The small cross-section of Raman scattering poses a great challenge for its direct study at the single-molecule level. By exploiting the high Franck-Condon factor of a common-mode resonance, choosing a large vibrational frequency difference in electronic ground and excited states and operating at $T<2\mathrm{K}$, we succeed at driving a coherent stimulated Raman transition in individual molecules. We observe and model a spectral splitting that serves as a characteristic signature of the phenomenon at hand. Our study sets the ground for exploiting the intrinsic optomechanical degrees of freedom of molecules for applications in solid-state quantum optics and information processing.

We investigate deep-learning-unique first-order and second-order phase transitions, whose phenomenology closely follows that in statistical physics. In particular, we prove that the competition between prediction error and model complexity in the training loss leads to the second-order phase transition for deep linear nets with one hidden layer and the first-order phase transition for nets with more than one hidden layer. We also prove the linear origin theorem, which states that common deep nonlinear models are equivalent to a linear network of the same depth and connection structure close to the origin. Therefore, the proposed theory is directly relevant to understanding the optimization and initialization of neural networks and serves as a minimal model of the ubiquitous collapse phenomenon in deep learning.

Two hybrid quantum-classical reservoir computing models are presented to reproduce the low-order statistical properties of a two-dimensional turbulent Rayleigh-Bénard convection flow at a Rayleigh number $Ra={10}^5$ and Prandtl number $Pr=10$. These properties comprise the mean vertical profiles of the root mean square velocity and temperature and the turbulent convective heat flux. The latter is composed of vertical velocity and temperature and measures the global turbulent heat transfer across the convection layer; it manifests locally in coherent hot and cold thermal plumes that rise from the bottom and fall from the top boundaries. Both quantum algorithms differ by the arrangement of the circuit layers of the quantum reservoir, in particular the entanglement layers. The second of the two quantum circuit architectures, denoted H2, enables a complete execution of the reservoir update inside the quantum circuit without the usage of external memory. Their performance is compared with that of a classical reservoir computing model. Therefore, all three models have to learn the nonlinear and chaotic dynamics of the turbulent flow at hand in a lower-dimensional latent data space which is spanned by the time-dependent expansion coefficients of the 16 most energetic proper orthogonal decomposition (POD) modes. These training data are generated by a POD snapshot analysis from direct numerical simulations of the original turbulent flow. All reservoir computing models are operated in the reconstruction or open-loop mode, i.e., they receive three POD modes as an input at each step and reconstruct the 13 missing modes. We analyze different measures of the reconstruction error in dependence on the hyperparameters which are specific for the quantum cases or shared with the classical counterpart, such as the reservoir size and the leaking rate. We show that both quantum algorithms are able to reconstruct the essential statistical properties of the turbulent convection flow successfully with similar performance compared with the classical reservoir network. Most importantly, the quantum reservoirs are by a factor of four to eight smaller in comparison with the classical case.

We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e., integrals of motion. The core idea of the algorithm is based on the knowledge that the evolution of an integrable system in the phase space is restricted to a lower-dimensional submanifold. Limiting ourselves to polygon invariants of motion, we analyze the shape of individual trajectories thus successfully distinguishing integrable motion from chaotic cases. For example, our method rediscovers some of the famous McMillan-Suris integrable mappings and ultradiscrete Painlevé equations. In total, over 100 new integrable families are presented and analyzed; some of them are isolated in the space of parameters, and some of them are families with one parameter (or the ratio of parameters) being continuous or discrete. At the end of the paper, we suggest how newly discovered maps are related to a general 2D symplectic map via an introduction of discrete perturbation theory and propose a method on how to construct smooth near-integrable dynamical systems based on mappings with polygon invariants.

Light and matter can now interact in a regime where their coupling is stronger than their bare energies. This deep-strong coupling (DSC) regime of quantum electrodynamics promises to challenge many conventional assumptions about the physics of light and matter. Here we show how light-matter interactions in this regime give rise to electromagnetic nonlinearities dramatically different from those of naturally existing materials. Excitations in the DSC regime act as photons with a linear energy spectrum up to a critical excitation number, after which the system suddenly becomes strongly anharmonic, thus acting as an effective intensity-dependent nonlinearity of an extremely high order. We show that this behavior allows for N-photon blockade (with $N\gg 1$), enabling qualitatively new kinds of quantum light sources. For example, this nonlinearity forms the basis for a new type of gain medium, which when integrated into a laser or maser produces large Fock states (rather than coherent states). Such Fock states could in principle have photon numbers orders of magnitude larger than any realized previously, and would be protected from dissipation by a new type of equilibrium between nonlinear gain and linear loss. We discuss paths to experimental realization of the effects described here.

We investigate the phenomenon of Hilbert space fragmentation (HSF) in open quantum systems and find that it can stabilize highly entangled steady states. For concreteness, we consider the Temperley-Lieb model, which exhibits quantum HSF in an entangled basis, and investigate the Lindblad dynamics under two different couplings. First, we couple the system to a dephasing bath that reduces quantum fragmentation to a classical one with the resulting stationary state being separable. We observe that despite vanishing quantum correlations, classical correlations develop due to fluctuations of the remaining conserved quantities, which we show can be captured by a classical stochastic circuit evolution. Second, we use a coupling that preserves the quantum fragmentation structure. We derive a general expression for the steady state, which has a strong coherent memory of the initial state due to the extensive number of noncommuting conserved quantities. We then show that it is highly entangled as quantified by logarithmic negativity.

Since the discovery of superconductivity, the realization of room-temperature superconductivity has been the long dream of mankind. Recently, it has been reported that nitrogen-doped lutetium hydride has room-temperature superconductivity at near-ambient conditions. However, there is no solid evidence of such tantalizing superconductivity in nitrogen-doped lutetium hydride synthesized by follow-up experiments. The compositions and crystal structures of the nitrogen-doped lutetium hydride are still unclear. Therefore, we here systematically study the structural stability and electronic properties of $Fm\overline{3}m \mathrm{Lu}{\mathrm{H}}_3$ and N-doped $\mathit{Fm}\overline{3}m \mathrm{Lu}{\mathrm{H}}_3$, such as 1, 2, 3, 4, and 8% N, by first-principles calculations. Our further electronic properties calculations show that all the simulated Lu-N-H ternary compounds are metallic, except for a semiconducting phase of ${\mathrm{Lu}}_4{\mathrm{H}}_{11}\mathrm{N} \left(\mathrm{Lu}{\mathrm{H}}_{2.75}{\mathrm{N}}_{0.25}\right)$. Remarkably, the contribution of the H atoms to the electronic density of states at the Fermi level could be tuned by the increasing N concentration. Electron-phonon coupling calculations also show that both $\mathit{Fm}\overline{3}m \mathrm{Lu}{\mathrm{H}}_3$ and $\mathit{Pm}\overline{3}m {\mathrm{Lu}}_4{\mathrm{H}}_{11}\mathrm{N}$ are superconducting with critical temperature $T_c$'s of 23 and 32 K at 24 and 60 GPa, respectively. Our current results suggest that $\mathrm{Lu}{\mathrm{H}}_3$ and N-doped $\mathrm{Lu}{\mathrm{H}}_3$ could be potential superconductors only at high pressure, while the estimated $T_c$ values are much lower than room temperature.

Directing indistinguishable photons from one input port into separate output ports is a fundamental operation in quantum information processing. The simplest scheme for achieving routing beyond random chance uses the photon blockade effect of a two-level emitter. But this approach is limited by a time-energy uncertainty relation. We show that a linear optical unitary transformation applied after the atom enables splitting efficiencies that exceed this time-energy limit. We show that the linear optical unitary improves the splitting efficiency from 67% to 82% for unentangled photon inputs, and from 77% to 90% for entangled photon inputs. We then optimize the temporal mode profile of the entangled photon wave function to attain the optimal splitting efficiency of 92%, a significant improvement over previous limits derived using a two-level atom alone. These results provide a path towards optimizing single photon nonlinearities and engineering programmable and robust photon-photon interactions for practical, high-fidelity quantum operations.

In the context of adiabatic quantum computation (AQC), it has been argued that first-order quantum phase transitions (QPTs) due to localization phenomena cause AQC to fail by exponentially decreasing the minimal spectral gap of the Hamiltonian along the annealing path as a function of the qubit number. The vanishing of the spectral gap is often linked to the localization of the ground state in a local minimum, requiring the system to tunnel into the global minimum at a later stage of the annealing. Recent methods have been proposed to avoid this phenomenon by carefully designing the involved Hamiltonians. However, it remains a challenge to formulate a comprehensive theory of the effect of the various parameters and the conditions under which QPTs make the AQC algorithm fail. Equipped with concepts from graph theory, in this work we link graph quantities associated with the Hamiltonians along the annealing path with the occurrence of QPTs. These links allow us to derive bounds on the location of the minimal spectral gap along the annealing path, augmenting the toolbox for the analysis of strategies to improve the runtime of AQC algorithms.

As a simple way to enhance catalytical performance, it has long been believed that catalyst loading increases the number of sites available for reaction. The overall reaction rate will increase and saturate eventually as catalyst loading increases. Here, we report a counterintuitive optimal catalyst loading for electrocatalytic carbon dioxide reduction (${\mathrm{eCO}}_2\mathrm{R}$) on nanocatalysts. Numerical analysis based on a comprehensive kinetic model reveals that nanocurved electric field (NEF) resulted from the comparable size of nanocatalysts and the electric double layer can essentially affect ${\mathrm{eCO}}_2\mathrm{R}$. While NEF induces extra mass transfer raising the overall reaction rate for low catalyst loading, such extra mass transfer is sharply reduced due to the overlap of NEF for high catalyst loading. These findings challenge the conventional physical picture of loading-dependent overall catalytical performance, and provide a new concept for design of nanocatalysis.

The Mandelstam-Tamm and Margolus-Levitin quantum speed limits are two well-known evolution time estimates for isolated quantum systems. These bounds are usually formulated for fully distinguishable initial and final states, but both have tight extensions to systems that evolve between states with an arbitrary fidelity. However, the foundations of these extensions differ in some essential respects. The extended Mandelstam-Tamm quantum speed limit has been proven analytically and has a clear geometric interpretation. Furthermore, which systems saturate the limit is known. The derivation of the extended Margolus-Levitin quantum speed limit, on the other hand, is based on numerical estimates. Moreover, the limit lacks a geometric interpretation, and no complete characterization of the systems reaching it exists. In this paper, we derive the extended Margolus-Levitin quantum speed limit analytically and describe the systems that saturate the limit in detail. We also provide the limit with a symplectic-geometric interpretation, which indicates that it is of a different character than most existing quantum speed limits. At the end of the paper, we analyze the maximum of the extended Mandelstam-Tamm and Margolus-Levitin quantum speed limits and derive a dual version of the extended Margolus-Levitin quantum speed limit. The maximum limit is tight regardless of the fidelity of the initial and final states. However, the conditions under which the maximum limit is saturated differ depending on whether or not the initial state and the final state are fully distinguishable. The dual limit is also tight and follows from a time reversal argument. We describe the systems that saturate the dual quantum speed limit.

The electron's electric dipole moment (eEDM) can be determined by polarizing the spin of an atom or a molecule and then measuring the spin precession frequency in an applied electric field. Radiation is used to polarize the spin and then analyze the precession angle, and the measurement is often sensitive to the polarization of this radiation. We show how systematic errors can arise when both the polarization of the radiation and the magnitude of the electric field are imperfectly controlled. We derive approximate analytical expressions for these errors, confirm their accuracy numerically, and show how they can be corrected empirically. We consider spin manipulation using single-photon pulses, Raman pulses, and stimulated Raman adiabatic passage (STIRAP), and we show that STIRAP provides better immunity to these systematic errors. An experimental study of these errors partly supports our findings but also reveals another potential error that is not captured by this analysis.

A general quantum mechanical theory is developed for the isomeric excitation of ${}^{229}\mathrm{Th}$ in strong femtosecond laser pulses. The theory describes the tripartite interaction between the nucleus, the atomic electrons, and the laser field. The nucleus can be excited both by the laser field and by laser-driven electronic transitions. Numerical results show that strong femtosecond laser pulses are very efficient in exciting the ${}^{229}\mathrm{Th}$ nucleus, yielding nuclear excitation probabilities on the order of ${10}^{-11}$ per nucleus per pulse. Laser-driven electronic excitations are found to be more efficient than direct optical excitations.

RhPb was initially recognized as one of CoSn-like compounds with $P6/mmm$ symmetry, containing an ideal kagome lattice of $d$-block atoms. However, theoretical calculations predict the realization of the phonon soft mode, which leads to the kagome lattice distortion and stabilization of the structure with $P\overline{6}2m$ symmetry [A. Ptok et al., Phys. Rev. B 104, 054305 (2021)]. Here, we present the single crystal x-ray diffraction results supporting this prediction. Furthermore, we discuss the main dynamical properties of RhPb with $P\overline{6}2m$ symmetry, i.e. phonon dispersions and surface Green's functions using the modern theoretical methods based on density functional theory. The bulk phononic dispersion curves contain several flattened bands, Dirac nodal lines, and triple degenerate Dirac points. As a consequence, the phononic drumhead surface state is realized for the (100) surface, terminated by the zigzaglike edge of Pb honeycomb sublattice.

One of the outstanding problems in the holographic approach to many-body physics is the explicit computation of correlation functions in nonequilibrium states. We provide a new and simple proof that the horizon cap prescription of Crossley-Glorioso-Liu for implementing the thermal Schwinger-Keldysh contour in the bulk is consistent with the Kubo-Martin-Schwinger periodicity and the ingoing boundary condition for the retarded propagator at any arbitrary frequency and momentum. The generalization to the hydrodynamic Bjorken flow is achieved by a Weyl rescaling in which the dual black hole's event horizon attains a constant surface gravity and area at late time although the directions longitudinal and transverse to the flow expand and contract, respectively. The dual state's temperature and entropy density thus become constants (instead of the perfect fluid expansion) although no time-translation symmetry emerges at late time. Undoing the Weyl rescaling, the correlation functions can be computed systematically in a large proper time expansion in inverse powers of the average of the two reparametrized proper time arguments. The horizon cap has to be pinned to the nonequilibrium event horizon so that regularity and consistency conditions are satisfied. Consequently, in the limit of perfect fluid expansion, the Schwinger-Keldysh correlation functions with space-time reparametrized arguments are simply thermal at an appropriate temperature. A generalized bilocal thermal structure holds to all orders. We argue that the Stokes data (which are functions rather than constants) for the hydrodynamic correlation functions can decode the quantum fluctuations behind the horizon cap pinned to the evolving event horizon, and thus the initial data.

We devise a generic and experimentally accessible recipe to prepare boundary states of topological or nontopological quantum systems through an interplay between coherent Hamiltonian dynamics and local dissipation. Intuitively, our recipe harnesses the spatial structure of boundary states which vanish on sublattices where losses are suitably engineered. This yields unique nontrivial steady states that populate the targeted boundary states with infinite lifetimes while all other states are exponentially damped in time. Remarkably, applying loss only at one boundary can yield a unique steady state localized at the very same boundary. We detail our construction and rigorously derive full Liouvillian spectra and dissipative gaps in the presence of a spectral mirror symmetry for a one-dimensional Su-Schrieffer-Heeger model and a two-dimensional Chern insulator. We outline how our recipe extends to generic noninteracting systems.

We develop a nonperturbative formulation based on the Green's function quantization method that can describe spontaneous parametric down-conversion in the high-gain regime in nonlinear optical structures with arbitrary amount of loss and dispersion. This formalism opens the way for description and design of arbitrary complex and/or open nanostructured nonlinear optical systems in quantum technology applications, such as squeezed-light generation, nonlinearity-based quantum sensing, and hybrid quantum systems mediated by nonlinear interactions. As an example case, we numerically investigate the scenario of integrated quantum spectroscopy with undetected photons, in the high-gain regime, and uncover novel gain-dependent effects in the performance of the system.

Living systems are chiral on multiple scales, from constituent biopolymers to large scale morphology, and their active mechanics is both driven by chiral components and serves to generate chiral morphologies. We describe the mechanics of active fluid membranes in coordinate-free form, with focus on chiral contributions to the stress. These generate geometric “odd elastic” forces in response to mean curvature gradients but directed perpendicularly. As a result, they induce tangential membrane flows that circulate around maxima and minima of membrane curvature. When the normal viscous force amplifies perturbations the membrane shape can become linearly unstable giving rise to shape instabilities controlled by an active Scriven-Love number. We describe examples for spheroids, membranes tubes, and helicoids, discussing the relevance and predictions such examples make for a variety of biological systems from the subcellular to tissue level.