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arXiv:1901.10896 · Physical Review A

Coherent and dissipative dynamics of entangled few-body systems of Rydberg atoms

Woojun Lee, Minhyuk Kim, Hanlae Jo, Yunheung Song, Jaewook Ahn

Published Apr 5, 2019• 57 citations
arXivHTMLPDF

Abstract

Experimentally observed quantum few-body dynamics of neutral atoms excited to a Rydberg state are numerically analyzed. For this, up to five rubidium atoms are trapped with optical tweezers, arranged in various two-dimensional configurations, and excited to the Rydberg $67S$ state in the nearest-neighbor blockade regime. Their coherent evolutions are measured with time-varying ground-state projections and the experimental results are analyzed with a model Lindblad equation with the homogeneous and inhomogeneous dampings determined by systematic and statistical error analysis. The coherent and dissipative dynamics of these entangled systems are successfully reproduced using the given model and external parameters optimally calibrated with the experimental results.

DOI
10.1103/physreva.99.043404

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Experimentally observed quantum few-body dynamics of neutral atoms excited to a Rydberg state are numerically analyzed. For this, up to five rubidium atoms are trapped with optical tweezers, arranged in various two-dimensional configurations, and excited to the Rydberg 67S67S67S state in the nearest-neighbor blockade regime. Their coherent evolutions are measured with time-varying ground-state projections and the experimental results are analyzed with a model Lindblad equation with the homogeneous and inhomogeneous dampings determined by systematic and statistical error analysis. The coherent and dissipative dynamics of these entangled systems are successfully reproduced using the given model and external parameters optimally calibrated with the experimental results.
Inevitably present in many current experiments with ultracold Rydberg atoms, dissipative effects such as dephasing and decay modify the dynamics of the examined system. In this thesis, the dynamics of many-body Rydberg systems in the incoherent regime is studied numerically. Specifically, a wave function Monte Carlo (MCWF) technique is integrated into a coherent two-level many-body Rydberg model, allowing a numerical simulation of dissipative dynamics. This model is used to benchmark a steady-state rate equation model and assess its range of validity. In addition, incoherent, off-resonant excitation dynamics is studied in a one-dimensional disordered geometry. We find that our simulation results can essentially be explained by the equilibration time scale as well as — for positive laser detuning — resonant excitations arising when the laser detuning compensates the Rydberg interaction. Eventually, we employ a rate equation model to investigate excitation spectra for an experimental trap geometry, which we benchmark using the MCWF technique. Based on numerical data, we deduce that in the considered parameter regime the dominant excitation mechanism can be characterized as sequential growth of aggregates of Rydberg excitations around an initial seed. Our simulation results highlight the impact of incoherent effects on observables such as Rydberg population, excitation number fluctuation and pair correlation function.
Single atoms in dipole microtraps or optical tweezers have recently become a promising platform for quantum computing and simulation. Here we report a detailed theoretical analysis of the physics underlying an implementation of a Rydberg two-qubit gate in such a system---a cornerstone protocol in quantum computing with single atoms. We focus on a blockade-type entangling gate and consider various decoherence processes limiting its performance in a real system. We provide numerical estimates for the limits on fidelity of the maximally entangled states and predict the full process matrix corresponding to the noisy two-qubit gate. We consider different excitation geometries and show certain advantages for the gate realization with linearly polarized driving beams. Our methods and results may find implementation in numerical models for simulation and optimization of neutral atom based quantum processors.
Generating entanglement between two Rydberg atoms is at the core of neutral-atom quantum computers. Current two-qubit gates operate in the Rydberg-blockade regime, in which the full strength of the van der Waals interaction between the two Rydberg atoms is not directly exploited, to avoid sensitivity to the position noise of the tweezer-trapped atoms, at the cost of a longer time spent in the Rydberg state. Here, we propose a set of techniques based on coherent control of the atomic motion obtained by combining optical tweezers and a two-dimensional optical lattice, and a sequence of multiple on/off pulses. The protocols keep the two-qubit gate error contribution from position noise below 10−410^{-4}10−4, heat the atom by less than~Δn=0.01Δn = 0.01Δn=0.01, while being robust to alignment errors of the potential up to 505050~nm and thermal excitation up to nˉ=3\bar{n} = 3nˉ=3. This toolbox opens the path for new two-qubit Rydberg gates directly, or partially, driven by the interaction, in which the atoms spend only ∼10\sim 10∼10~ns in the Rydberg state, minimizing the increasingly dominant error source originating from its finite lifetime.
Subject of this thesis is the theoretical investigation of ensembles of atoms that are coherently laser-excited to a Rydberg state. Rydberg excited atoms interact with each other over large distances, which leads to strongly correlated many-body dynamics, demanding powerful numerical tools for their modeling. The first part of the thesis deals with effective two-level atoms consisting of a ground and a Rydberg state only. For resonant laser excitation a modified scaling behavior of the excitation number is observed, which is caused by effects of finite system size and coarse graining of the medium due to the finite atomic density. For off-resonant excitation, ordered structures arise out of an initially homogeneous gas, which are reflected in strongly peaked spatial correlations and modified excitation statistics. In the second part a fast decaying intermediate level is additionally taken into account. In this situation the phenomenon of electromagnetically induced transparency (EIT) is encountered. This effect is suppressed in the presence of strong interactions between the Rydberg atoms leading to an optical nonlinearity. A model predicting the properties of a cloud of Rydberg atoms in EIT configuration is developed. In both parts the models are validated by comparing their predictions to recent experimental observations.
Individually trapped neutral atoms are a promising candidate for use in quantum computing and simulation applications. They are highly scalable, have long coherence times and can be entangled via strong dipole-dipole interactions by driving to highly excited Rydberg states. However, the fidelity of single atom operations as well as two-atom entangling operations is limited by intrinsic sources of decoherence such as atomic motion, as well as technical sources of noise such as laser intensity fluctuations and phase/frequency fluctuations. We study the effect of these factors on single atom Rabi oscillations and two-atom Rydberg blockaded Rabi oscillations, using perturbation theory and numerical simulation. We develop a window function approach which helps us qualitatively understand the significance of the different spectral components of the noise as well as quantitatively understand the dependence of the Rabi oscillation fidelity on Rabi frequency. This allows us to predict the maximum experimentally achievable fidelities using independent measurements of experimental parameters such as noise spectra and atomic temperature. Turning to the question of near-term scalability of the experimental system, we prototype and test a method of generating a ’ladder’ configuration of optical tweezers utilizing two independent lasers. Our setup allows us to fully tune the geometry of the ladder, namely the separation between the two rows, the angle between them, and their relative position along the axis of the ladder. This pseudo-2D configuration enables us to reach larger system sizes in the near future and allows us to access beyond 1D physics.