In nonrelativistic physics, the concepts of geometry and topology are usually applied to characterize spatial structures or structures in momentum space. We introduce the concept of temporal geometry, which encompasses the geometric and topological properties of temporal shapes, i.e., trajectories traced by the tip of a time-dependent vector. We apply it to electric field polarizations controlling ultrafast electron currents or induced polarization in chiral molecules. The central concepts of temporal geometry—Berry curvature and Berry connection—emerge as ubiquitous features of photoexcited, nonequilibrium, chiral electron dynamics. We demonstrate that the Berry curvature and Berry connection (1) rely on the polarization properties of light pulses, (2) can be introduced for multiphoton processes, and (3) control enantiosensitive geometric observables via nonequilibrium electronic dynamics excited by tailored laser fields. Our findings may open a way to ultrafast, topologically nontrivial, and enantiosensitive chemical dynamics.

We develop a mathematical formalism underlying the emergence of enantiosensitive molecular orientation due to photoionization or photoexitation of chiral molecules. We consider geometric quantities such as the Berry connection and Berry curvature in light-driven chiral electronic states in the space of complex light polarization vectors. The parametric dependence of the light-driven electronic wave function on such vectors is based on various possible mutual orientations between the laser field and a chiral molecule. Using the tools of differential geometry, we show how the enantiosensitive observables arise from the geometry of the molecular response in such spaces.

We investigate the nonequilibrium quantum dynamics and thermodynamics of free fermions suddenly coupled to a localized defect in a one-dimensional harmonic trap. This setup realizes a quantum quench transformation that gives rise to the orthogonalization of the system's wave function as an effect of the localized perturbation. Using the Loschmidt echo and the Kirkwood-Dirac quasiprobability (KDQ) distribution of the work done by the defect, we quantify the extent and rate of the orthogonalization dynamics. In particular, we show that initializing the system in a coherent superpositions of energy eigenstates leads to nonclassical features, such as Wigner function's negativity and nonpositivity of the work KDQ distribution. Starting from simple single-particle superpositions and then progressing with coherent and cat states of few-body fermionic systems, we uncover how quantum coherence and few-body correlations shape the out-of-equilibrium response due to the presence of the defect.

We study the impact of weak quenched disorder on the BCS-BEC crossover in the Hubbard model within a functional-integral approach. By deriving the thermodynamic potential up to second order in both the disorder potential and pairing fluctuations, we obtain self-consistent expressions for the number equation, condensate fraction, superfluid fraction, and sound speed at zero temperature. In the dilute BEC limit, our results analytically reproduce the known continuum limits of weakly interacting bosons, where weak disorder depletes the superfluid more strongly than the condensate due to broken translational symmetry, and it enhances the sound speed through the overcompensation of the static compressibility. These findings establish a unified and controlled approach for describing the BCS-BEC crossover in disordered lattice models, and they provide a foundation for future extensions to finite temperatures and multiband Hubbard models.

Fermionic cold atoms in optical traps provide viable quantum simulators of correlation effects in electronic systems. For dressed Rydberg atoms in two-dimensional traps with out-of-plane dipole moments, a realistic model of the pairwise interaction is of repulsive dipolar $1/r^3$ form at long range, softened to a constant at short range. This study provides parametrizations of fixed-node diffusion Monte Carlo energy data for ferromagnetic (one-component) and paramagnetic (two-component) two-dimensional homogeneous Fermi fluids of interacting dipolar atoms. We find itinerant ferromagnetism to be unstable within our parameter spaces for dipolar interactions both with and without softening. Our parametrization of the energy as a function of density will enable density functional theory to support experimental studies of inhomogeneous fermionic cold-atom systems.

The Efimov effect, a remarkable realization of discrete scale invariance, emerges in the three-body problem with short-range interactions and is understood as a renormalization group (RG) limit cycle within Short-Range Effective Field Theory (SREFT). While the analytic form of the three-body renormalization relation has been established for a sharp cutoff regulator, its universality for other regulators remains underexplored. In this work, we derive the universal functional form of the three-body renormalization relation for general separable regulators through a detailed analysis of the Skorniakov-Ter-Martirosian and Faddeev equations. We find that the relation follows from a real Möbius transformation characterized by three parameters. This universality is verified numerically for various regulators. Although the functional form remains the same, the parameters characterizing the limit cycle exhibit regulator dependence. These findings broaden the class of RG limit cycles in SREFT and offer a more complete understanding of three-body renormalization.

We demonstrate nonreciprocal optical transmission for both intense classical fields and weak quantum signals within a reconfigurable optomechanical platform driven by three-mode parametric interactions. The platform is modular, where each three-mode optomechanical system serves as a fundamental building block. Operating independently, a single block achieves nonreciprocity for classical fields. Specifically, asymmetric radiation pressure from intrinsic optomechanical nonlinearity induces nonreciprocal mechanical displacement, modulating the cavity intensity through optomechanical feedback. This enables full isolation of backward transmission without requiring parameter initialization. Alternatively, for quantum signals, the platform is reconfigured by activating photonic and phononic exchange channels between the two blocks. In this configuration, nonreciprocity arises from quantum interference between direct photon hopping and indirect conversion pathways. Constructive interference enables unidirectional low-loss transmission, while destructive interference completely suppresses the reverse direction. After adiabatically eliminating the auxiliary modes, the optimal nonreciprocal frequency and the trade-off between insertion loss and nonreciprocal bandwidth can be controlled by engineering optomechanically induced mechanical dissipation. Additionally, the three-mode-based device requires less control-field power than two-mode systems under resolved-sideband conditions, demonstrating versatile potential for optical nonreciprocity applications across classical and quantum domains.

In generic classical and quantum many-body systems, where typically energy and particle number are the only conserved quantities, stationary states are described by thermal equilibrium. In contrast, integrable systems showcase an infinite hierarchy of conserved quantities that inhibits conventional thermalization, forcing relaxation to a generalized Gibbs ensemble (GGE)—a concept first introduced in quantum many-body physics. In this study, we provide experimental evidence for the emergence of a GGE in a photonic system. By investigating partially coherent waves propagating in a normal dispersion optical fiber, governed by the one-dimensional defocusing nonlinear Schrödinger equation, we directly measure the density of states of the spectral parameter (rapidity) to confirm the time invariance of the full set of conserved charges. We also observe the relaxation of optical power statistics to the GGE's theoretical prediction, obtained using the experimentally measured density of states. These complementary measurements unambiguously establish the formation of a GGE in our photonic platform, highlighting its potential as a powerful tool for probing many-body integrability and bridging classical and quantum integrable systems.

In this paper, we propose and explore an experimentally viable scheme to realize tunable optomechanically induced transparency (OMIT) and optomechanically induced absorption (OMIA) phenomena in a hybrid microwave-optomechanical circuit in which two single-Cooper-pair transistors are coupled to a common microwave $LC$ resonator and two independent micromechanical resonators. We show that under special conditions such a system can be equivalently modeled as a two-mechanical-modes optomechanical cavity in which, aside from the standard radiation-pressure coupling, the cavity mode interacts with the mechanical modes through the cross-Kerr (CK), a higher-order generalized CK, and a three-mode CK type of coupling. Furthermore, there is an induced CK coupling between the two mechanical modes. Assuming that the cavity mode is simultaneously driven by a strong control field and a weak probe field, we analyze the response of the output probe field affected by the above-mentioned nonlinear couplings. In particular, our results reveal that the higher-order nonlinear CK and the three-mode CK couplings have remarkable impact on the characteristics of the OMIT and OMIA phenomena. Moreover, we find that these nonlinear couplings can give rise to the occurrence of the gain in the absorption profile and contribute to the amplification of the output probe field in specific frequency regions. We also show that the system offers tunable switching between slow and fast light behaviors. The proposed hybrid optomechanical circuit may find potential applications in light propagation, quantum sensing of physical quantities, and information processing.

The use of entangled gamma rays from positronium decay for quantum-enhanced imaging of dense materials is demonstrated. Quantum ghost images, where only one of the entangled 511-keV photons interacts with the object, are obtained for tantalum samples of varying density using a 210-ps time-resolution dual detector system and a Na-22 positron source. An analysis comparing both classical and quantum imaging modalities is employed to isolate true 511-keV events from background noise. Image quality is quantitatively assessed using transmission ratios and the Michelson contrast. Quantum-correlated images are found to exhibit superior (up to approximately 1.7x, from 0.49 to 0.83 in the thickest sample measured) contrast compared to classical methods and align well with theoretical expectations. These results suggest that quantum ghost imaging with positronium-based entangled gamma rays could significantly enhance noninvasive imaging of high-density objects, with potential applications in areas such as cargo inspection and security screening.

In this paper, we derive a general master equation for continuous feedback based on arbitrary linear signals. This result is an extension of the quantum Fokker-Planck master equation derived by Annby-Andersson et al. [Phys. Rev. Lett. 129, 050401 (2022)] to the case where the experiment has a general filtering structure. The filtering operation can include delayed information, memory effects, and non-Markovian signal processing. Using this general master equation, we derive analytical results for the ground-state cooling of a quantum harmonic oscillator. We compared our results with those derived by De Sousa et al. [Phys. Rev. E 111, 014152 (2025)]. Our framework aims to capture more realistic situations, to allow experiments to be better modeled, and to study non-Markovian effects in the spectral properties of the measurement signal.

We present a generalized Deutsch-Jozsa (DJ) quantum algorithm that determines not only the global type of an unknown Boolean function (constant or balanced) but also explicit output values of the function in a single oracle query. Unlike the original DJ algorithm, which identifies only whether a function is constant or balanced, our generalization retrieves actual function output values while at the same time using a Bell state as an ancilla. This makes a richer function characterization with minimal queries to have practical quantum advantages, e.g., data classification, logistic regression, and quantum cryptography.

This third paper in this series continues the investigation of atom-field interactions in the presence of a conductor or a dielectric medium, focusing on quantum information related basic issues such as decoherence and entanglement. Here we consider the entanglement between two atoms with internal degrees of freedom modeled by a harmonic oscillator, with varying separations between them and varying distances between them and a conducting surface. The coupling between the atoms and the field and the coupling between the atoms are allowed to go beyond the weak-coupling restrictions often found in the literature. A detailed analysis of how the entanglement depends on each variable involved enables us to come up with a spatial topography of quantum entanglement, facilitating a visualized understanding of the behavior of quantum field-mediated entanglement. In particular, we can quantify the definition of a three-dimensional entanglement domain between the two atoms, how it varies with their coupling, their separation and their distances from the conducting surface, and, for practical applications, how to exercise effective control of the entanglement between two atoms by changing these parameters. Our findings are expected to be useful for studies of atom-field-medium interactions in vacuum and surface physics.

High-precision variational calculations in Hylleraas coordinates are presented for all singlet and triplet $P$ states of helium up to principal quantum number $n=35$ with a uniform accuracy of 1 part in ${10}^{22}$ for the nonrelativistic energy. Mass polarization, relativistic, and quantum electrodynamic effects are included to achieve a final accuracy of $\pm 1\mathrm{kHz}$ or better for the ionization energy of the Rydberg states of ${}^4\mathrm{He}$ in the range $24\le n\le 35$. The results are combined with 11 transition frequency measurements of Clausen et al. [Phys. Rev. A 111, 012817 (2025)] to obtain complementary measurements of the ionization energy of the $1s2s{}^3{S}_1$ state that do not depend on quantum-defect extrapolations to the series limit. The result from the triplet spectrum yields an ionization energy of 1 152 842 742.728(6) MHz, which agrees with but is larger than the experimental value by $14\pm 17\mathrm{kHz}$. However, it confirms a much larger $9\sigma$ discrepancy of $0.468\pm 0.055\mathrm{MHz}$ with the theoretical ionization energy of Patkóš et al. [Phys. Rev. A 103, 042809 (2021)]. The results provide a test of the quantum-defect-extrapolation method at the level of $\pm 17\mathrm{kHz}$.

Understanding energy relaxation dynamics in weakly bound systems following excitation is fundamental to diverse phenomena, from radiation-induced biological damage to interstellar chemistry. Here, we investigate the photoinduced fragmentation dynamics of both isolated ${\mathrm{N}}_2\mathrm{O}$ molecules and their molecular clusters using a broadband extreme ultraviolet light source. Beyond direct photoionization processes, we observe indirect ionization pathways that generate low-energy electrons (LEEs) in the 0–10 eV range. This process originates from the population of neutral superexcited states in ${\mathrm{N}}_2\mathrm{O}$, followed by either intramolecular autoionization or resonant intermolecular Coulombic decay. In large clusters, we observe a remarkable enhancement of LEE production, with yields becoming comparable to those from direct ionization. Additionally, among all fragmentation products correlated with indirect LEEs, the ionic fragments containing ${\mathrm{N}}^{+}$ and ${\mathrm{O}}^{+}$ are significantly reduced, which is in contrast to the situation for isolated ${\mathrm{N}}_2\mathrm{O}$ molecules. Our observations demonstrate that the decay of superexcited states is significantly influenced by the molecular cluster environment and may extend to the radiation-induced biological damage processes.

We have investigated theoretically the formation of photoelectron holograms in the momentum distribution of the continuum electrons generated during the ionization of H atoms by ultrashort laser pulses. In previous theoretical and experimental works the observation of a clear holographic interference pattern was hindered by other secondary processes like the temporal interference or the presence of electron trajectories with multiple scattering events. In the present work we present a two-pulse setup for the production of clear photoelectron holograms. In this pump-drive setup an attosecond laser pulse is used for the creation of the continuum wave packet, while a second longer laser pulse is used to drive the dynamics of the continuum wave packet. By performing calculations for different pump-drive delays for a given drive-pulse shape, we have identified the optimal delay value for the production of the photoelectron holograms. We also verified for this optimal delay value how the photoelectron hologram can be shaped by varying the wavelength and intensity of the drive pulse.

We systematically investigate the attosecond joint energy spectra (JESs) of the dissociative wave packet of ${\mathrm{H}}_2^{+}$ by numerically solving the time-dependent Schrödinger equation. The dissociative wave packet, initially prepared by a resonant pump pulse and subsequently ionized by a single-attosecond extreme-ultraviolet pulse with a variable time delay, produces time-resolved JESs that exhibit splitting and distorted structures, encoding rich information on ultrafast molecular dynamics. Interestingly, variations in the slopes of the energy-sharing lines in the JESs are observed, in contrast to the ground-state scenario where the slope is $-1$. The origin of the slope variations is well explained by an analytical model combined with the Wentzel-Kramers-Brillouin approximation, and is attributed to the dispersion relation of the dissociative nuclear wave packet. Based on these findings, we propose a novel method for imaging the molecular potential energy curves, which remains robust even when the JESs are distorted by two-center interference.

We explore degenerate Raman sideband cooling in which neighboring Zeeman states of a fixed hyperfine level are coupled via a two-photon Raman transition. The degenerate coupling between $|F,m_F\rangle \to |F,m_F-1\rangle$ facilitates the removal of multiple motional quanta in a single cycle. This method greatly reduces the number of cooling cycles required to reach the ground state compared to traditional sideband cooling. We show that near ground state cooling can be achieved with a pulse number as low as $\overline{n}$ where $\overline{n}$ is the average phonon number in the initial thermal state. We demonstrate proof of concept in ${}^{176}\mathrm{Lu}^{+}$ by coupling neighboring Zeeman levels on the motional sideband for the $F=7$ hyperfine level in ${}^{3}D_1$. Starting from a thermal distribution with an average phonon number of 6, we demonstrate near ground-state cooling with $\sim 10$ pulses. A theoretical description is given that applies to any $F$ level and demonstrates how effective this approach can be.