Inspired by the narrow Feshbach resonance in systems with the two-body interaction, we propose a two-channel model of three-component fermions with a three-body interaction that takes into account finite-range effects in low dimensions. Within this model, the $p$-wave Efimov-like effect in the four-body sector is predicted in fractional dimensions between $d=1$ and $d=2$. The impact of the finite-range interaction on the formation of the four-body bound states in $d=1$ is also discussed in detail.

Motivated by recent cold atom experiments exploring the phase structure of Bose-Fermi mixtures, we propose novel emergent bound states. Cold atoms embedded in a degenerate Fermi system interact via a fermionic analog of the Casimir force, which is an attraction of a $-1/r$ form at distances shorter than the Fermi wavelength. Interestingly, the hydrogenic two-body bound states do not form in this regime because the interaction strength is too weak under realistic conditions, and yet the three-body bound states can have a considerably higher degree of stability. As a result, the trimer bound states can form even when the dimer states are unstable. A quasiclassical analysis of quantum states supported by periodic orbits singles out the figure-eight orbits, predicting bound states that are more stable than the ones originating from circular orbits. The discrete energies of these states form families of resonances with a distinct structure, enabling a direct observation of signatures of figure-eight braiding dynamics.

We investigate the ground-state phase diagram of a binary mixture of Bose-Einstein condensates (BECs) with competing interspecies $s$- and $p$-wave interactions. Exploiting a pseudopotential model for the $l=1$ partial wave, we derive an extended Gross-Pitaevskii (GP) equation for the BEC mixture that incorporates both $s$- and $p$-wave interactions. Based on it, we study the miscible-immiscible transition of a binary BEC mixture in the presence of interspecies $p$-wave interaction, by combining numerical solution of the GP equation and Gaussian variational analysis. Our paper uncovers a dual effect—to either enhance or reduce miscibility—of positive interspecies $p$-wave interaction, which can be precisely controlled by adjusting relevant experimental parameters. By completely characterizing the miscibility phase diagram, we establish a promising avenue towards experimental control of the miscibility of binary BEC mixtures via high partial-wave interactions.

The transverse optical force adds an extra degree of freedom for optical manipulation. In this paper, based on the full wave simulation, we find that an achiral sphere can experience a transverse optical force in the field of a circularly polarized or linearly diagonally polarized electric dipole source in the vicinity of a doped InSb substrate. When the dipole is circularly polarized, the transverse force results from the asymmetrical distribution of the excited surface waves. However, when the dipole is linearly diagonally polarized, the transverse force stems from the combined effect of the surface waves and asymmetrical propagating waves. More importantly, the magnitude and direction of the transverse force can be adjusted by applying a magnetic field parallel to the InSb substrate, due to the generated additional nonreciprocity. Our paper expands the scope of transverse optical force by nonreciprocity.

Leveraging operator techniques, we address the paraxial wave equation governing a field formed by the multiplication of a Gaussian function and an entire function; notably, the latter adheres to the Laplace equation, ${\nabla }_{\perp }^{2}f(x+iy)=0$, a direct consequence of satisfying the Cauchy-Riemann equations. Our theoretical and experimental exploration brings to light the intrinsic rotation of this field during propagation, elucidated by the incorporation of the quantum (Bohm) potential. This straightforward result holds promise, enabling the analytical deduction of the Fraunhofer or Fresnel diffraction pattern. Essentially, it simplifies the extraction of the Fresnel or Fourier transform from a function satisfying the Cauchy-Riemann equations.

High-fidelity entanglement plays an important role in quantum networks for guaranteeing the integrity of quantum information processing. We present an error identification entanglement purification protocol (EIEPP) for maintaining high-fidelity entanglement of stationary systems. In EIEPP, the hybrid controlled-x gate for stationary systems and high-dimensional spatial-mode state of photons has been constructed using a stationary-whispering gallery mode resonator-waveguides system, and it is used to construct an error number gate (ENG) and error position gate (EPG) for noisy entangled stationary systems. Using ENG and EPG, the stationary systems with errors are discarded according to the measurement results of high-dimensional entangled photon states, and typically high-fidelity entangled states of stationary systems can be achieved with high yield in both ideal and practical situations. This EIEPP has superior performance for stationary systems with amplitude damping noise, and it is also applicable for stationary systems with other types of noise.

Efficient control over entanglement in spin chains is useful for quantum information processing applications. In this paper, we propose the use of a combination of two different configurations of strong static and oscillating fields to control and generate near-perfect entanglement between any two spins in a spin chain, even in the presence of noise. This is made possible by the fact that our control fields not only decouple the spin chain from its environment but also selectively modify the spin-spin interactions. By suitably tuning these spin-spin interactions via the control fields, we show that the quantum state of any two spins in the spin chain can be made to be a Bell state. We illustrate our results for various spin chains, such as the $\mathit{XY}$ model, the XYZ model, and the Ising spin chain.

The refined values of the magnetic octupole moments of ${}^{113}\mathrm{In}$ and ${}^{115}\mathrm{In}$ are obtained by combining high-precision atomic calculations with the corresponding hyperfine structure (HFS) spectrum. We perform ab initio calculations of HFS properties for the low-lying states of the In atom using the single- and double-approximated relativistic coupled-cluster method. The HFS properties includes first-order HFS constants and the second-order magnetic dipole-magnetic dipole, magnetic dipole-electric quadrupole, and electric quadrupole-electric quadrupole effects caused by the off-diagonal hyperfine interaction (HFI). Based on our theoretical results, we reanalyze the previously measurements of hyperfine splitting in the $5p_{3/2}$ state of ${}^{113}\mathrm{In}$ and ${}^{115}\mathrm{In}$ [T. G. Eck and P. Kusch, Phys. Rev. 106, 958 (1957)], determining the corresponding hyperfine-structure constants $A, B$, and $C$. By combining these undated HFS constants and our theoretical results, the magnetic octupole moments of ${}^{113}\mathrm{In}$ and ${}^{115}\mathrm{In}$ nuclei are extracted to be $\mathrm{\Omega }\left({}^{113}\mathrm{In}\right)=0.456\left(44\right){\mu }_N\times b$, and $\mathrm{\Omega }\left({}^{115}\mathrm{In}\right)=0.447\left(42\right){\mu }_N\times b$, respectively. The refined values of the magnetic octupole moments are about 21% smaller than the previously reported results by Eck and Kusch [T. G. Eck and P. Kusch, Phys. Rev. 106, 958 (1957)]. Additionally, we also determine the electric quadrupole moment of ${}^{115}\mathrm{In}$ nuclei to be $Q\left({}^{115}\mathrm{In}\right)=0.758\left(12\right)b$ by combining our theoretical result and the measured value for the HFS constant of the $5p_{3/2}$ state. Our results are compared with available experimental and theoretical results.

The proton, deuteron, and triton masses can be determined relative to the electron mass via rovibrational spectroscopy of molecular hydrogen ions. This has to occur via comparison of the experimentally measured transition frequencies and the ab initio calculated frequencies, whose dependence on the mass ratios can be calculated precisely. In precision experiments to date (on ${\mathrm{HD}}^{+}$ and ${\mathrm{H}}_2{}^{+}$), the transitions have involved the ground vibrational level $v=0$ and excited vibrational levels with quantum numbers up to $v^{\prime }=9$. For these transitions, the sensitivity of the ab initio frequency to the high-order QED contributions is correlated with that to the mass ratios. This prevents an efficient simultaneous determination of these quantities from experimental data, so the accuracy of the mass ratios is essentially limited by the theoretical uncertainty. Here we analyze how the accuracy of mass ratios may be improved by providing experimental transition frequencies between levels with larger quantum numbers, whose sensitivity to the mass ratio is positive rather than negative, or close to zero. This allows the unknown QED contributions and involved fundamental constants to be much more efficiently determined from a joint analysis of several measurements. We also consider scenarios where transitions of ${\mathrm{D}}_2{}^{+}$ are included. We find these to be powerful approaches, allowing us in principle to reach uncertainties for the mass ratios approximately three orders smaller than reported by CODATA 2018. Improvements by a factor of 3.5 for the Rydberg constant, and 11 (14) for the proton (deuteron) charge radius, are also projected.

The inherent polarization gradients in tight optical tweezers can be used to couple the atomic spins to the two-body motion under the action of a microwave spin-flip transition, so that such a spin-motion coupling offers an important control knob on the motional states of optically trapped two colliding atoms. Here, after preparing two elastically scattering ${}^{85}\mathrm{Rb}$ atoms in the three-dimensional ground-state in the optical tweezer, we employed this control in order to probe the colliding energies of elastic and inelastic channels. The combination of microwave spectra and corresponding s-wave pseudopotential model allows us to infer the effect of the state-dependent trapping potentials on the elastic colliding energies, as well as to reveal how the presence of inelastic interactions affects elastic part of the relative potential. Our work shows that the spin-motion coupling in a tight optical tweezer expand the experimental toolbox for fundamental studies of ultracold collisions in the two body systems with reactive collisions, and potentially for that of more complex interactions, such as optically trapped atom-molecule and molecule-molecule interactions.

We measure the fluorescence spectrum of broadband emitters in an open optical microcavity with radius of curvature $R=17.7\left(3\right)\mu \mathrm{m}$ and finesse $F\approx 1000$. This geometry enables a combined measurement of emission spectra versus cavity length, which has several benefits over measurements at fixed wavelength or fixed cavity length alone. We demonstrate the role of the optical penetration depths on the cavity modes and provide practical working equations for its analysis. Furthermore, we show the ability to measure the coupling of cavity modes within a small scan range of the cavity length. By measuring these cavity emission spectra as a function of cavity length, we thus obtain a rich and complete picture of the optical microcavity.

The problem of resolving pointlike light sources not only serves as a benchmark for optical resolution but also holds various practical applications ranging from microscopy to astronomy. In this paper, we aim to resolve two thermal sources sharing arbitrary mutual coherence using the spatial mode demultiplexing technique. Our analytical study includes scenarios where the coherence and the emission rate depend on the separation between the sources, and is not limited to the faint sources limit. We consider the fluorescence of two interacting dipoles to demonstrate that the dependence of emission characteristics on the parameter of interest can boost the sensitivity of the estimation and noticeably prolong the duration of information decay.

Spin-orbit coupling is of fundamental interest in both quantum optical and condensed matter systems alike. In this work, we show that optically induced electronic excitations in lattices of V-type atoms exhibit an emergent spin-orbit coupling when the geometry is chiral. This spin-orbit coupling arises naturally from the electric dipole interaction between the atomic sites and leads to a nontrivial topology for the lattice band structure. Using a general quantum optical model, we determine analytically the conditions that give rise to spin-orbit coupling and characterize the behavior under various symmetry transformations. We demonstrate that chirality-induced spin-orbit coupling can result from either the chirality of the underlying lattice geometry or the combination of an achiral lattice with a suitably chosen external quantization axis. We then discuss how these results are influenced by dissipation, which breaks time-reversal symmetry and illuminates the distinction between true and false chirality. Our results demonstrate that chiral atom arrays are a robust platform for realizing spin-orbit-coupled topological states of matter.

In quantum electrodynamics, vacuum becomes a nonlinear optical medium: its optical index should be modified in the presence of intense external electromagnetic fields. The DeLLight project (Deflection of Light by Light) aims to observe this effect using intense focused femtosecond laser pulses delivered by LASERIX. The principle is to measure with a Sagnac interferometer the deflection of a low-intensity focused pulse (probe) crossing the vacuum index gradient induced by a high-intensity pulse (pump). A Sagnac interferometer working with femtosecond laser pulses has been developed for the DeLLight project. Compared to previous prototypes, the interferometer now includes the focusing of the probe beam in the interaction area. In this article, we measure and characterize the critical experimental parameters limiting the sensitivity of the interferometer, namely, the extinction factor, the spatial resolution, and the waist at focus of the probe pulse. We discuss future improvements.

The study of temporal coherence in a Bose-Einstein condensate of photons can be challenging, especially in the presence of correlations between the photonic modes. In this work, we use a microscopic, multimode model of photonic condensation inside a dye-filled microcavity and the quantum regression theorem to derive an analytical expression for the equation of motion of the photon-photon correlation function. This allows us to derive the coherence time of the photonic modes and identify a nonmonotonic dependence of the temporal coherence of the condensed light with the cutoff frequency of the microcavity.

Parameterized quantum circuits as machine learning models are typically well described by their representation as a partial Fourier series of the input features, with frequencies uniquely determined by the feature map's generator Hamiltonians. Ordinarily, these data-encoding generators are chosen in advance, fixing the space of functions that can be represented. In this work we consider a generalization of quantum models to include a set of trainable parameters in the generator, leading to a trainable-frequency (TF) quantum model. We numerically demonstrate how TF models can learn generators with desirable properties for solving the task at hand, including nonregularly spaced frequencies in their spectra and flexible spectral richness. Finally, we showcase the real-world effectiveness of our approach, demonstrating an improved accuracy in solving the Navier-Stokes equations using a TF model with only a single parameter added to each encoding operation. Since TF models encompass conventional fixed-frequency models, they may offer a sensible default choice for variational quantum machine learning.

Among the various types of quantum entanglement, the most fascinating and interesting one is genuine entanglement undoubtedly. In this paper, the unique genuine decomposition theorem with respect to any pure state is given and the relations between battery capacity gap and ergtropic gap are studied. By exploiting the battery capacity of multipartite systems, we introduce a vector-valued genuine measure compared with other existing measures and find that the one is superior to some other existing measures in confirming whether the deterministic LOCC transformation between two multipartite pure states is prohibited. Through some proper constructions, one can derive many GME measures. We also give the explicit expression of bipartite battery capacity gap with respect to mixed states by the convex roof extension and investigate some monogamy relations related to the battery capacity gap.

Closed-shell atoms and molecules such as Hg and TlF provide some of the best low-energy tests of hadronic $\mathcal{CP}$ violation beyond the standard model of particle physics, which is considered to be a necessary ingredient to explain the observed excess of matter over antimatter in our universe. $\mathcal{CP}$ violation is expected to be strongly enhanced in octupole-deformed nuclei such as ${}^{225}\mathrm{Ra}$. Recently, closed-shell radium-containing symmetric-top molecular ions were cooled sympathetically in a Coulomb crystal [Fan et al., Phys. Rev. Lett. 126, 023002 (2021)] and shown to be well suited for precision spectroscopy in the search for fundamental physics [Yu and Hutzler, Phys. Rev. Lett. 126, 023003 (2021)]. In closed-shell molecules hadronic $\mathcal{CP}$ violation contributes to a net electric dipole moment (EDM) that violates parity and time-reversal symmetries ($\mathcal{P},\mathcal{T}$), which is the target of measurements. To interpret experiments, it is indispensable to know the electronic-structure-enhancement parameters for the various sources of $\mathcal{P},\mathcal{T}$ violation which contribute to the net $\mathcal{P},\mathcal{T}$-odd EDM. We employ relativistic density-functional-theory calculations to determine relevant parameters for interpretation of possible EDM measurements in ${\mathrm{RaOCH}}_3{}^{+}, {\mathrm{RaSH}}^{+}, {\mathrm{RaCH}}_3^{+}, {\mathrm{RaCN}}^{+}$, and ${\mathrm{RaNC}}^{+}$ and perform accurate relativistic coupled-cluster calculations of the Schiff-moment enhancement in ${\mathrm{RaSH}}^{+}$ to gauge the quality of the density-functional-theory approach. Finally, we project to bounds on various $\mathcal{P},\mathcal{T}$-odd parameters that could be achievable from an experiment with ${\mathrm{RaOCH}}_3{}^{+}$ in the near future and assess its complementarity to experiments with Hg and TlF.

Doppler-free two-photon (DFTP) spectroscopy is a standard technique for precision measurement of transition frequencies of dipole-forbidden transitions. Here, we report the observation of quantum interference (QI) of optical transition pathways in DFTP spectroscopy of the cesium $6S\text{−}7D$ transitions chosen as a prototype system. The QI manifests itself as asymmetric line shapes of the hyperfine lines of the $7D$ states, observed through spontaneous emission following excitation by a narrow-linewidth cw laser. The interference persists despite the lines being spectrally well resolved. Ignoring the effect and fitting the spectrum to a Voigt profile causes large systematic shifts in the determination of the line centers, while accounting for QI resolves the apparent line shift and enables the precise determination of hyperfine splitting in the $7D$ states. We calculate the spectral line shape including the effect of QI and show that it agrees with the experimental observations. Our results are broadly applicable to other species and have implications for portable secondary optical clocks and precision measurements of hyperfine splittings, isotope shifts, and transition frequencies.