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arXiv:0709.2849 · New Journal of Physics

Trapped Rydberg ions: from spin chains to fast quantum gates

Markus Müller, Lin-Mei Liang, Igor Lesanovsky, P. Zoller

Published Sep 10, 2008• 106 citations
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Abstract

We study the dynamics of Rydberg ions trapped in a linear Paul trap, and discuss the properties of ionic Rydberg states in the presence of the static and time-dependent electric fields constituting the trap. The interactions in a system of many ions are investigated and coupled equations of the internal electronic states and the external oscillator modes of a linear ion chain are derived. We show that strong dipole–dipole interactions among the ions can be achieved by microwave dressing fields. Using low-angular momentum states with large quantum defect, the internal dynamics can be mapped onto an effective spin model of a pair of dressed Rydberg states that describes the dynamics of Rydberg excitations in the ion crystal. We demonstrate that excitation transfer through the ion chain can be achieved on a nanosecond timescale and discuss the implementation of a fast two-qubit gate in the ion chain.

DOI
10.1088/1367-2630/10/9/093009

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We study the dynamics of Rydberg ions trapped in a linear Paul trap, and discuss the properties of ionic Rydberg states in the presence of the static and time-dependent electric fields constituting the trap. The interactions in a system of many ions are investigated and coupled equations of the internal electronic states and the external oscillator modes of a linear ion chain are derived. We show that strong dipole–dipole interactions among the ions can be achieved by microwave dressing fields. Using low-angular momentum states with large quantum defect, the internal dynamics can be mapped onto an effective spin model of a pair of dressed Rydberg states that describes the dynamics of Rydberg excitations in the ion crystal. We demonstrate that excitation transfer through the ion chain can be achieved on a nanosecond timescale and discuss the implementation of a fast two-qubit gate in the ion chain.
Combining the strong and long-range interaction of cold Rydberg atoms with the controllability of trapped ions, ultracold trapped Rydberg ions provide a promising platform for scalable quantum computing. We demonstrate how microwave-dressed Rydberg states result in rotating permanent dipole moments causing strong dipole-dipole interaction between ions in highly excited Rydberg states. Due to the large difference in time scales, the fast electronic dynamics of the Rydberg ions decouple from the slower oscillator modes in the linear Coulomb crystal. These properties allow us to realize a submicrosecond two-qubit gate between two Rydberg ions confined in a Paul trap reaching fidelities of > 99% under consideration of the finite lifetime of the Rydberg states at room temperature.
We present a detailed theoretical and conceptual study of a planned experiment to excite Rydberg states of ions trapped in a Paul trap. The ultimate goal is to exploit the strong state-dependent interactions between Rydberg ions to implement quantum information processing protocols and simulate the dynamics of strongly interacting spin systems. We highlight the promise of this approach when combining the high degree of control and readout of quantum states in trapped ion crystals with the novel and fast gate schemes based on interacting giant Rydberg atomic dipole moments. We discuss anticipated theoretical and experimental challenges on the way to its realization.
Abstract Ultracold trapped atomic ions excited into highly energetic Rydberg states constitute a promising platform for scalable quantum information processing. Elementary building blocks for such tasks are high-fidelity and sufficiently fast entangling two-qubit gates, which can be achieved via strong dipole–dipole interactions between microwave-dressed Rydberg ions, as recently demonstrated experimentally (Zhang et al 2020 Nature 580 345). We theoretically investigate the performance of three protocols leading to controlled-phase gate operations. Starting from a microscopic description of Rydberg ions in a linear Paul trap, we derive an effective Hamiltonian that faithfully captures the essential dynamics underlying the gate protocols. We then use an optimization scheme to fine-tune experimentally controllable parameters like laser detuning and Rabi frequency to yield maximal gate fidelity under each studied protocol. We show how non-adiabatic transitions resulting from fast laser driving relative to the characteristic time scales of the system detrimentally affect the fidelity. Despite this, we demonstrate that in the realistic scenario of Rydberg ions with finite radiative lifetimes, optimizing the best found gate protocol enables achievement of fidelities as high as 99.25 % for a gate time of 0.2 μ s . This considerably undercuts entangling gate durations between ground state ions, for which gate times are typically limited by the comparably slower time scales of vibrational modes. Overall, this places trapped Rydberg ions into the regime where fast high-accuracy quantum computing and eventually quantum error correction become possible.
Combining the strong, long-range interactions of cold Rydberg atoms with the controllability of trapped ions, trapped Rydberg ions provide a promising platform for scalable quantum information processing. As demonstrated in a breakthrough experiment [1], microwave dressing of Rydberg states induces permanent rotating dipole moments leading to strong interactions between highly excited ions. Due to the separation of timescales, the fast electronic dynamics of Rydberg ions decouple from the slower motional modes of the linear Coulomb crystal, which typically mediate entangling gates in ground-state ion systems. Therefore, Rydberg ions enable significantly faster gate operations. We demonstrate how the unique properties of trapped Rydberg ions can be exploited to realize fast and high-fidelity entangling gates, along with the associated challenges and strategies to overcome them. Different types of gate protocols for two- and three-qubit entangling gates with trapped Rydberg ions are presented and sources of infidelity are analyzed.
We report on the observation of interactions between ultracold Rydberg atoms and ions in a Paul trap. The rate of observed inelastic collisions, which manifest themselves as charge transfer between the Rydberg atoms and ions, exceeds that of Langevin collisions for ground state atoms by about 3 orders of magnitude. This indicates a huge increase in interaction strength. We study the effect of the vacant Paul trap's electric fields on the Rydberg excitation spectra. To quantitatively describe the exhibited shape of the ion loss spectra, we need to include the ion-induced Stark shift on the Rydberg atoms. Furthermore, we demonstrate Rydberg excitation on a dipole-forbidden transition with the aid of the electric field of a single trapped ion. Our results confirm that interactions between ultracold atoms and trapped ions can be controlled by laser coupling to Rydberg states. Adding dynamic Rydberg dressing may allow for the creation of spin-spin interactions between atoms and ions, and the elimination of collisional heating due to ionic micromotion in atom-ion mixtures.
Trapped ions as one of the most promising quantum-information-processing platforms, yet conventional entangling gates mediated by collective motion remain slow and difficult to scale. Exciting trapped ions to high-lying electronic Rydberg states provides a promising route to overcome these limitations by enabling strong, long-range dipole-dipole interactions that support much faster multi-qubit operations. Here, we introduce the first scheme for implementing a native controlled-controlled-Z gate with microwave-dressed Rydberg ions by optimizing a single-pulse protocol that accounts for the finite Rydberg-state lifetime. The resulting gate outperforms standard decompositions into one- and two-qubit gates by achieving fidelities above 97% under realistic conditions, with execution times of about 2 microseconds at cryogenic temperatures. To explore the potential of trapped Rydberg ions for fault-tolerant quantum error correction, and to illustrate the utility of three-qubit Rydberg-ion gates in this context, we develop and analyze a proposal for fault-tolerant, measurement-free quantum error correction using the nine-qubit Bacon-Shor code. Our simulations confirm that quantum error correction can be performed in a fully fault-tolerant manner on a linear Rydberg-ion chain despite its limited qubit connectivity. These results establish native multiqubit Rydberg-ion gates as a valuable resource for fast, high-fidelity quantum computing and highlight their potential for fault-tolerant quantum error correction.