We investigate the joint (separable) numerical range of multiple measurements, i.e., the regions of expectation values accessible with (separable) quantum states for given observables. This not only enables efficient entanglement detection, but also sheds light on the geometry of the set of quantum states. More precisely, in an experiment, if the confidence region for the obtained data and the separable numerical range are disjoint, entanglement is reliably detected. Generically, the success of such an experiment is more likely the smaller the separable numerical range is, compared to the standard numerical range of the observables measured. We quantify this relation using the ratio between these two volumes and show that it cannot be arbitrarily small, giving analytical bounds for any number of particles, local dimensions, as well as number of measurements. Moreover, we explicitly compute the volume of separable and standard numerical range for two locally traceless two-qubit product observables, which are of particular interest as they are easier to measure in practice. Furthermore, we consider typical volume ratios for generic observables and extreme instances.

In this paper, we discuss in some detail how multiparty quantum key agreement protocols must be carefully designed and present a collusion attack to illustrate this point. Then, a secure circle-type multiparty quantum key agreement with Bell states is proposed. Bell states are used as the information carriers and transmitted among the participants, who embed their secrets into the traveling particles via certain encoding operations. In this way, all participants simultaneously obtain the same agreement key, i.e., the sum of their secret inputs, at the end of the protocol. Here, quantum state discrimination is utilized to design the encoding operations, which ensures that the proposed protocol is correct and secure against the presented collusion attack. Furthermore, it is shown that the proposed protocol satisfies three conditions of a secure quantum key agreement protocol in theory. In addition, these encoding operations consist of some common single-qubit gates, the Hadamard operator and four Pauli operators, which makes the proposed protocol feasible using current technology.

Hyperentanglement (HE), the simultaneous entanglement between two particles in more than one degree of freedom, is relevant to both fundamental physics and quantum technology. Previous study on HE has been focusing on photons. Here, we study HE in individual neutral atoms. In most alkaline-earth-like atoms with two valence electrons and a nonzero nuclear spin, there are two stable electronic states, the ground state and the long-lived clock state, which can define an electronic qubit. Meanwhile, their nuclear spin states can define a nuclear qubit. By the Rydberg blockade effect, we show that the controlled-$Z$ (cz) operation can be generated in the electronic qubits of two nearby atoms, and simultaneously in their nuclear qubits as well, leading to a cz$\otimes$cz operation which is capable to induce HE. The possibility to induce HE in individual neutral atoms offers opportunities to study quantum science and technology based on neutral atoms.

Alkaline-earth-like transition-metal atoms such as Zn and Cd are promising candidates for precision measurements and quantum many-body physics experiments. Here, we theoretically investigate the properties of diatomic molecules containing these closed-shell atoms. We calculate potential-energy curves, permanent electric dipole moments, and spectroscopic constants for molecules consisting of either a Zn or Cd atom interacting with an alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atom. We use the ab initio electronic-structure coupled-cluster method with single, double, and triple excitations combined with large Gaussian basis sets and small-core relativistic energy-consistent pseudopotentials for heavier atoms. We predict that the studied molecules in the ground electronic state are chemically reactive weakly bound van der Waals complexes with small permanent electric dipole moments. The present results may be useful for spectroscopy and application of the studied molecules in modern ultracold physics and chemistry experiments.

Motivated by recent direct measurement of the forbidden $2{}^3{S}_1\to 3{}^3{S}_1$ transition in helium [Thomas et al., Phys. Rev. Lett. 125, 013002 (2020)], where the ac Stark shift is one of the main systematic uncertainties, we propose a dichroic two-photon transition measurement for $2{}^3{S}_1\to 3{}^3{S}_1$, which could effectively suppress the ac Stark shift by utilizing magic wavelengths: one magic wavelength is used to realize state-insensitive optical trapping; the other magic wavelength is used as one of the two lasers driving the two-photon transition. Carrying out calculations based on the no-pair Dirac-Coulomb-Breit Hamiltonian with mass shift operator included, we report the magic wavelength of 1265.615 9(4) nm for ${}^4\mathrm{He}$ [or 1265.683 9(2) nm for ${}^3\mathrm{He}]$ can be used to design an optical dipole trap; the magic wavelength of 934.234 5(2) nm for ${}^4\mathrm{He}$ [or 934.255 4(4) nm for ${}^3\mathrm{He}]$ can be as one excitation laser in the two-photon process and the ac Stark shift can be reduced to less than 100 kHz, as long as the intensity of the other excitation laser does not exceed $1\times {10}^4{\text{W/cm}}^2$. Alternatively, by selecting detuning frequencies relative to the $2{}^{3}P$ state in the region of 82–103 THz, as well as adjusting the intensity ratios of the two lasers, the ac Stark shift in the $2{}^3{S}_1\to 3{}^3{S}_1$ two-photon transition can be canceled.

We have put forward the time-dependent Hartree-Fock approach to investigate ionization dynamics of HCl molecules subjected to strong few-cycle laser pulses, which is based on the finite-element discrete-variable representation in prolate spheroidal coordinates and the Crank-Nicolson method. It is demonstrated that the electron is favored to be freed by the peak electric field pointing towards the H atom for the HCl molecule possessing the bonding length $R=2.5$ a.u., while the ionization prefers to occur for the maximum electric field pointing from the H nucleus to Cl nucleus with increasing internuclear separations. Analysis indicates that the ionization yield of $5\sigma$ electrons becomes significant with respect to that of $2\pi$ electrons with stretching bonding lengths, and the relative contributions of the ionization from $5\sigma$ and $2\pi$ electrons change as a function of internuclear separations, which gives rise to the above distinct oriented ionization of HCl molecules.

The below- and near-threshold harmonics generated by ${\mathrm{O}}_2$ molecules and Xe atoms have been investigated experimentally by using an extreme-ultraviolet (XUV)-comb setup that is driven by an intense 1040-nm laser field. It is found that the yields of the below- and near-threshold harmonics generated by ${\mathrm{O}}_2$ molecules show a significant suppression when compared to Xe, although the two species have nearly identical ionization potentials. Our theoretical analysis shows that the harmonic yield suppression is related to the two-center interference effect of ${\mathrm{O}}_2$ and the tightly bounded orbital of the O atom. Our study provides useful information for the XUV-comb technique when extending the working media from atoms to complex systems.

Using strong-field ionization as a probe, we observe highly nonperiodic evolution of the spin-rotation wave packet launched by a nonionizing femtosecond pulse in oxygen. The nonperiodicity is readily apparent only in rotationally cold molecules that are pumped with a weak alignment pulse. We show that this behavior is a consequence of the spin-rotation and the spin-spin couplings in the triplet ground state of the neutral molecule. A model that includes these couplings in the field-free Hamiltonian but in neither the alignment nor the ionization step explains most of the observed dynamics, suggesting that neither process depends explicitly on the electronic spin. We also show that the angle dependence of strong-field ionization can be retrieved from the delay-dependent signal even when coupling to spin complicates the rotational dynamics.

This paper presents a study of the grand canonical Bose-Einstein (BE) statistics for a finite number of particles in an arbitrary quantum system. The thermodynamical quantities that identify BE condensation—namely, the fraction of particles in the ground state and the specific heat—are calculated here exactly in terms of temperature and fugacity. These calculations are complemented by a numerical calculation of fugacity in terms of the number of particles, without taking the thermodynamic limit. The main advantage of this approach is that it does not rely on approximations made in the vicinity of the usually defined critical temperature, rather it makes calculations with arbitrary precision possible, irrespective of temperature. Graphs for the calculated thermodynamical quantities are presented in comparison to the results previously obtained in the thermodynamic limit. In particular, it is observed that for the gas trapped in a three-dimensional box, the derivative of specific heat reaches smaller values than what was expected in the thermodynamic limit—here, this result is also verified with analytical calculations. This is an important result for understanding the role of the thermodynamic limit in phase transitions and makes possible to further study BE statistics without relying neither on the thermodynamic limit nor on approximations near critical temperature.

We analyze the collision of three identical spin-polarized fermions at zero collision energy, assuming arbitrary finite-range potentials, and define the corresponding three-body scattering hypervolume $D_F$. The scattering hypervolume $D$ was first defined for identical bosons in 2008. It is the three-body analog of the two-body scattering length. We solve the three-body Schrödinger equation asymptotically when the three fermions are far apart or one pair and the third fermion are far apart, deriving two asymptotic expansions of the wave function. Unlike the case of bosons for which $D$ has the dimension of length to the fourth power, here the $D_F$ we define has the dimension of length to the eighth power. We then analyze the interaction energy of three such fermions with momenta $\hslash {\mathbf{k}}_1$, $\hslash {\mathbf{k}}_2$, and $\hslash {\mathbf{k}}_3$ in a large periodic cubic box. The energy shift due to $D_F$ is proportional to $D_F/{\mathrm{\Omega }}^2$, where $\mathrm{\Omega }$ is the volume of the box. We also calculate the shifts of energy and pressure of spin-polarized Fermi gases due to a nonzero $D_F$ and the three-body recombination rate of spin-polarized ultracold atomic Fermi gases at finite temperatures.

We investigate the quantum phase transitions of a two-dimensional Bose-Hubbard model in the presence of a Rashba spin-orbit coupling with and without thermal fluctuations. The interplay of single-particle hopping, strength of spin-orbit coupling, and interspin interaction leads to superfluid phases with distinct properties. With interspin interactions weaker than intraspin interactions, the spin-orbit coupling induces two finite-momentum superfluid phases. One of them is a phase-twisted superfluid that exists at low hopping strengths and reduces the domain of insulating phases. At comparatively higher hopping strengths, there is a transition from the phase-twisted to a finite-momentum stripe superfluid. With interspin interactions stronger than the intraspin interactions, the system exhibits a phase-twisted to ferromagnetic phase transition. At finite temperatures, the thermal fluctuations destroy the phase-twisted superfluidity and lead to a wide region of normal-fluid states. These findings can be observed in recent quantum gas experiments with spin-orbit coupling in optical lattices.

Ultrafast laser-plasma interactions driven by ultrashort terawatt laser pulses are shown to give rise to a bright multioctave microwave radiation, whose polarization and spatial mode structure provides a sensitive probe for laser-driven plasma electrodynamics, helping detect the symmetries of plasma currents and signatures of multiple ionization. Polarization mode structure of this radiation is dominated, as polarization-resolved measurements show, by a radially polarized mode, indicating the significance of ponderomotively driven plasma currents as sources of microwave emission. Angle-resolved analysis of microwave supercontinua reveals regimes in which the microwave emission is drastically enhanced, via coherence buildup, manifested in a well-resolved Cherenkov-emission cone.

Nonmagnetic and spherically symmetric dielectric material media are investigated in their generality as analog models, in the domains of geometrical optics, for a few relevant static and spherically symmetric solutions of gravitation, including black holes and wormholes. Typical and desirable gravitational features are systematically linked to the nonlinear properties of the phenomenological dielectric permittivity of the medium. From this, the limitations of such analogies are explored in terms of their corresponding geometric flexibility, dielectric configurations, and causal structure.

Abruptly autofocusing beams were proposed and tested for a variety of applications such as optical manipulation, yet their trapping performance associated with the optical forces and trap stiffness remains largely unexplored. In this work, we design and demonstrate specially modulated autofocusing beams. We theoretically and experimentally show improved properties of such beams and their trapping capabilities as compared to their unmodulated counterparts. In particular, an autofocusing beam tailored with a Bessel function exhibits a shorter focal length and a much stronger peak intensity than that of an unmodulated circular Airy beam. Moreover, we perform optical tweezer experiments using both the modulated and unmodulated autofocusing beams to trap microbeads and red blood cells for direct comparison, and find that the Bessel-modulated beam displays an enhanced trapping capability, thanks to a stronger optical trapping force due to its peculiar intensity landscape. Compared with the conventional circular Airy beams, optical tweezers based on our modulated autofocusing beams exhibit a superior performance, which may lead to new photonic tools for optical trapping and manipulation.

Using the quantum map formalism, we provide a framework to construct fuzzy and coarse-grained quantum maps of many-body systems that account for limitations in the resolution of real measurement devices probing them. The first set of maps handles particle-indexing errors, while the second deals with the effects of detectors that can only resolve a fraction of the system constituents. We apply these maps to a spin-$1/2 \mathit{XX}$ chain, obtaining a blurred picture of the entanglement generation and propagation in the system. By construction, both maps are simply related via a partial trace, which allows us to concentrate on the properties of the former. We fully characterize the fuzzy map, identifying its symmetries and invariant spaces. We show that the volume of the tomographically accessible states decreases at a double-exponential rate in the number of particles, imposing severe bounds on the ability to read and use information of a many-body quantum system.

A theory for excitation of molecular resonances by a train of precursors is developed. Right at the vacuum-medium interface, a train of incident square waves interacts with light electrons and is converted into a train of precursors, which further excite molecular dipoles. Analytic calculations indicate that these excited dipoles generate radiation, including secondary precursors propagating in the backward direction. Encoded in this radiation are proper frequencies of excited molecular dipoles allowing for spectroscopic measurements. The frequency of the train of incident square pulses can be, by several orders of magnitude, smaller than the proper frequencies of molecular resonances.

A simple theoretical model used to treat the formation of negative ions during ${\mathrm{H}}^{–}/{\mathrm{H}}^0$ grazing scattering from the MgO(100) surface is presented. It is revealed that the resonant transfer from projectiles to the conduction band and the detachment of tunneling Coulomb repulsive barrier to the vacuum of the affinity electron of ${\mathrm{H}}^{–}$ ions both play an important role in the electron-loss processes. The negative-ion destruction is dominated by a nearly resonant electron loss in the low projectile energy region of $E\le 0.7\mathrm{keV}$ (velocities $v\le 0.17\mathrm{a}.\mathrm{u}.$), whereas the detachment by Coulomb repulsive barrier tunneling during the interaction between projectiles and surface anion sites becomes efficient in the high-energy region of $E\ge 1.2\mathrm{keV}$ ($v\ge 0.22\mathrm{a}.\mathrm{u}$). Combined with the valence-band electron capture, our present calculation results of the negative ion yields are in good agreement with the available experimental data in the whole velocity region.

Solitons in general are configurations of extended fields which move like isolated particles. Vector bright solitons can occur in a two-component self-attractive Bose-Einstein condensate. If the components of the condensate have different chemical potentials, the total spin of the soliton can serve as an internal energy depot that makes the soliton into an active particle, able to move against an external force using energy carried within the particle—if there is a dynamical mechanism for steadily transferring energy from soliton spin into soliton motion. Here we present such a dynamical mechanism, embed it in an experimentally feasible way within the larger system of a spinor condensate mean field, and show how the mechanism works to realize a solitonic active particle. In what can be considered a toy model for the project of going beyond toy models for active particles, we test the robustness of the activity mechanism by exploring a range of deformations to the simplest model for embedding the nonlinear mechanism in the condensate system.

Photon accelerators can spectrally broaden laser pulses with high efficiency in moving electron density gradients driven in a rapidly ionizing plasma. When driven by a conventional laser pulse, the group velocity walk-off experienced by the accelerated photons and deterioration of the gradient from diffraction and plasma refraction limit the extent of spectral broadening. Here we show that a laser pulse with a shaped space-time and transverse intensity profile overcomes these limitations by creating a guiding density profile at a tunable velocity. Self-photon acceleration in this profile leads to dramatic spectral broadening and intensity steepening, forming an optical shock that further enhances the rate of spectral broadening. In this new regime, multi-octave spectra extending from 400 to 60 nm wavelengths, which support near-transform-limited $<400$ as pulses, are generated over $<100 \mu \mathrm{m}$ of interaction length.