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arXiv:1909.03857 · Physical Review Applied

Suppressing Motional Dephasing of Ground-Rydberg Transition for High-Fidelity Quantum Control with Neutral Atoms

Xiao-Feng Shi

Published Feb 6, 2020• 40 citations
arXivHTMLPDF

Abstract

The performance of many control tasks with Rydberg atoms can be improved via suppression of the motion-induced dephasing between the ground state and Rydberg states of neutral atoms. This dephasing often occurs during the gap time when the atom is shelved in a Rydberg state before its deexcitation. This paper presents two theories about how to suppress this dephasing. First, by using laser fields to induce a specific extra phase change in the Rydberg state during the gap time, it is possible to faithfully transfer the Rydberg state back to the ground state after the gap. Although the Rydberg state transitions back and forth between different eigenstates during the gap time, it preserves the blockade interaction between the atom of interest and a nearby Rydberg excitation. This simple method of suppressing the motional dephasing of a flying Rydberg atom can be used in a broad range of methods of quantum control of neutral atoms. Second, we find that the motional dephasing can also be suppressed by using a transition in a ``V''-type dual-rail configuration. The left (right) arm of this ``V'' represents a transition to a Rydberg state $|{r}_{1(2)}⟩$ with a Rabi frequency $\mathrm{\ensuremath{\Omega}}{e}^{ikz}\phantom{\rule{0.2em}{0ex}}(\mathrm{\ensuremath{\Omega}}{e}^{\ensuremath{-}ikz})$, where $z$ is frozen without atomic drift, but changes linearly in each experimental cycle. Such a configuration is equivalent to a transition between the ground state and a hybrid time-dependent Rydberg state with a Rabi frequency $\sqrt{2}\mathrm{\ensuremath{\Omega}}$, such that there is no phase error whenever the state returns to the ground state. We study two applications of the second theory: (i) it is possible to faithfully transfer the atomic state between a hyperfine ground state and Rydberg states $|{r}_{1(2)}⟩$ with no gap time between the excitation and deexcitation; and (ii) if infrared laser fields are added to induce a transition between $|{r}_{1(2)}⟩$ and a nearby Rydberg state $|{r}_{3}⟩$ via a greatly detuned low-lying intermediate state during the gap time, the atom can keep its internal state in the Rydberg level as well as adjust the population branching in $|{r}_{1(2)}⟩$ during the gap time. This allows an almost perfect Rydberg deexcitation after the gap time, making it possible to recover a high fidelity in a Rydberg blockade gate. These theories pave the way for high-fidelity quantum control over neutral Rydberg atoms without cooling qubits to motional ground states in optical traps.

DOI
10.1103/physrevapplied.13.024008

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The performance of many control tasks with Rydberg atoms can be improved via suppression of the motion-induced dephasing between the ground state and Rydberg states of neutral atoms. This dephasing often occurs during the gap time when the atom is shelved in a Rydberg state before its deexcitation. This paper presents two theories about how to suppress this dephasing. First, by using laser fields to induce a specific extra phase change in the Rydberg state during the gap time, it is possible to faithfully transfer the Rydberg state back to the ground state after the gap. Although the Rydberg state transitions back and forth between different eigenstates during the gap time, it preserves the blockade interaction between the atom of interest and a nearby Rydberg excitation. This simple method of suppressing the motional dephasing of a flying Rydberg atom can be used in a broad range of methods of quantum control of neutral atoms. Second, we find that the motional dephasing can also be suppressed by using a transition in a V''-type dual-rail configuration. The left (right) arm of this V'' represents a transition to a Rydberg state ∣r1(2)⟩|{r}_{1(2)}⟩∣r1(2)​⟩ with a Rabi frequency \ensuremathΩeikz(\ensuremathΩe\ensuremath−ikz)\mathrm{\ensuremath{\Omega}}{e}^{ikz}\phantom{\rule{0.2em}{0ex}}(\mathrm{\ensuremath{\Omega}}{e}^{\ensuremath{-}ikz})\ensuremathΩeikz(\ensuremathΩe\ensuremath−ikz), where zzz is frozen without atomic drift, but changes linearly in each experimental cycle. Such a configuration is equivalent to a transition between the ground state and a hybrid time-dependent Rydberg state with a Rabi frequency 2\ensuremathΩ\sqrt{2}\mathrm{\ensuremath{\Omega}}2​\ensuremathΩ, such that there is no phase error whenever the state returns to the ground state. We study two applications of the second theory: (i) it is possible to faithfully transfer the atomic state between a hyperfine ground state and Rydberg states ∣r1(2)⟩|{r}_{1(2)}⟩∣r1(2)​⟩ with no gap time between the excitation and deexcitation; and (ii) if infrared laser fields are added to induce a transition between ∣r1(2)⟩|{r}_{1(2)}⟩∣r1(2)​⟩ and a nearby Rydberg state ∣r3⟩|{r}_{3}⟩∣r3​⟩ via a greatly detuned low-lying intermediate state during the gap time, the atom can keep its internal state in the Rydberg level as well as adjust the population branching in ∣r1(2)⟩|{r}_{1(2)}⟩∣r1(2)​⟩ during the gap time. This allows an almost perfect Rydberg deexcitation after the gap time, making it possible to recover a high fidelity in a Rydberg blockade gate. These theories pave the way for high-fidelity quantum control over neutral Rydberg atoms without cooling qubits to motional ground states in optical traps.
Abstract The Doppler dephasing error due to residual thermal motion of atoms is a major cause of infidelity in neutral-atom quantum gates. Besides cooling and trapping advancements, few effective methods exist to mitigate this error. In the present work, we first propose an error-erasing strategy that utilizes a pair of off-resonant fields to continuously dress the protected Rydberg state with an auxiliary state, which can induce an opposite but enhanced sensitivity to the same source of Doppler dephasing error. Combining with the optimal control of laser pulses, we have realized a family of Rydberg two-qubit controlled-NOT gates in Rb and Cs atoms that are fully immune to the Doppler dephasing error. We numerically simulate this gate operation with fidelity F ≈ 0.9906 at any temperature for a lower-excited auxiliary state, and a higher fidelity of F ≈ 0.9960 can be attained for a ground auxiliary state even at a temperature of 500 µK. Finally, we predict a super-high fidelity of F > 0.9999 for 50 μ K is possible by using the robust pulses with a larger amplitude. Our results significantly reduce atomic temperature requirements for high-fidelity quantum gates, and may provide fundamental guidance to practical fault-tolerant quantum computing with neutral atoms.
Quantum nonlinear optics by Rydberg polaritons can enable single-photon transistor and switch, single-photon source, and deterministic quantum information processing. A major hindrance in this study is the fast motional decoherence. Here, we devise a scheme to significantly enhance the coherence of Rydberg polariton by letting the atoms {\it remember} their velocities, or, alternatively, by {\it changing} the phase of Rydberg polariton according to its storage time. After the Rydberg polariton is prepared with a Rydberg state ∣r1⟩|r_1\rangle∣r1​⟩, i.e., during the storage time, two laser fields induce a transition between ∣r1⟩|r_1\rangle∣r1​⟩ and a nearby Rydberg state ∣r2⟩|r_2\rangle∣r2​⟩ via a low-lying intermediate state ∣f⟩\lvert f\rangle∣f⟩ which is largely detuned. In particular, we find that either a 2πN2π\mathbb{N}2πN protocol, a πππ-wait-πππ protocol, or a wait-πππ protocol, along with an appropriate choice of ∣f⟩\lvert f\rangle∣f⟩ can lead to a phase-coherent Rydberg polariton upon its retrieval. Importantly, the coherent transition between ∣r1⟩|r_1\rangle∣r1​⟩ and ∣r2⟩|r_2\rangle∣r2​⟩ ensures that the Rydberg polariton can block the Rydberg excitation of nearby atoms as in usual applications of Rydberg polaritons. Numerics show that the theory can nearly completely eliminate the motional dephasing, leaving Rydberg-state decay as the only fundamental channel of decoherence. This sheds light on a broad application of Rydberg-mediated quantum nonlinear optics.
Exploring controllable interactions lies at the heart of quantum science. Neutral Rydberg atoms provide a versatile route toward flexible interactions between single quanta. Previous efforts mainly focused on the excitation annihilation (EA) effect of the Rydberg blockade due to its robustness against interaction fluctuation. We study another effect of the Rydberg blockade, namely transition slow-down (TSD). In TSD, a ground-Rydberg cycling in one atom slows down a Rydberg-involved state transition of a nearby atom, which is in contrast to EA that annihilates a presumed state transition. TSD can lead to an accurate controlled-not (cnot) gate with a submicrosecond duration of about $2\ensuremath{\pi}/\mathrm{\ensuremath{\Omega}}+ϵ$ by two pulses, where ϵϵϵ is a negligible transient time to implement a phase change in the pulse and $\mathrm{\ensuremath{\Omega}}$ is the Rydberg Rabi frequency. The speedy and accurate TSD-based cnot gate makes neutral atoms comparable (superior) to superconducting (ion-trap) systems.
Abstract We analyse in detail various multi-level Rydberg excitation schemes which can be used to suppress motional dephasing in optically trapped Cesium atom qubits in the context of quantum information processing. To explore the dephasing mechanism on a quantitative level, we analyse the time evolution of the atom’s wavefunction, under the application of a composite pulse sequence ( π − 4 π − π ), taking into account controllable experimental parameters like the Rabi frequency and temperature. Our study determines the characteristics of a three level system that can be used with this pulse sequence for eliminating motional dephasing. Such systems can hence be directly employed in state-of-the-art quantum simulation and quantum computation experiments to reduce the trap induced decoherence. This paves the way towards the realization of large scale quantum information processing architecture using optically trapped alkali atom qubits.
We propose a versatile control protocol based on modulated zero-pulse-area fields that dynamically suppresses Rydberg excitation while retaining Rydberg-Rydberg interactions as an entangling phase resource. This mechanism enables single-step, perfectly entangling phase gates for arbitrary blockade strengths, eliminating finite-blockade errors even when the Rabi frequency approaches or exceeds the interaction energy. The approach defines a new operational regime for Rydberg-blockade quantum logic in which speed, fidelity, and robustness are achieved simultaneously within a simple dynamical framework. Owing to its simplicity and generality, the technique is compatible with a wide range of neutral-atom architectures and offers a promising route toward scalable, high-fidelity quantum computation and simulation.
Combining adiabatic passage and Rydberg antiblockade, we propose a scheme to implement a two-qubit phase gate between two Rydberg atoms. Detuning parameters between frequencies of atomic transitions and those of the corresponding driving lasers are carefully chosen to offset the blockade effect of two Rydberg atoms, so that an effective Hamiltonian, representing a single-photon detuning Λ-type three-level system and concluding the quantum state of two Rydberg atoms excited simultaneously, is obtained. The adiabatic-passage technique, based on the effective Hamiltonian, is adopted to implement a two-atom phase gate by using two time-dependent Rabi frequencies. Numerical simulations indicate that a high-fidelity two-qubit π -phase gate is constructed and its operation time does not have to be controlled accurately. Besides, owing to the long coherence time of the Rydberg state, the phase gate is robust against atomic spontaneous emission.