Coherent scattering of an elliptically polarized tweezer into a cavity mode provides a promising platform for cooling levitated nanoparticles into their combined rotational and translational quantum regime [J. Schäfer, H. Rudolph, K. Hornberger, and B. A. Stickler, Cooling Nanorotors by Elliptic Coherent Scattering, Phys. Rev. Lett. 126, 163603 (2021)]. This article presents the theory of how aspherical nanoparticles are affected by elliptically polarized laser beams, how two orthogonal cavity modes enable rotational and translational cooling, and how the resulting power spectra contain signatures of rotational nonlinearities. We provide analytic expressions for the resulting trapping frequencies, optomechanical coupling strengths, cooling rates, and steady-state occupations, and we study their dependence on the tweezer ellipticity.

Ordered atomic arrays trapped in the vicinity of nanoscale waveguides offer original light-matter interfaces, with applications to quantum information and quantum nonlinear optics. Here, we study the decay dynamics of a single collective atomic excitation coupled to a waveguide in different configurations. The atoms are arranged as a linear array and only a segment of them is excited to a superradiant mode and emits light into the waveguide. Additional atomic chains placed on one or both sides play a passive role, either reflecting or absorbing this emission. We show that when varying the geometry, such a one-dimensional atomic system could be able to redirect the emitted light, to directionally reduce or enhance it, and in some cases to localize it in a cavity formed by the atomic mirrors bounding the system.

We report on experimental results obtained from collisions of slow highly charged ${\mathrm{Ar}}^{9+}$ ions with a carbon monoxide dimer ${\left(\mathrm{CO}\right)}_2$ target. A cold target recoil ion momentum spectroscopy setup and a Coulomb explosion imaging approach are used to reconstruct the structure of the $\mathrm{CO}$ dimers. The three-dimensional structure is deduced from the two-body and three-body dissociation channels from which both the intermolecular bond length and the relative orientation of the two molecules are determined. For the three-body channels, the experimental data are interpreted with the help of a classical model in which the trajectories of the three emitted fragments are numerically integrated. We measured the equilibrium intermolecular distance to be $R_e=4.2\text{Å}$. The orientation of both CO molecules with respect to the dimer axis is found to be quasi-isotropic due to the large vibrational temperature of the gas jet.

Coupling between standard model particles and theoretically well-motivated ultralight dark matter (UDM) candidates can lead to time variation of fundamental constants, including the proton-to-electron mass ratio $\mu \equiv m_p/m_e\approx 1836$. The presence of nearly degenerate vibrational energy levels of different character in polyatomic molecules can result in significantly enhanced relative energy shifts in molecular spectra originating from ${\partial }_t\mu$, relaxing experimental complexity required for high-sensitivity measurements. We analyze the amplification of UDM effects in the spectrum of laser-cooled strontium monohydroxide (SrOH). SrOH was the first polyatomic molecule to be directly laser cooled to submillikelvin temperatures [Kozyryev et al., Phys. Rev. Lett. 118, 173201 (2017)], opening the possibility of long experimental coherence times and providing a promising platform for suppressing systematic errors. Because of the high enhancement factors $(\left|Q_{\mu }\right|\approx {10}^3)$, measurements of the $\tilde{X}\left(200\right)\leftrightarrow \tilde{X}\left({03}^{1}0\right)$ rovibrational transitions of SrOH in the microwave regime can result in $\sim {10}^{-17}$ fractional uncertainty in $\delta \mu /\mu$ with one day of integration, leading to significantly improved constraints for UDM coupling constants. We also detail how the use of more complex MOR-type radicals with additional vibrational modes arising from larger ligands R could lead to even greater enhancement factors, while still being susceptible to direct laser cooling.

The Fermi National Accelerator Laboratory (FNAL) Muon $g-2$ Experiment has measured the anomalous precession frequency $a_{\mu }^{}\equiv (g_{\mu }^{}-2)/2$ of the muon to a combined precision of 0.46 parts per million with data collected during its first physics run in 2018. This paper documents the measurement of the magnetic field in the muon storage ring. The magnetic field is monitored by systems and calibrated in terms of the equivalent proton spin precession frequency in a spherical water sample at $34.7{}^{\circ }\mathrm{C}$. The measured field is weighted by the muon distribution resulting in ${\tilde{\omega }}_p^{\prime }$, the denominator in the ratio ${\omega }_a^{}$/${\tilde{\omega }}_p^{\prime }$ that together with known fundamental constants yields $a_{\mu }^{}$. The reported uncertainty on ${\tilde{\omega }}_p^{\prime }$ for the Run-1 data set is 114 ppb consisting of uncertainty contributions from frequency extraction, calibration, mapping, tracking, and averaging of 56 ppb, and contributions from fast transient fields of 99 ppb.

We investigate magic-wavelength trapping of ultracold bialkali molecules in the vicinity of weak optical transitions from the vibrational ground state of the $X{}^1\mathrm{\Sigma }^{+}$ potential to low-lying rovibrational states of the $b{}^3{\mathrm{\Pi }}_0$ potential, focusing our discussion on the ${}^{87}\mathrm{Rb}{}^{133}\mathrm{Cs}$ molecule in a magnetic field of $B=181$ G. We show that a frequency window exists between two nearest-neighbor vibrational poles in the dynamic polarizability where the trapping potential is “near magic” for multiple rotational states simultaneously. We show that the addition of a modest DC electric field of $E=0.13$ kV/cm leads to an exact magic-wavelength trap for the lowest three rotational states at a angular-frequency detuning of ${\mathrm{\Delta }}_{v^{\prime }=0}=2\pi \times 218.22$ GHz from the $X{}^1\mathrm{\Sigma }^{+}(v=0,J=0)\to b{}^3\mathrm{\Pi }_0(v^{\prime }=0,J=1)$ transition. We derive a set of analytical criteria that must be fulfilled to ensure the existence of such magic frequency windows and present an analytic expression for the position of the frequency window in terms of a set of experimentally measurable parameters. These results should inform future experiments requiring long coherence times on multiple rotational transitions in ultracold polar molecules.

Quantum computers are expected to break today's public key cryptography within a few decades. New cryptosystems are being designed and standardized for the postquantum era, and a significant proportion of these rely on the hardness of problems like the shortest-vector problem to a quantum adversary. In this paper we describe two variants of a quantum Ising algorithm to solve this problem. One variant is spatially efficient, requiring only $O\left(N{log}_{2}N\right)$ qubits, where $N$ is the lattice dimension, while the other variant is more robust to noise. Analysis of the algorithms' performance on a quantum annealer and in numerical simulations shows that the more qubit-efficient variant will outperform in the long run, while the other variant is more suitable for near-term implementation.

Direct double ionization of the ${\mathrm{Ar}}^{+}\left(3p^{-1}\right)$ ion by a single photon is investigated both experimentally and theoretically. The photon-ion merged-beams technique was employed at the Advanced Light Source in Berkeley, USA, to measure absolute cross sections in the energy range from 60 to 150 eV. In this range, three contributions to the double ionization of ${\mathrm{Ar}}^{+}$ are to be expected: the removal of two $3p$ electrons, of a $3s$ and a $3p$ electron, and of two $3s$ electrons. Among the possible mechanisms leading to double ionization, the TS1 (two-step one) process dominates in the near-threshold region. In TS1, a photoelectron is ejected and, on its way out, knocks out a secondary electron. This two-step mechanism is treated theoretically by multiplying the calculated cross section for direct single photoionization of a given subshell with the calculated $(e,2e)$ ionization probability for the ejected photoelectron to knock off a secondary electron. The calculated cross section is in very good agreement with the experiment.

We present a quantum algorithm for European option pricing in finance, where the key idea is to work in the unary representation of the asset value. The algorithm needs novel circuitry and is divided in three parts: first, the amplitude distribution corresponding to the asset value at maturity is generated using a low-depth circuit; second, the computation of the expected return is computed with simple controlled gates; and third, standard amplitude estimation is used to gain quantum advantage. On the positive side, unary representation remarkably simplifies the structure and depth of the quantum circuit. Amplitude distributions use quantum superposition to bypass the role of classical Monte Carlo simulation. The unary representation also provides a postselection consistency check that allows for a substantial mitigation in the error of the computation. On the negative side, unary representation requires linearly many qubits to represent a target probability distribution, as compared to the logarithmic scaling of binary algorithms. We compare the performance of both unary vs binary option pricing algorithms using error maps, and find that unary representation may bring a relevant advantage in practice for near-term devices.

The concept of an embodied intelligent agent is a key concept in modern artificial intelligence and robotics. Physically, an agent is an open system embedded in an environment that it interacts with through sensors and actuators. It contains a learning algorithm that correlates the sensor and actuator results by learning features about its environment. In this article, we present a simple optical agent that uses light to probe and learn components of its environment. In our scenario, the quantum agent outperforms a classical agent: The quantum agent probes the world using single-photon pulses, where its classical counterpart uses a weak coherent state with an average photon number equal to one. We analyze the thermodynamic behavior of both agents, showing that improving the agent's estimate of the world corresponds to an increase in average work done on the sensor by the actuator pulse. Thus, our model provides a useful toy model for studying the interface between machine learning, optics, and statistical thermodynamics.

In heavy atoms and ions, nuclear structure effects are significantly enhanced due to the overlap of the electron wave functions with the nucleus. This overlap rapidly increases with the nuclear charge $Z$. We study the energy-level shifts induced by the electric-dipole and electric-quadrupole nuclear polarization effects in atoms and ions with $Z\ge 20$. The electric-dipole polarization effect is enhanced by the nuclear giant dipole resonance. The electric-quadrupole polarization effect is enhanced because the electrons in a heavy atom or ion move faster than the rotation of the deformed nucleus, thus experiencing significant corrections to the conventional approximation in which they “see” an averaged nuclear charge density. The electric nuclear polarization effects are computed numerically for $1s,$ $2s,$ $2p_{1/2},$ and high-$ns$ electrons. The results are fit with elementary functions of nuclear parameters (nuclear charge, mass number, nuclear radius, and deformation). We construct an effective potential which models the energy-level shifts due to nuclear polarization. This effective potential, when added to the nuclear Coulomb interaction, may be used to find energy-level shifts in multi-electron ions, atoms, and molecules. The fitting functions and effective potentials of the nuclear polarization effects are important for the studies of isotope shifts and nonlinearity in the King plot which are now used to search for new interactions and particles.

The energy deposition of hydrogen projectiles in material targets is of great importance in material damage, as well as in radiotherapy and dosimetry, particularly for the treatment of cancer tumors. The energy-loss description has to take into account electronic excitation, electron transfer, and nuclear displacement for collisions with atomic targets. Each of these processes become relevant at different projectile collision energies, making the modeling of the full energy-loss curve difficult to accomplish. In this article, an analytical expression for the electronic stopping cross section of atomic gas targets at nonrelativistic velocities for hydrogen ions is reported. As the energy deposition process requires a correct description of the energy-loss and scattering process, our formulation uses theoretical results at low collision energies derived from ab initio electron-nuclear dynamics (END), which accounts for the nuclear displacement, electronic excitation, and charge-transfer process. At high collision energies, the expression is based on the independent particle orbital description [R. Cabrera-Trujillo, Phys. Rev. A 60, 3044 (1999)] combined with Bethe's analytical expression obtained through a harmonic oscillator representation of a target [L. Trujillo-Lopez et al., Radiat. Phys. Chem. 156, 150 (2019)]. The two approaches are matched at intermediate energies through the charge-exchange cross sections obtained from the END approach in a probabilistic interpretation of the processes [E. Montenegro et al. Phys. Lett. A 92, 195 (1982)]. The excellent agreement obtained when compared to experimental data for H to Ar gas targets ($Z\le 18$) when hydrogen projectiles impinge gives support to the theoretical arguments implied in its derivation. The analytical expression is simple and has the correct asymptotic behavior at low and high collision energies. Furthermore, the formula explains properly the threshold effects at low collision energies which are the result of polarization effects and energy gaps in the excitation process of the target, as confirmed by our ab initio results.

Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimization, eigenvalue estimation, and machine learning. Here we establish the quantum computational universality of variational quantum computation by developing two objective functions which minimize to prepare outputs of arbitrary quantum circuits. The fleeting resource of variational quantum computation is the number of expected values which must be iteratively minimized using classical-to-quantum outer loop optimization. An efficient solution to this optimization problem is given by the quantum circuit being simulated itself. The first construction is efficient in the number of expected values for $n$-qubit circuits containing $O(polylnn)$ non-Clifford gates—the number of expected values has no dependence on Clifford gates appearing in the simulated circuit. The second approach yields $O\left(L^2\right)$ expected values whereas introducing not more than $O(lnL)$ slack qubits for a quantum circuit partitioned into $L$ gates. Hence, the utilitarian variational quantum programming procedure—based on the classical evaluation of objective functions and iterated feedback—is, in principle, as powerful as any other model of quantum computation. This result elevates the formal standing of the variational approach whereas establishing a universal model of quantum computation.

We report the production of quantum degenerate Bose-Bose mixtures of Cs and Yb with both attractive ($\mathrm{Cs}+{}^{174}\mathrm{Yb}$) and repulsive ($\mathrm{Cs}+{}^{170}\mathrm{Yb}$) interspecies interactions. Dual-species evaporation is performed in a bichromatic optical dipole trap that combines light at 1070 nm and 532 nm to enable control of the relative trap depths for Cs and Yb. Maintaining a trap which is shallower for Yb throughout the evaporation leads to highly efficient sympathetic cooling of Cs for both isotopic combinations at magnetic fields close to the Efimov minimum in the Cs three-body recombination rate at around 22 G. For $\mathrm{Cs}+{}^{174}\mathrm{Yb}$, we produce quantum mixtures with typical atom numbers of $N_{\mathrm{Yb}}\sim 5\times {10}^4$ and $N_{\mathrm{Cs}}\sim 5\times {10}^3$. We find that the attractive interspecies interaction (characterized by the scattering length $a_{\mathrm{CsYb}}=-75a_0$) is stabilized by the repulsive intraspecies interactions. For $\mathrm{Cs}+{}^{170}\mathrm{Yb}$, we produce quantum mixtures with typical atom numbers of $N_{\mathrm{Yb}}\sim 4\times {10}^4$ and $N_{\mathrm{Cs}}\sim 1\times {10}^4$. Here, the repulsive interspecies interaction ($a_{\mathrm{CsYb}}=96a_0$) can overwhelm the intraspecies interactions, such that the mixture sits in a region of partial miscibility.

The cross section of a given process fundamentally quantifies the probability for that process to occur. In the quantum regime of low energies, the cross section can greatly vary with collision energy due to quantum effects. Here, we report on a method to directly measure the atom-ion collisional cross section in the energy range of 0.2–$12\mathrm{mK}\times k_B$, by shuttling ultracold atoms trapped in an optical-lattice across a radio-frequency trapped ion. Using this method, the average number of atom-ion collisions per experiment is below one, such that the energy resolution is not limited by the broad (power-law) steady-state atom-ion energy distribution. Here, we estimate that the energy resolution is below $200\mu \mathrm{K}\times k_B$, limited by drifts in the ion's excess micromotion compensation and can be reduced to the tens of $\mu \mathrm{K}\times k_B$ regime. This resolution is one order-of-magnitude better than previous experiments measuring cold atom-ion collisional cross-section energy dependence. We used our method to measure the energy dependence of the inelastic collision cross sections of a nonadiabatic electronic-excitation-exchange (EEE) and spin-orbit change (SOC) processes. We found that, in the measured energy range, the EEE and SOC cross sections statistically agree with the classical Langevin cross section. This method allows for measuring the cross sections of various inelastic processes and opens the possibility to search for atom-ion quantum signatures such as shape resonances.

We present experiments revealing the competing effect of quantum fluctuations and of a coherent seed in the dynamics of a spin-1 Bose-Einstein condensate and discuss the relevance of a mean-field description of our system. We first explore a near-equilibrium situation, where the mean-field equations can be linearized around a fixed point corresponding to all atoms in the same Zeeman state $m=0$. Preparing the system at this classical fixed point, we observe a reversible dynamics triggered by quantum fluctuations, which cannot be understood within a classical framework. We demonstrate that the classical description becomes accurate provided a coherent seed of a few atoms only is present in the other Zeeman states $m=\pm 1$. In a second regime characterized by a strong nonlinearity of the mean-field equations, we observe a collapse dynamics driven by quantum fluctuations. This behavior cannot be accounted for by a classical description and persists for a large range of initial states. We show that all our experimental results can be explained with a semiclassical description (truncated Wigner approximation), using stochastic classical variables to model the quantum noise.

Geometrical chirality is a property of objects that describes a three-dimensional mirror-symmetry violation and therefore it requires a nonvanishing spatial extent. In contrary, optical chirality describes only the local handedness of electromagnetic fields and neglects the spatial geometrical structure of optical beams. In this Letter we put forward the physical significance of geometrical chirality of spatial structure of optical beams, which we term Kelvin's chirality. Furthermore, we report on an experiment revealing the coupling of Kelvin's chirality to optical chirality upon transmission of a focused beam through a planar medium. Our work emphasizes the importance of Kelvin's chirality in all light-matter interaction experiments involving structured light beams with spatially inhomogeneous phase and polarization distributions.

Limits to Rydberg gate fidelity that arise from the entanglement of internal states of neutral atoms with the motional degrees of freedom due to the momentum kick from photon absorption and re-emission is quantified. This occurs when the atom is in a superposition of internal states but only one of these states is manipulated by visible or UV photons. The Schrödinger equation that describes this situation is presented and two cases are explored. In the first case, the entanglement arises because the spatial wave function shifts due to the separation in time between excitation and stimulated emission. For neutral atoms in a harmonic trap, the decoherence can be expressed within a sudden approximation when the duration of the laser pulses are shorter than the harmonic oscillator period. In this limit, the decoherence is given by simple analytic formulas that account for the momentum of the photon, the temperature of the atoms, the harmonic oscillator frequency, and atomic mass. In the second case, there is a reduction in gate fidelity because the photons causing absorption and stimulated emission are in focused beam modes. This leads to a dependence of the optically induced changes in the internal states on the center of mass atomic position. In the limit where the time between pulses is short, the decoherence can be expressed as a simple analytic formula involving the laser waist, temperature of the atoms, the trap frequency, and the atomic mass. These limits on gate fidelity are studied for the standard $\pi \text{−}2\pi \text{−}\pi$ Rydberg gate and a protocol based on a single adiabatic pulse with a Gaussian envelope.

A matrix representation is introduced for stationary beamlike light fields that allows for simultaneous treatment of the orbital angular momentum (OAM) and the second-order state of spatial coherence. This coherence-OAM matrix is a counterpart of the $2\times 2$ beam coherence-polarization matrix in a Cartesian polarization basis or coherence-spin angular momentum (SAM) matrix in a circular polarization basis. The general properties of the coherence-OAM matrix are discussed and then the coherence-SAM-OAM matrix is introduced as a unifying entity for treating beams with any coherence, spin, and orbital angular momentum states.

Atom interferometers in optical cavities benefit from strong laser intensities and high-quality wave fronts. The laser frequency pairs that are needed for driving Raman transitions (often generated by phase modulating a monochromatic beam) form multiple standing waves in the cavity, resulting in a periodic spatial variation of the properties of the atom-light interaction along the cavity axis. Here, we model this spatial dependence and calculate two-photon Rabi frequencies and AC Stark shifts. We compare the model to measurements performed with varying cavity and pulse parameters such as cavity offset from the carrier frequency and the longitudinal position of the atom cloud. We show how setting cavity parameters to optimal values can increase the Raman transition efficiency at all positions in the cavity and nearly double the contrast in a Mach-Zehnder cavity atom interferometer in comparison to the unoptimized case.