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arXiv:1806.09775 · Physical Review A

Robust Rydberg gate via Landau-Zener control of Förster resonance

Xi-Rong Huang, Zong-Xing Ding, Chang‐Sheng Hu, Li-Tuo Shen, Weibin Li, Huai‐Zhi Wu, Shi‐Biao Zheng

Published Nov 19, 2018• 45 citations
arXivHTMLPDF

Abstract

In this paper, we propose a scheme to implement the two-qubit controlled-$Z$ gate via the Stark-tuned F\"orster interaction of Rydberg atoms, where the F\"orster defect is driven by a time-dependent electric field of a simple sinusoidal function while the matrix elements of the dipole-dipole interaction are time independent. It is shown that when the system is initially in a specific state, it makes a cyclic evolution after a preset interaction time, returning to the initial state, but picks up a phase, which can be used for realizing a two-atom controlled-$Z$ gate. Due to the interference of sequential Landau-Zener transitions, the population and phase of the state is quasideterministic after the cyclic evolution and therefore the gate fidelity is insensitive to fluctuations of the interaction time and the dipole-dipole matrix elements. Feasibility of the scheme realized with Cs atoms is discussed in detail, which shows that the two-qubit gate via Landau-Zener control can be realized with the state-of-the-art experimental setup.

DOI
10.1103/physreva.98.052324

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In this paper, we propose a scheme to implement the two-qubit controlled-ZZZ gate via the Stark-tuned F"orster interaction of Rydberg atoms, where the F"orster defect is driven by a time-dependent electric field of a simple sinusoidal function while the matrix elements of the dipole-dipole interaction are time independent. It is shown that when the system is initially in a specific state, it makes a cyclic evolution after a preset interaction time, returning to the initial state, but picks up a phase, which can be used for realizing a two-atom controlled-ZZZ gate. Due to the interference of sequential Landau-Zener transitions, the population and phase of the state is quasideterministic after the cyclic evolution and therefore the gate fidelity is insensitive to fluctuations of the interaction time and the dipole-dipole matrix elements. Feasibility of the scheme realized with Cs atoms is discussed in detail, which shows that the two-qubit gate via Landau-Zener control can be realized with the state-of-the-art experimental setup.
Fault-tolerant implementation of quantum gates is one of preconditions for realizing quantum computation. The platform of Rydberg atoms is one of the most promising candidates for achieving quantum computation. We propose to implement a controlled-ZZZ gate on Rydberg atoms where an amplitude-modulated field is employed to induce Rydberg antiblockade. Gate robustness against the fluctuations in the Rydberg-Rydberg interaction can be largely enhanced by adjusting amplitude-modulated field. Furthermore, we introduce a Landau-Zener-St\"uckelberg transition on the target atom so as to improve the gate resilience to the deviation in the gate time and the drift in the pulse amplitude. With feasible experimental parameters, one can achieve the gate with low fidelity errors caused by atomic decay, interatomic dipole-dipole force, and Doppler effects. Finally, we generalize the gate scheme into multiqubit cases, where resilient multiqubit phase gates can be obtained in one step with an unchanged gate time as the number of qubits increases.
We propose schemes of controlled-Z and controlled-not gates with ultracold neutral atoms based on deterministic phase accumulation during double adiabatic passage of the Stark-tuned F\"orster resonance of Rydberg states. The effect of deterministic phase accumulation during double adiabatic passage in a two-level quantum system has been analyzed in detail. Adiabatic rapid passage using nonlinearly chirped pulses with rectangle intensity profile has been discussed. Nonlinear time dependence of the energy detuning from the F\"orster resonance is used to achieve a high fidelity of population transfer between Rydberg states. Fidelity of two-qubit gates has been studied with an example of the $90S+96S\ensuremath{\rightarrow}90P+95P$ Stark-tuned F\"orster resonance in Cs Rydberg atoms.
Abstract We present a scheme for implementation of controlled-Z and controlled-NOT gates via rapid adiabatic passage and Stark-tuned Förster resonance. By sweeping the Förster resonance once without passing through it and adiabatically tuning the angle-dependent Rydberg–Rydberg interaction of the dipolar nature, the system can be effectively described by a two-level system with the adiabatic theorem. The single adiabatic passage leads to a gate fidelity as high as 0.999 and a greatly reduced gate operation time. We investigate the scheme by considering an actual atomic level configuration with rubidium atoms, where the fidelity of the controlled-Z gate is still higher than 0.99 under the influence of the Zeeman effect.
Adiabatic controlled-ZZZ gate for neutral atoms with Förster-enhanced Rydberg dressing
We study an adiabatic controlled-ZZZ (CZ) gate for neutral atoms in which dipole-dipole coupling between nearly degenerate Rydberg pair states enhances the interaction between dressed ground states. This coupling produces an avoided crossing in the two-atom dressed-state spectrum. Approaching the crossing enhances the dressed interaction, but also reduces the dressed-state gap and increases the Rydberg admixture. We identify a Förster-enhanced operating range in which the required conditional phase is accumulated with adiabatic return and small transient Rydberg population. We then analyze the finite-time dynamics of the two-qubit computational states under a smooth pulse. Reducing the dressing strength weakens the dressed interaction, so maintaining the target phase at the same pulse duration requires operation closer to the avoided crossing, where the Rydberg admixture increases. This dependence is then used to select the shortest gate at a fixed peak Rabi frequency in the Förster-enhanced operating range that accumulates the CZ phase with high Bell-state fidelity while keeping the Rydberg population small. Changing the Förster defect shifts the avoided crossing, while the gate parameters change only weakly. For a specific rubidium Förster channel, the selected gate corresponds to experimentally relevant laser coupling, pulse duration, and interatomic separation. We also estimate errors from the finite Rydberg lifetime and from weak excitation of a neighboring spectator atom. For the parameters considered, the spectator-induced error remains below the finite-lifetime contribution.
The advent of digital neutral-atom quantum computers relies on the development of fast and robust protocols for high-fidelity quantum operations. In this work, we introduce a novel scheme for entangling gates using four atomic levels per atom: a ground-state qubit and two Rydberg states. A laser field couples the qubit to one of the two Rydberg states, while a microwave field drives transitions between the two Rydberg states, enabling a resonant dipole-dipole interaction between different atoms. We show that controlled- Z gates can be realized in this scheme without requiring optical phase modulation and relying solely on a microwave field with time-dependent phase and amplitude. We demonstrate that such gates are faster and less sensitive to Rydberg decay than state-of-the-art Rydberg gates based on van der Waals interactions. Moreover, we systematically stabilize our protocol against interatomic distance fluctuations and analyze its performance in realistic setups with rubidium or cesium atoms. Our results open up new avenues to the use of microwave-driven dipolar interactions for quantum computation with neutral atoms.
Cold atoms in highly excited Rydberg states are promising candidates to implement quantum logic gates of a quantum computer via long-range dipole-dipole interaction. Two-qubit gates require a controlled interaction of only two close Rydberg atoms. We report on the first spectroscopic observation of the resonant dipole-dipole interaction between two cold rubidium Rydberg atoms confined in a small laser excitation volume. The interaction strength was controlled by fine-tuning of the Rydberg levels into a Förster resonance using the Stark effect. The observed resonance line shapes are in good agreement with numerical Monte Carlo simulations.