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Optimal metrology with programmable quantum sensors

Quantum sensors are an established technology that has created new opportunities for precision sensing across the breadth of science. Using entanglement for quantum-enhancement will allow us to construct the next generation of sensors that can approach the fundamental limits of precision allowed by quantum physics. However, determining how state-of-the-art sensing platforms may be used to converge to these ultimate limits is an outstanding challenge. In this work we merge concepts from the field of quantum information processing with metrology, and successfully implement experimentally a *programmable quantum sensor* operating close to the fundamental limits imposed by the laws of quantum mechanics. We achieve this by using low-depth, parametrized quantum circuits implementing optimal input states and measurement operators for a sensing task on a trapped ion experiment. With 26 ions, we approach the fundamental sensing limit up to a factor of 1.45(1), outperforming conventional spin-squeezing with a factor of 1.87(3). Our approach reduces the number of averages to reach a given Allan deviation by a factor of 1.59(6) compared to traditional methods not employing entanglement-enabled protocols. We further perform on-device quantum-classical feedback optimization to `self-calibrate' the programmable quantum sensor with comparable performance. This ability illustrates that this next generation of quantum sensor can be employed without prior knowledge of the device or its noise environment.

quant-ph↗

A quantum processor based on coherent transport of entangled atom arrays

The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is central for building scalable quantum information systems. In most state-of-the-art approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here, we demonstrate a quantum processor with dynamic, nonlocal connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, in between layers of single- and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation. We use this architecture to realize programmable generation of entangled graph states such as cluster states and a 7-qubit Steane code state. Furthermore, we shuttle entangled ancilla arrays to realize a surface code with 19 qubits and a toric code state on a torus with 24 qubits. Finally, we use this architecture to realize a hybrid analog-digital evolution and employ it for measuring entanglement entropy in quantum simulations, experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars. Realizing a long-standing goal, these results pave the way toward scalable quantum processing and enable new applications ranging from simulation to metrology.

quant-ph↗

Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer

Gate model quantum computers promise to solve currently intractable computational problems if they can be operated at scale with long coherence times and high fidelity logic. Neutral atom hyperfine qubits provide inherent scalability due to their identical characteristics, long coherence times, and ability to be trapped in dense multi-dimensional arrays\cite{Saffman2010}. Combined with the strong entangling interactions provided by Rydberg states\cite{Jaksch2000,Gaetan2009,Urban2009}, all the necessary characteristics for quantum computation are available. Here we demonstrate several quantum algorithms on a programmable gate model neutral atom quantum computer in an architecture based on individual addressing of single atoms with tightly focused optical beams scanned across a two-dimensional array of qubits. Preparation of entangled Greenberger-Horne-Zeilinger (GHZ) states\cite{Greenberger1989} with up to 6 qubits, quantum phase estimation for a chemistry problem\cite{Aspuru-Guzik2005}, and the Quantum Approximate Optimization Algorithm (QAOA)\cite{Farhi2014} for the MaxCut graph problem are demonstrated. These results highlight the emergent capability of neutral atom qubit arrays for universal, programmable quantum computation, as well as preparation of non-classical states of use for quantum enhanced sensing.

quant-ph↗

Hybrid setup for stable magnetic fields enabling robust quantum control

Well controlled and highly stable magnetic fields are desired for a wide range of applications in physical research, including quantum metrology, sensing, information processing, and simulation. Here we introduce a low-cost hybrid assembly of rare-earth magnets and magnetic field coils to generate a field strength of $\simeq\,10.9\,$mT with a spatial variation of less than 10$^{-6}$ within a diameter of spherical volume of $150\,$um. We characterise its tuneability and stability performance using a single Mg$^{+}$ atom confined in a radio-frequency surface-electrode trap under ultra-high vacuum conditions. The strength of the field can be tuned with a relative precision of $\leq 2\,\times\,10^{-5}$ and we find a passive temporal stability of our setup of better than $1.0\,\times\,10^{-4}$ over the course of one hour. Slow drifts on time scales of a few minutes are actively stabilised by adjusting electric currents in the magnetic field coils. In this way, we observe coherence times of electronic superposition states of greater than six seconds using a first-order field insensitive (clock) transition. In a first application, we demonstrate sensing of magnetic fields with amplitudes of $\geq0.2\,$uT oscillating at $\simeq 2π\,\times\,60\,$MHz. Our approach can be implemented in compact and robust applications with strict power and load requirements.

quant-ph↗

Exploring gravity with the MIGA large scale atom interferometer

We present an underground long baseline atom interferometer to study gravity at large scale. The hybrid atom-laser antenna will use several atom interferometers simultaneously interrogated by the resonant mode of an optical cavity. The instrument will be a demonstrator for gravitational wave detection in a frequency band (100 mHz - 1 Hz) not explored by classical ground and space-based observatories, and interesting for potential astrophysical sources. In the initial instrument configuration, standard atom interferometry techniques will be adopted, which will bring to a peak strain sensitivity of 2$\cdot 10^{-13}/\sqrt{\mathrm{Hz}}$ at 2 Hz. The experiment will be realized at the underground facility of the Laboratoire Souterrain à Bas Bruit (LSBB) in Rustrel--France, an exceptional site located away from major anthropogenic disturbances and showing very low background noise. In the following, we present the measurement principle of an in-cavity atom interferometer, derive signal extraction for Gravitational Wave measurement from the antenna and determine the expected strain sensitivity. We then detail the functioning of the different systems of the antenna and describe the properties of the installation site.

physics.atom-ph↗

Transverse optical pumping of spin states

Optical pumping is an efficient method for initializing and maintaining atomic spin ensembles in a well-defined quantum spin state. Standard optical-pumping methods orient the spins by transferring photonic angular momentum to spin polarization. Generally the spins are oriented along the propagation direction of the light due to selection rules of the dipole interaction. Here we present and experimentally demonstrate that by modulating the light polarization, angular momentum perpendicular to the optical axis can be transferred efficiently to cesium vapor. The transverse pumping scheme employs transversely oriented dark states, allowing for control of the trajectory of the spins on the Bloch sphere. This new mechanism is suitable and potentially beneficial for diverse applications, particularly in quantum metrology.

quant-ph↗

Superradiant decay in non-Markovian Waveguide Quantum Electrodynamics

An array of initially excited emitters coupled to a one-dimensional waveguide exhibits superradiant decay under the Born-Markov approximation, manifested as a coherent burst of photons in the output field. In this work, we employ tensor-network methods to investigate its non-Markovian dynamics induced by finite time delays in photon exchange among the emitters. We find that the superradiant burst breaks into a structured train of correlated photons, each intensity peak corresponding to a specific photon number. We quantify the emitter-photon and emitter-emitter entanglement generated during this process and show that the latter emerges in the long-time limit, as part of the excitation becomes trapped within the emitters' singlet subspace. We finally consider the decay of the system's most radiant state, the symmetric Dicke state, and show that time delay can lead to decay rates exceeding those predicted by the Markovian approximation.

quant-ph↗

Cascaded two-photon nonlinearity in a one-dimensional waveguide with multiple two-level emitters

We propose and theoretically investigate a model to realize cascaded optical nonlinearity with few atoms and photons in one-dimension (1D). The optical nonlinearity in our system is mediated by resonant interactions of photons with two-level emitters, such as atoms or quantum dots in a 1D photonic waveguide. Multi-photon transmission in the waveguide is nonreciprocal when the emitters have different transition energies. Our theory provides a clear physical understanding of the origin of nonreciprocity in the presence of cascaded nonlinearity. We show how various two-photon nonlinear effects including spatial attraction and repulsion between photons, background fluorescence can be tuned by changing the number of emitters and the coupling between emitters (controlled by the separation).

physics.optics↗

Goldstone and Higgs modes of photons inside a cavity

Goldstone and Higgs modes have been detected in various condensed matter, cold atom and particle physics experiments. Here, we demonstrate that the two modes can also be observed in optical systems with only a few (artificial) atoms inside a cavity. We establish this connection by studying the $ U(1)/Z_2 $ Dicke model where $ N $ qubits (atoms) coupled to a single photon mode. We determine the Goldstone and Higgs modes inside the super-radiant phase and their corresponding spectral weights by performing both $ 1/J=2/N $ expansion and exact diagonization (ED) study at a finite $ N $. We find nearly perfect agreements between the results achieved by the two approaches when $ N $ gets down even to $ N = 2 $. The quantum finite size effects at a few qubits make the two modes quite robust against an effectively small counter-rotating wave term. We present a few schemes to reduce the critical coupling strength, so the two modes can be observed in several experimental systems of (artificial) atoms inside a cavity by just conventional optical measurements.

quant-ph↗

Correlated Diskoid-like Electronic States

We study highly excited diskoid-like electronic states formed in the vicinity of charged and strongly polarizable diskotic nanostructures, such as circular graphene flakes. First, we study the nature of such extended states in a simple two-electron model. The two electrons are attached to a point-like nucleus with a charge 2+, where the material electron is forced to move within a 2D disk area centered at the nucleus, while the extended electron is free to move in 3D. Pronounced and complex correlations are revealed in the diskoid-like states. We also develop semiclassical one-electron models of such diskotic systems and explain how the one-electron and many-electron solutions are related.

cond-mat.mes-hall↗

Photophysics of indole upon x-ray absorption

A photofragmentation study of gas-phase indole (C$_8$H$_7$N) upon single-photon ionization at a photon energy of 420 eV is presented. Indole was primarily inner-shell ionized at its nitrogen and carbon $1s$ orbitals. Electrons and ions were measured in coincidence by means of velocity map imaging. The angular relationship between ionic fragments is discussed along with the possibility to use the angle-resolved coincidence detection to perform experiments on molecules that are strongly oriented in their recoil-frame. The coincident measurement of electrons and ions revealed fragmentation-pathway-dependent electron spectra, linking the structural fragmentation dynamics to different electronic excitations. Evidence for photoelectron-impact self-ionization was observed.

physics.atm-clus↗

Developing effective electronic-only coupled-cluster and Muller-Plesset perturbation theories for the muonic molecules

Recently we have proposed an effective Hartree-Fock (EHF) theory for the electrons of the muonic molecules that is formally equivalent to the HF theory within the context of the Nuclear-Electronic Orbital theory [Phys. Chem. Chem. Phys. 20, 4466 (2018)]. In the present report we extend the muon-specific effective electronic structure theory beyond the EHF level by introducing the effective second order Muller-Plesset perturbation theory (EMP2) and the effective coupled-cluster theory at single and double excitation levels (ECCSD) as well as an improved version including perturbative triple excitations (ECCSD(T)). These theories incorporate electron-electron correlation into the effective paradigm and through their computational implementation, a diverse set of small muonic species is considered as a benchmark at these post-EHF levels. A comparative computational study on this set demonstrates that the muonic bond length is in general non-negligibly longer than corresponding hydrogenic analogs. Next, the developed post-EHF theories are applied for the muoniated N-Heterocyclic carbene/silylene/germylene and the muoniated triazolium cation revealing the relative stability of the sticking sites of the muon in each species. The computational results, in line with previously reported experimental data demonstrate that the muon generally prefers to attach to the divalent atom with carbeneic nature. A detailed comparison of these muonic adducts with the corresponding hydrogenic adducts reveals subtle differences that have already been overlooked.

physics.atm-clus↗

The RbSr $^2Σ^+$ ground state investigated via spectroscopy of hot & ultracold molecules

We report on spectroscopic studies of hot and ultracold RbSr molecules, and combine the results in an analysis that allows us to fit a potential energy curve (PEC) for the X(1)$^2Σ^+$ ground state bridging the short-to-long-range domains. The ultracold RbSr molecules are created in a $μ$K sample of Rb and Sr atoms and probed by two-colour photoassociation spectroscopy. The data yield the long-range dispersion coefficients $C_6$ and $C_8$, along with the total number of supported bound levels. The hot RbSr molecules are created in a $1000 \,$K gas mixture of Rb and Sr in a heat-pipe oven and probed by thermoluminescence and laser-induced fluorescence spectroscopy. We compare the hot molecule data with spectra we simulated using previously published PECs determined by three different ab-initio theoretical methods. We identify several band heads corresponding to radiative decay from the B(2)$^2Σ^+$ state to the deepest bound levels of X(1)$^2Σ^+$. We determine a mass-scaled high-precision model for X(1)$^2Σ^+$ by fitting all data using a single fit procedure. The corresponding PEC is consistent with all data, thus spanning short-to-long internuclear distances and bridging an energy gap of about 75% of the potential well depth, still uncharted by any experiment. We benchmark ab-initio PECs against our results, and give the PEC fit parameters for both X(1)$^2Σ^+$ and B(2)$^2Σ^+$ states. As first outcomes of our analysis, we calculate the $s$-wave scattering properties for all stable isotopic combinations and corroborate the locations of Fano-Feshbach resonances between alkali Rb and closed-shell Sr atoms recently observed [Barbé et al., Nat. Phys., 2018, DOI:10.1038/s41567-018-0169-x]. These results should greatly contribute to the generation of ultracold alkali$-$alkaline-earth dimers, whose applications range from quantum simulation to quantum chemistry.

physics.atom-ph↗

Infrared absorption of dense helium and its importance in the atmospheres of cool white dwarfs

Aims: Hydrogen deficient white dwarfs are characterized by very dense, fluid-like atmospheres of complex physics and chemistry that are still poorly understood. The incomplete description of these atmospheres by the models results in serious problems with the description of spectra of these stars and subsequent difficulties in derivation of their surface parameters. Here, we address the problem of infrared (IR) opacities in the atmospheres of cool white dwarfs by direct $ab$ $initio$ simulations of IR absorption of dense helium. Methods: We applied state-of-the-art density functional theory-based quantum molecular dynamics simulations to obtain the time evolution of the induced dipole moment. The IR absorption coefficients were obtained by the Fourier transform of the dipole moment time autocorrelation function. Results: We found that a dipole moment is induced due to three- and more-body simultaneous collisions between helium atoms in highly compressed helium. This results in a significant IR absorption that is directly proportional to $\rm ρ_{\rm He}^3$, where $ρ_{\rm He}$ is the density of helium. To our knowledge, this absorption mechanism has never been measured or computed before and is therefore not accounted for in the current atmosphere models. It should dominate the other collisionally induced absorptions (CIA), arising from $\rm H-He$ and $\rm H_2-He$ pair collisions, and therefore shape the IR spectra of helium-dominated and pure helium atmosphere cool white dwarfs for $\rm He/H>10^4$. Conclusions: Our work shows that there exists an unaccounted IR absorption mechanism arising from the multi-collisions between He atoms in the helium-rich atmospheres of cool white dwarfs, including pure helium atmospheres. This absorption may be responsible for a yet unexplained frequency dependence of near- and mid- IR spectra of helium-rich stars.

astro-ph.SR↗

Structure of the Balmer jump. The isolated hydrogen atom

Context. The spectrum of the hydrogen atom was explained by Bohr more than one century ago. We revisit here some of the aspects of the underlying quantum structure, with a modern formalism, focusing on the limit of the Balmer series. Aims. We investigate the behaviour of the absorption coefficient of the isolated hydrogen atom in the neighbourhood of the Balmer limit. Methods. We analytically computed the total cross-section arising from bound-bound and bound-free transitions in the isolated hydrogen atom at the Balmer limit, and established a simplified semi-analytical model for the surroundings of that limit. We worked within the framework of the formalism of Landi Degl'Innocenti & Landolfi (2004, Astrophys. Space Sci. Lib., 307), which permits an almost straight-forward generalization of our results to other atoms and molecules, and which is perfectly suitable for including polarization phenomena in the problem. Results. We analytically show that there is no discontinuity at the Balmer limit, even though the concept of a "Balmer jump" is still meaningful. Furthermore, we give a possible definition of the location of the Balmer jump, and we check that this location is dependent on the broadening mechanisms. At the Balmer limit, we compute the cross-section in a fully analytical way. Conclusions. The Balmer jump is produced by a rapid drop of the total Balmer cross-section, yet this variation is smooth and continuous when both bound-bound and bound-free processes are taken into account, and its shape and location is dependent on the broadening mechanisms.

physics.atom-ph↗

K-shell photoabsorption and photoionization of trace elements. II. Isoelectronic sequences with electron number $12\leq N \leq 18$

We are concerned with improving the diagnostic potential of the K lines and edges of elements with low cosmic abundances that are observed in the X-ray spectra of supernova remnants, galaxy clusters and accreting black holes and neutron stars. Since accurate photoabsorption and photoionization cross sections are needed in their spectral models, they have been computed for isoelectronic sequences with electron number $12\leq N\leq 18$ using a multi-channel method. Target representations are obtained with the atomic structure code AUTOSTRUCTURE, and ground-state cross sections are computed with the Breit--Pauli $R$-matrix method (BPRM) in intermediate coupling, including damping (radiative and Auger) effects. The contributions from channels associated with the 2s-hole $[2{\rm s}]μ$ target configurations and those containing 3d orbitals are studied in the Mg and Ar isoelectronic sequences. Cross sections for the latter ions are also calculated in the isolated-resonance approximation as implemented in AUTOSTRUCTURE and compared with BPRM to test their accuracy. It is confirmed that the collisional channels associated with the $[2{\rm s}]μ$ target configurations must be taken into account owing to significant increases in the monotonic background cross section between the L and K edges. Target configurations with 3d orbitals give rise to fairly conspicuous unresolved transition arrays in the L-edge region, but to a much lesser extent in the K-edge which is our main concern; therefore, they have been neglected throughout owing to their computationally intractable channel inventory, thus allowing the computation of cross sections for all the ions with $12\leq N\leq 18$ in intermediate coupling with BPRM. We find that the isolated-resonance approximations performs satisfactorily.

astro-ph.IM↗

Extended transition rates and lifetimes in Al I and Al II from systematic multiconfiguration calculations

Multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) calculations were performed for 28 and 78 states in neutral and singly ionized aluminium, respectively. In Al I, the configurations of interest are $3s^2nl$ for $n=3,4,5$ with $l=0$ to $4$, as well as $3s3p^2$ and $3s^26l$ for $l=0,1,2$. In Al II, the studied configurations are, besides the ground configuration $3s^2$, $3snl$ with $n=3$ to $6$ and $l=0$ to $5$, $3p^2$, $3s7s$, $3s7p$ and $3p3d$. Valence and core-valence electron correlation effects are systematically accounted for through large configuration state function (CSF) expansions. Calculated excitation energies are found to be in excellent agreement with experimental data from the NIST database. Lifetimes and transition data for radiative electric dipole (E1) transitions are given and compared with results from previous calculations and available measurements, for both Al I and Al II. The computed lifetimes of Al I are in very good agreement with the measured lifetimes in high-precision laser spectroscopy experiments. The present calculations provide a substantial amount of updated atomic data, including transition data in the infrared region. This is particularly important since the new generation of telescopes are designed for this region. There is a significant improvement in accuracy, in particular for the more complex system of neutral Al I. The complete tables of transition data are available.

physics.atom-ph↗

Plasma environment effects on K lines of astrophysical interest I. Atomic structure, radiative rates and Auger widths of oxygen ions

Aims. In the context of black-hole accretion disks, the main goal of the present study is to estimate the plasma environment effects on the atomic structure and radiative parameters associated with the K-vacancy states in ions of the oxygen isonuclear sequence. Methods. We use a time-averaged Debye-Huckel potential for both the electron-nucleus and the electron-electron interactions implemented in the fully relativistic multiconfiguration Dirac-Fock (MCDF) method. Results. Modified ionization potentials, K thresholds, Auger widths and radiative transition wavelengths and rates are reported for O I - O VII in plasma environments with electron temperature and density ranges 10E5 - 10E7 K and 10E18 - 10E22 cm-3 .

physics.atom-ph↗