We investigate the Coulomb explosion dynamics of ${\mathrm{H}}_2$ molecules embedded in helium nanodroplets, induced by an intense ultraviolet femtosecond laser pulse. By employing ion-ion coincidence and momentum correlation spectroscopy, we identify the Coulomb-exploded double ionization of ${\mathrm{H}}_2$ molecules within the droplets. Our results demonstrate that the collisions between dissociating ${\mathrm{H}}^{+}$ ions and surrounding He atoms significantly alter both the kinetic energy distributions and the emission direction of the ion fragments. Notably, the $\mathrm{He}{\mathrm{H}}^{+}$ fragments originating from the Coulomb explosion channel exhibit higher kinetic energies in larger droplets, a phenomenon driven by the solvation dynamics that depend on the fragment's kinetic energy and droplet size. This study provides deep insights into the translation, dissociation, and solvation processes of light impurities in quantum liquid, underscoring the critical role of droplet size in shaping fragment kinetics during these processes.

Bose-Einstein condensates (BECs) of neutral atoms constitute an important quantum system for fundamental research and precision metrology. Many applications require short preparation times of BECs, for example, for optimized data acquisition rates in scientific applications, and reduced dead times and improved bandwidths for atomic quantum sensors. Here, we report on the generation of rubidium BECs with a repetition rate of more than $2\mathrm{Hz}$. The system relies on forced evaporation in a dynamically adjusted optical potential, which is created by the spatial modulation of laser beams. Our system provides a versatile source of the ubiquitous rubidium BECs, and promotes their exploitation for high-precision atom interferometers.

Alkali-metal–noble-gas comagnetometers are precision probes well suited for tests of fundamental physics and inertial rotation sensing, combining the high sensitivity of the spin-exchange-relaxation-free magnetometers with inherent suppression of magnetic field noise. Past versions of the device utilizing continuous-wave optical pumping are sensitive to rotation and anomalous spin couplings along a single axis perpendicular to the plane spanned by the orthogonal pump and probe laser beams. These devices are susceptible to light shifts in the alkali atoms, and to power and beam pointing fluctuations of both the probe and pump lasers, the latter of which is a dominant source of $1/f$ noise. In this work, we model and implement an approach to alkali-metal–noble-gas comagnetometers using pulsed optical pumping. After each pump laser pulse, an off-resonance probe beam measures the precession of noble-gas-spins-coupled alkali spins via optical rotation in the dark, thus eliminating effects from pump laser light shift and power fluctuations. Performing nonlinear fitting on the sinusoidal transient signal with a proper phase enables independent and simultaneous measurement of signals along two orthogonal axes in the plane perpendicular to the pump beam. Effects from beam pointing fluctuations of the probe beam in the pump-probe plane are fundamentally eliminated, and signal response to pump beam pointing fluctuations is suppressed by compensation from noble-gas nuclear spins.

We engineer angular momentum eigenstates of a single atom by using an all-optical approach based on the interference of Laguerre-Gaussian beams. We confirm the imprint of angular momentum by measuring the two-dimensional density distribution and by performing Ramsey spectroscopy in a slightly anisotropic trap, which additionally reveals the sense of rotation. This article provides the experimental details on the quantum state control of angular momentum eigenstates reported in P. Lunt et al., Phys. Rev. Lett. 133, 253401 (2024).

On the millisecond to second time scale, stored beams of diatomic carbon anions ${\mathrm{C}}_2{}^{-}$ from a sputter ion source feature unimolecular decay of yet unexplained origin by electron emission and fragmentation. To account for the magnitude and time dependence of the experimental rates, levels with high rotational and vibrational excitation are modeled for the lowest electronic states of ${\mathrm{C}}_2{}^{-}$, also including the lowest quartet potential. Energies, spontaneous radiative decay rates (including spin-forbidden quartet-level decay), and tunneling dissociation rates are determined for a large number of highly excited ${\mathrm{C}}_2{}^{-}$ levels and their population in sputter-type ion sources is considered. For the quartet levels, the stability against autodetachment is addressed and recently calculated rates of rotationally assisted autodetachment are applied. Nonadiabatic vibrational autodetachment rates of high vibrational levels in the doublet ${\mathrm{C}}_2{}^{-}$ ground potential are also calculated. The results are combined to model the experimental unimolecular decay signals. Comparison of the modeled to the experimental rates measured at the cryogenic storage ring facility CSR gives strong evidence that ${\mathrm{C}}_2{}^{-}$ ions in quasistable levels of the quartet electronic states are the so far unidentified source of unimolecular decay.

Magic-state resource theory is a powerful tool with applications in quantum error correction, many-body physics, and classical simulation of quantum dynamics. Despite its broad scope, finding tractable resource monotones has been challenging. Stabilizer entropies have recently emerged as promising candidates (being easily computable and experimentally measurable detectors of nonstabilizerness) though their status as true resource monotones has been an open question ever since. In this Letter, we establish the monotonicity of stabilizer entropies for $\alpha \ge 2$ within the context of magic-state resource theory restricted to pure states. Additionally, we show that linear stabilizer entropies serve as strong monotones. Furthermore, we extend stabilizer entropies to mixed states as monotones via convex roof constructions whose computational evaluation significantly outperforms optimization over stabilizer decompositions for low-rank density matrices. As a direct corollary, we provide improved conversion bounds between resource states, revealing a preferred direction of conversion between magic states. These results conclusively validate the use of stabilizer entropies within magic-state resource theory and establish them as the only known family of monotones that are experimentally measurable and computationally tractable.

Direct measurement of the elastic scattering of real photons on an electromagnetic field would allow the fundamental low-energy constants of quantum electrodynamics to be experimentally determined. We show that scenarios involving the collision of three laser beams have several advantages over conventional two-beam scenarios. The kinematics of a three-beam collision allows for a higher signal-to-background ratio in the detection region, without the need for polarimetry, and separates out contributions from different orders of photon scattering. A planar configuration of colliding a photon beam from an x-ray free-electron laser with two optical beams is studied in detail. We show that measurements of elastic photon scattering and vacuum birefringence are possible with currently available technology.

Ion-neutral reactions are driving the formation of small molecules in the gas phase of interstellar clouds, where hydrogen molecules and their ions are by far the most important collision partners for any species in the astrochemical network. Here we present absolute rate coefficient measurements for the reactions ${\mathrm{HD}}^{+}+\mathrm{C}\to {\mathrm{CH}}^{+}/{\mathrm{CD}}^{+}+\mathrm{D}/\mathrm{H}$ and ${\mathrm{H}}_3^{+}+\mathrm{C}\to {\mathrm{CH}}^{+}/{\mathrm{CH}}_2^{+}+{\mathrm{H}}_2/\mathrm{H}$ obtained using a recently commissioned ion-neutral collision setup at the Cryogenic Storage Ring. Our measurements with vibrationally cold ions result in significantly higher rate coefficients when compared with previous studies using internally excited ions, bringing them in better agreement with classical capture theories. Moreover, we have performed detailed quasiclassical trajectory (QCT) calculations for the ${\mathrm{HD}}^{+}+\mathrm{C}$ reaction, using new potential energy surfaces. Our experimental results and the QCT calculations show very good agreement for the absolute cross section of the reactions, as well as for the isotope effect. These results have great potential relevance for the chemistry of the interstellar medium and the onset of organic chemistry in space.

Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. A complete quantification of uncertainties is necessary in order to make precise predictions using simulations on modern-day devices. Therefore, the inherent physical limitations of the device on the parameters of the simulation must be understood. This paper examines the interplay of errors arising from simulation of approximate time evolution with those due to practical, real-world device constraints. These errors are studied in Heisenberg-type systems on analog quantum devices described by the Ising Hamiltonian. A general framework for quantifying these errors is introduced and applied to several proposed time evolution methods, including Trotter-like methods and Floquet-engineered constant-field approaches. The limitations placed on the accuracy of time evolution methods by current devices are discussed. Characterization of the scaling of coherent effects of different error sources provides a way to extend the presented Hamiltonian engineering methods to take advantage of forthcoming device capabilities.

We demonstrate a method for determining the three-dimensional location of single atoms in a quantum gas microscopy system using a phase-only spatial light modulator to modify the point-spread function of the high-resolution imaging system. Here, the typical diffracted spot generated by a single atom as a point source is modified to a double spot that rotates as a function of the atom's distance from the focal plane of the imaging system. We present and numerically validate a simple model linking the rotation angle of the point-spread function with the distance to the focal plane. We show that, when aberrations in the system are carefully calibrated and compensated for, this method can be used to determine an atom's position to within a single lattice site in a single experimental image, extending quantum simulation with microscopy systems further into the regime of three dimensions.

We investigate the contribution of negative-energy states on the $E2$ and $M1$ polarizabilities for the ${}^{1}S_0$ and ${}^{3}P_0$ states of the Sr clock and find that they dominate the $E2\text{−}M1$ polarizability difference. Our calculated result is $-7.74\left(3.92\right)\times {10}^{-5}$ a.u., which resolves the sign inconsistency between theory and experiment. Additionally, we extend our method to other optical clocks, confirming the crucial role of negative-energy states in determining the $M1$ polarizability.

We address the problem of lattice light shifts in the Sr clock caused by multipolar $M1$ and $E2$ atom-field interactions. We present a simple but accurate formula for the magnetic-dipole polarizability that takes into account the contributions of both the positive- and negative-energy states. We calculate the contribution of negative-energy states to the $M1$ polarizabilities of the clock ${}^1{S}_0$ and ${}^3{P}_0^o$ states at the magic frequency. Taking these contributions into account, we obtain good agreement with the experimental results, explaining the major discrepancy between theory and experiment.

We present a technique to assess the focal volume of petawatt-class lasers at full power. Our approach exploits quantitative measurement of the angular distribution of electrons born in the focus via ionization of rarefied gas, which are accelerated forward and ejected ponderomotively by the field. We show that a bivariate ($\theta ,\varphi$) angular distribution, which was obtained with image plates, not only enables the peak intensity to be extracted, but also reflects nonideality of the focal-spot intensity distribution. In our prototype demonstration at intensities of a few $\times {10}^{19}$ to a few $\times {10}^{20}\mathrm{W}/{\mathrm{cm}}^2$, an f/10 optic produced a focal spot in the paraxial regime. This allows a plane-wave parametrization of the peak intensity given by $tan{\theta }_c=2/a_0$ ($a_0$ being the normalized vector potential and ${\theta }_c$ the minimum ejection angle) to be compared with our measurements. Qualitative agreement was found using an $a_0$ inferred from the pulse energy, pulse duration, and focal spot distribution with a modified parametrization, $tan{\theta }_c=2\eta /a_0$ ($\eta =2.{02}_{-0.22}^{+0.26}$). This highlights the need for (i) better understanding of intensity degradation due to focal-spot distortions and (ii) more robust modeling of the ejection dynamics. Using single-shot detection of electrons, we showed that while there is significant shot-to-shot variation in the number of electrons ejected at a given angular position, the average distribution scales with the pulse energy in a way that is consistent with that seen with the image plates. Finally, we note that the asymptotic behavior as $\theta \to 0^{\circ }$ limits the usability of angular measurement. For 800 nm, this limit is at an intensity $\sim {10}^{21}\mathrm{W}/{\mathrm{cm}}^2$.

We investigate a scalable trapped-ion array architecture for quantum control of many particles, extending techniques to access multiple dimensions. Our experimental study focuses on automated loading and shuttling of single ${\mathrm{Mg}}^{+}$ ions within our platform that contains up to 13 trapping sites in a three-dimensional arrangement. When shuttling ions from a loading hub to multiple sites, we achieve a success rate of over 0.99 999 and demonstrate coherence preservation and coherent manipulation of superposition states of a hyperfine qubit during the process. Our findings suggest promising applications of these techniques in future large-scale quantum architectures.

The opportunity to manipulate small-scale objects pushes us to the limits of our understanding of physics. Particularly promising in this regard is the interdisciplinary field of levitation, in which light fields can be harnessed to isolate nanoparticles from their environment by levitating them optically. When cooled towards their motional quantum ground state, levitated systems offer the tantalizing prospect of displaying mesoscopic quantum properties. While the interest in levitation has so far been focused mainly on manipulating individual objects with simple shapes, the field is currently moving towards the control of more complex structures, such as those featuring multiple particles or different degrees of freedom. Unfortunately, current cooling techniques are mostly designed for single objects and thus cannot easily be multiplexed to address such coupled many-body systems. Here we present an approach based on the spatial modulation of light in the far field to cool multiple nano-objects in parallel. Our procedure is based on the experimentally measurable scattering matrix and on its changes with time. We demonstrate how to compose from these ingredients a linear energy-shift operator, whose eigenstates are identified as the incoming wavefronts that implement the most efficient cooling of complex moving ensembles of levitated particles. Submitted in parallel with Hüpfl et al. [Phys. Rev. Lett. 130, 083203 (2023)], this article provides a theoretical and numerical study of the expected cooling performance as well as of the robustness of the method against environmental parameters.

We demonstrate an intense, continuous cold atomic beam generated via post-nozzle seeding of a supersonic ${}^4\mathrm{He}$ jet with ${}^7\mathrm{Li}$ atoms. The nozzle is cooled to about 4.4 K to reduce the forward velocity of the atoms. The atomic beam is brought to a focus 176 cm from the nozzle by a 10 cm bore diameter magnetic hexapole lens. Absorption and fluorescence imaging of the focus show a flux of $2.3\left(4\right)\times {10}^{12}{\text{s}}^{-1}$, brightness of $1.8\left(6\right)\times {10}^{19}{\text{m}}^{-2}{\text{s}}^{-1}{\text{sr}}^{-1}$, forward velocity of 211(2) m/s, and longitudinal temperature of 7(3) mK. Results agree with a Monte Carlo simulation of the seeding dynamics and a particle-tracing simulation of the atom lens. We predict that 10 times higher flux would be possible with improved vacuum system design. Our method should provide a useful high-brightness source for atom-optical and other atomic and molecular physics applications.

Two optically pumped atomic magnetometer geometries, with sub-$\mathrm{fT}/\sqrt{\mathrm{Hz}}$ sensitivity for radio frequencies, are contrasted: one with a probe beam of high power and few passes through the atoms, the other with low power and many passes. Theoretical noise sensitivity for these conditions is modeled and compared to experimental values, with the latter geometry achieving a sensitivity of 0.19 $\pm$ 0.02 $\mathrm{fT}/\sqrt{\mathrm{Hz}}$. Further, a general approach for choosing probe parameters to optimize sensitivity is given. With the use of a $\lambda$/2 wave plate, both systems are also configured to act as an intrinsic gradiometer, enabling the rejection of common-mode interference. Common-mode interference is reduced by over 50 dB in both geometries.

The standard dynamical approach to quantum thermodynamics is based on Markovian master equations describing the thermalization of a system weakly coupled to a large environment, and on tools such as entropy production relations. Here we develop a framework overcoming the limitations that the current dynamical and information theory approaches encounter when applied to this setting. More precisely, we introduce the notion of continuous thermomajorization and employ it to obtain necessary and sufficient conditions for the existence of a Markovian thermal process transforming between given initial and final energy distributions of the system. These lead to a complete set of generalized entropy production inequalities including the standard one as a special case. Importantly, these conditions can be reduced to a finitely verifiable set of constraints governing nonequilibrium transformations under master equations. What is more, the framework is also constructive, i.e., it returns explicit protocols realizing any allowed transformation. These protocols use as building blocks elementary thermalizations, which we prove to be universal controls. Finally, we also present an algorithm constructing the full set of energy distributions achievable from a given initial state via Markovian thermal processes and provide a Mathematica implementation solving $d=6$ on a laptop computer in minutes.

In general, the optical binding force between identical particles is thought to be symmetric. However, we demonstrate analytically a counterintuitively asymmetric longitudinal optical binding force between two identical electric and magnetic dipolar dielectric particles. This homodimer is confined in two counterpropagating incoherent plane waves along the dimer's axis. The force consists of the electric dipolar, magnetic dipolar, and electric-magnetic dipolar coupling interactions. The combined effect of these interactions is markedly different than the expected behavior in the Rayleigh approximation. The asymmetric force is a result of the asymmetric forward and backward scattering of the particles due to the dipolar hybridization and coupling interactions. Consequently, it leads to a harmonic driving force on the pair, which decays with the interparticle distance to the first power. We show the rich nonequilibrium dynamics of the dimer and of the two particles impelled by the driving and binding forces and discuss the ranges of particle refractive index and size in which the asymmetric binding force arises. Our results open perspectives for nonequilibrium light-driven multiparticle transport and self-assembly.

We realize the first magneto-optical trap of an atom in main group III of the Periodic Table. Our atom of choice (indium) does not have a transition out of its ground state suitable for laser cooling; therefore, laser cooling is performed on the $|5P_{3/2},F=6\rangle \to |5D_{5/2},F=7\rangle$ transition, where $|5P_{3/2},F=6\rangle$ is a long-lived metastable state. Optimization of our trap parameters results in atoms numbers as large as $5\times {10}^8$ atoms with temperatures of order 1 mK. Additionally, through trap decay measurements, we infer a one-body trap lifetime of $12.3\mathrm{s}$. This lifetime is consistent with background gas collisions and indicates that our repumpers have closed all leakage pathways. We also infer a two-body loss rate of $1.6\times {10}^{-11}{\mathrm{cm}}^3/\mathrm{s}$, which is comparable to those measured in alkali atoms. The techniques demonstrated in this Letter can be straightforwardly applied to other group-III atoms, and our results pave the way for realizing quantum degenerate gases of these particles.