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Quantum state-resolved spectroscopy of the low energy thorium-229 nuclear transition was recently achieved. The five allowed transitions within the electric quadrupole splitting structure were measured to the kilohertz level in a calcium fluoride host crystal, opening the field of nuclear-based optical clocks. Central to the performance of solid-state clock operation is an understanding of systematic shifts such as the temperature dependence of the clock transitions. In this work, we measure the four strongest transitions of thorium-229 in the same crystal at three temperature values: 150 K, 229 K, and 293 K. We find shifts of the unsplit frequency and the electric quadrupole splittings, corresponding to decreases in the electron density, electric field gradient, and field gradient asymmetry at the nucleus as temperature increases. The $\textit{m}$ = $\pm 5/2 \rightarrow \pm 3/2$ line shifts only 62(6) kHz over the temperature range, i.e., approximately 0.4 kHz/K, representing a promising candidate for a future solid-state optical clock. Achieving 10$^{-18}$ precision requires crystal temperature stability of 5$\mu$K., Comment: 7 pages, 3 figures, 2 tables

We use a multi-phase transport (AMPT) model to study multi-pion and multi-kaon Hanbury Brown-Twiss (HBT) correlations for the partially coherent particle-emitting sources in relativistic heavy-ion collisions. A density-dependent longitudinal coherent emission length and density-dependent transverse coherent emission length are introduced in calculating the multi-boson HBT correlation functions of the partially coherent sources. We compare the model results of three- and four-pion HBT correlation functions with experimental data in Pb-Pb collisions at center-of-mass energy $\sqrt{s_{NN}}=$2.76 TeV, and investigate the influences of boson coherent emissions on the multi-pion and multi-kaon correlation functions, respectively. We find that all of the three- and four-pion correlation functions of the partially coherent sources are consistent with experimental data. Coherent emission leads to the intercept decreases of the multi-boson correlation functions. The intercepts of the multi-kaon correlation functions of the partially coherent source are higher than those of the multi-pion correlation functions, because low kaon densities lead to smaller kaon coherent emission lengths than pion emission lengths. The intercepts of multi-boson correlation functions of partially coherent sources in high transverse momentum intervals are higher than those in low transverse momentum intervals because particle de Broglie wavelengths are small at high momenta., Comment: 19 pages, 12 figures

State-resolved laser spectroscopy at the 10$^{-12}$ precision level recently reported in $arXiv$:2406.18719 determined the fractional change in nuclear quadrupole moment between the ground and isomeric state of $^{229}\rm{Th}$, $\Delta Q_0/Q_0$=1.791(2) %. Assuming a prolate spheroid nucleus, this allows to quantify the sensitivity of the nuclear transition frequency to variations of the fine-structure constant $\alpha$ to $K=5900(2300)$, with the uncertainty dominated by the experimentally measured charge radius difference $\Delta \langle r^2 \rangle$ between the ground and isomeric state. This result indicates a three orders of magnitude enhancement over atomic clock schemes based on electron shell transitions. We find that $\Delta Q_0$ is highly sensitive to tiny changes in the nuclear volume, thus the constant volume approximation cannot be used to accurately relate changes in $\langle r^2 \rangle$ and $Q_0$. The difference between the experimental and estimated values in $\Delta Q_0/Q_0$ raises a further question on the octupole contribution to the alpha-sensitivity., Comment: 10 pages, 2 figures

Optical atomic clocks$^{1,2}$ use electronic energy levels to precisely keep track of time. A clock based on nuclear energy levels promises a next-generation platform for precision metrology and fundamental physics studies. Thorium-229 nuclei exhibit a uniquely low energy nuclear transition within reach of state-of-the-art vacuum ultraviolet (VUV) laser light sources and have therefore been proposed for construction of the first nuclear clock$^{3,4}$. However, quantum state-resolved spectroscopy of the $^{229m}$Th isomer to determine the underlying nuclear structure and establish a direct frequency connection with existing atomic clocks has yet to be performed. Here, we use a VUV frequency comb to directly excite the narrow $^{229}$Th nuclear clock transition in a solid-state CaF$_2$ host material and determine the absolute transition frequency. We stabilize the fundamental frequency comb to the JILA $^{87}$Sr clock$^2$ and coherently upconvert the fundamental to its 7th harmonic in the VUV range using a femtosecond enhancement cavity. This VUV comb establishes a frequency link between nuclear and electronic energy levels and allows us to directly measure the frequency ratio of the $^{229}$Th nuclear clock transition and the $^{87}$Sr atomic clock. We also precisely measure the nuclear quadrupole splittings and extract intrinsic properties of the isomer. These results mark the start of nuclear-based solid-state optical clock and demonstrate the first comparison of nuclear and atomic clocks for fundamental physics studies. This work represents a confluence of precision metrology, ultrafast strong field physics, nuclear physics, and fundamental physics., Comment: 22 pages, 5 figures, 1 extended data figure

The quantum mechanical nature of spherical top molecules is particularly evident at low angular momentum quantum number J. Using infrared spectroscopy on the 8.4$\mu$m rovibrational band of buffer gas cooled $^{12}$C$_{60}$, we observe the hitherto unseen R(J = 0 - 29) rotational progression, including the complete disappearance of certain transitions due to the molecule's perfect icosahedral symmetry and identical bosonic nuclei. The observation of extremely weak C$_{60}$ absorption is facilitated by a laser desorption C$_{60}$ vapor source, which transfers 1000-fold less heat to the cryogenic buffer gas cell than a traditional oven source. This technique paves the way to cooling C$_{60}$ and other large gas phase molecules to much lower temperatures, providing continued advances for spectral resolution and sensitivity.

We propose protocols that probe manifestations of the mass-energy equivalence in an optical lattice clock (OLC) interrogated with spin coherent and entangled quantum states. To tune and uniquely distinguish the mass-energy equivalence effects (gravitational redshift and second order Doppler shift) in such setting, we devise a dressing protocol using an additional nuclear spin state. We then analyze the interplay between photon-mediated interactions and gravitational redshift and show that such interplay can lead to entanglement generation and frequency synchronization. In the regime where all atomic spins synchronize, we show the synchronization time depends on the initial entanglement of the state and can be used as a proxy of its metrological gain compared to a classical state. Our work opens new possibilities for exploring the effects of general relativity on quantum coherence and entanglement in OLC experiments., Comment: 7+17 pages, 4+6 figures

Gas samples relevant to health and environment typically contain a plethora of molecular species that span a huge concentration dynamic range. High-concentration molecules impose a strong absorption background that hinders robust identification of low-concentration species. While mid-infrared frequency comb spectroscopy with high-finesse cavity enhancement has realized many of the most sensitive multi-species trace gas detection to date, its robust performance requires gas samples to contain only weak absorption features to avoid dispersing cavity resonances from the comb line frequencies. Here we introduce a new technique that is free from this restriction, thus enabling the development of next-generation multi-species trace gas sensing with broad applicability to complex and dynamic molecular compositions. The principle of Modulated Ringdown Comb Interferometry is to resolve ringdown dynamics carried by massively parallel comb lines transmitted through a length-modulated cavity. This method leverages both periodicity of the field dynamics and Doppler frequency shifts introduced from a Michelson interferometer. Scalable enhancement of both spectral coverage and cavity finesse is enabled with dispersion immune and high-efficiency data collection. Built upon this platform, we realize in the mid-infrared a product of finesse and spectral coverage that is orders of magnitude better than all prior experiments. We demonstrate the power of this technique by measuring highly dispersive exhaled human breath samples over a vastly expanded spectral coverage of 1,010 cm-1 and with cavity finesse of 23,000. This allows for the first time simultaneous quantification of 20 distinct molecular species at > 1 part-per-trillion sensitivity with their concentrations varying by 7 orders of magnitude.

We propose how to achieve nonreciprocal quantum phase transition in a spinning microwave magnonic system composed of a spinning microwave resonator coupled with an yttrium iron garnet sphere with magnon Kerr effect. Sagnac-Fizeau shift caused by the spinning of the resonator brings about a significant modification in the critical driving strengths for second- and one-order quantum phase transitions, which means that the highly controllable quantum phase can be realized by the spinning speed of the resonator. More importantly, based on the difference in the detunings of the counterclockwise and clockwise modes induced by spinning direction of the resonator, the phase transition in this system is nonreciprocal, that is, the quantum phase transition occurs when the system is driven in one direction but not the other. Our work offers an alternative path to engineer and design nonreciprocal magnonic devices., Comment: 8 pages, 6 figures

Atomic, molecular, and optical (AMO) physics has been at the forefront of the development of quantum science while laying the foundation for modern technology. With the growing capabilities of quantum control of many atoms for engineered many-body states and quantum entanglement, a key question emerges: what critical impact will the second quantum revolution with ubiquitous applications of entanglement bring to bear on fundamental physics? In this Essay, we argue that a compelling long-term vision for fundamental physics and novel applications is to harness the rapid development of quantum information science to define and advance the frontiers of measurement physics, with strong potential for fundamental discoveries. As quantum technologies, such as fault-tolerant quantum computing and entangled quantum sensor networks, become much more advanced than today's realization, we wonder what doors of basic science can these tools unlock? We anticipate that some of the most intriguing and challenging problems, such as quantum aspects of gravity, fundamental symmetries, or new physics beyond the minimal standard model, will be tackled at the emerging quantum measurement frontier., Comment: 17 pages, 1 figure, Part of a series of Phys. Rev. Lett. Essays which concisely present author visions for the future of their field

Long-range and anisotropic dipolar interactions profoundly modify the dynamics of particles hopping in a periodic lattice potential. Here, we report the realization of a generalized t-J model with dipolar interactions using a system of ultracold fermionic molecules with spin encoded in the two lowest rotational states. We systematically explore the role of dipolar Ising and spin-exchange couplings and the effect of motion on spin dynamics. The model parameters can be controlled independently, with dipolar couplings tuned by electric fields and motion regulated by optical lattices. Using Ramsey spectroscopy, we observed interaction-driven contrast decay that depends strongly both on the strength of the anisotropy between Ising and spin-exchange couplings and on motion. These observations are supported by theory models established in different motional regimes that provide intuitive pictures of the underlying physics. This study paves the way for future exploration of kinetic spin dynamics and quantum magnetism with highly tunable molecular platforms in regimes challenging for existing numerical and analytical methods, and it could shed light on the complex behaviors observed in real materials.

Polar molecules confined in an optical lattice are a versatile platform to explore spin-motion dynamics based on strong, long-range dipolar interactions. The precise tunability of Ising and spin-exchange interactions with both microwave and dc electric fields makes the molecular system particularly suitable for engineering complex many-body dynamics. Here, we used Floquet engineering to realize interesting quantum many-body systems of polar molecules. Using a spin encoded in the two lowest rotational states of ultracold KRb molecules, we mutually validated XXZ spin models tuned by a Floquet microwave pulse sequence against those tuned by a dc electric field through observations of Ramsey contrast dynamics, setting the stage for the realization of Hamiltonians inaccessible with static fields. In particular, we observed two-axis twisting mean-field dynamics, generated by a Floquet-engineered XYZ model using itinerant molecules in 2D layers. In the future, Floquet-engineered Hamiltonians could generate entangled states for molecule-based precision measurement or could take advantage of the rich molecular structure for quantum simulation of multi-level systems., Comment: 20 pages, 4 figures + 4 extended data figures

Efficient sub-Doppler laser cooling and optical trapping of YO molecules offer new opportunities to study collisional dynamics in the quantum regime. Confined in a crossed optical dipole trap, we achieve the highest phase-space density of $2.5 \times 10^{-5}$ for a bulk laser-cooled molecular sample. This sets the stage to study YO-YO collisions in the microkelvin temperature regime, and reveal state-dependent, single-partial-wave two-body collisional loss rates. We determine the partial-wave contributions to specific rotational states (first excited $N=1$ and ground $N=0$) following two strategies. First, we measure the change of the collision rate in a spin mixture of $N=1$ by tuning the kinetic energy with respect to the p- and d-wave centrifugal barriers. Second, we compare loss rates between a spin mixture and a spin-polarized state in $N=0$. Using quantum defect theory with a partially absorbing boundary condition at short range, we show that the dependence on temperature for $N=1$ can be reproduced in the presence of a d-wave or f-wave resonance, and the dependence on a spin mixture for $N=0$ with a p-wave resonance., Comment: 5 Pages, 4 Figures

We report an optical lattice clock with a total systematic uncertainty of $8.1 \times 10^{-19}$ in fractional frequency units, representing the lowest uncertainty of any clock to date. The clock relies on interrogating the ultra-narrow ${}^1S_0 \rightarrow {}^3P_0$ transition in a dilute ensemble of fermionic strontium atoms trapped in a vertically-oriented, shallow, one-dimensional optical lattice. Using imaging spectroscopy, we previously demonstrated record high atomic coherence time and measurement precision enabled by precise control of collisional shifts and the lattice light shift. In this work, we revise the black body radiation shift correction by evaluating the $5s4d$ $^3D_1$ lifetime, necessitating precise characterization and control of many body effects in the $5s4d$ $^3D_1$ decay. Lastly, we measure the second order Zeeman coefficient on the least magnetically sensitive clock transition. All other systematic effects have uncertainties below $1 \times 10^{-19}$.

We explore a scheme for entanglement generation and optimization in giant atoms by coupling them to finite one-dimensional arrays of spins that behave as cavities. We find that high values for the concurrence can be achieved in small-sized cavities, being the generation time very short. When exciting the system by external means, optimal concurrence is obtained for very weak drivings. We also analyze the effect of disorder in these systems, showing that although the average concurrence decreases with disorder, high concurrences can still be obtained even in scenarios presenting strong disorder. This result leads us to propose an optimization procedure in which by engineering the on-site energies or hoppings in the cavity, concurrences close to 1 can be reached within an extremely short period of time.

Many-particle entanglement is a key resource for achieving the fundamental precision limits of a quantum sensor. Optical atomic clocks, the current state-of-the-art in frequency precision, are a rapidly emerging area of focus for entanglement-enhanced metrology. Augmenting tweezer-based clocks featuring microscopic control and detection with the high-fidelity entangling gates developed for atom-array information processing offers a promising route towards leveraging highly entangled quantum states for improved optical clocks. Here we develop and employ a family of multi-qubit Rydberg gates to generate Schr\"odinger cat states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 9 optical clock qubits in a programmable atom array. In an atom-laser comparison at sufficiently short dark times, we demonstrate a fractional frequency instability below the standard quantum limit using GHZ states of up to 4 qubits. However, due to their reduced dynamic range, GHZ states of a single size fail to improve the achievable clock precision at the optimal dark time compared to unentangled atoms. Towards overcoming this hurdle, we simultaneously prepare a cascade of varying-size GHZ states to perform unambiguous phase estimation over an extended interval. These results demonstrate key building blocks for approaching Heisenberg-limited scaling of optical atomic clock precision., Comment: 22 pages, 7 figures, 2 tables, added additional Methods sections and gate error modeling

Measurement science now connects strongly with engineering of quantum coherence, many-body states, and entanglement. To scale up the performance of an atomic clock using a degenerate Fermi gas loaded in a three-dimensional optical lattice, we must understand complex many-body Hamiltonians to ensure meaningful gains for metrological applications. In this work, we use a near unity filled Sr 3D lattice to study the effect of a tunable Fermi-Hubbard Hamiltonian. The clock laser introduces a spin-orbit coupling spiral phase and breaks the isotropy of superexchange interactions, changing the Heisenberg spin model into one exhibiting XXZ-type spin anisotropy. By tuning the lattice confinement and applying imaging spectroscopy we map out favorable atomic coherence regimes. With weak transverse confinement, both s- and p-wave interactions contribute to decoherence and atom loss, and their contributions can be balanced. At deep transverse confinement, we directly observe coherent superexchange interactions, tunable via on-site interaction and site-to-site energy shift, on the clock Ramsey fringe contrast over timescales of multiple seconds. This study provides a groundwork for using a 3D optical lattice clock to probe quantum magnetism and spin entanglement

It is important to develop a unified theoretical framework to describe the nuclear experiments and astrophysical observations based on the same effective nuclear interactions. Based on the so-called Skyrme pseudopotential up to next-to-next-to-next-to-leading order, we construct a series of extended Skyrme interactions by modifying the density-dependent term and fitting the empirical nucleon optical potential up to above $1$ GeV, the empirical properties of isospin symmetric nuclear matter, the microscopic calculations of pure neutron matter and the properties of neutron stars from astrophysical observations. The modification of the density-dependent term in the extended Skyrme interactions follows the idea of Fermi momentum expansion and this leads to a highly flexible density behavior of the symmetry energy. In particular, the values of the density slope parameter $L$ of the symmetry energy for the new extended Skyrme interactions range from $L = -5$ MeV to $L = 125$ MeV by construction, to cover the large uncertainty of the density dependence of the symmetry energy. Furthermore, in order to consider the effects of isoscalar and isovector nucleon effective masses, we adjust the momentum dependency of the single-nucleon optical potential and the symmetry potential of these new extended Skyrme interactions and construct a parameter set family, by which we systematically study the impacts of the symmetry energy and the nucleon effective masses on the properties of nuclear matter and neutron stars. The new extended Skyrme interactions constructed in the present work will be useful to determine the equation of state of isospin asymmetric nuclear matter, especially the symmetry energy, as well as the nucleon effective masses and their isospin splitting, in transport model simulations for heavy-ion collisions, nuclear structure calculations and neutron star studies., Comment: 38 pages, 16 figures, 8 tables. Discussions added and typos fixed. Accepted version to appear in PRC

The Pound-Drever-Hall (PDH) cavity-locking scheme has found prevalent uses in precision optical interferometry and laser frequency stabilization. A form of frequency modulation spectroscopy, PDH enjoys superior signal-to-noise recovery, large acquisition dynamic range, wide servo bandwidth, and robust rejection of spurious effects. However, residual amplitude modulation at the signal frequency, while significantly suppressed, still presents an important concern for further advancing the state-of-the-art performances. Here we present a simplified and improved scheme for PDH using an acousto-optic modulator to generate digital phase reference sidebands instead of the traditionally used electro-optic modulator approach. We demonstrate four key advantages: (1) the carrier and two modulation tones are individually synthesized and easily reconfigured, (2) robust and orthogonal control of the modulated optical field is applied directly to the amplitude and phase quadratures, (3) modulation synthesis, demodulation, and feedback are implemented in a self-contained and easily reproducible electronic unit, and (4) superior active and passive control of residual amplitude modulation is achieved, especially when the carrier power is vanishingly low. These distinct merits stimulate new ideas on how we optimally enact PDH for a wide range of applications.

We perform two-pion Hanbury Brown-Twiss (HBT) interferometry for the partially coherent pion-emitting sources in relativistic heavy-ion collisions, using a multi-phase transport (AMPT) model. A longitudinal coherent emission length, as well as a transverse coherent emission length, are introduced to the pion generation coordinates in calculating the HBT correlation functions of the partially coherent sources. We compare the model results with and without coherent emission conditions with experimental data in Au-Au collisions at center-of-mass energy $\sqrt{s_{NN}}=$200 GeV, and in Pb-Pb collisions at center-of-mass energy $\sqrt{s_{NN}}=$2.76 TeV, and find that the HBT results of the partially coherent sources are closer to the experimental data than those of chaotic sources., Comment: 20 pages,8 figures

We demonstrate photon-counting single-pixel imaging in the ultraviolet region. Toward this target, we develop a high-performance compact single-photon detector based on a 4H-SiC single-photon avalanche diode (SPAD), where a tailored readout circuit with active hold-off time is designed to restrain detector noise and operate the SPAD in free-running mode. We use structured illumination to reconstruct 192$\times$192 compressed images at a 4 fps frame rate. To show the superior capability of ultraviolet characteristics, we use our single-pixel imaging system to identify and distinguish different transparent objects under low-intensity irradiation, and image ultraviolet light sources. The results provide a practical solution for general ultraviolet imaging applications., Comment: 5 pages, 5 figures, accepted for publication in Applied Physics Letters

An increasingly large variety of molecular species are being cooled down to low energies in recent years, and innovative ideas and powerful techniques continue to emerge to gain ever more precise control of molecular motion. In this brief review we focus our discussions on two widely employed cooling techniques that have brought molecular gases into the quantum regime: association of ultracold atomic gases into quantum gases of molecules and direct laser cooling of molecules. These advances have brought into reality our capability to prepare and manipulate both internal and external states of molecules quantum mechanically, opening the field of cold molecules to a wide range of scientific explorations., Comment: 5 figures

Ergodicity, the central tenet of statistical mechanics, requires that an isolated system will explore all of its available phase space permitted by energetic and symmetry constraints. Mechanisms for violating ergodicity are of great interest for probing non-equilibrium matter and for protecting quantum coherence in complex systems. For decades, polyatomic molecules have served as an intriguing and challenging platform for probing ergodicity breaking in vibrational energy transport, particularly in the context of controlling chemical reactions. Here, we report the observation of rotational ergodicity breaking in an unprecedentedly large and symmetric molecule, 12C60. This is facilitated by the first ever observation of icosahedral ro-vibrational fine structure in any physical system, first predicted for 12C60 in 1986. The ergodicity breaking exhibits several surprising features: first, there are multiple transitions between ergodic and non-ergodic regimes as the total angular momentum is increased, and second, they occur well below the traditional vibrational ergodicity threshold. These peculiar dynamics result from the molecules' unique combination of symmetry, size, and rigidity, highlighting the potential of fullerenes to uncover emergent phenomena in mesoscopic quantum systems.