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In this work, we examine the consequences of the existence of a finite group of matrix product unitary (MPU) symmetries for matrix product states (MPS). We generalize the well-understood picture of onsite unitary symmetries, which give rise to virtual symmetry defects given by insertions of operators in the bonds of the MPS. In the MPU case, we can define analogous defect tensors, this time sitting on lattice sites, that can be created, moved, and fused by local unitary operators. We leverage this formalism to study the gauging of MPU symmetries. We introduce a condition, block independence, under which we can gauge the symmetries by promoting the symmetry defects to gauge degrees of freedom, yielding an MPS of the same bond dimension that supports a local version of the symmetry given by commuting gauge constraints. Whenever block independence does not hold (which happens, in particular, whenever the symmetry representation is anomalous), a modification of our method which we call state-level gauging still gives rise to a locally symmetric MPS by promotion of the symmetry defects, at the expense of producing gauge constraints that do not commute on different sites., Comment: 28 pages

Global sensing enables parameter estimation across arbitrary parameter ranges with a finite number of shots. While various formulations exist, the Bayesian paradigm offers a flexible approach to optimal protocol design under minimal assumptions. However, there are several sets of assumptions capturing the notions of prior ignorance and uninformed estimation, leading to two main approaches: invariance of the prior distribution under specific parameter transformations, and adherence to the geometry of a state space. While the first approach often leads to simpler priors and estimators and is more broadly applicable in adaptive settings, the second can lead to faster posterior convergence in a well-defined measurement setting. We examine the practical consequences of both approaches and show how to apply them in examples of rate and coherence estimation in noisy scenarios. More importantly, by employing the notion of location-isomorphic parameters, we unify the two approaches into a practical and versatile framework for optimal global quantum sensing, detailing when and how each set of assumptions should be employed - a blueprint for the design of quantum sensors., Comment: 17 pages, 5 figures

We consider a linear array of trapped ions subjected to local parametric modulation of the trapping potential and continuous laser cooling. In our model, the phase of the parametric modulation varies linearly along the array, breaking time-reversal symmetry and inducing non-trivial topological effects. The linear response to an external force is investigated with the Green's function formalism. We predict the appearance of topological amplification regimes in which the trapped ion array behaves as a directional amplifier of vibrational excitations. The emergence of topological phases is determined by a winding number related to non-Hermitian point-gap topology. Beyond its fundamental interests as a topological driven-dissipative system, our setup can be used for quantum sensing of ultra-weak forces and electric fields. We consider a scheme in which a trapped ion at one edge of the array acts as a sensor of an ultra-weak force, and the vibrational signal gets amplified towards the last trapped ion, which acts as a detector. We consider arrays of 2-30 $^{25}$Mg$^+$ ions, assuming that the detector ion's displacement is measured via fluorescence with a spatial resolution of 200-500 nm, and predict sensitivities as small as 1 yN $\cdot$ Hz$^{-1/2}$. Our system has the advantage that the detected force frequency can be tuned by adjusting the frequency of the periodic drive., Comment: 17 pages, 17 figures

Confining electromagnetic fields inside an optical cavity can enhance the light-matter coupling between quantum materials embedded inside the cavity and the confined photon fields. When the interaction between the matter and the photon fields is strong enough, even the quantum vacuum field fluctuations of the photons confined in the cavity can alter the properties of the cavity-embedded solid-state materials at equilibrium and room temperature. This approach to engineering materials with light avoids fundamental issues of laser-induced transient matter states. To clearly differentiate this field from phenomena in driven systems, we call this emerging field cavity materials engineering. In this review, we first present theoretical frameworks, especially, ab initio methods, for describing light-matter interactions in solid-state materials embedded inside a realistic optical cavity. Next, we overview a few experimental breakthroughs in this domain, detailing how the ground state properties of materials can be altered within such confined photonic environments. Moreover, we discuss state-of-the-art theoretical proposals for tailoring material properties within cavities. Finally, we outline the key challenges and promising avenues for future research in this exciting field., Comment: 75 pages, 8 figures

We identify a property of the local tensors of matrix product states (MPS) that guarantees that their parent Hamiltonians satisfy the intersection property. The intersection property ensures that the ground space consists of MPS, with degeneracy bounded by the square of the bond dimension. The new local property, dubbed stability, generalizes (block) injectivity and is satisfied by the MPS tensors that construct the W state, domain wall superposition states, and their generalizations.

We perform extensive simulations of the two-dimensional cavity-coupled electron gas in a modulating potential as a minimal model for cavity quantum materials. These simulations are enabled by a newly developed quantum-electrodynamical (QED) auxiliary-field quantum Monte Carlo method. We present a procedure to greatly reduce finite-size effects in such calculations. Based on our results, we show that a modified version of weak-coupling perturbation theory is remarkably accurate for a large parameter region. We further provide a simple parameterization of the light-matter correlation energy as a functional of the cavity parameters and the electronic density. These results provide a numerical foundation for the development of the QED density functional theory, which was previously reliant on analytical approximations, to allow quantitative modeling of a wide range of systems with light-matter coupling., Comment: 6 pages, 3 figures

Embedding materials in optical cavities has emerged as an intriguing perspective for controlling quantum materials, but a key challenge lies in measuring properties of the embedded matter. Here, we propose a framework for probing strongly correlated cavity-embedded materials through direct measurements of cavity photons. We derive general relations between photon and matter observables inside the cavity, and show how these can be measured via the emitted photons. As an example, we demonstrate how the entanglement phase transition of an embedded H$_2$ molecule can be accessed by measuring the cavity photon occupation, and showcase how dynamical spin correlation functions can be accessed by measuring dynamical photon correlation functions. Our framework provides an all-optical method to measure static and dynamic properties of cavity-embedded materials., Comment: 5 pages, 3 figures + supplemental material (20 pages)

Projected entangled pair states (PEPS) are very useful in the description of strongly correlated systems, partly because they allow encoding symmetries, either global or local (gauge), naturally. In recent years, PEPS with local symmetries have increasingly been used in the study of non-perturbative regimes of lattice gauge theories, most prominently as a way to construct variational ansatz states depending only on a small number of parameters and yet capturing the relevant physical properties. For the case of one-dimensional PEPS (Matrix Product States - MPS) a bidirectional connection was established between the internal structure of the tensor network, i.e. the mathematical properties of the constituent tensors, and the symmetry. In higher dimensions this has only been done for global symmetries, where in the local (gauge) case it is known only how to construct gauge-invariant states, but not what the symmetry implies on the internal structure of the PEPS. In the present work we complete this missing piece and study the internal structure of projected entangled pair states with a gauge symmetry. The PEPS we consider consist of matter and gauge field tensors placed on the vertices and edges, respectively, of arbitrary graphs., Comment: 24 pages, 4 figures; included example section

Quantum-enhanced sensors, which surpass the standard quantum limit (SQL) and approach the fundamental precision limits dictated by quantum mechanics, are finding applications across a wide range of scientific fields. This quantum advantage becomes particularly significant when a large number of particles are included in the sensing circuit. Achieving such enhancement requires introducing and preserving entanglement among many particles, posing significant experimental challenges. In this work, we integrate concepts from Floquet theory and quantum information to design an entangler capable of generating the desired entanglement between two paths of a quantum interferometer. We demonstrate that our path-entangled states enable sensing beyond the SQL, reaching the fundamental Heisenberg limit (HL) of quantum mechanics. Moreover, we show that a decoding parity measurement maintains the HL when specific conditions from Floquet theory are satisfied$\unicode{x2013}$particularly those related to the periodic driving parameters that preserve entanglement during evolution. We address the effects of a priori phase uncertainty and imperfect transmission, showing that our method remains robust under realistic conditions. Finally, we propose a superconducting-circuit implementation of our sensor in the microwave regime, highlighting its potential for practical applications in high-precision measurements.

Bayesian methods promise enhanced device performance and accelerated data collection. We demonstrate an adaptive Bayesian measurement strategy for atom number estimation in a quantum technology experiment, utilising a symmetry-informed loss function. Compared to a standard unoptimised strategy, our method yields a five-fold reduction in the fractional variance of the atom number estimate. Equivalently, it achieves the target precision with a third of the data points previously required. We provide general expressions for the optimal estimator and error for any quantity amenable to symmetry-informed strategies, facilitating the application of these strategies in quantum computing, communication, metrology, and the wider quantum technology sector., Comment: 6 + 5 pages, 3 + 2 figures, 1 + 1 tables. Updated references and minor revisions

We propose a systematic framework to construct a (d+1)-dimensional stabilizer model from an initial generic d-dimensional abelian symmetry. Our approach builds upon the iterative gauging procedure, developed by one of the authors in [J. Garre-Rubio, Nature Commun. 15, 7986 (2024)], in which an initial symmetric state is repeatedly gauged to obtain an emergent model in one dimension higher that supports the initial symmetry at its boundary. This method not only enables the construction of emergent states and corresponding commuting stabilizer Hamiltonians of which they are ground states, but it also provides a way to construct gapped boundary conditions for these models that amount to spontaneously breaking part of the boundary symmetry. In a detailed introductory example, we showcase our paradigm by constructing three-dimensional Clifford-deformed surface codes from iteratively gauging a global 0-form symmetry that lives in two dimensions. We then provide a proof of our main result, hereby drawing upon a slight extension of the gauging procedure of Williamson. We additionally provide two more examples in d=2 in which different type-I fracton orders emerge from gauging initial linear subsystem and Sierpinski fractal symmetries. En passant, we provide explicit tensor network representations of all of the involved gauging maps and the emergent states.

We present a series of algorithms in tensor networks for anomaly detection in datasets, by using data compression in a Tensor Train representation. These algorithms consist of preserving the structure of normal data in compression and deleting the structure of anomalous data. The algorithms can be applied to any tensor network representation. We test the effectiveness of the methods with digits and Olivetti faces datasets and a cybersecurity dataset to determine cyber-attacks., Comment: 10 pages, 13 figures

The field of Quantum Computation is plagued by issues that limit the implementation and development of quantum systems and quantum algorithms. Issues which force the development of Hybrid Quantum-Classical algorithms, such as the quantum DisCoCat implementation for Natural Language Processing. These require a high processing cost and are susceptible to errors due to Out of Vocabulary words. In this work, we develop a framework to implement Few Shot Learning for Quantum Natural Language Processing, by modifying the encoding ans\"atze and dividing it into two parts, the first one leveraging the vast corpus of classical training already available, and the second variationally training on the task. This framework is then put to the test to explore its behaviour and its power in extracting as much useful work from each call to a quantum system as possible.

Engineering phases of matter in cavities requires effective light-matter coupling strengths that are on the same order of magnitude as the bare system energetics, coined the ultra-strong coupling regime. For models of itinerant electron systems, which do not have discrete energy levels, a clear definition of this regime is outstanding to date. Here we argue that a change of the electronic mass exceeding $10\%$ of its bare value may serve as such a definition. We propose a quantitative computational scheme for obtaining the electronic mass in relation to its bare vacuum value and show that coupling to surface polariton modes can induce such mass changes. Our results have important implications for cavity design principles that enable the engineering of electronic properties with quantum light., Comment: 5 pages, 3 figes + Supplement: 4 pages, 1 figure

Polaritonic chemistry has garnered increasing attention in recent years due to pioneering experimental results, which show that site- and bond-selective chemistry at room temperature is achievable through strong collective coupling to field fluctuations in optical cavities. Despite these notable experimental strides, the underlying theoretical mechanisms remain unclear. In this focus review, we highlight a fundamental theoretical link between the seemingly unrelated fields of polaritonic chemistry and spin glasses, exploring its profound implications for the theoretical framework of polaritonic chemistry. Specifically, we present a mapping of the dressed electronic structure problem under collective vibrational strong coupling to the iconic Sherrington-Kirkpatrick model of spin glasses. This mapping uncovers a collectively induced instability in the dressed electronic structure (spontaneous replica symmetry breaking), which could provide the long-sought seed for significant local chemical modifications in polaritonic chemistry. This mapping paves the way to incorporate, adjust and probe numerous spin glass concepts in polaritonic chemistry, such as frustration, aging dynamics, excess of thermal fluctuations, time-reversal symmetry breaking or stochastic resonances. Ultimately, the mapping also offers fresh insights into the applicability of spin glass theory beyond condensed matter systems and it suggests novel theoretical directions such as polarization glasses with explicitly time-dependent order parameter functions.

In this work we explore theoretically whether a parity-violating/chiral light-matter interaction is required to capture all relevant aspects of chiral polaritonics or if a parity-conserving/achiral theory is sufficient (e.g. long-wavelength/dipole approximation). This question is non-trivial to answer, since achiral theories (Hamiltonians) still possess chiral solutions. To elucidate this fundamental theoretical question, a simple GaAs quantum ring model is coupled to an effective chiral mode of a single-handedness optical cavity in dipole approximation. The bare matter GaAs quantum ring possesses a non-degenerate ground state and a doubly degenerate first excited state. The chiral or achiral nature (superpositions) of the degenerate excited states remains undetermined for an isolated matter system. However, inside our parity-conserving description of a chiral cavity, we find that the dressed eigenstates automatically (ab-initio) attain chiral character and become energetically discriminated based on the handedness of the cavity. In contrast, the non-degenerate bare matter state (ground state) does not show an energetic discrimination inside a chiral cavity within dipole approximation. Nevertheless, our results suggest that the handedness of the cavity can still be imprinted onto these states (e.g. angular momentum and chiral current densities). Overall, above findings highlight the relevance of degenerate states in chiral polaritonics. In particular, because recent theoretical results for linearly polarized cavities indicate the formation of a frustrated and highly-degenerate electronic ground-state under collective strong coupling conditions, which, likewise, is expected to form in chiral polaritonics and thus could be prone to chiral symmetry breaking effects.

We study the statistics of domain wall excitations in quantum spin chains. We focus on systems with finite symmetry groups represented by matrix product unitaries (MPUs), i.e. finite depth quantum circuits. Such symmetries can be anomalous, in which case gapped phases which they support must break the symmetry. The lowest lying excitations of those systems are thus domain wall excitations. We investigate the behavior of these domain walls under exchange, and find that they can exhibit non-trivial exchange statistics. This statistics is completely determined by the anomaly of the symmetry, and we provide a direct relation between the known classification of MPU symmetry actions on ground states and the domain wall statistics. Already for the simplest case of a $\mathbb Z_2$ symmetry, we obtain that the presence of an anomalous MPU symmetry gives rise to domain wall excitations which behave neither as bosons nor as fermions, but rather exhibit fractional statistics. Finally, we show that the exchange statistics of domain walls is a physically accessible quantity, by devising explicit measurement operators through which it can be determined., Comment: v2: A few typos corrected

The propagation of errors severely compromises the reliability of quantum computations. The quantum adiabatic algorithm is a physically motivated method to prepare ground states of classical and quantum Hamiltonians. Here, we analyze the proliferation of a single error event in the adiabatic algorithm. We give numerical evidence using tensor network methods that the intrinsic properties of adiabatic processes effectively constrain the amplification of errors during the evolution for geometrically local Hamiltonians. Our findings indicate that low energy states could remain attainable even in the presence of a single error event, which contrasts with results for error propagation in typical quantum circuits., Comment: 6+3 pages, 4+2 figures, comments welcome

We consider the classification problem of quantum spin chains invariant under local decomposable group actions, covering matrix product unitaries (MPUs), using an operator algebraic approach. We focus on finite group symmetries hosting both symmetric and symmetry broken phases. The local-decomposable group actions we consider have a 3-cocycle class of the symmetry group associated to them. We derive invariants for our classification that naturally cover one-dimensional symmetry protected topological (SPT) phases. We prove that these invariants coincide with the ones of [J. Garre Rubio et al, Quantum 7, 927 (2023)] using matrix product states (MPSs) techniques, by explicitly working out the GNS representation of MPSs and MPUs, resulting in a useful dictionary between both approaches that could be of independent interest.

Gauging introduces gauge fields in order to localize an existing global symmetry, resulting in a dual global symmetry on the gauge fields that can be gauged again. By iterating the gauging process on spin chains with Abelian group symmetries and arranging the gauge fields in a 2D lattice, the local symmetries become the stabilizer of the $XZZX$-code for any Abelian group. By twisting the gauging map we obtain new codes that explicitly confine anyons, which violate an odd number of plaquette terms and whose fusion results in mobile dipole excitations. Our construction naturally realizes any gapped boundary by taking different quantum phases of the initial (1+1)D globally symmetric system. Our method establishes a new route to obtain higher dimensional topological codes from lower ones, to identify their gapped boundaries and their tensor network representations., Comment: Short version: 5+3 pages. Complete boundary study and new bulk Hamiltonian using twisted gauging

Pure dephasing and spontaneous emission are two non-unitary processes of atoms or spins interacting with fluctuating electromagnetic (EM) modes. The dissipative collective emission processes (e.g., superradiance) originate from interactions with EM modes in resonance with atoms and have received considerable attention. Meanwhile, the analogous non-dissipative collective dephasing phenomena mediated by EM environments remain poorly understood. Here, we introduce the nano-EM super-dephasing phenomenon arising in the photonic environments near materials. We show that collective dephasing in this nano-EM environment is enhanced by over 10 orders of magnitude compared to free space or cavities. This giant enhancement originates from long-range correlations in off-resonant, low-frequency evanescent EM fluctuations, which lead to collectively accelerated (super-) or suppressed (sub-) dephasing in many-body entangled states. We further unravel that nano-EM collective dephasing exhibits universal interaction ranges near materials with different anisotropy that can be reciprocal or non-reciprocal. This nano-EM interaction range, which is not present in free-space and cavities, leads to unique scaling laws of super-dephasing in GHZ states different from the conventional $N^2$ scaling of superradiance. Finally, we discuss how to experimentally isolate and control super-dephasing to open interesting frontiers for scalable quantum systems., Comment: 5 pages (main text) + 12 pages (appendices), 8 figures

We study dynamical (quasi)-condensation in the Fermi-Hubbard model starting from a completely uncorrelated initial state of adjacent doubly occupied sites. We show that upon expansion of the system in one dimension, dynamical (quasi)-condensation occurs not only for large interactions via the condensation of doublons, but also for small interactions. The behavior of the system is distinctly different in the two parameter regimes, underlining a different mechanism at work. We address the question whether the dynamical (quasi-)condensation effect persists in the thermodynamic limit. For this purpose, we use the two-particle reduced density matrix method, which allows the extension to large system sizes, long propagation times, and two-dimensional (2D) systems. Our results indicate that the effect vanishes in the thermodynamic limit. However, especially in 2D, further investigation beyond numerically tractable system sizes calls for the use of quantum simulators, for which we show that the described effect can be investigated by probing density fluctuations., Comment: 15 pages, 13 figures

Combining quantum and Bayesian principles leads to optimality in metrology, but the optimisation equations involved are often hard to solve. This work mitigates this problem with a novel class of measurement strategies for quantities isomorphic to location parameters, which are shown to admit a closed-form optimisation. The resulting framework admits any parameter range, prior information, or state, and the associated estimators apply to finite samples. As an example, the metrology of relative weights is formulated from first principles and shown to require hyperbolic errors. The primary advantage of this approach lies in its simplifying power: it reduces the search for good strategies to identifying which symmetry leaves a state of maximum ignorance invariant. This will facilitate the application of quantum metrology to fundamental physics, where symmetries play a key role., Comment: 6 pages, 1 figure, 1 table. Accepted as a Letter in Physical Review A

Quantum-electrodynamical density-functional theory (QEDFT) provides a promising avenue for exploring complex light-matter interactions in optical cavities for real materials. Similar to conventional density-functional theory, the Kohn-Sham formulation of QEDFT needs approximations for the generally unknown exchange-correlation functional. In addition to the usual electron-electron exchange-correlation potential, an approximation for the electron-photon exchange-correlation potential is needed. A recent electron-photon exchange functional [C. Sch\"afer et al., Proc. Natl. Acad. Sci. USA, 118, e2110464118 (2021), https://www.pnas.org/doi/abs/10.1073/pnas.2110464118], derived from the equation of motion of the non-relativistic Pauli-Fierz Hamiltonian, shows robust performance in one-dimensional systems across weak- and strong-coupling regimes. Yet, its performance in reproducing electron densities in higher dimensions remains unexplored. Here we consider this QEDFT functional approximation from one to three-dimensional finite systems and across weak to strong light-matter couplings. The electron-photon exchange approximation provides excellent results in the ultra-strong-coupling regime. However, to ensure accuracy also in the weak-coupling regime across higher dimensions, we introduce a computationally efficient renormalization factor for the electron-photon exchange functional, which accounts for part of the electron-photon correlation contribution. These findings extend the applicability of photon-exchange-based functionals to realistic cavity-matter systems, fostering the field of cavity QED (quantum electrodynamics) materials engineering., Comment: 15 pages, 4 figures

Despite recent numerical evidence, one of the fundamental theoretical mysteries of polaritonic chemistry is how and if collective strong coupling can induce local changes of the electronic structure to modify chemical properties. Here we present non-perturbative analytic results for a model system consisting of an ensemble of $N$ harmonic molecules under vibrational strong coupling (VSC) that alters our present understanding of this fundamental question. By applying the cavity Born-Oppenheimer partitioning on the Pauli-Fierz Hamiltonian in dipole approximation, the dressed many-molecule problem can be solved self-consistently and analytically in the dilute limit. We discover that the electronic molecular polarizabilities are modified even in the case of vanishingly small single-molecule couplings. Consequently, this non-perturbative local polarization mechanism persists even in the large-$N$ limit. In contrast, a perturbative calculation of the polarizabilities leads to a qualitatively erroneous scaling behavior with vanishing effects in the large-$N$ limit. Nevertheless, the exact (self-consistent) polarizabilities can be determined from single-molecule strong coupling simulations instead. Our fundamental theoretical observations demonstrate that hitherto existing collective-scaling arguments are insufficient for polaritonic chemistry and they pave the way for refined single- (or few-) molecule strong-coupling ab-initio simulations of chemical systems under collective strong coupling.

When light and matter interact strongly, the coupled system inherits properties from both constituents. It is consequently possible to alter the properties of either by engineering the other. This intriguing possibility has lead to the emergence of the cavity-materials-engineering paradigm which seeks to tailor material properties by engineering the fluctuations of a dark electromagnetic environment. The theoretical description of hybrid light-matter systems is complicated by the combined complexity of a realistic description of the extended electronic and quantum electromagnetic fields. Here we derive an effective, non-perturbative theory for low dimensional crystals embedded in a paradigmatic Fabry-P\'erot resonator in the long-wavelength limit. The theory encodes the multi-mode nature of the electromagnetic field into an effective single-mode scheme and it naturally follows from requiring a negligible momentum transfer from the photonic system to the matter. Crucially, in the effective theory the single light mode is characterized by a finite effective mode volume even in the limit of bulk cavity-matter systems and can be directly determined by realistic cavity parameters. As a consequence, the coupling of the effective mode to matter remains finite for bulk materials. By leveraging on the realistic description of the cavity system we make our effective theory free from the double counting of the coupling of matter to the electromagnetic vacuum fluctuations of free space. Our results provide a substantial step towards the realistic description of interacting cavity-matter systems at the level of the fundamental Hamiltonian, by effectively including the electromagnetic environment and going beyond the perfect mirrors approximation.

The development of quantum-gas microscopes has brought novel ways of probing quantum degenerate many-body systems at the single-atom level. Until now, most of these setups have focused on alkali atoms. Expanding quantum-gas microscopy to alkaline-earth elements will provide new tools, such as SU(N)-symmetric fermionic isotopes or ultranarrow optical transitions, to the field of quantum simulation. Here, we demonstrate the site-resolved imaging of a $^{84}$Sr bosonic quantum gas in a Hubbard-regime optical lattice. The quantum gas is confined by a two-dimensional in-plane lattice and a light-sheet potential, which operate at the strontium clock-magic wavelength of 813.4 nm. We realize fluorescence imaging using the broad 461 nm transition, which provides high spatial resolution. Simultaneously, we perform attractive Sisyphus cooling with the narrow 689 nm intercombination line. We reconstruct the atomic occupation from the fluorescence images, obtaining imaging fidelities above 94%. Finally, we realize a $^{84}$Sr superfluid in the Bose-Hubbard regime. We observe its interference pattern upon expansion, a probe of phase coherence, with single-atom resolution. Our strontium quantum-gas microscope provides a new platform to study dissipative Hubbard models, quantum optics in atomic arrays, and SU(N) fermions at the microscopic level., Comment: 11 pages, 6 figures

Parametric resonances and amplification have led to extraordinary photoinduced phenomena in pump-probe experiments. While these phenomena manifest themselves in out-of-equilibrium settings, here, we present the striking result of parametric amplification in equilibrium. In particular, we demonstrate that quantum and thermal fluctuations of a Raman-active mode amplifies light inside a cavity, at equilibrium, when the Raman mode frequency is twice the cavity mode frequency. This noise-driven amplification leads to the creation of an unusual parametric Raman polariton, intertwining the Raman mode with cavity squeezing fluctuations, with smoking gun signatures in Raman spectroscopy. In the resonant regime, we show the emergence of not only quantum light amplification but also localization and static shift of the Raman mode. Apart from the fundamental interest of equilibrium parametric amplification our study suggests a resonant mechanism for controlling Raman modes and thus matter properties by cavity fluctuations. We conclude by outlining how to compute the Raman-cavity coupling, and suggest possible experimental realization, Comment: as accepted in PRL

In this study, we conducted a detailed investigation into the time evolution of the probability density within a 1D double-well potential hosting a Bose-Fermi mixture. This system comprised spinless bosons and spin one-half fermions with weak repulsive contact interactions. Notably, even at very low effective coupling constants, periodic probabilities were observed, indicating correlated tunneling of both bosons and fermions, leading to complete miscibility, which disappears when an external electric field is turned on. The electric field accentuated fermion-fermion interactions due to the Pauli exclusion principle, altering both boson density and interactions and leading to spatial redistribution of particles. These findings underscore the complex interplay between interactions, external fields, and spatial distributions within confined quantum systems. Our exploration of higher interaction strengths revealed conditions under which probability density functions are decoupled. Furthermore, we observed that increased fermion interaction, driven by the electric field, led to higher tunneling frequencies for both species because of the repulsive nature of the boson-fermion interaction. Conversely, increased boson-boson interaction resulted in complete tunneling of both species, especially when boson density was high, leading to effective fermion repulsion. Expanding our analysis to scenarios involving four bosons demonstrated that higher interaction values corresponded to increased oscillation frequencies in tunneling probabilities. Finally, by manipulating interaction parameters and activating the electric field, we achieved complete tunneling of both species, further increasing oscillation frequencies and resulting in intervals characterized by overlapping probability functions.

The exchange-only virial relation due to Levy and Perdew is revisited. Invoking the adiabatic connection, we introduce the exchange energy in terms of the right-derivative of the universal density functional w.r.t. the coupling strength $\lambda$ at $\lambda=0$. This agrees with the Levy-Perdew definition of the exchange energy as a high-density limit of the full exchange-correlation energy. By relying on $v$-representability for a fixed density at varying coupling strength, we prove an exchange-only virial relation without an explicit local-exchange potential. Instead, the relation is in terms of a limit ($\lambda \searrow 0$) involving the exchange-correlation potential $v_\mathrm{xc}^\lambda$, which exists by assumption of $v$-representability. On the other hand, a local-exchange potential $v_\mathrm{x}$ is not warranted to exist as such a limit.

In this work we investigate the effects that multi-mode photonic environments, e.g., optical cavities, have on the properties of quantum matter. We highlight the importance of the non-perturbative mass renormalization procedure for ab initio quantum electrodynamics simulations and how it connects to common approximations used in polaritonic chemistry and cavity materials engineering. We focus on one-dimensional systems which can be solved exactly for large number of photon modes. First, we apply mass renormalization to free particles. The value of the renormalized mass depends on the details of the photonic environment and on the number of particles. We then show how the multi-mode photon field influences various ground- and excited-state properties of atomic and molecular systems. For instance, we observe the enhancement of particle confinement in the binding potential for the atomic system, and the modification of the potential energy surfaces of the molecular dimer due to photon-mediated long-range interactions. We also highlight how these changes compare to the common free-space mass-renormalization approximation employed in electronic structure theory and quantum chemistry. Since such phenomena are enhanced under strong light-matter coupling in a cavity environment they will become relevant for the emerging fields of polaritonic chemistry and cavity materials engineering., Comment: 19 pages, 18 figures

Coherent control over electron dynamics in atoms and molecules using high-intensity circularly-polarized laser pulses gives rise to current loops, resulting in the emission of magnetic fields. We propose and demonstrate with ab-initio calculations ``current-gating" schemes to generate direct or alternating-current magnetic pulses in the infrared spectral region, with highly tunable waveform and frequency, and showing femtosecond-to-attosecond pulse duration. In optimal conditions, the magnetic pulse can be highly isolated from the driving laser and exhibits a high flux density ($\sim1$ Tesla at few hundred nanometers from the source, with a pulse duration of 787 attoseconds) for application in forefront experiments of ultrafast spectroscopy. Our work paves the way toward the generation of attosecond magnetic fields to probe ultrafast magnetization, chiral responses, and spin dynamics., Comment: Main text (7 pages including references, 3 figures), Supplementary material (8 pages, 3 figures)

Photon statistics of an optical field can be used for quantum optical sensing in low light level scenarios free of bulky optical components. However, photon-number-resolving detection to unravel the photon statistics is challenging. Here, we propose a novel detection approach, that we call `photon discerning', which uses adaptive photon thresholding for photon statistical estimation without recording exact photon numbers. Our photon discerner is motivated by the field of neural networks where tunable thresholds have proven efficient for isolating optimal decision boundaries in machine learning tasks. The photon discerner maximizes Fisher information per photon by iteratively choosing the optimal threshold in real-time to approach the shot noise limit. Our proposed scheme of adaptive photon thresholding leads to unique remote-sensing applications of quantum DoLP (degree of linear polarization) camera and quantum LiDAR. We investigate optimal thresholds and show that the optimal photon threshold can be counter-intuitive (not equal to 1) even for weak signals (mean photon number much less than 1), due to the photon bunching effect. We also put forth a superconducting nanowire realization of the photon discerner which can be experimentally implemented in the near-term. We show that the adaptivity of our photon discerner enables it to beat realistic photon-number-resolving detectors with limited photon-number resolution. Our work suggests a new class of detectors for information-theory driven, compact, and learning-based quantum optical sensing., Comment: 12 pages, 9 figures

Experimental studies indicate that optical cavities can affect chemical reactions, through either vibrational or electronic strong coupling and the quantized cavity modes. However, the current understanding of the interplay between molecules and confined light modes is incomplete. Accurate theoretical models, that take into account inter-molecular interactions to describe ensembles, are therefore essential to understand the mechanisms governing polaritonic chemistry. We present an ab-initio Hartree-Fock ansatz in the framework of the cavity Born-Oppenheimer approximation and study molecules strongly interacting with an optical cavity. This ansatz provides a non-perturbative, self-consistent description of strongly coupled molecular ensembles taking into account the cavity-mediated dipole self-energy contributions. To demonstrate the capability of the cavity Born-Oppenheimer Hartree-Fock ansatz, we study the collective effects in ensembles of strongly coupled diatomic hydrogen fluoride molecules. Our results highlight the importance of the cavity-mediated inter-molecular dipole-dipole interactions, which lead to energetic changes of individual molecules in the coupled ensemble.

An important goal of modern condensed matter physics involves the search for states of matter with new emergent properties and desirable functionalities. Although the tools for material design remain relatively limited, notable advances have been recently achieved by controlling interactions at hetero-interfaces, precise alignment of low-dimensional materials and the use of extreme pressures . Here, we highlight a new paradigm, based on controlling light-matter interactions, which provides a new way to manipulate and synthesize strongly correlated quantum matter. We consider the case in which both electron-electron and electron-photon interactions are strong and give rise to a variety of novel phenomena. Photon-mediated superconductivity, cavity-fractional quantum Hall physics and optically driven topological phenomena in low dimensions are amongst the frontiers discussed in this perspective, which puts a spotlight on a new field that we term here "strongly-correlated electron-photon science.", Comment: 15 pages, 5 figures

We demonstrate that collective vibrational strong coupling of molecules in thermal equilibrium can give rise to significant local electronic polarizations in the thermodynamic limit. We do so by first showing that the full non-relativistic Pauli-Fierz problem of an ensemble of strongly-coupled molecules in the dilute-gas limit reduces in the cavity Born-Oppenheimer approximation to a cavity-Hartree equation for the electronic structure. Consequently, each individual molecule experiences a self-consistent coupling to the dipoles of all other molecules, which amount to non-negligible values in the thermodynamic limit (large ensembles). Thus collective vibrational strong coupling can alter individual molecules strongly for localized "hotspots" within the ensemble. Moreover, the discovered cavity-induced polarization pattern possesses a zero net polarization, which resembles a continuous form of a spin glass (or better polarization glass). Our findings suggest that the thorough understanding of polaritonic chemistry, requires a self-consistent treatment of dressed electronic structure, which can give rise to numerous, so far overlooked, physical mechanisms.

The emerging field of strongly coupled light-matter systems has drawn significant attention in recent years due to the prospect of altering physical and chemical properties of molecules and materials. Because this emerging field draws on ideas from both condensed-matter physics and quantum optics, it has attracted attention from theoreticians from both fields. While the former employ accurate descriptions of the electronic structure of the matter the description of the electromagnetic environment is often oversimplified. Contrastingly, the latter often employs sophisticated descriptions of the electromagnetic environment, while using simple few-level approximations for the matter. Both approaches are problematic because the oversimplified descriptions of the electronic system are incapable of describing effects such as light-induced structural changes, while the oversimplified descriptions of the electromagnetic environments can lead to unphysical predictions because the light-matter interactions strengths are misrepresented. Here we overcome these shortcomings and present the first method which can quantitatively describe both the electronic system and general electromagnetic environments from first principles. We realize this by combining macroscopic QED (MQED) with Quantum Electrodynamical Density-functional Theory. To exemplify this approach, we consider an absorbing spherical cavity and study the impact of different parameters of both the environment and the electronic system on the transition from weak-to-strong coupling for different aromatic molecules. As part of this work, we also provide an easy-to-use tool to calculate the cavity coupling strengths for simple cavity setups. Our work is a step towards parameter-free ab initio calculations for strongly coupled quantum light-matter systems and will help bridge the gap between theoretical methods and experiments in the field.

The effect of spin-orbit (and Darwin) interaction on a 2D electron gas subject to a radial symmetric, inhomogeneous $1/r$-magnetic field is discussed analytically in a perturbative and non-perturbative manner. For this purpose, we investigate the radial Hall conductivity that emerges from an additional homogeneous electric field perturbation perpendicular to the 2D electron gas, which solely interacts via spin-orbit coupling. Numerical calculations of the absorptive spin-orbit spectra show for an ideal InSb electron gas a behaviour that is dominated by the localized (atomic) part of the distorted Landau levels. In contrast, however, we also find analytically that a (non-local) divergent static response emerges for Fermi energies close to the ionization energy in the thermodynamic limit. The divergent linear response implies that the external electric field is entirely absorbed outside the 2D electron gas by induced radial spin-orbit currents, as it would be the case inside a perfect conductor. This spin-orbit induced polarization mechanism depends on the effective $g^*$-factor of the material for which it shows a critical behaviour at $g^*_c=2$, where it abruptly switches direction. The diverging absorption relies on the presence of degenerate energies with allowed selection rules that are imposed by the radial symmetry of our inhomogeneous setup. We show analytically the presence of a discrete Rydberg-like band structure that obeys these symmetry properties. In a last step, we investigate the robustness of the spectra by solving analytically the Dirac equation expanded up to order $1/(mc)^2$. We find that the distorted Landau-levels, and thus the divergent spin-orbit polarization, remain protected with respect to slow changes of the applied $1/r$-magnetic field.

Strong light-matter interactions as realized in an optical cavity provide a tantalizing opportunity to control the properties of condensed matter systems. Inspired by experimental advances in cavity quantum electrodynamics and the fabrication and control of two-dimensional magnets, we investigate the fate of a quantum critical antiferromagnet coupled to an optical cavity field. Using unbiased quantum Monte Carlo simulations, we compute the scaling behavior of the magnetic structure factor and other observables. While the position and universality class are not changed by a single cavity mode, the critical fluctuations themselves obtain a sizable enhancement, scaling with a fractional exponent that defies expectations based on simple perturbation theory. The scaling exponent can be understood using a generic scaling argument, based on which we predict that the effect may be even stronger in other universality classes. Our microscopic model is based on realistic parameters for two-dimensional magnetic quantum materials and the effect may be within the range of experimental detection., Comment: 16 pages, 10 figures

Quantum computing has emerged as a promising platform for simulating strongly correlated systems in chemistry, for which the standard quantum chemistry methods are either qualitatively inaccurate or too expensive. However, due to the hardware limitations of the available noisy near-term quantum devices, their application is currently limited only to small chemical systems. One way for extending the range of applicability can be achieved within the quantum embedding approach. Herein, we employ the projection-based embedding method for combining the variational quantum eigensolver (VQE) algorithm, although not limited to, with density functional theory (DFT). The developed VQE-in-DFT method is then implemented efficiently on a real quantum device and employed for simulating the triple bond breaking process in butyronitrile. The results presented herein show that the developed method is a promising approach for simulating systems with a strongly correlated fragment on a quantum computer. The developments as well as the accompanying implementation will benefit many different chemical areas including the computer aided drug design as well as the study of metalloenzymes with a strongly correlated fragment.

We present a scheme to enhance the atom number in magneto-optical traps of strontium atoms operating on the 461 nm transition. This scheme consists of resonantly driving the $^1$S$_0\to^3$P$_1$ intercombination line at 689 nm, which continuously populates a short-lived reservoir state and, as expected from a theoretical model, partially shields the atomic cloud from losses arising in the 461 nm cooling cycle. We show a factor of two enhancement in the atom number for the bosonic isotopes $^{88}$Sr and $^{84}$Sr, and the fermionic isotope $^{87}$Sr, in good agreement with our model. Our scheme can be applied in the majority of strontium experiments without increasing the experimental complexity of the apparatus, since the employed 689 nm transition is commonly used for further cooling. Our method should thus be beneficial to a broad range of quantum science and technology applications exploiting cold strontium atoms, and could be extended to other atomic species., Comment: 10 pages, 6 figures, 4 tables. Accepted version

In this work, we use the quantum-jump approach to study light-matter interactions in a four-level scheme giving rise to frequency up-conversion amplification without inversion (AWI). The results obtained apply to the case of neutral Hg vapour where, recently, it has been reported AWI of a probe field in the UV regime, opening the way for lasing without inversion in this range of frequencies. We show that, in this scheme, the key element to obtain maximum amplification is the fulfillment of the three-photon resonance condition, which favors coherent evolution periods associated with the probe field gain. We also investigate the parameter values in order to optimize amplification. The present study extends the theoretical understanding of the underlying mechanisms involved in AWI., Comment: 10 pages, 9 figures

Several quantum hardware platforms, while being unable to perform fully fault-tolerant quantum computation, can still be operated as analogue quantum simulators for addressing many-body problems. However, due to the presence of errors, it is not clear to what extent those devices can provide us with an advantage with respect to classical computers. In this work we consider the use of noisy analogue quantum simulators for computing physically relevant properties of many-body systems both in equilibrium and undergoing dynamics. We first formulate a system-size independent notion of stability against extensive errors, which we prove for Gaussian fermion models, as well as for a restricted class of spin systems. Remarkably, for the Gaussian fermion models, our analysis shows the stability of critical models which have long-range correlations. Furthermore, we analyze how this stability may lead to a quantum advantage, for the problem of computing the thermodynamic limit of many-body models, in the presence of a constant error rate and without any explicit error correction.

In this review we present the theoretical foundations and first principles frameworks to describe quantum matter within quantum electrodynamics (QED) in the low-energy regime. Having a rigorous and fully quantized description of interacting photons, electrons and nuclei/ions, from weak to strong light-matter coupling regimes, is pivotal for a detailed understanding of the emerging fields of polaritonic chemistry and cavity materials engineering. The use of rigorous first principles avoids ambiguities and problems stemming from using approximate models based on phenomenological descriptions of light, matter and their interactions. By starting from fundamental physical and mathematical principles, we first review in great detail non-relativistic QED, which allows to study polaritonic systems non-perturbatively by solving a Schr\"odinger-type equation. The resulting Pauli-Fierz quantum field theory serves as a cornerstone for the development of computational methods, such as quantum-electrodynamical density functional theory, QED coupled cluster or cavity Born-Oppenheimer molecular dynamics. These methods treat light and matter on equal footing and have the same level of accuracy and reliability as established methods of computational chemistry and electronic structure theory. After an overview of the key-ideas behind those novel ab initio QED methods, we explain their benefits for a better understanding of photon-induced changes of chemical properties and reactions. Based on results obtained by ab initio QED methods we identify the open theoretical questions and how a so far missing mechanistic understanding of polaritonic chemistry can be established. We finally give an outlook on future directions within polaritonic chemistry and first principles QED and address the open questions that need to be solved in the next years both from a theoretical as well as experimental viewpoint.

The levitation of nanoparticles is essential in various branches of research. Casimir forces are natural candidates to tackle it but the lack of broadband metamaterials precluded repulsive forces in vacuum. We show sub-micron nanoparticle levitation in vacuum only based on the design of a broadband metamaterial perfect magnetic conductor surface, where the force is mostly given by the (quantum) zero-point contribution. In the harmonic regime of the center of mass dynamics, the characteristic frequency depends linearly on Planck's constant $\hbar$ while independent of the nanoparticle's volume., Comment: 6 pages manuscript, with 3 figures; and 9 pages supplementary material, with 2 figures

Portfolio optimization is an important process in finance that consists in finding the optimal asset allocation that maximizes expected returns while minimizing risk. When assets are allocated in discrete units, this is a combinatorial optimization problem that can be addressed by quantum and quantum-inspired algorithms. In this work we present an integer simulated annealing method to find optimal portfolios in the presence of discretized convex and non-convex cost functions. Our algorithm can deal with large size portfolios with hundreds of assets. We introduce a performance metric, the time to target, based on a lower bound to the cost function obtained with the continuous relaxation of the combinatorial optimization problem. This metric allows us to quantify the time required to achieve a solution with a given quality. We carry out numerical experiments and we benchmark the algorithm in two situations: (i) Monte Carlo instances are started at random, and (ii) the algorithm is warm-started with an initial instance close to the continuous relaxation of the problem. We find that in the case of warm-starting with convex cost functions, the time to target does not grow with the size of the optimization problem, so discretized versions of convex portfolio optimization problems are not hard to solve using classical resources. We have applied our method to the problem of re-balancing in the presence of non-convex transaction costs, and we have found that our algorithm can efficiently minimize those terms., Comment: 9 pages, 3 figures

Gauging a global symmetry of a system amounts to introducing new degrees of freedom whose transformation rule makes the overall system observe a local symmetry. In quantum systems there can be obstructions to gauging a global symmetry. When this happens the symmetry is dubbed anomalous. Such obstructions are related to the fact that the global symmetry cannot be written as a tensor product of local operators. In this manuscript we study non-local symmetries that have an additional structure: they take the form of a matrix product operator (MPO). We exploit the tensor network structure of the MPOs to construct local operators from them satisfying the same group relations, that is, we are able to localize even anomalous MPOs. For non-anomalous MPOs, we use these local operators to explicitly gauge the MPO symmetry of a one-dimensional quantum state obtaining non-trivial gauged states. We show that our gauging procedure satisfies all the desired properties as the standard on-site case does. We also show how this procedure is naturally represented in matrix product states protected by MPO symmetries. In the case of anomalous MPOs, we shed light on the obstructions to gauging these symmetries., Comment: 13 pages, 1 figure v2: minor typos corrected, projection to ungauge added and section with examples added