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arXiv:1802.10424 · Physical Review A

Analysis of imperfections in the coherent optical excitation of single atoms to Rydberg states

Sylvain de Léséleuc, Daniel Barredo, Vincent Lienhard, Antoine Browaeys, Thierry Lahaye

Published May 3, 2018• 207 citations
arXivHTMLPDF

Abstract

Arrays of single atoms promoted to Rydberg states offer a versatile platform for quantum simulation and implementation of two-qubit gates. A comprehensive account of the limiting factors and sources of errors in their experimental preparation is presented.
DOI
10.1103/physreva.97.053803

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Arrays of optically trapped atoms excited to Rydberg states have recently emerged as a competitive physical platform for quantum simulation and computing, where high-fidelity state preparation and readout, quantum logic gates, and controlled quantum dynamics of more than 100 qubits have all been demonstrated. These systems are now approaching the point where reliable quantum computations with hundreds of qubits and realistically thousands of multiqubit gates with low error rates should be within reach for the first time. In this article, the authors give an overview of the Rydberg quantum toolbox, emphasizing the high degree of flexibility for encoding qubits, performing quantum operations, and engineering quantum many-body Hamiltonians. The authors then review the state-of-the-art concerning high-fidelity quantum operations and logic gates as well as quantum simulations in many-body regimes. Finally, the authors discuss computing schemes that are particularly suited to the Rydberg platform and some of the remaining challenges on the road to general purpose quantum simulators and quantum computers.
Neutral atoms trapped and manipulated by laser light provide experimentally well accessible quantum systems allowing for a high degree of control over external and internal degrees of freedom. Arrays of dipole traps in which the atoms are confined individually in a configurable geometry constitute a versatile platform for quantum simulation and information applications. By exciting these atoms into Rydberg states, interactions of variable strength and range can be introduced into the system, allowing for the implementation of entangling gate operations or spin Hamiltonians. A crucial requirement for these schemes to function in a reliable way is the ability to create defect-free arrays of single atoms. This is generally a challenge in these types of systems, as common atom loading schemes are limited to roughly 50% probability of filling each site. In this work, a technique for the rearrangement of atoms within a scalable architecture based on micro-optical lens arrays was developed and implemented, resulting in the creation of uniformly filled regions containing more than 100 atoms, which represent the largest defect-free structures realized so far in systems of this kind. This was accomplished by filling the empty traps in a pre-defined pattern with an atom one by one using an optical tweezer. Thus, structures with up to 5 x 5 atoms could be rendered defect-free in more than 99% of attempts. Although the success rate drops below unity for larger clusters, a value of 3.1% for a 100-atom structure is still viable for experiments working with post-selection methods. The filling fraction of even the largest examined structures was observed to be higher than 88%, surpassing common loading schemes by a significant margin. The measurements presented in this thesis build on a region of the array containing 361 sites, being limited by available laser power. In contrast, the addressable range of the optical tweezer includes more than 1500 sites and microlens arrays with up to a million lenses are commercially available. By implementing coherent Rydberg excitation of this assembled atom array, significant progress toward a universal quantum computer or flexible quantum simulator has been made. Using a two-photon excitation scheme, coherent dynamics between the ground and Rydberg state could be observed simultaneously in a 5 x 5 region of the array, with two-photon Rabi frequencies on the order of Omega = 2Pi x 500kHz measured for a Rydberg laser beam waist of w_0,B = 18.7(10) µm. The choice of an appropriate Rydberg state and interatomic spacing led to the presence of strong nearest-neighbor interactions and allowed for the demonstration of the Rydberg blockade effect by observing a collective enhancement of the Rabi frequency consistent with the expected scaling ~ sqrt(N) as well as the suppression of multiple excitations. This mechanism represents the fundamental constituent of a two-qubit gate operation. The architecture introduced in this work offers a scalability unique among quantum simulation platforms and the presented results underpin its potential to propel the atom-optical approach for quantum information processing beyond the threshold of quantum supremacy. Different approaches for scaling up the system have been explored, indicating that defect-free structures of more than 1000 atoms are within range with feasible experimental improvements. Through a detailed analysis of the factors limiting the coherence of the observed dynamics, strategies for future experimental improvements have been developed. Among these, increasing the coupling strength to the Rydberg state into the megahertz regime by increasing laser power and implementing single-site addressing represents the most straight-forward and promising approach.
Precise individual addressing of single atoms in quantum registers formed by optical trap arrays is essential to achieve high-fidelity quantum gates in neutral-atom quantum computers and simulators. Two-qubit quantum gates are typically implemented using coherent two-photon laser excitation of atoms to strongly interacting Rydberg states. However, two-photon excitation encounters challenges in individual addressing with tightly focused laser beams due to atom position uncertainty and the spatial inhomogeneity in both Rabi frequencies and light shifts. In this work, we theoretically demonstrate that the fidelity of individual addressing is significantly enhanced by employing coherent three-photon laser excitation of Rydberg states. For a specific example of $5{s}_{1/2}\stackrel{{\mathrm{\ensuremath{\Omega}}}_{1}}{\ensuremath{\rightarrow}}5{p}_{3/2}\stackrel{{\mathrm{\ensuremath{\Omega}}}_{2}}{\ensuremath{\rightarrow}}7{s}_{1/2}\stackrel{{\mathrm{\ensuremath{\Omega}}}_{3}}{\ensuremath{\rightarrow}}np$ excitation in 87Rb^{87}\mathrm{Rb}87Rb atoms, we find that upon strong laser coupling in the second step (Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{2}$) and moderate coupling in the first and third steps (Rabi frequencies ${\mathrm{\ensuremath{\Omega}}}_{1}$ and ${\mathrm{\ensuremath{\Omega}}}_{3}$), the three-photon Rabi frequency is given by $\mathrm{\ensuremath{\Omega}}={\mathrm{\ensuremath{\Omega}}}_{1}{\mathrm{\ensuremath{\Omega}}}_{3}/{\mathrm{\ensuremath{\Omega}}}_{2}$. If the spatial distributions of $({\mathrm{\ensuremath{\Omega}}}_{1}{\mathrm{\ensuremath{\Omega}}}_{3})$ and ${\mathrm{\ensuremath{\Omega}}}_{2}$ are arranged to be identical, $\mathrm{\ensuremath{\Omega}}$ becomes independent of atom position, even within very tightly focused laser beams. This approach dramatically improves individual addressing of Rydberg excitation for neighboring atoms in trap arrays compared to conventional two-photon excitation schemes. Our findings are crucial for large-scale quantum registers of neutral atoms, where distances between adjacent atoms should be minimized to ensure stronger Rydberg interactions and compact arrangement of atom arrays.
We present the coherent excitation of a single Rubidium atom to the Rydberg state 58d3/258{d}_{3/2}58d3/2​ using a two-photon transition. The experimental setup is described in detail, as are experimental techniques and procedures. The coherence of the excitation is revealed by observing Rabi oscillations between ground and Rydberg states of the atom. We analyze the observed oscillations in detail and compare them to numerical simulations which include imperfections of our experimental system. Strategies for future improvements on the coherent manipulation of a single atom in our settings are given.
We propose a parity-controlled gate within a two-dimensional Rydberg atom array, enabling efficient discrimination between even and odd parities of virtually excited control atoms by monitoring the dynamic evolution of an auxiliary atom. This is achieved through the use of spin-exchange dipolar interactions between Rydberg states and coupling between ground states and Rydberg states. For practical applications, we explore its implementation in three-qubit repetition codes and rotated surface codes featuring XZZXXZZXXZZX stabilizers, enabling single-shot readout of stabilizer measurements. Comprehensive numerical simulations are conducted to assess the feasibility of the proposed approach, taking into account potential experimental imperfections such as unwanted interactions between Rydberg states, atomic position fluctuations, laser phase noise, and Rabi amplitude noise. Our study highlights the inherent advantages of the physical mechanisms underlying parity measurement, demonstrating its reliability and practicality. These findings establish our protocol as a highly promising solution for quantum error detection and computation within Rydberg atom systems, with significant potential for future experimental realizations.