapless-gapped transition in the spin sector. Our findings could be observed experimentally in state-of-the-art cold-atom setups.