In the present study we determine from the available experimental data the cross section of muon transfer to molecular oxygen at low energies with an account of the oxygen molecule structure. Building on an earlier work, the results highlight the role of the molecular structure effects and significantly improve the agreement with theoretical calculations of the muon transfer rate. An efficient computational model of the kinetics of the processes involving muonic hydrogen atoms in a gaseous mixture of ${\mathrm{H}}_2$ and ${\mathrm{O}}_2$ is developed and analyzed. The model is applied in the description of the FAMU experiment for the measurement of the hyperfine splitting in muonic hydrogen and the Zemach radius of the proton.

This paper presents a combined theoretical and experimental study of the collisions between oxygen anions $\left({\mathrm{O}}^{-}\right)$ and HD molecules. The thermal rate coefficients for associative electron detachment (HDO molecule formation), hydrogen transfer (${\mathrm{OH}}^{-}$ ion formation), and deuterium transfer (${\mathrm{OD}}^{-}$ ion formation) were measured at temperatures between 10 and 200 K in a radio-frequency ion trap. The experimental data are compared with theoretical reaction rate coefficients, which were computed over a temperature range of 10–4000 K using the classical-trajectory Monte Carlo method on an ab initio calculated potential energy surface. The thermal rate coefficients for reactions with other deuterated or tritiated variants of the ${\mathrm{H}}_2$ molecule were also calculated. We analyze the results in terms of cross sections and the dependence of reaction and detachment probabilities on the impact parameter. Additionally, we demonstrate that the scattering dynamics for this system exhibits signatures of deterministic chaos at the classical level.

Coherent control aims to manipulate chemical processes on the latent length and timescales of atoms and bonds, scales that are intrinsic to molecular dynamics but not directly resolved by most experimental probes. As a result, existing coherent-control experiments, which overwhelmingly rely on spectroscopic observables, leave a crucial blind spot: the direct, real-space recovery of all atomic and molecular rearrangements in response to coherently controlled excitations. Here, we overcome this limitation by integrating a Tannor–Kosloff–Rice pump-control-probe scheme with ultrafast x-ray scattering to capture snapshots of the wave-packet motion in a benchmark molecular system. We demonstrate this by photoexciting diatomic iodine vapor with a visible pump pulse, selectively steering the wave packet toward ground-state recombination or dissociative pathways with a time-delayed near-IR control pulse and recording the dynamics with angstrom and femtosecond precision with an ultrashort hard x-ray probe pulse. By comparing these structural observations with numerical solutions of the time-dependent Schrödinger equation, we reveal how coherent control actively reshapes the molecular charge density distribution. Our results pave the way for leveraging structural feedback as a control handle and provide a fundamental microscopic visualization of quantum decoherence and energy redistribution at the atomic level.

We study the motion of an impurity under the action of a constant force through a one-dimensional system of weakly interacting homogeneous bosons. The interplay of the impurity-boson interaction, the boson-boson interaction, and the driving force gives rise to a rich dynamics. We focus on the influence of a finite external force. Under these far-from-equilibrium conditions, we show that in a wide range of forces, one part of the momentum transferred to the system is periodically channeled into the Bose gas through the emission of dispersive density shock waves, solitons, density waves, and the creation of additional phase gradients. As a result, the impurity velocity does not increase indefinitely, but periodically oscillates in time around the drift velocity. We uncover and characterize different dynamical regimes in a wide range of the impurity-boson coupling, the impurity mass, and the external force. At a sufficiently large force, the Bloch oscillations cease and the impurity exhibits an unlimited acceleration.

A method is proposed for the formation of femtosecond and subfemtosecond pulses of the deep ultraviolet and vacuum ultraviolet radiation via generation of the third harmonic of femtosecond laser pulses during their resonant interaction with alkali-metal atoms or alkaline-earth-metal ions. The pulse formation occurs due to two-photon Rabi oscillations between quasiequidistant energy levels of atoms or ions. The duration of the generated third-harmonic pulse is several times shorter than far from resonance, while the generation efficiency is up to three to four orders of magnitude higher.

We present a theoretical investigation of third-order cross-nonlinearity in an $N$-type four-level system and a ladder-type three-level system, as a major extension of prior work [Phys. Rev. Lett. 91, 093601 (2003)]. The third-order cross-nonlinearity in the $N$-type four-level system can be enhanced with compressed linewidth under two-photon resonance between the probe and coupling fields, by reducing the coupling Rabi frequency or increasing the coupling detuning. The enhanced cross-nonlinearity can also be obtained in the ladder-type system and it shows that the cross-nonlinearity in the ladder-type system can be one order of magnitude larger than that in the $N$-type system under the same parameters. Furthermore, the cross-nonlinearity arising between the probe and coupling fields in the $N$-type system is also explored and the enhanced cross-nonlinearity with compressed linewidth can be achieved by reducing the signal Rabi frequency or increasing the signal detuning. Our study shows that this enhanced cross-nonlinearity stems from the $\mathrm{\Lambda }$-type system and is not larger than that of the $\mathrm{\Lambda }$-type system.

We conduct a theoretical study to understand the periodic superradiance observed in an Er:YSO crystal. First, we construct a model based on the Maxwell-Bloch equations for a reduced level system, a pair of superradiance states, and a population reservoir state. Analysis of the eigenvalues of the linearized differential equations shows that periodic superradiance can be realized only for certain parameters. We also derive two-variable equations consisting of the coherence and population difference between the two superradiance states, which contain the essential feature of the periodic superradiance. The two-variable equations clarify the mathematical structure of this periodic phenomenon and give analytical forms of the period, pulse duration, and number of emitted photons. Our model successfully reproduces the periodic behavior, but the actual experimental parameters are found to be outside the parameter region for the periodic superradiance. This result implies that some other mechanism(s) is (are) required. As one example, assuming that the field decay rate varies with the electric field, the periodic superradiance can be reproduced even under the actual experimental conditions.

Beats arising from the interference among waves with different frequencies have emerged as a powerful tool for precision measurements. In a $lin\left|\right|lin$ coherent-population-trapping (CPT) clock, such beats can be induced by a double-$\mathrm{\Lambda }$ CPT transition that shares a common excited state. Here we employ CPT-Ramsey interferometry to experimentally explore the underlying beating dynamics in such a double-$\mathrm{\Lambda }$ CPT transition. The observed beating results from the differential Zeeman shifts between the two $\mathrm{\Lambda }$ subsystems, which are caused by the opposite nuclear spin projections in the involved states. The amplitude of the frequency-domain Ramsey fringes depends strongly on both the magnetic field strength and the Ramsey time, exhibiting clear constructive and destructive interference patterns. This dependence enables the optimization of signal contrast in CPT clocks by tuning the magnetic field and Ramsey time. The overall light shift ${\nu }_{\mathrm{LS}}$ relates to the sum of two initial phases ${\mathrm{\Theta }}_{+}$ for the two $\mathrm{\Lambda }$ structures: ${\nu }_{\mathrm{LS}}=-{\mathrm{\Theta }}_{+}/\left(2\pi T\right)$ for a given Ramsey time $T$. In the vicinity of resonance, this light shift is approximately proportional to the two-photon detuning $\delta$ if $\left|\delta \right|\le$ 4 kHz. Through enabling the precise measurement and effective suppression of light shifts, our approach provides a direct path toward improved stability and accuracy in cold-atom CPT clocks. Our work provides promising application prospects in the field of quantum sensing, such as ultra-weak magnetic field measurement.

We introduce and study coherent polarization self-rotation (CPSR), a two-photon light-matter interaction in dense alkali-metal vapors that enables both narrowband optical spectroscopy of magnetic transitions and coherent coupling between light and collective atomic spins. Unlike conventional polarization self-rotation, CPSR requires initial spin polarization and a predominantly linearly polarized probe. It operates efficiently even in optically thick vapors with high buffer-gas pressure, rapid spin-exchange collisions, and optically unresolved hyperfine structure. We demonstrate CPSR with near-unity contrast in rubidium and achieve an exceptionally narrow two-photon linewidth of 10 Hz in potassium. CPSR realizes a coherent interface between one optical quadrature and the long-lived collective electronic spin, offering a robust and scalable spin-light coupling in optically thick platforms. This opens opportunities for quantum optics, including quantum-enhanced metrology in the audio-frequency band and coherent transduction between light and ultralong-lived noble-gas spins via alkali-metal spins.

We study a class of feedback oscillators realized by a phase-insensitive amplifier in positive feedback, where either the amplifier or the feedback element may determine the oscillator's linewidth. The spectral purity of the output of such a device originates from basic demands of quantum mechanics and causality. The resulting expression generalizes the Schawlow-Townes limit, which is itself one component of a standard quantum limit for feedback oscillators. Recently realized bad-cavity oscillators, such as superradiant lasers and solid-state masers, can saturate this generalized Schawlow-Townes limit. This limit can be surpassed through appropriate quantum engineering, for example, by atomic spin squeezing in a superradiant laser.

We show that a simple model of non-Hermitian noise gives rise to the telegraph switching behavior seen in experiments with single qubits, without any reference to the existence of photons as corpuscles. This lends support to a continuous collapse interpretation of quantum mechanics, but can also be viewed as a model of continuous detection of a steady-state process in the incoherent limit. We show explicitly that such a system obeys the Born rule for particle counting statistics, even though no particle behavior has been invoked at any point in the calculation.

Quantum steering, as a manifestation of nonlocal quantum correlations, plays a crucial role in enabling various quantum information processing tasks. However, practical implementations are often hindered by significant challenges arising from imperfect or untrusted measurement devices. This study investigates the impact of measurement inaccuracies on quantum steering, with a particular focus on errors in the untrusted party's measurement devices. We first analyze how such errors affect the evaluation of steering inequalities and then derive bipartite steering inequalities based on correlation matrices under imperfect measurements. Our findings show that even small measurement errors can significantly compromise the certification of quantum steerability, an effect that becomes particularly pronounced as the system dimension increases. Furthermore, by extending the proposed steering inequality to a modified tripartite scenario via correlation matrices, we demonstrate that the influence of measurement imperfections is far more severe in multipartite quantum steering than in the bipartite case. Our results underscore the critical need to account for measurement imperfections in experimental quantum steering and provide a theoretical framework for characterizing and mitigating these effects in high-dimensional quantum systems.

We present benchmarking results for single-qubit gates implemented on a neutral-atom quantum processor using direct randomized benchmarking (DRB) and gate-set tomography (GST). The DRB protocol involves preparing stabilizer states, applying $m$ layers of native single-qubit gates, and measuring in the computational basis, providing an efficient error characterization under a stochastic Pauli noise model. GST enables the full, self-consistent reconstruction of quantum processes, including gates, input states, and measurements. Both protocols provide estimations of gate performance robust to state preparation and measurement (SPAM) errors, offering complementary perspectives on quantum gate fidelity. For single-qubit gates, DRB yields an average fidelity of $99.963\%$. The protocol was further applied to a 25-qubit array under global single-qubit control. GST results are consistent with those obtained via DRB. We also introduce a gauge-optimization procedure for GST that brings the reconstructed gates, input states, and measurements into a canonical frame, enabling meaningful fidelity comparisons while preserving physical constraints. These constraints on the operators, such as complete positivity and trace preservation, are enforced by performing the optimization over the Stiefel manifold. The combined analysis supports the use of complementary benchmarking techniques for characterizing scalable quantum architectures.

A qubit, or quantum bit, is conventionally defined as “a physical system for storing information that is capable of existing in either of two quantum states or in a superposition of both” [Oxford English Dictionary (Oxford University Press, 2025)]. In this paper, we examine the simple question of whether two distinct levels, each consisting of multiply degenerate substates, could serve as a practical quantum bit using two fine-structure energy levels containing degeneracy as a model. We find that, in the continuous presence of the field, the atom still undergoes Rabi oscillations, which are suitable for quantum gate construction. In addition, we compute the average fidelity in Hadamard gate performance for a single degenerate atom and postulate the required form of two-atom interaction to construct a controlled-$Z$ gate.

Several high-power laser facilities are reaching field strengths where leading-order strong-field quantum electrodynamical (QED) processes can be measured in the regime of nonperturbative charge-field interaction. At very high, as yet unobtainable in the laboratory, field strengths, the contribution of higher-order processes is predicted to dominate, implying a breakdown of current calculational methods. Focusing on nonlinear showers and considering currently available experimental parameters, we find that if the momentum spectrum of the incident particles is well known, asymmetries in the outgoing particle spectrum may provide a useful signature of higher orders of nonlinear phototrident, trident, and Compton scattering. These signatures could be used by experiment to test how accurate the current calculational framework is when applied to strong-field QED at higher orders.

We report a joint experimental and theoretical study using a combination of polarization-controlled free-electron-laser (FEL) and near-infrared (NIR) pulses in a synchronized two-color photoionization scheme. Excited ${\mathrm{He}}^{+}$ ions, created by extreme ultraviolet (XUV) circularly polarized radiation from the XUV-FEL FERMI in the oriented $3p(m=+1)$ state, are exposed to circularly polarized 784-nm NIR radiation with peak intensities from ${10}^{12}$ to ${10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. The angular distribution of the ejected electrons exhibit a strong dichroism depending on the NIR intensity. While the corotating case is defined by a single path, for the counterrotating case, there are two dominant pathways whose relative strength and phase difference are determined.

In this work we investigate the influence of atomic diffusion effects on the resonance of electromagnetically induced transparency (EIT) in gas cells filled with three-level atoms and a buffer gas. The influence of the end walls and diffusion of atoms at the wavelength of laser field beats is studied. Analytical expressions are obtained for the local absorption coefficient of the probe field and for the full absorption spectrum of the gas cell. It is shown that the diffusion contribution to the EIT resonance linewidth can be suppressed near the walls. It was found that the influence of end walls can lead to both inhomogeneous broadening and narrowing of the EIT line. This can be controlled by changing the intensity of the control field. The dispersion characteristics of the medium were analyzed. Expressions for the group velocity and group delay were obtained, and it is shown that under certain conditions the influence of the walls leads to an increase in the group delay.

Collective emission of light from distributions of two-level systems was first predicted in 1954 by Robert Dicke, who showed that when $N$ quantum emitters absorb photons, their collective radiative decay rate can be significantly enhanced (superradiance) or suppressed (subradiance) relative to the single-emitter decay rate. In this work, we derive analytical expressions for the collective decay rates and collective Lamb shifts for the coherent interaction of a single photon with topologically one-dimensional, continuous distributions of quantum two-level systems: an infinite line and an infinite helix. We compare our solution with arrangements where the distribution of transition dipole vector emitters is discrete rather than continuous, and when short- ($1/r^3$), intermediate- ($1/r^2$), and long-range ($1/r$) interaction terms are included. We conduct a detailed comparison of our results averaging out polarization effects, with eigensolutions of similar systems maintaining the dot product between transition dipole vectors and the electric field, finding that the thermally averaged collective decay rate is enhanced in both approaches. Our analytical solution for the helix is then used to make order-of-magnitude estimates of the maximally superradiant state, thermally averaged collective decay rate, and percentage of trapped states in helical architectures of molecular quantum emitters in protein fibers. Given the inclusion of short- and intermediate-range interaction terms in our numerical models for realistic protein fiber architectures and the averaging out of polarization effects in our analytical solution, these results show excellent agreement for sparse arrangements of emitters. Our work thus bridges the theoretical gap between different formalisms for treating superradiant matter distributions, aids the engineering of helical devices to harness quantum optical effects for computing with superradiant error correction and subradiant memories, and motivates the discovery and creation of flexible platforms for quantum information processing using the intrinsic helical geometries of biomatter.

Parametrically driven oscillators can emerge as a basis for the next generation of qubits. Classically, these systems exhibit two stable oscillatory states with opposite phases. Upon quantization, these states turn into a pair of closely spaced Floquet states, which can serve as the logical basis for a qubit. However, interaction with the environment induces phase-slip events which set a limit on qubit coherence. Such phase slips persist even at zero temperature due to a mechanism known as quantum activation. In contrast to conventional tunneling, the quantum activation is described by a real-time instanton trajectory in the complexified phase space of the system. In this work, we show that the phase-slip rate is exponentially sensitive to weak ac perturbations. The spectrum of the system's response—captured by the so-called logarithmic susceptibility—enables a direct observation of characteristic features of real-time instantons. Studying this spectrum suggests new means of efficient qubit control.