There has recently been a growing effort to understand the physics and intricate dynamics of many-body and many-state (multimode) interacting bosonic systems in a comprehensive manner. For instance, in photonics, nonlinear multimode fibers are being intensely investigated nowadays due to their promise for ultrahigh-bandwidth and high-power capabilities. Similar prospects are being pursued in connection with magnon Bose-Einstein (BE) condensates, and ultracold atoms in periodic lattices for room-temperature quantum devices and quantum computation, respectively. While it is practically impossible to monitor the phase space of such complex systems (classically or quantum mechanically), thermodynamics has succeeded in predicting their thermal state: the Rayleigh-Jeans (RJ) distribution for classical fields and the BE distribution for quantum systems. These distributions are monotonic and promote either the ground state or the most excited mode. Here, we demonstrate the possibility to advance the participation of other modes in the thermal state of bosonic oligomers. The resulting nonmonotonic modal occupancies are described by a microcanonical treatment, while they deviate drastically from the RJ/BE predictions of canonical and grand-canonical ensembles. Our results provide a paradigm of ensemble equivalence violation and can be used for designing the shape of thermal states.

Recent progress in the design and optimization of neural-network quantum states (NQSs) has made them an effective method to investigate ground-state properties of quantum many-body systems. In contrast to the standard approach of training a separate NQS from scratch at every point of the phase diagram, we demonstrate that the optimization of a NQS at a highly expressive point of the phase diagram (i.e., close to a phase transition) yields features that can be reused to accurately describe a wide region across the transition. We demonstrate the feasibility of our approach on different systems in one and two dimensions by initially pretraining a NQS at a given point of the phase diagram, followed by fine-tuning only the output layer for all other points. Notably, the computational cost of the fine-tuning step is very low compared to the pretraining stage. We argue that the reduced cost of this paradigm has significant potential to advance the exploration of strongly correlated systems using NQS, mirroring the success of fine-tuning in machine learning and natural language processing.

Lattice-based cryptography has emerged as one of the most prominent candidates for postquantum cryptography, projected to be secure against the imminent threat of large-scale fault-tolerant quantum computers. The Shortest Vector Problem (SVP) is to find the shortest nonzero vector in a given lattice. It is fundamental to lattice-based cryptography and believed to be hard even for quantum computers. We study a natural generalization of the SVP known as the $K$-Densest Sublattice Problem ($K$-DSP): to find the densest $K$-dimensional sublattice of a given lattice. We formulate $K$-DSP as finding the first excited state of a $Z$-basis Hamiltonian, making $K$-DSP amenable to investigation via an array of quantum algorithms, including Grover search, quantum Gibbs sampling, adiabatic, and variational quantum algorithms. The complexity of the algorithms depends on the basis through which the input lattice is presented. We present a classical polynomial-time algorithm that takes an arbitrary input basis and preprocesses it into inputs suited to quantum algorithms. With preprocessing, we prove that $O\left(K{N}^2\right)$ qubits suffice for solving $K$-DSP for $N$-dimensional input lattices. We empirically demonstrate the performance of a quantum approximate optimization algorithm $K$-DSP solver for low dimensions, highlighting the influence of a good preprocessed input basis. We then discuss the hardness of $K$-DSP in relation to the SVP, to see if there is a reason to build postquantum cryptography on $K$-DSP. We devise a quantum algorithm that solves $K$-DSP with runtime exponent $\left(5KN{log}_{2}N\right)/2$. Therefore, for fixed $K, K$-DSP is no more than polynomially harder than the SVP. The central insight we use is similar in spirit to those underlying the best-known classical $K$-DSP algorithm due to Dadush and Micciancio. Whether the exponential dependence on $K$ can be lowered remains an open question.

The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit compilation, or Monte Carlo sampling. We introduce two ideas for the time-efficient approximation of matrix exponentials of linear multiparametric Hamiltonians. We modify the Suzuki-Trotter product formula from an approximation to an interpolation scheme to improve both accuracy and walltime. This allows us to achieve high fidelities within a single interpolation step, which can be computed directly from cached matrices. Furthermore, we define the interpolation on a grid of system parameters, and show that the interpolation infidelity converges with fourth-order accuracy in the number of interpolation bins.

Starting with Hedin's equations, simple expressions for the irreducible self-energy are derived. The derivation with vertex effects included in the self-energy results in a number of terms beyond $GW$ such as second-order screened exchange (the term that also gives rise to vertex/excitonic effects in the polarization) and an infinite series describing correlations between the added-particle (removed-hole) and the excited electrons and holes: the screened $T$-matrix channels. Two-body correlated propagation is considered, with the third propagating freely, however, three-body correlations are discussed and these can be added hierarchically to the method. For electron-hole propagation, the reducible polarization is calculated, which results in an expression for the self-energy that can be solved analytically without the need for widely used expensive numerical methods for frequency integration or having to adopt the plasmon-pole approximation. The method requires diagonalization of the usual particle-hole matrix—derived from the Bethe-Salpter equation—and also a particle-particle$+\mathrm{hole}$-hole matrix that has a similar structure; with the second-order exchange present in all channels. The method goes beyond current widely used methods that adopt the $GW$ approximation, whilst being ab initio in nature and requiring relatively modest extensions to existing functionality, e.g., it could be implemented in the sophisticated quasiparticle self-consistent framework. It is anticipated the method will significantly improve on the accuracy of current state-of-the-art calculations, improving our understanding of processes in simple and strongly correlated systems, with the additional contributions demanding a similar cost to methods that include vertex effects in the polarization only.

Single-sized clusters of ${\mathrm{Ag}}_{309}^{-}$ are accumulated within a digital Paul trap and exposed to intense optical laser pulses, leading to the formation of nanoplasmas of known initial conditions, not yet feasible. Using field-free diagnostics, the resulting Coulomb explosion is analyzed, giving electron distributions and charge-state resolved ion energy spectra. Experiments on the well-defined target result in comprehensive information on the particle emission and reveals details of nanoplasma dynamics not available before. These are for example the particle size-specific intensity-dependent transition towards a fully ionized plasma state as well as the subtle interplay between electron and ion dynamics, which becomes apparent in the intensity-dependent development of maximum and average values of energy and charge state.

Real-world systems are shaped by both their complex internal interactions and the changes in their noisy environments. In this work, we study how a shared active bath affects the statistical dependencies between two interacting Brownian particles by evaluating their mutual information. We decompose the mutual information into three terms: information stemming from the internal interactions between the particles; information induced by the shared bath, which encodes environmental changes; a term describing information interference that quantifies how the combined presence of both internal interactions and environment either masks (destructive interference) or boosts (constructive interference) information. By studying exactly the case of linear interactions, we find that the sign of information interference depends solely on that of the internal coupling. However, when internal interactions are described by a nonlinear activation function, we show that both constructive and destructive interference appear depending on the interplay between the timescale of the active environment, the internal interactions, and the environmental coupling. Finally, we show that our results generalize to hierarchical systems where asymmetric couplings to the environment mimic the scenario where the active bath is only partially accessible to one particle. This setting allows us to quantify how this asymmetry drives information interference. Our work underscores how information and functional relationships in complex multiscale systems are fundamentally shaped by the environmental context.

The spatial and spectral distributions of terahertz (THz) pulses emitted by two-color air plasmas are theoretically investigated for focused laser pulses and in the filamentation regime. We derive a so-called augmented conical emission model, which, like the one proposed by You et al. [Phys. Rev. Lett. 109, 183902 (2012)], involves phase matching between laser harmonics along the plasma channel, the plasma density and length, and the emitted frequency as key parameters. Our augmented model, however, treats envelope effects and accounts for transverse variations of both plasma- and Kerr-driven potential THz emitters. We highlight the importance of the characteristic spatiospectral distributions of these two conversion mechanisms in the expression of the angular radiated power. The results of our model are successfully compared with data provided by a comprehensive, fully space- and time-resolved unidirectional solver. Importantly, these numerical simulations clear up the effective plasma length along which THz emission develops, compared with the dephasing length over which the laser fundamental and second harmonic shift out-of-phase. The impact of common optical aberrations, such as sphericity, astigmatism, and coma, on the THz generation is also investigated. Aberrations are shown to generally decrease the laser-to-THz conversion efficiency and potentially induce spatial asymmetries and narrowing of the THz spectra.

In quantum mechanics, supersymmetry (SUSY) posits an equivalence between two elementary degrees of freedom, bosons, and fermions defined by local rules. Here we apply it to find connections between bosonic and fermionic lattice models in the realm of condensed-matter physics and uncover a novel fivefold way topology it demands in these systems. At the single-particle level, our connections pair a bosonic and fermionic lattice model, either describing the hopping of number-conserving particles or local couplings between fermion parity-conserving particles. The pair are isospectral except for zero modes, such as flat bands, quadratic band touchings, and nexus points, whose existence is undergirded by the Witten index of the SUSY theory. We develop a unifying framework to formulate these SUSY connections in terms of general lattice graph correspondences. Notably, in this framework, the supercharge operator that generates SUSY is Hermitian and can itself be interpreted as a hopping Hamiltonian on a bipartite lattice, a feature that enables the discovery of materials or model lattices hosting the SUSY partners. To illustrate the power of SUSY, we present 16 use cases of SUSY, that span topics including frustrated magnets, Kitaev spin liquids, and topological superconductors, the majority of which turn out to provide insights into the discovery and design of flat bands and topological materials.

We demonstrate two-dimensional arrays of Bose-Einstein condensates (BECs) as a new experimental platform with parallel quantum simulation capability. A defect-free array of up to 49 BECs is formed by loading a single BEC with $50000$ atoms into $7\times 7$ optical wells. Each BEC is prepared with independent phases, confirmed by matterwave interference. Based on BEC arrays, we realize fast determination of the phase boundary of BECs with attractive interactions. We also observe the stochastic collapse dynamics from the distribution of atom numbers in the array. We show that the collapse of a BEC can occur much faster than the averaged decay of an ensemble. The BEC arrays enable new forms of experiments to drastically increase the measurement throughput and to quantum simulate, say, large 2D Josephson-junction arrays.

Fano resonances are ubiquitous phenomena appearing in many fields of physics, e.g., atomic or molecular photoionization, or electron transport in quantum dots. Recently, attosecond interferometric techniques have been used to measure the amplitude and phase of photoelectron wave packets close to Fano resonances in argon and helium, allowing for the retrieval of the temporal dynamics of the photoionization process. In this work, we study the photoionization of argon atoms close to the $3s^{1}3p^{6}4p$ autoionizing state using an interferometric technique with high spectral resolution. The phase shows a monotonic $2\pi$ variation across the resonance or a nonmonotonic less than $\pi$ variation depending on experimental conditions, e.g., the probe laser bandwidth. Using three different, state-of-the-art calculations, we show that the measured phase is influenced by the interaction between final states reached by two-photon transitions.

We show that matter-wave diffraction off a single standing laser wave can be used as an accurate measurement scheme for photophysical molecular parameters. These include state-dependent optical polarizabilities and photon-absorption cross sections, the relaxation rates for fluorescence, internal conversion, and intersystem crossing, as well as ionization or cleavage probabilities. We discuss how the different photophysical processes manifest as features of the interference pattern, and we determine the accuracy of molecular parameters estimated from a realistic measurement with finite particle numbers. The analysis is based on an analytic calculation in Wigner representation, which accounts for the laser-induced coherent and incoherent dynamics, for the finite longitudinal and transverse coherence in the matter-wave beam, the gravitational and Coriolis acceleration, and an imperfect standing laser wave.

Communication complexity is a fundamental aspect of information science, concerned with the amount of communication required to solve a problem distributed among multiple parties. The standard quantification of one-way communication complexity relies on the minimal dimension of the communicated systems. In this paper, we measure the communication complexity of a task by the minimal distinguishability required to accomplish it, while leaving the dimension of the communicated systems unconstrained. Distinguishability is defined as the maximum probability of correctly guessing the sender's input from the message, quantifying the message's distinctiveness relative to the sender's input. This measure becomes especially relevant when maintaining the confidentiality of the sender's input is essential. After establishing the generic framework, we focus on three relevant families of communication complexity tasks—the random access codes, equality problems defined by graphs, and the pair-distinguishability tasks. We derive general lower bounds on the minimal classical distinguishability as a function of the success metric of these tasks. We demonstrate that quantum communication outperforms classical communication presenting explicit protocols and utilizing semidefinite programming methods. In particular, we demonstrate unbounded quantum advantage for random access codes and Hadamard graph-based equality problems. Specifically, we show that the classical-to-quantum ratio of minimal distinguishability required to achieve the same success metric escalates polynomially and exponentially with the complexity of these tasks, reaching arbitrarily large values.

Addressing the optical clock transition of alkaline-earth-like atoms has garnered increasing interest in the context of a future redefinition of the Système International second, as well as for fundamental physics based on inertial sensors. To be accessible in bosonic alkaline-earth-like atoms, this transition necessitates external coupling. Here we propose a scheme utilizing midinfrared to deep-infrared optical dressing to drive a three-level coherence that mixes into and therefore addresses the optical clock transition of bosonic alkaline-earth-like atoms.

Optical quantum sensing promises measurement precision beyond classical sensors termed the Heisenberg limit (HL). However, conventional methodologies often rely on prior knowledge of the target system to achieve HL, presenting challenges in practical applications. Addressing this limitation, we introduce an innovative deep-learning-based quantum sensing scheme (DQS), enabling optical quantum sensors to attain HL in agnostic environments. DQS incorporates two essential components: a graph neural network (GNN) predictor and a trigonometric interpolation algorithm. Operating within a data-driven paradigm, DQS utilizes the GNN predictor, trained on offline data, to unveil the intrinsic relationships between the optical setups employed in preparing the probe state and the resulting quantum Fisher information (QFI) after interaction with the agnostic environment. This distilled knowledge facilitates the identification of optimal optical setups associated with maximal QFI. Subsequently, DQS employs a trigonometric interpolation algorithm to recover the unknown parameter estimates for the identified optical setups. Extensive experiments are conducted to investigate the performance of DQS under different settings up to eight photons. Our findings not only offer a different lens through which to accelerate optical quantum sensing tasks but also catalyze future research integrating deep learning and quantum mechanics.

Communications in space are rapidly increasing in both capacity and extension. A satellite network in space calls for efficient and lightweight optical transmitters, suitable to communicate over distances going from the low-Earth-orbit to interplanetary links and beyond. To this aims, here we study the use of novel resources as an array of nanoptical coupler from guided sources and modulators to free space modes, that is phased with a suitable correction systems as well as efficient coding with error corrections capable of bearing large values of losses. We develop a method for designing such an array, which achieve a main lobe divergence of 1 $\mu \mathrm{rad}$. We also discuss the lower and upper limits of the beam steering technique as a function of the array and emitter size, respectively. The optimization of grating couples (GCs) resulted an apodized structure with approximately $0.7$ coupling efficiency and 70-$\mu \mathrm{m}$ beam waist. We also demonstrate the feasibility of phase correction and polarization modulation of the output mode by means of metalenses. The resulting link budget in terms of received photons on the Earth sets exceptional conditions for the digital optical communication system, for which a power efficient modulation scheme such as pulse position modulation (PPM) is considered. Here, we assess the PPM performance and we propose suitable channel coding schemes, essential to reduce the high bit error rate obtained in few-photon regime at the receiver.