We obtain time-resolved spectra of spontaneous emission and resonance fluorescence of a single multilevel emitter where two antiparallel transitions interfere and cause quantum beats. After rising as a single broad peak, the spontaneous emission spectrum turns into a doublet of subnatural peaks and then fades for long times. For strong field resonance fluorescence, the beat signature is the formation of doublet sidebands, which initially grow asymmetrically but end up symmetrical. We stress the filter bandwidth's crucial role in the spectral resolution and causal evolution.

The single-photon Raman interaction has emerged as a promising tool for deterministic photon subtraction, acting as a photon-activated switch in which the first arriving photon renders the system transparent to subsequent photons. Here, we employ the input-output formalism to perform a single-photon transport analysis within a photon subtractor consisting of a three-level quantum emitter coupled to a bimodal cavity-waveguide system. The analysis provides the frequency response of the system and reveals how it is affected by the key physical parameters of the cavity modes, such as coupling strengths and decay rates. We utilize these results to calculate the probability of successful photon subtraction from pulses of different temporal shapes, durations, and carrier frequencies. Subsequent analysis combines the input-output formalism with the quantum trajectory method to numerically verify the analytical findings as well as to assess the impact of photon number of the input pulse on the subtractor's performance. Our findings highlight the single-photon model's capability in predicting the system's response to multiphoton inputs in the pulsed regime as well as its potential utility in the design of efficient single-photon subtractors.

Continuous-time Markov processes are governed by the Chapman-Kolmogorov differential equation. We show that replacing the standard time derivative of the governing equation with a Caputo fractional derivative of order $0<\alpha <1$, leads to a fractional differential equation whose solution can describe the state probabilities of a class of non-Markovian stochastic processes. We show that the same state probabilities also solve a system of equations that describe semi-Markov processes in which the sojourn times follow a Mittag-Leffler distribution, contrasting the usual Markov processes with exponentially distributed sojourn times. We apply the fractional framework to the $\varepsilon \text{−}\mathrm{SIS}$ epidemic process on any contact graph and we propose a microscopic epidemic description in which infection and curing events follow a Mittag-Leffler distribution and are not independent. We analytically prove that the description exactly solves the fractional extension of the Chapman-Kolmogorov differential equation, and we provide an extensive study of how the dependence between events strongly affects the dynamics of the spreading process. We conclude verifying the proposed framework with Monte Carlo simulations.

Precision measurements of gravitational acceleration, or gravimetry, enable the testing of physical theories and find numerous applications in geodesy and space exploration. By harnessing quantum effects, high-precision sensors can achieve sensitivity and accuracy far beyond their classical counterparts when using the same number of sensing resources. Therefore, developing gravimeters with quantum-enhanced sensitivity is essential for advancing theoretical and applied physics. While novel quantum gravimeters have already been proposed for this purpose, the ultimate sensing precision, known as the Heisenberg limit, remains largely elusive. Here, we demonstrate that the gravimetry precision of a conditional displacement spin-mechanical system increases quadratically with the number of spins: a Heisenberg-limited spin-mechanical gravimeter. In general, the gravitational parameter is dynamically encoded into the entire entangled spin-mechanical probe. However, at some specific times, the mechanical degree of freedom disentangles from the spin subsystem, transferring all the information about the gravitational acceleration to the spin subsystem. Hence, we prove that a feasible spin magnetization measurement can reveal the ultimate gravimetry precision at such disentangling times. We predict an absolute gravimetry uncertainty of ${10}^{-11}{\text{m/s}}^2$ to ${10}^{-6}{\text{m/s}}^2$, without relying on free-fall methodologies, ground-state cooling of the mechanical object, and robust against spin-mechanical coupling anisotropies.

We study the transport of self-propelled noninteracting active Brownian particles and run-and-tumble particles in long tubes of varying widths. Using a moment expansion, we construct a generalized Fick-Jacobs framework for the active particles when the tube width is large and slowly varying. We show that the variation of the particle density along the tube is well described by a one-dimensional generalized entropy potential. This potential resembles its passive counterpart, albeit with an effective temperature and an effective tube width that are renormalized by the activity. Our generalized entropy potential approach allows us to predict the steady-state density distribution along the tube as well as the mean-escape time out of a spindle chamber. Finally, we show how to account for the emergence of spontaneous ratchet flows in asymmetric channels by including higher-order corrections neglected in the effective entropy potential approach.

Alternative computing paradigms open the door to exploiting recent innovations in computational hardware to probe the fundamental thermodynamic limits of information processing. One such paradigm employs superconducting quantum interference devices (SQUIDs) to execute classical computations. This, though, requires constructing sufficiently complex superconducting circuits that support a suite of useful information processing tasks and storage operations, as well as understanding these circuits' energetics. First-principles circuit design leads to prohibitive algebraic complications when deriving the effective equations of motion—complications that to date have precluded achieving these goals, let alone doing so efficiently. We circumvent these complications by (i) specializing our class of circuits and physical operating regimes, (ii) synthesizing existing derivation techniques to suit these specializations, and (iii) implementing solution-finding optimizations which facilitate physically interpreting circuit degrees of freedom that respect physically grounded constraints. This leads to efficient and practical circuit prototyping, as well as accessing scalable circuit architectures. The analytical efficiency is demonstrated by reproducing the potential energy landscape generated by a SQUID. We then show how inductively coupling two SQUIDs produces a device that is capable of executing two-bit computations via its composite potential energy landscape. More generally, the synthesized methods detailed here provide a basis for constructing universal logic gates and investigating their thermodynamic performance.

Synthetic gauge fields have provided physicists with a unique tool to explore a wide range of fundamentally important phenomena. However, most experiments have focused on synthetic vector gauge fields. The very rich physics brought about by coupling tensor gauge fields to fracton phases of matter remains unexplored in laboratories. Here, we propose schemes to realize synthetic tensor gauge fields that address dipoles instead of single particles. A lattice tilted by a strong linear potential and a weak quadratic potential yields a rank-2 electric field for a dipole formed by a particle-hole pair. Such a rank-2 electric field leads to a new type of Bloch oscillations, which modulates the quadrupole moment and preserves the dipole moment of the system. In higher dimensions, the interplay between interactions and vector gauge potentials imprints a phase to the ring-exchange interaction and thus generates synthetic tensor gauge fields. Such tensor gauge fields make it possible to realize a dipolar Harper-Hofstadter model in laboratories. The resultant dipolar Chern insulators feature chiral edge currents of dipoles in the absence of net charge currents.

The second harmonic (SH) of an axicon generated Bessel-Gauss beam is created through the nonlinear interaction of photons with a crystal, resulting in the energy doubling of the output photons. In this work, we show experimentally that in addition to frequency doubling, the SH of Bessel-Gauss beams under asymmetric aberrations from an elliptic axicon exhibit intriguing beam formation. Particularly, the central region of the SH beam profile is composed of two central spots of various geometries surrounded by nested ellipses; one of which is the configuration of two central gamma dots with similar radius knotted by nested ellipses for a zeroth-order Bessel-Gauss pump. These SH beams consistently maintain their spatial profile throughout propagation, reminiscing the behavior of screw dislocations in wave patterns. Our numerical simulations produce beam dynamics consistent with that of experiments and further implicate the remarkable interweaving of bright spots with dark vortices. This is especially noticeable when the beams dynamically oscillate along the optical axis, resulting in the genesis of spatially polarized beams with a knotted framework. The insights gained from our study establish a novel paradigm for exploring interactions of Bessel-like beams with vortex dynamics. This, in turn, has the potential to spark innovations in optical applications, fostering new methodologies to harness and manipulate complex light structures. Our experimental findings could spur new methods of generating logical states of light and new opportunities for material processing control.

Counting the microwave photons emitted by an ensemble of electron spins when they relax radiatively has recently been introduced as a sensitive new method for electron paramagnetic resonance spectroscopy at millikelvin temperatures. Here, we apply this spin fluorescence method to a scheelite crystal of ${\mathrm{CaWO}}_4$, finding some known (${\mathrm{Er}}^{3+}, {\mathrm{Yb}}^{3+}, {\mathrm{Nd}}^{3+}$, and ${\mathrm{Fe}}^{3+}$) and other unknown paramagnetic impurities. Investigating the zero nuclear spin isotope ($I=0$) transition of ${\mathrm{Er}}^{3+}:{\mathrm{CaWO}}_4$ as a model system, we provide a quantitative analysis of the time-dependent photon counting rate following an excitation pulse, as a function of its power. The achieved signal-to-noise ratio is found to be an order of magnitude higher than the one obtained by inductively detected Hahn echo under identical conditions. Finally, we use spin fluorescence spectroscopy at low excitation power to probe the properties of rare-earth ions close to a metallic wire deposited on the surface; our data reveal line distortion caused by the mechanical strain imparted by the thermal contractions of the metal relative to the underlying crystal. Coherent oscillations are also observed for the most highly strained ions.

We present a method to sample Markov-chain trajectories constrained to both the initial and final conditions, which we term Markov bridges. The trajectories are conditioned to end in a specific state at a given time. We derive the master equation for Markov bridges, which exhibits the original transition rates scaled by a time-dependent factor. Trajectories can then be generated using a refined version of the Gillespie algorithm. We illustrate the benefits of our method by sampling trajectories in the Müller-Brown potential. This allows us to generate transition paths which would otherwise be obtained at a high computational cost with standard kinetic Monte Carlo methods because commitment to a transition path is essentially a rare event. We then apply our method to a single-cell RNA sequencing dataset from mouse pancreatic cells to investigate the cell differentiation pathways of endocrine-cell precursors. By sampling Markov bridges for a specific differentiation pathway, we obtain a time-resolved dynamics that can reveal features such as cell types which behave as bottlenecks. The ensemble of trajectories also gives information about the fluctuations around the most likely path. For example, we quantify the statistical weights of different branches in the differentiation pathway to alpha cells.

Finding the optimal implosion design on existing experimental facilities for inertial confinement fusion requires an exhaustive search of the vast design parameter space. This is infeasible both with experiments and with simulations. Consequently, a large fraction of the experimentally realizable design space remains unexplored, and new design schemes are challenging to optimize in a reasonable time frame. On the OMEGA laser facility, predictive machine learning models have been developed to accurately forecast the result of an experiment using only inexpensive simulations and the large dataset of prior experimental data. However, the full design space remains vast enough to be unassailable with simple optimization techniques. Here we develop an automated and optimally parallel Bayesian optimization algorithm that can entirely optimize the target and pulse shape of a direct-drive ICF implosion under a given design paradigm. We use this algorithm to find a markedly improved design for the performance implosions on OMEGA that is predicted to hydroequivalently scale to ignition at 2.15 MJ.

Noise is both ubiquitous and generally deleterious in settings where precision is required. This is especially true in the quantum technology sector where system utility typically decays rapidly under its influence. Understanding the noise in quantum devices is thus a prerequisite for efficient strategies to mitigate or even eliminate its harmful effects. However, this requires resources that are often prohibitive, such that the typically used noise models rely on simplifications that sometimes depart from experimental reality. Here we derive a compact microscopic error model for single-qubit gates that only requires a single experimental input—the noise power spectral density. Our model goes beyond standard depolarizing or Pauli-twirled noise models, explicitly including non-Clifford and non-Markovian contributions to the dynamical error map. We gauge our predictions for experimentally relevant metrics against established characterization techniques run on a trapped-ion quantum computer. In particular, we find that experimental estimates of average gate errors measured through randomized benchmarking and reconstructed via quantum process tomography are tightly lower-bounded by our analytical estimates, while the depolarizing model overestimates the gate error. Our noise modeling including non-Markovian contributions can be readily applied to established frameworks such as dynamical decoupling and dynamically corrected gates, or to provide more realistic thresholds for quantum error correction.

Quantum computing is a promising candidate for accelerating machine learning tasks. Limited by the control accuracy of current quantum hardware, reducing the consumption of quantum resources is the key to achieving quantum advantage. Here, we propose a quantum resonant dimensionality reduction (QRDR) algorithm based on the quantum resonant transition to reduce the dimension of input data and accelerate the quantum machine learning algorithms. After QRDR, the dimension of input data $N$ can be reduced into the desired scale $R$, and the effective information of the original data will be preserved correspondingly, which will reduce the computational complexity of subsequent quantum machine learning algorithms or quantum storage. QRDR operates with polylogarithmic time complexity and reduces the error dependency from the order of $1/{\epsilon }^3$ to the order of $1/\epsilon$, compared to existing algorithms. Meanwhile, by avoiding quantum phase estimation, the consumed qubits in QRDR is independent on error $\epsilon$. Therefore, compared with existing algorithms, our algorithm has achieved the optimal performance in terms of time complexity and space complexity. We demonstrate the performance of our algorithm combining with two types of quantum classifiers, quantum support vector machines and quantum convolutional neural networks, for classifying underwater detection targets and quantum many-body phase, respectively. The simulation results indicate that reduced data extremely improved the processing efficiency following the application of QRDR. As quantum machine learning continues to advance, our algorithm has the potential to be utilized in a variety of computing fields.

As part of the Vienna package for Erlangen LEED, low-energy electron diffraction (ViPErLEED) project, computer programs have been developed for facile and user-friendly data extraction from movies of LEED images. The programs make use of some concepts from astronomical image processing and analysis. As a first step, flat-field and dark-frame corrections reduce the effects of inhomogeneities of the camera and screen. In a second step, for identifying all diffraction maxima (“spots”), it is sufficient to manually mark and label a single spot or very few spots. Then the program can automatically identify all other spots and determine the distortions of the image. This forms the basis for automatic spot tracking (i.e., following the spots as they move across the LEED screen) and intensity measurement. Even for complex structures with hundreds to a few thousand diffraction beams, this step takes less than a minute. The package also includes a program for further processing of these $I\left(V\right)$ curves (averaging of equivalent beams, manual and/or automatic selection, smoothing) as well as several utilities. The software is implemented as a set of plugins for the public-domain image processing program ImageJ and provided as an open-source package.

Low-energy electron diffraction (LEED) is a widely used technique in surface-science laboratories. Yet, it is rarely used to its full potential. The quantitative information about the surface structure, contained in the modulation of the intensities of the diffracted beams as a function of incident electron energy, LEED $I\left(V\right)$, is underutilized. To acquire these data, only minor adjustments would be required in most experimental setups, but existing analysis software is cumbersome to use and often computationally inefficient. The ViPErLEED (Vienna package for Erlangen LEED) project lowers these barriers, introducing a combined solution for user-friendly data acquisition, extraction, and computational analysis. These parts are discussed in three separate publications. Here, the focus is on the computational part of ViPErLEED, which performs highly automated LEED-$I\left(V\right)$ calculations and structural optimizations. Minimal user input is required, and the functionality is significantly enhanced compared to existing solutions. Computation is performed by embedding the existing Erlangen tensor-LEED package (TensErLEED). ViPErLEED manages additional parallelization, monitors convergence, and processes all input and output. This makes LEED $I\left(V\right)$ more accessible to new users while minimizing the potential for errors and the manual labor. Added functionalities include intelligent structure-dependent defaults for most calculation parameters, automatic detection of bulk and surface symmetries and their relationship, automated search procedures that preserve the symmetry and speed up convergence, adjustments to the TensErLEED code to handle larger systems than before, as well as parallelization and optimization. Modern file formats are used as input and output, and there is a direct interface to the atomic simulation environment (ASE) package. The software is implemented primarily in Python (version $\ge 3.7$) and provided as an open-source package (GNU GPLv3 or any later version). A structure determination of the $\alpha {\text{-Fe}}_2{\text{O}}_3\left(1\overline{1}02\right)-(1\times 1)$ surface is presented as an example for the application of the software.

The centrosomal aster is a mobile and adaptable cellular organelle that exerts and transmits forces necessary for tasks such as nuclear migration and spindle positioning. Recent experimental and theoretical studies of nematode and human cells demonstrate that pulling forces on asters by cortically anchored force generators are dominant during such processes. Here, we present a comprehensive investigation of the S-model (S for stoichiometry) of aster dynamics based solely on such forces. The model evolves the astral centrosome position, a probability field of cell-surface motor occupancy by centrosomal microtubules (under an assumption of stoichiometric binding), and free boundaries of unattached, growing microtubules. We show how cell shape affects the stability of centering of the aster, and its transition to oscillations with increasing motor number. Seeking to understand observations in single-cell nematode embryos, we use highly accurate simulations to examine the nonlinear structures of the bifurcations, and demonstrate the importance of binding domain overlap to interpreting genetic perturbation experiments. We find a generally rich dynamical landscape, dependent upon cell shape, such as internal constant-velocity equatorial orbits of asters that can be seen as traveling wave solutions. Finally, we study the interactions of multiple asters which we demonstrate an effective mutual repulsion due to their competition for surface force generators. We find, amazingly, that centrosomes can relax onto the vertices of platonic and nonplatonic solids, very closely mirroring the results of the classical Thomson problem for energy-minimizing configurations of electrons constrained to a sphere and interacting via repulsive Coulomb potentials. Our findings both explain experimental observations, providing insights into the mechanisms governing spindle positioning and cell division dynamics, and show the possibility of new nonlinear phenomena in cell biology.

We consider the quantum memory assisted quantum state verification task, where an adversary prepares independent multipartite entangled states and sends them to the local verifiers, who then store several copies in the quantum memory and measure them collectively to make a decision. We establish an exact analytic formula for optimizing two-copy state verification, where the verifiers store two copies, and give a globally optimal two-copy strategy for multiqubit graph states involving only Bell measurements. When the verifiers can store arbitrarily many copies, we present a dimension expansion technique that designs efficient verification strategies for this case, showcasing its application to efficiently verifying Greenberger-Horne-Zeilinger (GHZ)-like states. These strategies become increasingly advantageous with growing memory resources, ultimately approaching the theoretical limit of efficiency. Our findings demonstrate that quantum memories enhance state verification efficiency, shedding light on error-resistant strategies and practical applications of large-scale quantum memory assisted verification.

Fano resonances originate from the interaction of a discrete state with a continuum of propagation modes. They have been observed in various quantum and classical systems. Here, we provide experimental observation of the Fano resonance in two coupled micromechanical oscillator systems. The system consists of a pair of electrostatically coupled silicon micromechanical resonators. The coupling strength between the two resonators and their stiffness can be electrically tuned. The damping of one resonator can be regulated by an external proportional feedback control system. We have achieved the switching from the Lorentzian line shape to the Fano line shape, indicating that the quality factor of the Fano resonance is more than three times that of the Lorentzian resonance. This work supplies a flexible platform for exploring the physics of Fano resonances in a mechanical system and paves the way for developing a new generation of silicon resonant sensors with superior resolution.

We study the classical hardness of learning the output distribution from instantaneous quantum polynomial-time circuits with a varying density of two-qubit gates. We first investigate the complexity phases relevant to simulating the output distribution. In addition to a known parameter regime for anticoncentration, where the classical simulation is believed to be infeasible, we identify a novel parameter condition such that the classically simulability of the circuit can be proven rigorously. Next, we explore the classical learnability of the output distribution. We prove that a circuit instance whose output distribution is not classically learnable exists, assuming the hardness of learning parity with noise. We numerically study this phenomenon deeply using a classical energy-based model, where we find that the classical model fails to learn the output distribution even when the density of two-qubit gates is much smaller than that for the anticoncentration. We argue that this is mainly due to the fact that an accurate classical description of the output distribution requires exponentially large amount of resources.