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arXiv:1606.08198 · Physical Review A

Two-qubit gates using adiabatic passage of the Stark-tuned Förster resonances in Rydberg atoms

Ilya I. Beterov, Mark E. Saffman, Elena A. Yakshina, Denis B. Tretyakov, Vasily M. Entin, S. Bergamini, Elena A. Kuznetsova, I. I. Ryabtsev

Published Dec 6, 2016• 61 citations
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Abstract

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.

DOI
10.1103/physreva.94.062307

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quant-pharXiv:2610.24755•Oct 20, 2026•0 citations
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→90P+95P90S+96S\ensuremath{\rightarrow}90P+95P90S+96S\ensuremath→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.
High-fidelity entangled Bell states are of great interest in quantum physics. Entanglement of ultracold neutral atoms in two spatially separated optical dipole traps is promising for implementation of quantum computing and quantum simulation and for investigation of Bell states of material objects. We propose a method to entangle two atoms via long-range Rydberg-Rydberg interaction. Alternative to previous approaches, based on Rydberg blockade, we consider radio-frequency-assisted Stark-tuned F\"orster resonances in Rb Rydberg atoms. To reduce the sensitivity of the fidelity of Bell states to the fluctuations of interatomic distance, we propose to use the double adiabatic passage across the radio-frequency-assisted Stark-tuned F\"orster resonances, which results in a deterministic phase shift of the collective two-atom state.
We have studied the regimes of deterministic single-atom Rydberg excitation in the conditions of Rydberg blockade and the methods of compensation for the dynamic phase of the wave function during the adiabatic passage. Using these methods, we have proposed schemes of single-qubit and two-qubit quantum states with mesoscopic atomic ensembles containing a random number of atoms, considred as quibits. The double adiabatic passage of the Förster resonance for two interacting atoms with a deterministic phase shift can be used for the implementation of two-qubit gates with reduced sensitivity of the gate fidelity to the fluctuations of the interatomic distance.
We propose a controlled-Z gate scheme for Rydberg atoms based on level-crossing-free echoing rapid adiabatic population transfer. We design antisymmetric Rabi frequency pulses and symmetric detuning pulses, enabling the system to completely avoid level-crossing points throughout the evolution, and the dynamical phase is naturally eliminated by the time-reversal symmetry of the double-pulse sequence. We incorporate dissipative effects through the Lindblad master equation. The numerical simulation yields a two-qubit CZ gate fidelity of 0.9999. When the Rabi-frequency fluctuation is within ±2%\pm 2\%±2%, and the detuning offset is within ±1%\pm 1\%±1%, the fidelity can still remain above 0.999. Under the same dissipative model, the three-qubit CCZ gate achieves a fidelity of 0.999. When a single-parameter fluctuation does not exceed ±3%\pm 3\%±3%, the fidelity is always higher than 0.997. Our scheme requires no laser phase jumps or fast switching operations. The zero-area pulse structure suppresses first-order intensity noise, and the symmetric double-pulse sequence avoids spatially resolved laser switching, making it suitable for parallel gate operations in large-scale neutral-atom arrays.
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.
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.