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Laser cooling is used to produce ultracold atoms and molecules for quantum science and precision measurement applications. Molecules are more challenging to cool than atoms due to their vibrational and rotational internal degrees of freedom. Molecular rotations lead to the use of type-II transitions ($F \geq F'$) for magneto-optical trapping (MOT). When typical red detuned light frequencies are applied to these transitions, sub-Doppler heating is induced, resulting in higher temperatures and larger molecular cloud sizes than realized with the type-I MOTs most often used with atoms. To improve type-II MOTs, Jarvis et al. PRL 120, 083201 (2018) proposed a blue-detuned MOT to be applied after initial cooling and capture with a red-detuned MOT. This was successfully implemented (Burau et al. PRL 130, 193401 (2023), Jorapur et al. PRL 132, 163403 (2024), Li et al. PRL 132, 233402 (2024)), realizing colder and denser molecular samples. Very recently, Hallas et al. arXiv:2404.03636 (2024) demonstrated a blue-detuned MOT with a "1+2" configuration that resulted in even stronger compression of the molecular cloud. Here, we describe and characterize theoretically the conveyor-belt mechanism that underlies this observed enhanced compression. We perform numerical simulations of the conveyor-belt mechanism using both stochastic Schr\"odinger equation (SSE) and optical Bloch equation (OBE) approaches. We investigate the conveyor-belt MOT characteristics in relation to laser parameters, g-factors, and the structure of the molecular system., Comment: 12 pages, 14 figures

We report the experimental realization of a conveyor-belt magneto-optical trap for calcium monofluoride (CaF) molecules. The obtained highly-compressed cloud has a mean radius of 64(5) $\mu$m and a peak number density of $3.6(5) \times 10^{10}$ cm$^{-3}$, a 600-fold increase over the conventional red-detuned MOTs of CaF, and the densest molecular MOT observed to date. Subsequent loading of these molecules into an optical dipole trap yields up to $2.6 \times 10^4$ trapped molecules at a temperature of 14(2) $\mu$K with a peak phase-space density of $\sim 2.4 \times 10^{-6}$. This opens new possibilities for a range of applications utilizing high-density, optically trapped ultracold molecules., Comment: 7 pages; 4 figures; typos corrected

We report a magneto-optical trap of strontium monohydroxide (SrOH) containing 2000(600) molecules at a temperature of 1.2(3) mK. The lifetime is 91(9) ms, which is limited by decay to optically unaddressed vibrational states. This provides the foundation for future sub-Doppler cooling and optical trapping of SrOH, a polyatomic molecule suited for precision searches for physics beyond the Standard Model including new CP violating particles and ultralight dark matter. We also identify important features in this system that guide cooling and trapping of complex and heavy polyatomic molecules into the ultracold regime.

Let $K$ be a function field of characteristic $p\geq0$ or a number field over which the $abc$ conjecture holds, and let $\phi(x)=x^d+c \in K[x]$ be a unicritical polynomial of degree $d\geq2$ with $d \not\equiv 0,1\pmod{p}$. We completely classify all portraits of $K$-rational preperiodic points for such $\phi$ for all sufficiently large degrees $d$. More precisely, we prove that, up to accounting for the natural action of $d$th roots of unity on the preperiodic points for $\phi$, there are exactly thirteen such portraits up to isomorphism. In particular, for all such global fields $K$, it follows from our results together with earlier work of Doyle-Poonen and Looper that the number of $K$-rational preperiodic points for $\phi$ is uniformly bounded -- independent of $d$. That is, there is a constant $B(K)$ depending only on $K$ such that \[\big|\text{PrePer}(x^d+c,K)\big|\leq B(K)\] for all $d\geq2$ and all $c\in K$. Moreover, we apply this work to construct many irreducible polynomials with large dynamical Galois groups in semigroups generated by sets of unicritical polynomials under composition.

We demonstrate production of cold atomic strontium (Sr) and strontium-containing molecules (SrOH) in a cryogenic buffer gas beam source via direct heating of strontium oxide (SrO) with 30 mJ laser pulses several milliseconds long. $3.7(2)\times10^{14}$ Sr atoms are released, which represents a factor of 7 increase in atomic production per pulse compared to nanosecond-scale ablation laser pulses. A peak atomic density of $1.93(6) \times 10^{12}$ atoms/cm$^3$ is achieved, which corresponds to a factor of 2 increase relative to ablation. We further propose extensions of this method to other atomic and molecular species., Comment: Typos corrected

Relativistic exact two-component coupled-cluster calculations of molecular sensitivity factors for nuclear Schiff moments (NSMs) are reported. We focus on molecules containing heavy nuclei, especially octupole-deformed nuclei. Analytic relativistic coupled-cluster gradient techniques are used and serve as useful tools for identifying candidate molecules that sensitively probe for physics beyond the Standard Model in the hadronic sector. Notably, these tools enable straightforward ``black-box'' calculations. Two competing chemical mechanisms that contribute to the NSM are analyzed, illuminating the physics of ligand effects on NSM sensitivity factors.

The vibrational branching ratios from the lowest excited electronic state for $\textrm{SrOCH}_3$, $\textrm{SrNH}_2$, and $\textrm{SrSH}$ are measured at the $< 0.1\%$ level. Spectra are obtained by driving the $\tilde{X} - \tilde{A}$ transitions and dispersing the fluorescence on a grating spectrometer. We also perform $\textit{ab initio}$ calculations for the energies of vibrational levels relevant for laser cooling, as well as branching ratios to support the interpretations of all molecular spectra. Symmetry group analysis is applied in conjunction with our data to study rotational closure in these molecules. These analyses indicate favorable prospects for laser cooling $\textrm{SrNH}_2$ and other similar alkaline-earth(-like) amides for future beyond the Standard Model physics searches using polyatomic molecules with long-lived parity doublets.

We establish upper bounds on the size of the largest subset of $\{1,2,\dots,N\}$ lacking nonzero differences of the form $h(p_1,\dots,p_{\ell})$, where $h\in \mathbb{Z}[x_1,\dots,x_{\ell}]$ is a fixed polynomial satisfying appropriate conditions and $p_1,\dots,p_{\ell}$ are prime. The bounds are of the same type as the best-known analogs for unrestricted integer inputs, due to Bloom-Maynard and Arala for $\ell=1$, and to the authors for $\ell \geq 2$., Comment: 22 pages. arXiv admin note: text overlap with arXiv:2006.15400

We demonstrate a blue-detuned magneto-optical trap (MOT) of a polyatomic molecule, calcium monohydroxide (CaOH). We identify a novel MOT frequency configuration that produces high spatial compression of the molecular cloud. This high compression MOT achieves a cloud radius of $59(5)~\mu\text{m}$ and a peak density of $8(2) \times 10^8~\text{cm}^{-3}$, the highest reported density for a molecular MOT to date. We compare our experimental studies of blue-detuned MOTs for CaOH and compare with Monte-Carlo simulations, finding good agreement.

This paper focuses on the need for a rigorous theory of layered control architectures (LCAs) for complex engineered and natural systems, such as power systems, communication networks, autonomous robotics, bacteria, and human sensorimotor control. All deliver extraordinary capabilities, but they lack a coherent theory of analysis and design, partly due to the diverse domains across which LCAs can be found. In contrast, there is a core universal set of control concepts and theory that applies very broadly and accommodates necessary domain-specific specializations. However, control methods are typically used only to design algorithms in components within a larger system designed by others, typically with minimal or no theory. This points towards a need for natural but large extensions of robust performance from control to the full decision and control stack. It is encouraging that the successes of extant architectures from bacteria to the Internet are due to strikingly universal mechanisms and design patterns. This is largely due to convergent evolution by natural selection and not intelligent design, particularly when compared with the sophisticated design of components. Our aim here is to describe the universals of architecture and sketch tentative paths towards a useful design theory., Comment: Submitted to IEEE Control Systems Magazine

Polyatomic molecules have rich structural features that make them uniquely suited to applications in quantum information science, quantum simulation, ultracold chemistry, and searches for physics beyond the Standard Model. However, a key challenge is fully controlling both the internal quantum state and the motional degrees of freedom of the molecules. Here, we demonstrate the creation of an optical tweezer array of individual polyatomic molecules, CaOH, with quantum control of their internal quantum state. The complex quantum structure of CaOH results in a non-trivial dependence of the molecules' behavior on the tweezer light wavelength. We control this interaction and directly and nondestructively image individual molecules in the tweezer array with >90% fidelity. The molecules are manipulated at the single internal quantum state level, thus demonstrating coherent state control in a tweezer array. The platform demonstrated here will enable a variety of experiments using individual polyatomic molecules with arbitrary spatial arrangement., Comment: 11 pages, 6 figures

Ultracold polar molecules are promising for quantum information processing and searches for physics beyond the Standard Model. Laser cooling to ultracold temperatures is an established technique for trapped diatomic and triatomic molecules. Further cooling of the molecules to near the motional ground state is crucial for reducing various dephasings in quantum and precision applications. In this work, we demonstrate Raman sideband cooling of CaF molecules in optical tweezers to near their motional ground state, with average motional occupation quantum numbers of $\bar{n}_{x}=0.16(12)$, $\bar{n}_{y}=0.17(17)$ (radial directions), $\bar{n}_{z}=0.22(16)$ (axial direction) and a 3-D motional ground state probability of $54\pm18\%$. This paves the way to increase molecular coherence times in optical tweezers for robust quantum computation and simulation applications., Comment: 10 pages, 6 figures

Incorporating pattern-learning for prediction (PLP) in many discrete-time or discrete-event systems allows for computation-efficient controller design by memorizing patterns to schedule control policies based on their future occurrences. In this paper, we demonstrate the effect of PLP by designing a controller architecture for a class of linear Markovian jump systems (MJS) where the aforementioned ``patterns'' correspond to finite-length sequences of modes. In our analysis of recurrent patterns, we use martingale theory to derive closed-form solutions to quantities pertaining to the occurrence of patterns: 1) the expected minimum occurrence time of any pattern from some predefined collection, 2) the probability of a pattern being the first to occur among the collection. Our method is applicable to real-world dynamics because we make two extensions to common assumptions in prior pattern-occurrence literature. First, the distribution of the mode process is unknown, and second, the true realization of the mode process is not observable. As demonstration, we consider fault-tolerant control of a dynamic topology-switching network, and empirically compare PLP to two controllers without PLP: a baseline based on the novel System Level Synthesis (SLS) approach and a topology-robust extension of the SLS baseline. We show that PLP is able to reject disturbances as effectively as the topology-robust controller at reduced computation time and control effort. We discuss several important tradeoffs, such as the size of the pattern collection and the system scale versus the accuracy of the mode predictions, which show how different PLP implementations affect stabilization and runtime performance., Comment: Preprint submitted to Automatica as of Jan 2023

We study the internal state dynamics of optically trapped polyatomic molecules subject to room temperature blackbody radiation. Using rate equations that account for radiative decay and blackbody excitation between rovibrational levels of the electronic ground state, we model the microscopic behavior of the molecules' thermalization with their environment. As an application of the model, we describe in detail the procedure used to determine the blackbody and radiative lifetimes of low-lying vibrational states in ultracold CaOH molecules, the values of which were reported in previous work [Hallas et al., arXiv:2208.13762]. Ab initio calculations are performed and are found to agree with the measured values. Vibrational state lifetimes for several other laser-coolable molecules, including SrOH and YbOH, are also calculated., Comment: arXiv admin note: substantial text overlap with arXiv:2208.13762

Over the past decade, tremendous progress has been made to extend the tools of laser cooling and trapping to molecules. Those same tools have recently been applied to polyatomic molecules (molecules containing three or more atoms). In this review, we discuss the scientific drive to bring larger molecules to ultralow temperatures, the features of molecular structure that provide the most promising molecules for this pursuit, and some technical aspects of how lasers can be used to control the motion and quantum states of polyatomic molecules. We also present opportunities for and challenges to the use of polyatomic molecules for science and technology., Comment: 112 pages, 32 figures; review article prepared for Advances in Atomic, Molecular and Optical Physics

Ultracold polyatomic molecules are promising candidates for experiments in quantum science, quantum sensing, ultracold chemistry, and precision measurements of physics beyond the Standard Model. A key, yet unrealized, requirement of these experiments is the ability to achieve full quantum control over the complex internal structure of the molecules. Here, we establish coherent control of individual quantum states in a polyatomic molecule, calcium monohydroxide (CaOH), and use these techniques to demonstrate a method for searching for the electron electric dipole moment (eEDM). Optically trapped, ultracold CaOH molecules are prepared in a single quantum state, polarized in an electric field, and coherently transferred into an eEDM sensitive state where an electron spin precession measurement is performed. To extend the coherence time of the measurement, we utilize eEDM sensitive states with tunable, near-zero magnetic field sensitivity. The spin precession coherence time is limited by AC Stark shifts and uncontrolled magnetic fields. These results establish a path for eEDM searches with trapped polyatomic molecules, towards orders-of-magnitude improved experimental sensitivity to time-reversal-violating physics.

Among all the dynamical modular curves associated to quadratic polynomial maps, we determine which curves have infinitely many quadratic points. This yields a classification statement on preperiodic points for quadratic polynomials over quadratic fields, extending previous work of Poonen, Faber, and the authors., Comment: Improvements to the exposition; stronger version of what is now Proposition 4.5

Due to their intrinsic electric dipole moments and rich internal structure, ultracold polar molecules are promising candidate qubits for quantum computing and for a wide range of quantum simulations. Their long-lived molecular rotational states form robust qubits while the long-range dipolar interaction between molecules provides quantum entanglement. Using a molecular optical tweezer array, single molecules can be moved and separately addressed for qubit operations using optical and microwave fields, creating a scalable quantum platform. Here, we demonstrate long-range dipolar spin-exchange interactions in pairs of CaF molecules trapped in an optical tweezer array. We control the anisotropic interaction and realize the spin-$\frac{1}{2}$ quantum XY model by encoding an effective spin-$\frac{1}{2}$ system into the rotational states of the molecules. We demonstrate a two-qubit (two-molecule) gate to generate entanglement deterministically, an essential resource for all quantum information applications. Employing interleaved tweezer arrays, we demonstrate high fidelity single site molecular addressability.

Animals move smoothly and reliably in unpredictable environments. Models of sensorimotor control have assumed that sensory information from the environment leads to actions, which then act back on the environment, creating a single, unidirectional perception-action loop. This loop contains internal delays in sensory and motor pathways, which can lead to unstable control. We show here that these delays can be compensated by internal feedback signals that flow backwards, from motor towards sensory areas. Internal feedback is ubiquitous in neural sensorimotor systems and recent advances in control theory show how internal feedback compensates internal delays. This is accomplished by filtering out self-generated and other predictable changes in early sensory areas so that unpredicted, actionable information can be rapidly transmitted toward action by the fastest components. For example, fast, giant neurons are necessarily less accurate than smaller neurons, but they are crucial for fast and accurate behavior. We use a mathematically tractable control model to show that internal feedback has an indispensable role in achieving state estimation, localization of function -- how different parts of cortex control different parts of the body -- and attention, all of which are crucial for effective sensorimotor control. This control model can explain anatomical, physiological and behavioral observations, including motor signals in visual cortex, heterogeneous kinetics of sensory receptors and the presence of giant Betz cells in motor cortex, Meynert cells in visual cortex and giant von Economo cells in the prefrontal cortex of humans as well as internal feedback patterns and unexplained heterogeneity in other neural systems., Comment: Submitted to PNAS

The application of silicon photomultiplier (SiPM) technology for weak-light detection at a single photon level has expanded thanks to its better photon detection efficiency in comparison to a conventional photomultiplier tube (PMT). SiPMs with large detection area have recently become commercially available, enabling applications where the photon flux is low both temporarily and spatially. On the other hand, several drawbacks exist in the usage of SiPMs such as a higher dark count rate, many readout channels, slow response time, and optical crosstalk; therefore, users need to carefully consider the trade-offs. This work presents a SiPM-embedded compact large-area photon detection module. Various techniques are adopted to overcome the disadvantages of SiPMs so that it can be generally utilized as an upgrade from a PMT. A simple cooling component and recently developed optical crosstalk suppression method are adopted to reduce the noise which is more serious for larger-area SiPMs. A dedicated readout circuit increases the response frequency and reduces the number of readout channels. We favorably compare this design with a conventional PMT and obtain both higher photon detection efficiency and larger-area acceptance.

We demonstrate and characterize Zeeman-Sisyphus (ZS) deceleration of a beam of ytterbium monohydroxide (YbOH). Our method uses a combination of large magnetic fields ($\sim$ 2.5 T) and optical spin-flip transitions to decelerate molecules while scattering only $\sim$ 10 photons per molecule. We study the challenges associated with the presence of internal molecular perturbations among the excited electronic states and discuss the methods used to overcome these challenges, including a modified ZS decelerator using microwave and optical transitions., Comment: 9 pages, 3 figures, 1 table

We present a high-resolution laser spectroscopic study of the $\tilde{A}\,^2B_2- \tilde{X}\,^2A_1$ and $\tilde{B}\,^2B_1- \tilde{X}\,^2A_1$ transitions of calcium (I) phenoxide, CaOPh (CaOC$_6$H$_5$). The rotationally resolved band systems are analyzed using an effective Hamiltonian model and are accurately modeled as independent perpendicular ($b$- or $c$-type) transitions. The structure of calcium monophenoxide is compared to previously observed Ca-containing radicals and implications for direct laser cooling are discussed. This work demonstrates that functionalization of aromatic molecules with optical cycling centers can preserve many of the properties needed for laser-based control.

We report optical trapping of a polyatomic molecule, calcium monohydroxide (CaOH). CaOH molecules from a magneto-optical trap are sub-Doppler laser cooled to $20(3)~\mu\text{K}$ in free space and loaded into an optical dipole trap. We attain an in-trap molecule number density of $3(1) \times 10^9~\text{cm}^{-3}$ at a temperature of $57(8)~\mu$K. Trapped CaOH molecules are optically pumped into an excited vibrational bending mode, whose $\ell$-type parity doublet structure is a potential resource for a wide range of proposed quantum science applications with polyatomic molecules. We measure the spontaneous, radiative lifetime of this bending mode state to be $\sim$$0.7~\text{s}$.

Laser spectroscopy of the $^{\mathrm{229m}}$Th nuclear clock transition is necessary for the future construction of a nuclear-based optical clock. Precision laser sources with broad spectral coverage in the vacuum ultraviolet are needed for this task. Here, we present a tunable vacuum-ultraviolet frequency comb based on cavity-enhanced seventh-harmonic generation. Its tunable spectrum covers the current uncertainty range of the $^{\mathrm{229m}}$Th nuclear clock transition.

The vibrational branching ratios of SrOH for radiative decay to the ground electronic state, $X^{2}\Sigma^{+}$, from the first two electronically excited states, $A^{2}\Pi$ and $B^{2}\Sigma^{+}$, are determined experimentally at the $\sim10^{-5}$ level. The observed small branching ratios enable the design of a full, practical laser-cooling scheme, including magneto-optical trapping and sub-Doppler laser cooling, with $>10^4$ photon scatters per molecule. Ab initio calculations sensitive to weak vibronic transitions are performed to facilitate the experimental measurement and analysis, and show good agreement with experiment., Comment: 6 pages, 3 figures, 3 tables

Optically trapped laser-cooled polar molecules hold promise for new science and technology in quantum information and quantum simulation. Large numerical aperture optical access and long trap lifetimes are needed for many studies, but these requirements are challenging to achieve in a magneto-optical trap (MOT) vacuum chamber that is connected to a cryogenic buffer gas beam source, as is the case for all molecule laser cooling experiments so far. Long distance transport of molecules greatly eases fulfilling these requirements as molecules are placed into a region separate from the MOT chamber. We realize a fast transport method for ultracold molecules based on an electronically focus-tunable lens combined with an optical lattice. The high transport speed is achieved by the 1D red-detuned optical lattice, which is generated by interference of a focus-tunable laser beam and a focus-fixed laser beam. Efficiency of 48(8)% is realized in the transport of ultracold calcium monofluoride (CaF) molecules over 46 cm distance in 50 ms, with a moderate heating from 32(2) {\mu}K to 53(4) {\mu}K. Positional stability of the molecular cloud allows for stable loading of an optical tweezer array with single molecules., Comment: 21 pages, 7 figures

The current best upper limit for electron electric dipole moment (EDM), $|d_e|<1.1\times10^{-29}\,$e$\cdot$cm ($90$% confidence), was set by the ACME collaboration in 2018. The ACME experiment uses a spin-precession measurement in a cold beam of ThO molecules to detect $d_e$. An improvement in statistical uncertainty would be possible with more efficient use of molecules from the cryogenic buffer gas beam source. Here, we demonstrate electrostatic focusing of the ThO beam with a hexapole lens. This results in a factor of $16$ enhancement in the molecular flux detectable downstream, in a beamline similar to that built for the next generation of ACME. We also demonstrate an upgraded rotational cooling scheme that increases the ground state population by $3.5$ times compared to no cooling, consistent with expectations and a factor of $1.4$ larger than previously in ACME. When combined with other demonstrated improvements, we project over an order of magnitude improvement in statistical sensitivity for the next generation ACME electron EDM search., Comment: 20 pages, 8 figures, 2 pages appendices

The best limit on the electron electric dipole moment (eEDM) comes from the ACME II experiment [Nature \textbf{562} (2018), 355-360] which probes physics beyond the Standard Model at energy scales well above 1 TeV. ACME II measured the eEDM by monitoring electron spin precession in a cold beam of the metastable H$^3\Delta_1$ state of thorium monoxide (ThO) molecules, with an observation time $\tau \approx 1$ ms for each molecule. We report here a new measurement of the lifetime of the ThO (H$^3\Delta_1$) state, $\tau_H = 4.2\pm 0.5$ ms. Using an apparatus within which $\tau \approx \tau_H$ will enable a substantial reduction in uncertainty of an eEDM measurement., Comment: 6 pages, 5 figures

We present a new, scalable alternative to the structured singular value, which we call $\nu$, provide a convex upper bound, study their properties and compare them to $\ell_1$ robust control. The analysis relies on a novel result on the relationship between robust control of dynamical systems and non-negative constant matrices., Comment: Submitted to CDC2022, six pages. Companion article: arXiv:2204.02493

We present D-Phi iteration: an algorithm for distributed, localized, and scalable robust control of systems with structured uncertainties. This algorithm combines the System Level Synthesis (SLS) parametrization for distributed control with stability criteria from L1, LInf, and nu robust control. We show in simulation that this algorithm achieves good nominal performance while greatly increasing the robust stability margin compared to the LQR controller. To the best of our knowledge, this is the first distributed and localized algorithm for structured robust control; furthermore, algorithm complexity depends only on the size of local neighborhoods and is independent of global system size. We additionally characterize the suitability of different robustness criteria for distributed and localized computation., Comment: To appear in CDC 2022

Static electric dipole moments of nondegenerate systems probe mass scales for physics beyond the Standard Model well beyond those reached directly at high energy colliders. Discrimination between different physics models, however, requires complementary searches in atomic-molecular-and-optical, nuclear and particle physics. In this report, we discuss the current status and prospects in the near future for a compelling suite of such experiments, along with developments needed in the encompassing theoretical framework., Comment: Contribution to Snowmass 2021; updated with community edits and endorsements

We extend a technique, originally due to the first author and Poonen, for proving cases of the Strong Uniform Boundedness Principle (SUBP) in algebraic dynamics over function fields of positive characteristic. The original method applied to unicritical polynomials for which the characteristic does not divide the degree. We show that many new 1-parameter families of polynomials satisfy the SUBP, including the family of all quadratic polynomials in even characteristic. We also give a new family of non-polynomial, non-Latt\`es rational functions that satisfies the SUBP., Comment: 14 pages; main results now hold over 1-dimensional function fields over arbitrary fields of positive characteristic (not just finite fields); to appear in Mathematische Annalen

Rapid and repeated photon cycling has enabled precision metrology and the development of quantum information systems using a variety of atoms and simple molecules. Extending optical cycling to structurally complex molecules would provide new capabilities in these areas, as well as in ultracold chemistry. Increased molecular complexity, however, makes realizing closed optical transitions more difficult. Building on the already established strong optical cycling of diatomic, linear triatomic, and symmetric top molecules, recent theoretical and experimental work has indicated that cycling will be extendable to phenol containing molecules, as well as other asymmetric species. The paradigm for these systems is the use of an optical cycling center bonded to a molecular ligand. Theory has suggested that cycling may be extended to even larger ligands, like naphthalene, pyrene and coronene. Here, we study the optical excitation and vibrational branching of the molecules CaO-2-naphthyl, SrO-2-naphthyl and CaO-1-naphthyl and find only weak decay to excited vibrational states, indicating a promising path to full quantum control and laser cooling of large arene-based molecules., Comment: 9 pages, 3 figures, 2 tables

In this paper we study two questions related to exceptional behavior of preperiodic points of polynomials in $\mathbb{Q}[x]$. We show that for all $d\geq 2$, there exists a polynomial $f_d(x) \in \mathbb{Q}[x]$ with $2\leq \mathrm{deg}(f_d) \leq d$ such that $f_d(x)$ has at least $d + \lfloor \log_2(d)\rfloor$ rational preperiodic points. Furthermore, we show that for infinitely many integers $d$, the polynomials $f_d(x)$ and $f_d(x) + 1$ have at least $d^2 + d\lfloor \log_2(d)\rfloor - 2d + 1$ common complex preperiodic points., Comment: Strengthened results, added new references

We report magneto-optical trapping (MOT) of a polyatomic molecule, calcium monohydroxide (CaOH). The MOT contains $2.0(5)\times 10^4$ CaOH molecules at a peak density of $3.0(8)\times10^{6}$ cm$^{-3}$. CaOH molecules are further sub-Doppler laser cooled in an optical molasses, to a temperature of 110(4) $\mu$K. The temperatures and densities achieved here make CaOH a viable candidate for a wide variety of quantum science applications, including the creation of optical tweezer arrays of CaOH molecules. This work also suggests that laser cooling and magneto-optical trapping of many other polyatomic species will be both feasible and practical., Comment: 6 pages, 4 figures

We study the dynamics of stochastic families of rational maps on the projective line. As such families can be infinite and may not typically be defined over a single number field, we introduce the concept of generalized adelic measures, generalizing previous notions introduced by Favre and Rivera-Letelier and Mavraki and Ye. Generalized adelic measures are defined over the measure space of places of an algebraic closure of the rationals, using a framework established by Allcock and Vaaler. This turns our heights from sums over places into integrals. We prove an equidistribution result for generalized adelic measures, and use this result to prove an equidistribution result for random backwards orbits in stochastic arithmetic dynamics., Comment: 54 pages

Feedback is ubiquitous in both biological and engineered control systems. In biology, in addition to typical feedback between plant and controller, we observe feedback pathways within control systems, which we call internal feedback pathways (IFPs), that are often very complex. IFPs are most familiar in neural systems, our primary motivation, but they appear everywhere from bacterial signal transduction to the human immune system. In this paper, we describe these very different motivating examples and introduce the concepts necessary to explain their complex IFPs, particularly the severe speed-accuracy tradeoffs that constrain the hardware in biology. We also sketch some minimal theory for extremely simplified toy models that nevertheless highlight the importance of diversity-enabled sweet spots (DESS) in mitigating the impact of hardware tradeoffs. For more realistic models, standard modern and robust control theory can give some insights into previously cryptic IFPs, and the new System Level Synthesis theory expands this substantially. These additional theories explaining IFPs will be explored in more detail in several companion papers., Comment: This paper is a companion to arXiv:2109.11752 and arXiv:2109.11757. v3: updated title + author metadata to match PDF

Neural architectures in organisms support efficient and robust control that is beyond the capability of engineered architectures. Unraveling the function of such architectures is challenging; their components are highly diverse and heterogeneous in their morphology, physiology, and biochemistry, and often obey severe speed-accuracy tradeoffs; they also contain many cryptic internal feedback pathways (IFPs). We claim that IFPs are crucial architectural features that strategically combine highly diverse components to give rise to optimal performance. We demonstrate this in a case study, and additionally describe how sensing and actuation delays in standard control (state feedback, full control, output feedback) give rise to independent and separable sources of IFPs. Our case study is an LQR problem with two types of sensors, one fast but sparse and one dense but slow. Controllers using only one type of sensor perform poorly, often failing even to stabilize; controllers using both types of sensors perform extremely well, demonstrating a strong diversity-enabled sweet spot (DESS). We demonstrate that IFPs are key in enabling this DESS, and additionally that with IFPs removed, controllers with delayed sensing perform poorly. The existence of strong DESS and IFP in this simple example suggest that these are fundamental architectural features in any complex system with diverse components, such as organisms and cyberphysical systems., Comment: To appear in 2022 ACC; Companion paper to arXiv:2110.05029, arXiv:2109.11757; Version updates: author + content changes, T.J.S., G.C., E.S.H., N.K. and their contributions have migrated to to arXiv:2110.05029

We present a robust, continuous molecular decelerator that employs high magnetic fields and few optical pumping steps. CaOH molecules are slowed, accumulating at low velocities in a range sufficient for loading both magnetic and magneto-optical traps. During the slowing, the molecules scatter only 7 photons, removing around 8 K of energy. Because large energies can be removed with only a few spontaneous radiative decays, this method can be applied to nearly any paramagnetic atomic or molecular species, opening a general path to trapping of complex molecules., Comment: 6 pages, 4 figures. Slightly revised text and updated citations

Given a set $S=\{x^2+c_1,\dots,x^2+c_s\}$ defined over a field and an infinite sequence $\gamma$ of elements of $S$, one can associate an arboreal representation to $\gamma$, generalizing the case of iterating a single polynomial. We study the probability that a random sequence $\gamma$ produces a ``large-image'' representation, meaning that infinitely many subquotients in the natural filtration are maximal. We prove that this probability is positive for most sets $S$ defined over $\mathbb{Z}[t]$, and we conjecture a similar positive-probability result for suitable sets over $\mathbb{Q}$. As an application of large-image representations, we prove a density-zero result for the set of prime divisors of some associated quadratic sequences. We also consider the stronger condition of the representation being finite-index, and we classify all $S$ possessing a particular kind of obstruction that generalizes the post-critically finite case in single-polynomial iteration., Comment: 22 pages

A portrait is a combinatorial model for a discrete dynamical system on a finite set. We study the geometry of portrait moduli spaces, whose points correspond to equivalence classes of point configurations on the affine line for which there exist polynomials realizing the dynamics of a given portrait. We present results and pose questions inspired by a large-scale computational survey of intersections of portrait moduli spaces for polynomials in low degree., Comment: 26 pages, comments welcome!

Given a generic polynomial $f(x)$, the generalized dynatomic polynomial $\Phi_{f,c,d}(x)$ vanishes at precisely those $\alpha$ such that $f^c(\alpha)$ has period exactly $d$ under iteration of $f(x)$. We show that the shifted dynatomic polynomials $\Phi_{f,c,d}(x) - 1$ often have generalized dynatomic factors, and that these factors are in correspondence with certain cyclotomic factors of necklace polynomials. These dynatomic factors of $\Phi_{f,c,d}(x) - 1$ have an interpretation in terms of new multiplicative relations between dynamical units which are uniform in the polynomial $f(x)$., Comment: 19 pages, comments welcome!

Qubit coherence times are critical to the performance of any robust quantum computing platform. For quantum information processing using arrays of polar molecules, a key performance parameter is the molecular rotational coherence time. We report a 93(7) ms coherence time for rotational state qubits of laser cooled CaF molecules in optical tweezer traps, over an order of magnitude longer than previous systems. Inhomogeneous broadening due to the differential polarizability between the qubit states is suppressed by tuning the tweezer polarization and applied magnetic field to a "magic" angle. The coherence time is limited by the residual differential polarizability, implying improvement with further cooling. A single spin-echo pulse is able to extend the coherence time to nearly half a second. The measured coherence times demonstrate the potential of polar molecules as high fidelity qubits.

We demonstrate the direct loading of a D$_2$ MOT of potassium-39 atoms from a cryogenic buffer gas beam source. We load $10^8$ atoms in a 10 ms pulse, with no degradation in performance up to a 10 Hz repetition rate. Observed densities reach $\sim10^{11}$ atoms/cm$^3$ in a single pulse, achieved with no sub-Doppler cooling or transverse compression. This system produces an ideal starting point for ultracold atom experiments where high experimental repetition rates are desirable and initial high densities are critical. Extension to other atomic species (e.g., refractory metals) that present technical challenges to high-yield production using oven-based sources is straightforward., Comment: 7 pages, 4 figures

We report a generally applicable computational and experimental approach to determine vibronic branching ratios in linear polyatomic molecules to the $10^{-5}$ level, including for nominally symmetry forbidden transitions. These methods are demonstrated in CaOH and YbOH, showing approximately two orders of magnitude improved sensitivity compared with the previous state of the art. Knowledge of branching ratios at this level is needed for the successful deep laser cooling of a broad range of molecular species.

We propose and study a method of optical crosstalk suppression for silicon photomultipliers (SiPMs) using optical filters. We demonstrate that attaching absorptive visible bandpass filters to the SiPM can substantially reduce the optical crosstalk. Measurements suggest that the absorption of near infrared light is important to achieve this suppression. The proposed technique can be easily applied to suppress the optical crosstalk in SiPMs in cases where filtering near infrared light is compatible with the application.