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This work discusses the problem of optimal excitation of a three-level atom of ladder-configuration by light in the two-photon state and coherent light carrying an average of two photons. The applied atom-light interaction model is based on the Wigner-Weisskopf approximation. We characterize the properties of the optimal two-photon state that excites an atom perfectly, i.e. with probability equal to one: We find that the spectro-temporal shape of the optimal state of light is determined by the lifetimes of the atomic states, with the degree of photonic entanglement in the optimal state depends on the lifetime ratio. In consequence, two distinct interaction regimes can be identified in which the entanglement of the input state of light has qualitatively different impact. As the optimal states may be challenging to prepare in general, we compare the results with those obtained for photon pairs of selected experimentally-relevant pulse shapes. As these shapes are optimized for maximal atomic excitation probability, the results can be interpreted in terms of the overlap between the optimal and investigated pulse shapes., Comment: 16 pages, 14 figures

We study a class of non-reversible, continuous-time random walks in random environments on $\mathbb{Z}^d$ that admit a cycle representation with finite cycle length. The law of the transition rates, taking values in $[0, \infty)$, is assumed to be stationary and ergodic with respect to space shifts. Moreover, the transition rate from $x$ to $y$, denoted by $c^\omega(x,y)$, is a superposition of non-negative random weights on oriented cycles that contain the edge $(x,y)$. We prove a quenched invariance principle under moment conditions that are comparable to the well-known p-q moment condition of Andres, Deuschel, and Slowik [2] for the random conductance model. A key ingredient in proving the sublinearity is an energy estimate for the non-symmetric generator. Our result extends that of Deuschel and K\"osters [12] beyond strong ellipticity and bounded cycle lengths.

The dressed atom approach provides a tool to investigate the dynamics of an atom-laser system by fully retaining the quantum nature of the coherent mode. In its standard derivation, the internal atom-laser evolution is described within the rotating-wave approximation, which determines a doublet structure of the spectrum and the peculiar fluorescence triplet in the steady state. However, the rotating wave approximation may fail to apply to atomic systems subject to femtosecond light pulses, light-matter systems in the strong-coupling regime or sustaining permanent dipole moments. This work aims to demonstrate how the general features of the steady-state radiative cascade are affected by the interaction of the dressed atom with propagating radiation modes. Rather than focusing on a specific model, we analyze how these features depend on the parameters characterizing the dressed eigenstates in arbitrary atom-laser dynamics, given that a set of general hypotheses is satisfied. Our findings clarify the general conditions in which a description of the radiative cascade in terms of transition between dressed states is self-consistent. We provide a guideline to determine the properties of photon emission for any atom-laser interaction model, which can be particularly relevant when the model should be tailored to enhance a specific line. We apply the general results to the case in which a permanent dipole moment is a source of low-energy emission, whose frequency is of the order of the Rabi coupling., Comment: 13 pages, 4 figures

Two-photon absorption in molecules, of significance for high-resolution imaging applications, is typically characterised with low cross sections. To enhance the TPA signal, one effective approach exploits plasmonic enhancement. For this method to be efficient, it must meet several criteria, including broadband operational capability and a high fluorescence rate to ensure effective signal detection. In this context, we introduce a novel plus-shaped silver nanostructure designed to exploit the coupling of bright and dark plasmonic modes. This configuration considerably improves both the absorption and fluorescence of molecules across near-infrared and visible spectra. By fine-tuning the geometrical parameters of the nanostructure, we align the plasmonic resonances with the optical properties of specific TPA-active dyes, i.e., ATTO 700, Rhodamine 6G, and ATTO 610. The expected TPA signal enhancement is evaluated using classical estimations based on the assumption of independent enhancement of absorption and fluorescence. These results are then compared with outcomes obtained in a quantum-mechanical approach to evaluate the stationary photon emission rate. Our findings reveal the important role of molecular saturation determining the regimes where either absorption or fluorescence enhancement leads to an improved TPA signal intensity, considerably below the classical predictions. The proposed nanostructure design not only addresses these findings, but also might serve for their experimental verification, allowing for active polarization tuning of the plasmonic response targeting the absorption, fluorescence, or both. The insight into quantum-mechanical mechanisms of plasmonic signal enhancement provided in our work is a step forward in the more effective control of light-matter interactions at the nanoscale.

We investigate the dynamics of polar systems coupled to classical external beams in the ultrastrong coupling regime. The permanent dipole moments (PDMs) sustained by polar systems can couple to the electromagnetic field, giving rise to a variety of processes such as difference-frequency and harmonic generation, reflected in complicated dynamics of the atomic system. Here, we demonstrate that the dynamics can be described simply in a dynamic reference frame. We derive a Jaynes-Cummings-like framework with effective parameters describing frequency shift, coupling strength with the driving field, and a rescaled relaxation rate. The familiar linear scaling of the interaction strength with the field amplitude is replaced with a nonlinear dependence, suggesting potential applications for improving the coherence of quantum system ensembles with permanent dipoles.

In this paper the total positivity of quasi-Riordan arrays is investigated with use of the sequence characterization of quasi-Riordan arrays. Due to the correlation between quasi-Riordan arrays and Riordan arrays, this study is an in-depth discussion of the total positivity of Riordan arrays.

In this paper we study the total positivity of almost-Riordan arrays $(d(t)|\, g(t), f(t))$ and establish its necessary conditions and sufficient conditions, particularly, for some well used formal power series $d(t)$. We present a semidirect product of an almost-array and use it to transfer a total positivity problem for an almost-Riordan array to the total positivity problem for a quasi-Riordan array. We find the sequence characterization of total positivity of the almost-Riordan arrays. The production matrix $J$ of an almost-Riordan array $(d|\, g,f)$ is presented so that $J$ is totally positive implies the total positivity of both the almost-Riordan array $(d|\, g,f)$ and the Riordan array $(g,f)$. We also present a counterexample to illustrate that this sufficient condition is not necessary. If the production matrix $J$ is tridiagonal, then the expressions of its principal minors are given. By using expressions, we find a sufficient and necessary condition of the total positivity of almost-Riordan arrays with tridiagonal production matrices. A numerous examples are given to demonstrate our results.

Quantifying the complex/multifractal organization of the brain signals is crucial to fully understanding the brain processes and structure. In this contribution, we performed the multifractal analysis of the electroencephalographic (EEG) data obtained from a controlled multiple sclerosis (MS) study, focusing on the correlation between the degree of multifractality, disease duration, and disability level. Our results reveal a significant correspondence between the complexity of the time series and multiple sclerosis development, quantified respectively by scaling exponents and the Expanded Disability Status Scale (EDSS). Namely, for some brain regions, a well-developed multifractality and little persistence of the time series were identified in patients with a high level of disability, whereas the control group and patients with low EDSS were characterised by persistence and monofractality of the signals. The analysis of the cross-correlations between EEG signals supported these results, with the most significant differences identified for patients with EDSS $> 1$ and the combined group of patients with EDSS $\leq 1$ and controls. No association between the multifractality and disease duration was observed, indicating that the multifractal organisation of the data is a hallmark of developing the disease. The observed complexity/multifractality of EEG signals is hypothetically a result of neuronal compensation -- i.e., of optimizing neural processes in the presence of structural brain degeneration. The presented study is highly relevant due to the multifractal formalism used to quantify complexity and due to scarce resting-state EEG evidence for cortical reorganization associated with compensation., Comment: 39 pages, including supplementary materials (11 figures, 4 tables)

Large multi-modal models (LMMs) hold the potential to usher in a new era of automated visual assistance for people who are blind or low vision (BLV). Yet, these models have not been systematically evaluated on data captured by BLV users. We address this by empirically assessing CLIP, a widely-used LMM likely to underpin many assistive technologies. Testing 25 CLIP variants in a zero-shot classification task, we find that their accuracy is 15 percentage points lower on average for images captured by BLV users than web-crawled images. This disparity stems from CLIP's sensitivities to 1) image content (e.g. not recognizing disability objects as well as other objects); 2) image quality (e.g. not being robust to lighting variation); and 3) text content (e.g. not recognizing objects described by tactile adjectives as well as visual ones). We delve deeper with a textual analysis of three common pre-training datasets: LAION-400M, LAION-2B and DataComp-1B, showing that disability content is rarely mentioned. We then provide three examples that illustrate how the performance disparities extend to three downstream models underpinned by CLIP: OWL-ViT, CLIPSeg and DALL-E2. We find that few-shot learning with as few as 5 images can mitigate CLIP's quality-of-service disparities for BLV users in some scenarios, which we discuss alongside a set of other possible mitigations., Comment: Accepted at 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

Readout errors contribute significantly to the overall noise affecting present-day quantum computers. However, the complete characterization of generic readout noise is infeasible for devices consisting of a large number of qubits. Here we introduce an appropriately tailored quantum detector tomography protocol, the so called Quantum Detector Overlapping Tomography, which enables efficient characterization of $k-$local cross-talk effects in the readout noise as the sample complexity of the protocol scales logarithmically with the total number of qubits. We show that QDOT data provides information about suitably defined reduced POVM operators, correlations and coherences in the readout noise, as well as allows to reconstruct the correlated clusters and neighbours readout noise model. Benchmarks are introduced to verify utility and accuracy of the reconstructed model. We apply our method to investigate cross-talk effects on 79 qubit Rigetti and 127 qubit IBM devices. We discuss their readout noise characteristics, and demonstrate effectiveness of our approach by showing superior performance of correlated clusters and neighbours over models without cross-talk in model-based readout error mitigation applied to energy estimation of MAX-2-SAT Hamiltonians, with the improvement on the order of 20% for both devices., Comment: comments and suggestions are welcome

We study continuous time random walks on $\mathbb{Z}^d$ (with $d \geq 2$) among random conductances $\{ \omega(\{x,y\}) : x,y \in \mathbb{Z}^d\}$ that permit jumps of arbitrary length. The law of the random variables $\omega(\{x,y\})$, taking values in $[0, \infty)$, is assumed to be stationary and ergodic with respect to space shifts. Assuming that the first moment of $\sum_{x \in \mathbb{Z}^d} \omega(\{0,x\}) |x|^2$ and the $q$-th moment of $1/\omega(0,x)$ for $x$ neighbouring the origin are finite for some $ q >d/2$, we show a quenched invariance principle and a quenched local limit theorem, where the moment condition is optimal for the latter. We also obtain H\"older regularity estimates for solutions of the heat equation for the associated non-local discrete operator, and deduce that the pointwise spectral dimension equals $d$ almost surely. Our results apply to random walks on long-range percolation graphs with connectivity exponents larger than $d+2$ when all nearest-neighbour edges are present., Comment: There is a gap in the proof of Proposition 4.2, step 3

In this paper we consider a time-continuous random walk in $\mathbb{Z}^d$ in a dynamical random environment with symmetric jump rates to nearest neighbours. We assume that these random conductances are stationary and ergodic and, moreover, that they are bounded from below but unbounded from above with finite first moment. We derive sharp on-diagonal estimates for the annealed first and second discrete space derivative of the heat kernel which then yield local limit theorems for the corresponding kernels. Assuming weak algebraic off-diagonal estimates, we then extend these results to the annealed Green function and its first and second derivative. Our proof which extends the result of Delmotte and Deuschel (2005) to unbounded conductances with first moment only, is an adaptation of the recent entropy method of Benjamini et. al. (2015)., Comment: 37 pages

We introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model on inhomogeneous dense random graphs and the randomly diluted Hopfield model. We are interested in quantitative estimates of metastability in large volumes at fixed temperatures when these systems evolve according to a Glauber dynamics, i.e.\ where spins flip with Metropolis transition probabilities at inverse temperature $\beta$. We identify conditions ensuring that with high probability the system behaves like the corresponding system where the random couplings are replaced by their averages. More precisely, we prove that the metastability of the former system is implied with high probability by the metastability of the latter. Moreover, we consider relevant metastable hitting times of the two systems and find the asymptotic tail behaviour and the moments of their ratio. This work provides an extension of the results known for the Ising model on the Erd\H{o}s--R{\'e}nyi random graph. The proofs use the potential-theoretic approach to metastability in combination with concentration inequalities., Comment: 30 pages