Quantum key distribution (QKD) allows remote parties to share secret keys with proven security. In practice, optical schemes based on the Faraday mirror and Sagnac loop are widely used in QKD systems to improve the stability of QKD systems. In these schemes, light transmits bidirectionally in the optical path, compensating the effects caused by the environment automatically. However, due to the finite extinction ratio of the light source, these schemes will modulate the leaked light between the signal pulses, resulting in time-dependent side channels. Here, we provide a comprehensive experimental study of the security for practical QKD with time-dependent side channels. We demonstrate the amount of information leakage from the encoding modules using a Faraday mirror and Sagnac loop in a high-speed QKD system. Based on experimental results, we analyze the security risks and the corresponding countermeasures.

Weakly bound systems provide possibilities to study nonlocal electronic decay processes, which present unique physical and chemical properties. Here we report the experimental observation of a nonlocal decay process, i.e., nonadiabatic-coupling-mediated charge transfer (NCMCT), in argon dimer. This process can be effectively produced and manipulated by the double electron capture in low-charge-state oxygen ion collisions. Compared to other common decay mechanisms of ${\mathrm{Ar}}_2$ dication, the NCMCT process results in notably different kinetic energy releases for the $\mathrm{A}{\mathrm{r}}^{+}+\mathrm{A}{\mathrm{r}}^{+}$ channel. It is due, revealed by theoretical calculations, to the special potential energy curve of the responsible $\mathrm{A}{\mathrm{r}}^{2+}-\mathrm{Ar}$ state that possesses many crossing points and thus nonadiabatically couples with the $\mathrm{A}{\mathrm{r}}^{+}-\mathrm{A}{\mathrm{r}}^{+*}$ states in a wide internuclear distance range. Such an NCMCT process is expected to be a general process occurring in weakly bound systems when highly excited. The present work provides a prime collision system to explore the charge transfer in ion-molecule reactions and also brings insight into cluster dissociation mechanism.

We experimentally investigate the dissociative frustrated triple ionization of ArKr dimers induced by a relative phase-controlled linearly polarized two-color femtosecond laser field. In this process, one of the three ionized electrons is recaptured by the triply ionized ArKr, leading to fragmentation via two distinct Rydberg channels: ($\mathrm{A}{\mathrm{r}}^{+*}$, $\mathrm{K}{\mathrm{r}}^{+}$) and ($\mathrm{A}{\mathrm{r}}^{+}$, $\mathrm{K}{\mathrm{r}}^{+*}$). Coincidence measurements are performed for the resulting fragments. By examining the sum momentum of the two fragments along the symmetry axis of the spectrometer in relation to their total kinetic energy release, we establish a method for selectively identifying events corresponding to each Rydberg channel from the raw data. Furthermore, we demonstrate that the emission directions of the Rydberg fragments in the ($\mathrm{A}{\mathrm{r}}^{+*}$, $\mathrm{K}{\mathrm{r}}^{+}$) and ($\mathrm{A}{\mathrm{r}}^{+}$, $\mathrm{K}{\mathrm{r}}^{+*}$) channels can be manipulated by adjusting the relative phase of the two-color laser fields. Notably, these two channels exhibit distinct behaviors in the relative phase-dependent asymmetry as a function of the kinetic energy release of the fragments. Based on the observed asymmetry patterns and the enhanced ionization mechanism, we elucidate the pathways leading to the formation of the ($\mathrm{A}{\mathrm{r}}^{+*}$, $\mathrm{K}{\mathrm{r}}^{+}$) and ($\mathrm{A}{\mathrm{r}}^{+}$, $\mathrm{K}{\mathrm{r}}^{+*}$). Our findings provide an experimental approach and deeper insight into molecular dissociative frustrated ionization in femtosecond laser fields.

Cumulant mapping has recently been suggested [Frasinski, Phys. Chem. Chem. Phys. 24, 20776 (2022)] as an efficient approach to observing multiparticle fragmentation pathways while bypassing the restrictions of the usual coincidence-measurement approach. We present a formal analysis of the cumulant-mapping technique in the presence of moderate external noise, which induces spurious correlations between the fragments. Suppression of a false-cumulant signal may impose severe restrictions on the stability of the experimental setup and/or the permissible average event rate, which increase with cumulant order. We demonstrate that cumulant mapping in an imperfect apparatus remains competitive for dominant processes and for pathways with a background-free marker fragment. We further show that the false-cumulant contributions increase faster than linearly with the average event rate, providing a simple test for the experimental data analysis.

We study the nonequilibrium dynamics of bosons in a two-dimensional optical lattice after a sudden quench from the superfluid phase to the free-boson regime. The initial superfluid state is described approximately using both the Bogoliubov theory and the Gaussian variational principle. The subsequent time evolution remains Gaussian, and we compare the results from each approximation of the initial state by examining different aspects of the dynamics. First, we analyze the entanglement entropy and observe that, in both cases, it increases linearly with time before reaching a saturation point. This behavior is attributed to the propagation of entangled pairs of quantum depletions in the superfluid state. Next, we explore the fate of particle-number symmetry, which is spontaneously broken in the superfluid phase. To do so, we use the entanglement asymmetry, a recently introduced observable that enables us to track symmetry breaking within a subsystem. We observe that its evolution varies qualitatively depending on the theory used to describe the initial state. However, in both cases, the symmetry remains broken and is never restored in the stationary state. Finally, we assess the time it takes to reach the stationary state by evaluating the quantum fidelity between the stationary reduced density matrix and the time-evolved one. Interestingly, within the Gaussian variational principle, we find that an initial state further from the stationary state can relax more quickly than one closer to it, indicating the presence of the recently discovered quantum Mpemba effect. We derive the microscopic conditions necessary for this effect to occur and demonstrate that these conditions are never met in the Bogoliubov theory.

We have determined the atomic mass of ${}^3\mathrm{He}$ to 12 parts per trillion relative precision from a measurement of the cyclotron frequency ratio of ${}^3\mathrm{He}^{+}$ and ${}^{12}\mathrm{C}^{4+}$ in a Penning trap. From the obtained mass of the ${}^3\mathrm{He}^{+}$ ion, the mass of the neutral atom can be calculated without loss of precision: $m\left({}^3\mathrm{He}\right)=3.016029322011\left(35\right)$ u. This result provides independent, high-precision data for the last missing link between the masses in the regime of light ions, thereby resolving discrepancies in the reported masses of light atomic nuclei from various experiments.

Gaussian boson sampling is a popular method for experimental demonstrations of quantum advantage, but many subtleties remain in fully understanding its theoretical underpinnings. An important component in the theoretical arguments for approximate average-case hardness of sampling is anticoncentration, which is a second-moment property of the output probabilities. In Gaussian boson sampling these are given by hafnians of generalized circular orthogonal ensemble matrices. In a companion work by Ehrenberg et al. [Phys. Rev. Lett. 134, 140601 (2025)], we develop a graph-theoretic method to study these moments and use it to identify a transition in anticoncentration. In this work, we find a recursive expression for the second moment using these graph-theoretic techniques. While we have not been able to solve this recursion by hand, we are able to solve it numerically exactly, which we do up to Fock sector $2n=80$. We further derive analytical results about the second moment. These results allow us to pinpoint the transition in anticoncentration and furthermore yield the expected linear cross-entropy benchmarking score for an ideal (error-free) device.

Trapped ions are among the most advanced platforms for quantum simulation and computation. Their capabilities can be further augmented by making use of electronically highly excited Rydberg states, which enable the realization of long-range electric dipolar interactions. Most experimental and theoretical studies so far have focused on the excitation of ionic Rydberg states in linear Paul traps, which generate confinement by a combination of static and oscillating electric fields. These two fields need to be carefully aligned to minimize so-called micromotion, caused by the time-dependent electric field. The purpose of this work is to systematically understand the qualitative impact of micromotion on the Rydberg excitation spectrum, when the symmetry axes of the two electric fields do not coincide. Considering this scenario not only is important in the case of possible field misalignment but becomes inevitable for Rydberg excitations in two- and three-dimensional ion crystals, we develop a minimal model describing a single trapped Rydberg ion, which we solve numerically via Floquet theory and analytically using a perturbative approach. We calculate the excitation spectra and analyze in which parameter regimes addressable and energetically isolated Rydberg lines persist, which are important requirements for conducting coherent manipulations.

Squeezed states of light are one of the most important fundamental resources for quantum optics, optical quantum information processing, and quantum sensing. Recently, it has been experimentally demonstrated that the squeezing of single-mode squeezed vacuum states can be enhanced by probabilistic two-photon subtraction. A further enhancement of the squeezing is subsequently possible by heralded Gaussification, which distills a Gaussian state from the de-Gaussified two-photon subtracted state. Here we provide an extended theoretical analysis of squeezing distillation and purification. We consider a more general scheme in which photon subtraction is combined with a weak coherent displacement. This more flexible scheme allows us to enhance squeezing for an arbitrary input squeezing value. Moreover, if the modified two-photon subtraction operation is properly chosen, then arbitrary strong squeezing can be distilled by subsequent Gaussification. We go beyond pure states and show that the combination of photon subtraction and heralded Gaussification cannot suppress losses that have affected the input state. To overcome this limitation, we propose an alternative de-Gaussifying operation based on a Fock-state filter that removes the single-photon state. With this de-Gaussifying operation and subsequent re-Gaussification, pure single-mode squeezed states can be distilled from a large class of mixed input states. Interestingly, we have found that squeezing distillation by two-photon subtraction is closely related to certain methods for generating Gottesman-Kitaev-Preskill states, which are crucial for optical quantum computing.

We investigate a mode-locking regime in the singly resonant optical parametric oscillator (OPO) employing simultaneous amplitude and frequency modulation of the intracavity field. This OPO exhibits deterministic, “turn-key” formation of a stable, broadband, chirped frequency comb with high conversion efficiency. Comb-forming dynamics follow a simple phase-space dynamical model, governed by cavity dispersion and modulator chirp, which agrees closely with full numerical simulations. The comb exhibits fast, mode-hop-free tuning over the full gain window of the optical parametric amplification crystal, controlled by the modulator frequency. Conditions for comb stability, and techniques to enhance comb bandwidth through intentional phase mismatch and chirping, are investigated.

Levitated optomechanical systems are rapidly becoming leading tools for precision sensing of forces and accelerations acting on particles in the femtogram to nanogram mass range. These systems enable a high level of control over the sensor's center-of-mass motion, rotational degrees of freedom, and electric charge state. For many sensing applications, extending these techniques to arrays of sensors enables rejection of correlated noise sources and increases sensitivity to interactions that may be too rare or weak to detect with a single particle. Here we present techniques capable of trapping defect-free, two-dimensional arrays of more than 25 microspheres in vacuum. These techniques provide independent control of the optical potential for each sphere. Simultaneous imaging of the motion of all spheres in the array is demonstrated using camera-based imaging, with optimized object tracking algorithms reaching a displacement sensitivity below 1 nm/$\sqrt{\mathrm{Hz}}$. Such arrays of levitated microspheres may find applications ranging from inertial sensing to searches for weakly interacting particles such as dark matter.

Dipolar Bose-Einstein condensates are excellent platforms for studying supersolidity, characterized by coexisting density modulation and superfluidity. The realization of dipolar mixtures opens intriguing new scenarios, most remarkably the possibility of realizing a double supersolid, composed of two interacting superfluids. We analyze the complex excitation spectrum of a miscible trapped dipolar Bose mixture, showing that it provides key insights about the double-supersolid regime. We show that this regime may be readily probed experimentally by monitoring the appearance of a doublet of superfluid compressional modes, linked to the different superfluid character of each component. Additionally, the dipolar supersolid mixture exhibits a nontrivial spin nature of the dipolar rotons, the Higgs excitation, and the low-lying Goldstone modes. Interestingly, the analysis of the lowest-lying modes allows for monitoring the transition of just one of the components into the incoherent-droplet regime, whereas the other remains coherent, highlighting their disparate superfluid properties.

The Hubbard model is a paradigmatic model of strongly correlated quantum matter, thus making it desirable to investigate with quantum simulators such as ultracold atomic gases. Here we consider the problem of two atoms interacting in a quasi-one- or quasi-two-dimensional optical lattice, geometries which are routinely realized in quantum-gas-microscope experiments. We perform an exact calculation of the low-energy scattering amplitude which accounts for the effects of the transverse confinement as well as all higher Bloch bands. This goes beyond standard perturbative treatments and allows us to precisely determine the effective Hubbard on-site interaction for arbitrary $s$-wave scattering length (see source code available at https://github.com/HaydnAdlong/Hubbard-Interaction-Optical-Lattices). In particular, we find that the Hubbard on-site interaction displays lattice-induced resonances for scattering lengths on the order of the lattice spacing, which are well within reach of current experiments. Furthermore, we show that our results are in excellent agreement with spectroscopic measurements of the Hubbard interaction for a quasi-two-dimensional square optical lattice in a quantum-gas microscope. Our formalism is very general and may be extended to multiband models and other atomlike scenarios in lattice geometries, such as exciton-exciton and exciton-electron scattering in moiré superlattices.

Alkali-metal optically pumped magnetometers that utilize vapor cells containing high buffer-gas pressure and operate at elevated temperatures are prone to inaccuracies arising from the overlap of the average $F=I+1/2$ and $F=I-1/2$ ground-state Zeeman resonances. We employ density-matrix simulations and experiments to investigate how this hyperfine systematic error varies with spin polarization in a ${}^{87}\mathrm{Rb}$ free-induction-decay (FID) magnetometer. At low spin polarizations $P\le 0.5$, this effect causes single-frequency magnetic-field-extraction techniques to exhibit inaccuracies up to approximately 3.5 nT. Density-matrix simulations reveal that this bias can be traced to the relative amplitude and phase between the $F=I\pm 1/2$ hyperfine ground-state manifolds in the FID spin precession signal. We show that this systematic error can be mitigated using either a double-frequency fitting model that accounts for the relative amplitude and phase or synchronous-pulse pumping that minimizes the $F=1$ contribution to the FID signal. Theoretical simulations predict accuracies within 0.5 nT for both techniques across a wide range of spin polarizations, suggesting a sevenfold enhancement over single-frequency extraction methods. Our experiments validate this, showcasing a variation in the extracted field below 1 nT, a 3.5-fold improvement compared to single-frequency extraction methods. Furthermore, the mitigation techniques demonstrate agreement of the extracted magnetic field within 1.5 nT.

We propose a scheme achieving the ultimate quantum precision for the estimation of the transverse displacement between two interfering photons. Such a transverse displacement could be caused, for example, by the refracting properties of the propagation medium or by the orientation of a system of mirrors. By performing transverse-momentum sampling interference between polarization-entangled pairs of photons that propagate with different momenta, we show that it is possible to perform transverse-displacement estimation with a precision that increases with the difference of the transverse momenta of the photons. We show that the precision achieved with our scheme is independent of the value of the displacement, which is useful when tracking a variable displacement. Moreover, only for small displacements, we show that the estimation can be performed without the need for transverse-momentum-resolving detectors. More fundamentally, we demonstrate that it is the quantum interference arising from two-photon entanglement in the transverse momenta at the very heart of the foreseen quantum-limited sensitivity in the spatial domain.

We investigate the potential of tensor-network-based machine-learning methods to scale to large image and text datasets. We study how the mutual information between a subregion and its complement scales with the subsystem size $L$, similarly to approaches used in quantum many-body physics. Using various mutual information (MI) estimation methods, including an autoregressive network-based estimator, we find that simple image datasets exhibit area law scaling, suggesting efficient representation by two-dimensional tensor networks. More complex image datasets exceed the area law, indicating the need for generalized tensor network states or hybrid models. For Wikipedia text data, we observe power-law scaling $I\left(L\right)\propto L^{\nu }$ with $\nu \approx 0.82$, approaching a volume law. This implies that one-dimensional tensor networks with area law entanglement may not efficiently capture the structure of text. We introduce two models to reproduce this scaling: a quantum-inspired random pair toy model and a linguistically motivated Markovian dependency tree model. In the latter model, matching the observed MI scaling allows us to infer the word-word correlation length distribution in text.

A two-body interaction or force between quantum particles is ubiquitous in nature, and the microscopic description in terms of the bare two-body interaction is the basis for quantitatively describing interacting few- and many-body systems. Alternatively, the effective description in terms of an effective two-body interaction successfully captures the essence of the systems. However, for several important observations, the explanation in terms of an effective two-body interaction is not satisfactory, and the effective three-body interaction has played an essential role in understanding the systems. In this study, we investigate a few-body system comprising of ultracold bosons tightly confined in a deep optical lattice site, which is effectively described as zero-dimensional bosons. By combining an occupancy-resolving high-resolution laser spectroscopy with an inter-orbital Feshbach resonance controlling the bare two-body interaction over a wide range, we experimentally reveal the behaviors of few-atom systems in a strongly interacting regime. Our results, for which perturbative calculations do not provide proper explanations, serve as a valuable and precise benchmark for theoretical approaches to strongly interacting few-body systems. As one important illustration, we obtain a clear signature of an effective four-body interaction evidenced by the binding energies of four and more atoms. This work is an important step for our deeper understanding of strongly interacting few-body systems.

Using time-resolved UV-laser spectroscopy up to a few seconds in a cryogenic ion storage ring, we observe that coupling of the stretching and bending modes via Fermi resonance considerably affects the vibrational radiative cooling process of the linear triatomic molecular ion ${\mathrm{N}}_2{\mathrm{O}}^{+}$ isolated in vacuum. We state-selectively compare the cooling rates of vibrational states in the electronic ground states $X{}^2\mathrm{\Pi }_{3/2}$ and $X{}^2\mathrm{\Pi }_{1/2}$, only one of which is under Fermi resonance. The vibrational radiative cooling rate of the vibrational state ($v_1{v}_2{v}_3$) = (2 0 0) in the electronic ground state $X{}^2\mathrm{\Pi }_{3/2}$, which couples with (1 2 0) via Fermi resonance, is determined through the excitation to a predissociation channel. Here, $v_1$, $v_2$, and $v_3$ represent the vibrational quantum numbers of NN–O stretching, N–N–O bending, and N–NO stretching, respectively. We successfully find that the vibrational radiative cooling rate for the (2 0 0) state of $X{}^2\mathrm{\Pi }_{3/2}$ is significantly slower than that of $X{}^2\mathrm{\Pi }_{1/2}$ without the Fermi resonance coupling.

We introduce a polarization-agnostic method for Gaussian-modulated coherent-state (GCMS) continuous-variable quantum key distribution (CVQKD). Due to the random and continuous nature of the GCMS protocol, Alice, the transmitter, can encode two distinct quadratures in each of two orthogonal polarization modes, such that Bob, the receiver, measures valid GCMS quadratures in a single polarization mode even when polarization changes occur during transmission. This method does not require polarization correction in the optical domain, does not require monitoring both polarization modes, reduces loss by eliminating optical components, and avoids the noise injected by polarization correction algorithms.

Multipartite entanglement plays a critical role in various applications of quantum internet. In these applications, the entanglement is usually shared by the distant parties. Experimentally, the distributed entanglement should be estimated by only local measurements. Furthermore, for network experiments, it is desirable to employ measurement techniques that are straightforward to implement. In this paper, we propose a method to measure arbitrary multipartite single-photon path entangled states by only local measurements. By considering practically reasonable assumptions, our method is relatively easy to implement. We experimentally demonstrate the utility of this method by reconstructing the density matrix of a 3-qubit $W$ state.