Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms.

Engineering controllable, strongly interacting many-body quantum systems is at the frontier of quantum simulation and quantum information processing. Arrays of laser-cooled neutral atoms in optical tweezers have emerged as a promising platform because of their flexibility and the potential for strong interactions via Rydberg states. Existing neutral atom array experiments utilize alkali atoms, but alkaline-earth atoms offer many advantages in terms of coherence and control, and also open the door to new applications in precision measurement and time keeping. In this Letter, we present a technique to trap individual alkaline-earth-like ytterbium (Yb) atoms in optical tweezer arrays. The narrow ^{1}S_{0}-^{3}P_{1} intercombination line is used for both cooling and imaging in a magic-wavelength optical tweezer at 532nm. The low Doppler temperature allows for imaging near the saturation intensity, resulting in a very high atom detection fidelity. We demonstrate the imaging fidelity concretely by observing rare (<1 in 10^{4} images) spontaneous quantum jumps into and out of a metastable state. We also demonstrate stochastic loading of atoms into a two-dimensional, 144-site tweezer array. This platform will enable advances in quantum information processing, quantum simulation, and precision measurement. The demonstrated narrow-line Doppler imaging may also be applied in tweezer arrays or quantum gas microscopes using other atoms with similar transitions, such as erbium and dysprosium.

The motion-induced dephasing is a severe problem that limits the accuracy of a quantum control process by using external laser fields in neutral Rydberg atoms. This dephasing is a major issue that limits the realizable fidelity of a quantum entangling gate with neutral atoms when there is a {\it gap} time for the Rydberg atom to drift freely. We find that such a dephasing can be largely suppressed by using a transition in a `V'-type dual-rail configuration. The left~(right) arm of this `V' represents a transition to a Rydberg state $|r_{1(2)}\rangle$ with a Rabi frequency $\Omega e^{ikz}~(\Omega e^{-ikz})$, where $z$ is frozen without atomic drift, but changes linearly in each experimental cycle. Such a configuration is equivalent to a transition between the ground state and a hybrid and time-dependent Rydberg state with a Rabi frequency $\sqrt2\Omega$, such that there is no phase error whenever the state returns to the ground state. We study two applications of this method. First, it is possible to faithfully transfer the atomic state between a hyperfine ground state $|1\rangle$ and Rydberg states $|r_{1(2)}\rangle$ with no {\it gap} time between the excitation and deexcitation. Second, by adding infrared laser fields to induce transition between $|r_{1(2)}\rangle$ and a nearby Rydberg state $|r_3\rangle$ via a largely detuned low-lying intermediate state in the {\it gap} time, the atom can keep its internal state in the Rydberg level as well as adjust the population branching in $|r_{1(2)}\rangle$ during the {\it gap} time. This allows an almost perfect Rydberg deexcitation after the {\it gap} time, making it possible to recover a high fidelity in the Rydberg blockade gate. The theory paves the way for high-fidelity quantum control over neutral Rydberg atoms without cooling qubits to the motional ground states in optical traps.

The spectra of Rydberg atoms are of great significance for studying the energy levels of Rydberg atoms and the interaction between neutral atoms, especially, the high-precision spectra of Rydberg atoms can be used to measure the energy level shifts of Rydberg atoms resulting from the dipole-dipole interactions in room-temperature vapor cells. In this paper we report the preparation of cesium Rydberg states based on the cascaded two-photon excitation of 509 nm laser and 852 nm laser in opposite, and the measurements of the fine structure of cesium Rydberg states. In this experiment, the 509 nm laser is generated by the cavity-enhanced second-harmonic generation from 1018 nm laser with a periodically-poled KTP crystal and has a maximum power of about 1 W, and the 852 nm probe laser is provided by an external-cavity diode laser with a maximum output power of 5 mW and a typical linewidth of 1 MHz. By scanning the frequency of 509 nm coupling laser, it is presented that the Doppler-free spectra based on electromagnetically-induced transparency (EIT) of 509 nm coupling laser and 852 nm probe laser. The velocity-selective EIT spectra are used to study the spectral splitting of 6S1/26P3/257S(D) ladder-type system of cesium Rydberg atoms in a room-temperature vapor cell. The powers of 852 nm probe laser and 509 nm coupling laser are 0.3 upW and 200 mW, respectively. Their waist radii are both approximately 50 m. The intervals of hyperfine splitting of the intermediate state 6P3/2(F'=3, 4, 5) and fine splitting of 57D3/2 and 57D5/2 Rydberg states are measured by a frequency calibrating. Concretely, the velocity-selective spectrum with a radio frequency (RF) modulation of 30 MHz is used as a reference to calibrate the Rydberg fine-structure states in the hot vapor cell, where the RF frequency precision is smaller than a hertz on long time scales and the EIT linewidth is smaller than 13 MHz. The experimental value of the fine structure splitting of 57D3/2 and 57D5/2 Rydberg states is (354.72.5) MHz, that is in consistence with the value of 346.8 MHz calculated by Rydberg-Ritz equation and quantum defects of 57D3/2 and 57D5/2 Rydberg states. The experimental values of hyperfine splitting of intermediate state 6P3/2(F'=3, 4, 5) are also coincident with the theoretical calculated values. The dominant discrepancy existing between the experimental and calculated results may arise from the nonlinear correspondence of the PZT while the 509 nm wavelength cavity is scanned, and the measurement accuracy influenced by the spectral linewidth. The velocity-selective spectroscopy technique can also be used to measure the energy level shifts caused by the interactions of Rydberg atoms.

In this thesis, the development of an experimental system for microscopic dipole trapping of ultracold neutral rubidium atoms is presented. The purpose of this system is to advance towards the experimental realisation of a quantum computational protocol utilising neutral atoms as qubits. It is intended that the quantum gate operations between qubits will be implemented by a scheme using Rydberg blockade, imposing a restriction on the maximum size of the dipole-trapped atom cloud; the spatial extent of the atomic ensemble contained in this trap must be smaller than the blockade radius to ensure that one single collective Rydberg state per qubit can be achieved. Therefore the experiment was designed with the intent of fulfilling these challenging requirements. This project involved the design and construction of an improved ultra-high vacuum chamber containing the optical setup for the experiment, successfully achieving pressures below 5 x 10-10 mbar. A magneto-optical trap was produced to act as a background reservoir of atoms from which to load the dipole trap. Numerous experimental measurements were done to characterise the physical properties of the trapped atoms, including the number, density and temperature of atoms, as well as the lifetime of the trap. The results of these measurements led to the conclusion that a suitable reservoir for loading the dipole trap had been produced. Significant work was carried out to set up and obtain the dipole trap in the laboratory. Measurements of the characteristic properties of the trap and the atoms confined in the trap were carried out to investigate the behaviour of the atoms and to validate our design. Ultimately a trap containing tens of atoms was achieved, with an atom cloud diameter of ~1.2 µm in two dimensions, being well within the estimated Rydberg blockade radius of ~4.4 µm for n ~ 60 as intended. The two-photon excitation laser system for the probing of Rydberg states, for future applications in Rydberg blockade-based quantum gate operations, was also developed during the course of this work. Different Rydberg states were detected experimentally by the observation of Autler-Townes splitting in a three-level atom scheme. Overall, the work presented in this thesis provides a strong groundwork for the advancement towards neutral atom-based quantum gates, including the development of the experimental system and the production of standard procedures to carry out characterisation measurements of the traps efficiently in the future. The main achievements of this work are the establishment of the experimental apparatus, the achievement of a microscopic dipole trap which conforms to the requirements of an atomic qubit, and the significant growth in the knowledge of atom trapping specific to our system.

Rydberg ions with orbital dimensions up to approximately 1000 a,, are found to traverse thin gas targets fairly undisturbed, indicating relatively small ionisation cross sections ui. Theoretical estimates which take into account screening of target nuclei reveal that q(n) becomes asymptotically independent of principal quantum number n. In recent years a number of reports have dealt with Rydberg ions which travel through gaseous targets and residual gas in beam lines prior to being observed by field ionisation or radiative decays (Braithwaite et a1 1975, Kim and Meyer 1980, Betz et a1 1980, 1983). It is well understood that the long lifetime of Rydberg states, 7,~ a n312, where n and 1 denote principal and angular quantum number, respectively, allows detection long after creation of the state, but no explanation was given for the fact that these ions could be observed and were not destroyed in collisions with atoms along the flight path. For obvious reasons, a steep rise of electron-loss cross section, cri(n) a n2, is expected only for ionisation by charged particles. We estimate ionisation by neutral atoms and find that ui(n) deviates significantly from a n2 dependence even for the lowest n values and becomes asymptotically independent of n. The latter result is in agreement with expectations from Butler and May (1965) and estimates by Matsuzawa (1980). 125 MeV sulphur ions from the Munich Tandem van de Graaff accelerator were prestripped to obtain bare nuclei (charge 16') and directed through a gas cell of length 3 cm containing target gases (N2, CH4) at pressures up to approximately 1 Torr. Two cryogenic pumping systems aided by two turbomolecular pumps served to achieve high vacuum (about Torr) behind the gas target. At a distance of 10 cm behind the centre of the gas target a Si(Li) detector observed K x-rays due to decays of Rydberg states formed by electron capture in the gas target. Energy resolution was sufficient to resolve hydrogen-like transitions. Separate experiments with other lengths of the gas cell and variation of target-detector distance showed that the observed x-ray decays contain negligible contributions due to states formed by collisions along the flight path between gas target and the end of the detection region. Beam intensity was monitored by means of a Faraday cup. Further experimental details and dis- cussions of the technique to observe Rydberg states via radiative decay cascades are

We propose a nonadiabatic non-Abelian geometric quantum operation scheme to realize universal quantum computation with mesoscopic Rydberg atoms. A single control atom entangles a mesoscopic ensemble of target atoms through long-range interactions between Rydberg states. We demonstrate theoretically that both the single qubit and two-qubit quantum gates can achieve high fidelities around or above 99.9% in ideal situations. Besides, to address the experimental issue of Rabi frequency fluctuation (Rabi error) in Rydberg atom and ensemble, we apply the dynamical-invariant-based zero systematic-error sensitivity (ZSS) optimal control theory to the proposed scheme. Our numerical simulations show that the average fidelity could be 99.98% for single ensemble qubit gate and 99.94% for two-qubit gate even when the Rabi frequency of the gate laser acquires 10% fluctuations. We also find that the optimized scheme can also reduce errors caused by higher-order perturbation terms in deriving the Hamiltonian of the ensemble atoms. To address the experimental issue of decoherence error between the ground state and Rydberg levels in Rydberg ensemble, we introduce a dispersive coupling regime between Rydberg and ground levels, based on which the Rydberg state is adiabatically discarded. The numerical simulation demonstrate that the quantum gate is enhanced. By combining strong Rydberg atom interactions, nonadiabatic geometric quantum computation, dynamical invariant and optimal control theory together, our scheme shows a new route to construct fast and robust quantum gates with mesoscopic atomic ensembles. Our study contributes to the ongoing effort in developing quantum information processing with Rydberg atoms trapped in optical lattices or tweezer arrays.

Neutral atoms are promising for large-scale quantum computing, but accurate neutral-atom entanglement depends on large Rydberg interactions which strongly limit the interatomic distances. Via a phase accumulation in detuned Rabi cycles enabled by a Rydberg interaction of similar magnitude to the Rydberg Rabi frequency, we study a controlled-phase gate with an arbitrary phase and extend it to the controlled-NOT gate. The gates need only three steps for coupling one Rydberg state, depend on easily accessible van der Waals interaction that naturally arises between distant atoms, and have no rotation error in the weak interaction regime. Importantly, they can work with very weak interactions so that well-separated qubits can be entangled. The gates are sensitive to the irremovable fluctuation of Rydberg interactions, but can still have a fidelity over 98\% with realistic position fluctuation of qubits separated over 20~$\mu$m.

The Rydberg blockade is a key ingredient for entangling atoms in arrays. However, it requires atoms to be spaced well within the blockade radius, which limits the range of local quantum gates. Here we break this constraint using Floquet frequency modulation, with which we demonstrate Rydberg-blockade entanglement beyond the traditional blockade radius and show how the enlarged entanglement range improves qubit connectivity in a neutral atom array. Further, we find that the coherence of entangled states can be extended under Floquet frequency modulation. Finally, we realize Rydberg anti-blockade states for two sodium Rydberg atoms within the blockade radius. Such Rydberg anti-blockade states for atoms at close range enables the robust preparation of strongly-interacting, long-lived Rydberg states, yet their steady-state population cannot be achieved with only the conventional static drive. Our work transforms between the paradigmatic regimes of Rydberg blockade versus anti-blockade and paves the way for realizing more connected, coherent, and tunable neutral atom quantum processors with a single approach.

Currently, the most accurate and stable clocks use optical interrogation of either a single ion or an ensemble of neutral atoms confined in an optical lattice. Here, we demonstrate a new optical clock system based on an array of individually trapped neutral atoms with single-atom readout, merging many of the benefits of ion and lattice clocks as well as creating a bridge to recently developed techniques in quantum simulation and computing with neutral atoms. We evaluate single-site-resolved frequency shifts and shortterm stability via self-comparison. Atom-by-atom feedback control enables direct experimental estimation of laser noise contributions. Results agree well with an ab initio Monte Carlo simulation that incorporates finite temperature, projective readout, laser noise, and feedback dynamics. Our approach, based on a tweezer array, also suppresses interaction shifts while retaining a short dead time, all in a comparatively simple experimental setup suited for transportable operation. These results establish the foundations for a third optical clock platform and provide a novel starting point for entanglement-enhanced metrology, quantum clock networks, and applications in quantum computing and communication with individual neutral atoms that require optical-clock-state control.

Quantum processors based on neutral atoms trapped in arrays of optical tweezers have appealing properties, including relatively easy qubit number scaling and the ability to engineer arbitrary gate connectivity with atom movement. However, these platforms are inherently prone to atom loss, and the ability to replace lost atoms during a quantum computation is an important but previously elusive capability. Here, we demonstrate the ability to measure and reinitialize, and if necessary replace, a subset of atoms while maintaining coherence in other atoms. This allows us to perform logical circuits that include single- and two-qubit gates as well as repeated midcircuit measurement while compensating for atom loss. We highlight this capability by performing up to 41 rounds of syndrome extraction in a repetition code, and combine midcircuit measurement and atom replacement with real-time conditional branching to demonstrate heralded state preparation of a logically encoded Bell state. Finally, we demonstrate the ability to replenish atoms in a tweezer array from an atomic beam while maintaining coherence of existing atoms—a key step toward execution of logical computations that last longer than the lifetime of an atom in the system.

A single Rydberg atom impurity excited in a BEC is a system that can be utilized to measure the quantum mechanical properties of electron - neutral scattering andthe electron probability density of a Rydberg atom. The Rydberg electron – neutral atom scattering process, is a fundamental scattering process, which can be described via Fermi’s pseudopotential as V{vec{r},vec{R} )=2pi textit{a}[k(R)]delta^{(3)}(vec{r}-vec{R}). The scattering length is dependent on the momentum of the Rydberg electron, and therefore is dependent on the separation of the Rydberg electron from the ion core. At the classical outermost turning point of the electron, it has the slowest momentum leading to s-wave dominated scattering potentials 10’s of MHz in depth for n<40 (Greene et al. PRL 85 2458 (2000), Bendkowsky et al. PRL 105 163201 (2010)). In alkali atoms there is a shape resonance for p-wave scattering, which becomes relevant at ion-neutral separations of ~75nm (I.I. Fabrikant J.Phys B 19, 1527 (1985)). This shape resonance potential is several GHz deep, spanning the energy level spacing between n and n-1 principal quantum numbers. At high BEC densities of 5x10^14cm-3 the nearest neighbor spacing is less than 70nm. A Rydberg atom excited within a BEC, is an excitation of the Rydberg atom and all N neutral atoms located within the Rydberg orbit, described as nS+N x 5S. The nS+N x 5S state is density shifted from the Rydberg resonance. Not only does the distribution of atoms within the Rydberg orbit lead to a density shift, but, at these high densities, atoms excited in the nS+N x 5S state near the shape resonance potential cause large perturbations to the density shift, leading to a line broadening. Therefore the spectroscopic line shape of a Rydberg atom in a BEC allows us to probe the theoretically calculated p-wave shape resonance potential. Furthermore, we can observe and measure the dynamics of neutrals excited in the nS+N x 5S state. In the ultracold regime of a BEC, the background neutral atoms within the Rydberg orbit have kinetic energies of a few kHz, and experience large forces due to the GHz-deep shape resonance potentials. An atom dragged into this deep potential leads to an exothermic state-changing collision. We measure the timescale of this state-changing collision and compare to semi-classical calculations of the neutral atoms evolving in the potential of the two-particle nS+ 5S system. We also measure the change in energy from the original nS state to the product state, (n-4)L (L<3). On time scales shorter than the state-changing collisions, which for n<100 is on the order of 10 microseconds, the neutral atoms will evolve and collect in the shallower electron-neutral potentials, which mimic the electron probability density of the Rydberg atom.With n<100, the Rydberg atom has a diameter greater than 2 micrometers. With an imaging system with <1 micrometer resolution, we expect to observe a macroscopic change in the density profile of the BEC indicating an nS versus nD Rydberg state. The BEC would serve as a contrast agent for observing textbook atomic wavefunctions (Karpiuk et al. New Journal of Physics 17, 053046 (2015)).

Optical tweezer arrays1,2 have transformed atomic and molecular physics, now forming the backbone for a range of leading experiments in quantum computing3–8, simulation1,9–12 and metrology13–15. Typical experiments trap tens to hundreds of atomic qubits and, recently, systems with around 1,000 atoms were realized without defining qubits or demonstrating coherent control16–18. However, scaling to thousands of atomic qubits with long coherence times and low-loss and high-fidelity imaging is an outstanding challenge and critical for progress in quantum science, particularly towards quantum error correction (QEC)19,20. Here we experimentally realize an array of optical tweezers trapping more than 6,100 neutral atoms in around 12,000 sites, simultaneously surpassing state-of-the-art performance for several metrics that underpin the success of the platform. Specifically, while scaling to such a large number of atoms, we demonstrate a coherence time of 12.6(1) s, a record for hyperfine qubits in an optical tweezer array. We show room-temperature trapping lifetimes of about 23 min, enabling record-high imaging survival of 99.98952(1)% with an imaging fidelity of more than 99.99%. We present a plan for zone-based quantum computing5,21 and demonstrate necessary coherence-preserving qubit transport and pick-up/drop-off operations on large spatial scales, characterized through interleaved randomized benchmarking. Our results, along with recent developments8,22–24, indicate that universal quantum computing and QEC with thousands to tens of thousands of physical qubits could be a near-term prospect.

The production and loss of ${\mathrm{He}}^{+}$ and $\mathrm{He}_{2}^{+}$ ions in the afterglow of a low pressure helium discharge are studied using a mass spectrometer to analyze the positive ions and microwave techniques to determine the electron density. The change of positive ion and electron density with time is explained by considering three dominant processes in the afterglow: the production of ${\mathrm{He}}^{+}$ ions and electrons by collisions between pairs of metastable atoms, the ambipolar diffusion of the ions and electrons, and the conversion of ${\mathrm{He}}^{+}$ ions to $\mathrm{He}_{2}^{+}$ ions by three-body collisions with neutral atoms. The time constants for the decay of the electron density at low pressures yield the ambipolar diffusion coefficient for ${\mathrm{He}}^{+}$ ions of 560 ${\mathrm{cm}}^{2}$/sec and a frequency for the conversion of ${\mathrm{He}}^{+}$ ions into $\mathrm{He}_{2}^{+}$ ions of 65 ${\mathrm{sec}}^{\ensuremath{-}1}$, both at 1 mm pressure and 300\ifmmode^\circ\else\textdegree\fi{}K. The mobility coefficient for ${\mathrm{He}}^{+}$ ions in helium obtained from the measured ambipolar diffusion coefficient is 14 ${\mathrm{cm}}^{2}$/volt-sec at 300\ifmmode^\circ\else\textdegree\fi{}K and 760-mm pressure and agrees satisfactorily with the value of 12 ${\mathrm{cm}}^{2}$/volt-sec calculated using the quantum-mechanical interaction of the ${\mathrm{He}}^{+}$ ion and the neutral helium atom.

Atomic scattering factors for electrons are strongly affected by the charge status of the scattering atoms. The difference in scattering factors for charged and neutral atoms is most pronounced in the resolution range below 5 A. As a result of the negative scattering factors of negatively charged atoms in the low-resolution range, charged glutamate or aspartate residues produce weaker densities in electron crystallographic maps than their neutral forms. Such charge effects were indeed observed in an experimental map of bacteriorhodopsin. Here we present mathematical simulations of this charge effect on electron crystallographic density maps that corroborate the experimental results. For the simulations, we first evaluated the errors introduced by approximating atomic scattering factors for neutral and charged atoms by Gaussians. The simulations then showed that the effect of a polarized pair of oxygen and hydrogen atoms on the density (polarization effect) was much smaller than that expected from the individual charged atoms (charge effect), due to charge compensation. Still, density maps obtained by electron crystallography are expected to show slightly elongated features toward the positively charged atoms.

Neutral atom arrays are particularly promising for large-scale quantum computing because it is possible to prepare large-scale qubit arrays. An unsolved issue is how to selectively excite one qubit deep in a 3D atomic array to Rydberg states. In this work, we show two methods for this purpose. The first method relies on a well-known result: in a dipole transition between two quantum states driven by two off-resonant fields of equal strength but opposite detunings ±Δ, the transition is characterized by two counter-rotating Rabi frequencies (or if the two fields have a π-phase difference). This pair of detuned fields lead to a time-dependent Rabi frequency (or ), so that a full transition between the two levels is recovered. We show that when the two detuned fields are sent in different directions, one atom in a 3D optical lattice can be selectively addressed for Rydberg excitation, and when its state is restored, the state of any nontarget atoms irradiated in the light path is also restored. Moreover, we find that the Rydberg excitation by this method can significantly suppress the fundamental blockade error of a Rydberg gate, paving the way for a high-fidelity entangling gate with a commonly used quasi-rectangular pulse that is easily obtained by pulse pickers. Along the way, we find a second method for single-site Rydberg addressing in 3D, where a selected target atom can be excited to the Rydberg state while preserving the state of any nontarget atom due to a spin-echo sequence. The capability to selectively address a target atom in 3D atomic arrays for Rydberg excitation makes it possible to design a large-scale neutral-atom information processor based on the Rydberg blockade.