The traditional framework of quantum metrology commonly assumes unlimited access to resources, overlooking resource constraints in realistic scenarios. As such, the optimal strategies therein can be infeasible in practice. Here, we investigate quantum metrology where the total energy consumption of the probe state preparation, intermediate control operations, and the final measurement is subject to a constraint. We establish a comprehensive theoretical framework for characterizing energy-constrained multistep quantum processes, based on which we develop a general optimization method for energy-constrained quantum metrology that determines both the optimal precision and the corresponding strategy. Using the method, we determine the ultimate precision limit of energy-constrained phase estimation and identify a novel advantage of quantum superpositions of causal orders in enhancing the energy efficiency of adaptive quantum estimation.

Quantum sensors hold considerable promise for precision measurement, yet their capabilities are inherently constrained by environmental noise. A fundamental task in quantum sensing is determining the precision limit of noisy sensor devices. For continuously monitored quantum sensors, characterizing the optimal precision in the presence of environments other than the measurement channel is an outstanding open theoretical challenge, due to the infinite-dimensional nature of the sensor output field and the complex temporal correlation of the photons therein. Here, we establish a numerically efficient method to determine the quantum Cramér-Rao bound for continuously monitored quantum sensors subject to general environmental noise—Markovian or non-Markovian, and showcase its application with paradigmatic models of continuously monitored quantum sensors. Applicable to both constant-parameter and waveform estimation, our method provides a rigorous and practical framework for assessing and enhancing the sensor performance in realistic settings, with broad applications across experimental quantum physics.

We reinterpret Starobinsky’s stochastic inflation as an open quantum system, where short-wavelength modes act as the environment for long-wavelength modes. Using the Schwinger-Keldysh formalism, we systematically trace out the environment and derive an effective theory for the reduced density matrix, including deviations from exact de Sitter space. The resulting master equation is a Lindblad equation, which reduces to a Fokker-Planck equation for the diagonal elements up to higher orders in the slow-roll expansion, while also yielding a more complete equation in phase space. Finally, we extend the formalism to global de Sitter space, for which the associated Fokker-Planck equation lacks equilibrium solutions until the late-time regime $aH\gg 1$.

For the first time, we implement the deep-neural-network-based variational Monte Carlo approach for the multiquark bound states, whose complexity surpasses that of electron or nucleon systems due to strong SU(3) color interactions. We design a novel and high-efficiency architecture, DeepQuark, to address the unique challenges in multiquark systems such as stronger correlations, extra discrete quantum numbers, and intractable confinement interaction. Our method demonstrates competitive performance with state-of-the-art approaches, including diffusion Monte Carlo and Gaussian expansion method, in the nucleon, doubly heavy tetraquark, and fully heavy tetraquark systems. Notably, it outperforms existing calculations for pentaquarks, exemplified by the triply heavy pentaquark. For the nucleon, we successfully incorporate three-body flux-tube confinement interactions without additional computational costs. In tetraquark systems, we consistently describe hadronic molecule $T_{cc}$ and compact tetraquark $T_{bb}$ with an unbiased form of wave function ansatz. In the pentaquark sector, we obtain weakly bound ${\overline{D}}^{*}{\mathrm{\Xi }}_{cc}^{*}$ molecule $P_{cc\overline{c}}(5715)$ with $S=\frac{5}{2}$ and its bottom partner $P_{bb\overline{b}}(15569)$. They can be viewed as the analogs of the molecular $T_{cc}$. We recommend experimental search of $P_{cc\overline{c}}(5715)$ in the D-wave $J/\psi {\mathrm{\Lambda }}_c$ channel. DeepQuark holds great promise for extension to larger multiquark systems, overcoming the computational barriers in conventional methods. It also serves as a powerful framework for exploring confining mechanism beyond two-body interactions in multiquark states, which may offer valuable insights into nonperturbative QCD and general many-body physics.

The identification of the first multiphonon $\gamma$-vibrational bands in an odd-odd neutron-rich nucleus of the nuclear chart is presented. These high-spin structures of hard to access ${}_{41}{}^{104}{\mathrm{Nb}}_{63}$, produced in fission, were studied by combining a spectrometer with isotopic resolution coupled to a $\gamma$-ray tracking array and independently from high-fold $\gamma$ coincidence measurements. Triaxial projected shell model calculations for the high-spin states are in good agreement with the measured observables for the yrast, one-phonon, and two-phonon $\gamma$ bands. The possibility of an oblate shape of an isomeric state and coexistence of triaxial and oblate configurations is investigated from the decay of the 141 keV isomer. The present Letter illustrates the robustness of vibration excitations in the presence of an odd valence proton and neutron as well as the possibly coexisting shapes beyond the $N=60$ transitional region.

Moiré physics has transcended spatial dimensions, extending into synthetic domains and enabling novel quantum phenomena. We propose a theoretical model for a two-dimensional (2D) moiré time crystal formed by ultracold atoms, induced by periodic perturbations applied to a nonlattice trap. Our analysis reveals the emergence of regional superfluid states exhibiting moiré-scale quantum coherence across temporal, spatial, and spatiotemporal domains. This Letter provides fundamental insights into temporal moiré phenomena and presents an alternative pathway to engineer spatial moiré phases without requiring twisted multilayer lattices.

Rydberg atom triangular arrays in an optical cavity serve as an ideal platform for understanding the interplay between geometric frustration and quantized photons. Using a large-scale quantum Monte Carlo method, we obtain a rich ground state phase diagram. Around half-filling, the infinite long-range light-matter interaction lifts the ground state degeneracy, resulting in a novel order-coexisted superradiant clock phase that completely destroys the fragile order-by-disorder phase observed in classical light fields. According to the Ginzburg-Landau theory, this replacement may result from the competition between threefold and sixfold clock terms. Similar to the spin supersolid, the clear first-order phase transition at the $Z_2$ symmetry line is attributed to the nonzero photon density, which couples to the threefold clock term. Finally, we discuss the low-energy physics in the dimer language and propose that cavity-mediated nonlocal ring exchange interactions may play a critical role in the rich physics induced by the attachment of cavity QED. Our Letter opens a new arena of research on the emergent phenomena of quantum phase transitions in many-body quantum optics.

Recent experiments demonstrate all-electric spinning of levitated nanodiamonds with embedded nitrogen-vacancy spins. Here, we argue that such gyroscopically stabilized spin rotors offer a promising platform for probing and exploiting quantum spin-rotation coupling of particles hosting a single spin degree of freedom. Specifically, we derive the effective Hamiltonian describing how an embedded spin affects the rotation of rapidly revolving quantum rotors due to the Einstein-de Haas and Barnett effects, which we use to devise experimental protocols for observing this coupling in state-of-the-art experiments. This will open the door for future exploitations of quantum spin rotors for superposition experiments with massive objects.

We investigate the transport dynamics of elongated particles in cellular vortical flows that undergo spatial oscillations over time. Experimental flow visualizations reveal mixed flow fields with chaotic and elliptic regions coexisting. Surprisingly, the particle transport rate does not increase monotonically with particle length, even though longer particles are expected to explore neighboring vortices more easily. Numerical simulations in a much larger system produce similar transport anomalies, characterized by subdiffusion due to frequent longtime trapping in vortices at certain lengths but normal diffusion at others. At moderate oscillation frequencies, these longtime trapping events occur within the chaotic region; at high frequencies, they occur in the elliptic regions, but only for particles whose lengths match these regions. In the latter case, subdiffusion is robust against random noise. Our results reveal new mechanisms for controlling particle random walks and dispersal in fluid flows.

This Letter reports the simultaneous excitation of two terahertz plasma waves in field-emission-driven microdischarges. As demonstrated by first-principle particle-in-cell simulations, we reveal that one wave results from intermittent field emission due to space-charge effects, while the other arises from a two-stream instability between cathode field-emission electrons and anode multipactor electrons, which can trap less energetic electrons, leading to circumnutation trajectories and increased collisionality. A dispersion relation is derived from fluid equations, showing good agreement with the simulated wave parameters. The findings of this Letter provide a foundation and potential pathway for designing novel terahertz sources at miniaturized scales.

We combine simulations with new analyses that overcome previous pitfalls to explicate how nonhelical mean-field dynamos grow and saturate in unstratified, magnetorotationally driven turbulence. Shear of the mean radial magnetic field amplifies the azimuthal component. Radial fields are regenerated by velocity fluctuations that induce shear of radial magnetic fluctuations, followed by Lorentz and Coriolis forces that source a negative off-diagonal component in the turbulent diffusivity tensor. We present a simple schematic to illustrate this dynamo growth. A different part of the Lorentz force forms a third-order correlator in the mean electromotive force that saturates the dynamo.

Electronic nematic and smectic liquid crystals are spontaneous symmetry-breaking phases that are seen to precede or coexist with enigmatic unconventional superconducting states in multiple classes of materials. In this Letter we describe scanning tunneling microscopy observations of a short ranged charge stripe (smectic) order in NaAlSi, whose superconductivity is speculated to have an unconventional origin. As well as this we resolve a clear spatial modulation of the superconducting gap amplitude, which arises due to the intertwined superconducting and smectic orders. Numerical calculations help to understand the possible driving mechanism as a suppression of kinetic energy on the Fermi surface formed in part by two large, flat-topped hole pockets of $p$-orbital character.

Thin film deposition on weakly interacting substrates exhibits a unique growth mode characterized by initially strong island formation and rapidly increasing roughness, which reaches a maximum and subsequently decreases as the film returns to a smooth morphology. Here we show this rough-to-smooth growth mode experimentally for two molecular systems with substantially different geometries, namely, the effectively spherical buckminsterfullerene (${\mathrm{C}}_{60}$) and the disk-like 1,4,5,8,9,11-hexaazatriphenylenehexacarbonitrile. This growth mode is explained by a geometrical model that captures the basic mechanisms of multilayer island growth, island coalescence, and formation of a continuous film. Additionally, kinetic Monte Carlo simulations with minimal ingredients demonstrate that this mode generally occurs for weakly interacting substrates, providing quantitative estimates of parameters that characterize adsorbate-adsorbate and adsorbate-substrate interactions. Both the model and simulations accurately describe the experimental data and highlight the generic nature of the phenomenon, independently of the details of the interactions and the molecular flux, which opens up a path for controlling nanoscale film roughness.

Collision of quantum particles remains an effective way of probing their mutual statistics. Colliders based on quantum point contacts in quantum Hall edge states have been successfully used to probe the statistics of the underlying quantum particles. Notwithstanding the extensive theoretical work focusing on pointlike colliders, when it comes to experiment, the colliders are rarely pointlike objects and can support a resonant level or multiple tunneling points. We present a study of a paradigmatic extended (non-point-like) fermionic collider (and an extension to bosonic colliders). As with particle interferometers, in an extended collider there is an infinite number of trajectories for any single- or multiparticle event. Self-interference of the former can lead to an apparent bunching of fermions when we compare the cross-current correlator with a classical benchmark representing two colliding beams. In view of this apparent bunching behavior of fermions, we identify an experimentally accessible current correlator, which reveals the true mutual statistics of fermions.

Fabricating room-temperature ferromagnetic insulators, which are crucial candidates for next-generation dissipation-free quantum and spintronic devices, remains a significant challenge. In this Letter, we report on the epitaxial synthesis of novel room-temperature ferromagnetic insulating thin films created through the precise construction of (111)-oriented $3\mathrm{d}/5\mathrm{d}$ interfaces. Our analysis indicates that, unlike conventional doping methods, the (111)-oriented ${\mathrm{SrIrO}}_3/{\mathrm{La}}_{2/3}{\mathrm{Sr}}_{1/3}{\mathrm{MnO}}_3$ ($\mathrm{SIO}/\mathrm{LSMO}$) interfaces exhibit markedly enhanced spin-orbit coupling. This enhanced interfacial spin-orbit coupling strengthens the electron-phonon coupling in LSMO, thereby shortening the electronic mean free path. As a result, the intrinsic metallicity of LSMO is suppressed, giving rise to a new ferromagnetic insulating phase that emerges between the ferromagnetic metal and paramagnetic insulator regimes of the LSMO phase diagram. Furthermore, the temperature window of the ferromagnetic insulating phase can be tuned by precisely controlling the thickness of the LSMO layers. Our Letter reveals a new strategy for developing ferromagnetic insulators by engineering $3\mathrm{d}/5\mathrm{d}$ interfaces and orientations, paving a way for the development of novel dissipation-free quantum and spintronic devices.

Transition metals exemplify correlated electronic systems, where electron-electron ($e\text{−}e$) scattering often results in a quadratic temperature dependence of the electrical resistivity, $\rho (T)\propto T^2$. In ${\mathrm{SrVO}}_3$ (SVO), a material with a $V\text{−}3{\mathrm{d}}^1$ electronic configuration that ensures metallicity through narrow $3d\text{−}{\mathrm{t}}_{2g}$ bands, a $\rho (T)\propto T^2$ dependence has been reported. While traditionally attributed to $e\text{−}e$ scattering, recent studies suggest that electron-phonon ($e$-ph) interactions may play a significant role. To unravel the influence of phonon interactions on carrier transport in SVO, we present a comparative study of the transport and optical properties of SVO films with partial substitution of ${}^{16}\mathrm{O}$ ions by their heavier isotope, ${}^{18}\mathrm{O}$. Our findings reveal that ${}^{18}\mathrm{O}$ substitution induces a change in the slope of $d\rho (T)/dT$ at nominal fixed carrier density, highlighting the dominant contribution of $e$-ph coupling over $e\text{−}e$ scattering in determining $\rho (T)$. Furthermore, it is found that the ${}^{18}\mathrm{O}$ substitution softens the phonon lattice and promotes a reduction in plasma frequency and an increase in the carrier effective mass. These results indicate that the $e$-ph coupling strength increases upon ${}^{18}\mathrm{O}$ substitution. Our findings suggest that $e$-ph interactions may surpass $e\text{−}e$ scattering in governing the resistivity of metallic ionic lattices.

We study the model for spin-$1/2$ $J_1\text{−}{J}_2$ Heisenberg antiferromagnets on a square lattice in the presence of spin vacancies. In order to overcome the methodological challenges associated with analyzing models with magnetic frustration and inhomogeneities, we introduce a new semiclassical approach in which singlet dimers are treated as effective classical degrees of freedom. The energetic and entropic aspects of the dimer formation are included via a classical Monte Carlo scheme that allows for the dynamical conversion of spin pairs into dimers and vice versa. We show that our semiclassical approach recovers the qualitative physics of the $J_1\text{−}{J}_2$ model in the absence of vacancies. The vacancies lead to a broadening of the spin-liquid regime between the Néel and the stripe antiferromagnetic phases. This suggests a possible new route to discover spin-liquid ground states by tuning the $J_2/J_1$ ratio in doped square lattice antiferromagnets.