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arXiv:1701.00081 · Physical Review A

Dissipative stabilization of quantum-feedback-based multipartite entanglement with Rydberg atoms

Xiao‐Qiang Shao, Jin-Hui Wu, X. X. Yi

Published Feb 10, 2017• 35 citations
arXivHTMLPDF

Abstract

A quantum-feedback-based scheme is proposed for generating multipartite entanglements of Rydberg atoms in a dissipative optical cavity. The Rydberg blockade mechanism efficiently prevents double excitations of the system, which is further exploited to speed up the stabilization of an entangled state with a single Rydberg state excitation. The corresponding feedback operations are greatly simplified, since only one regular atom needs to be controlled during the whole process, irrespective of the number of particles. The form of the entangled state is also adjustable via regulating the Rabi frequencies of driving fields. Moreover, a relatively long lifetime of the high-lying Rydberg level guarantees a high fidelity in a realistic situation.

DOI
10.1103/physreva.95.022317

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A quantum-feedback-based scheme is proposed for generating multipartite entanglements of Rydberg atoms in a dissipative optical cavity. The Rydberg blockade mechanism efficiently prevents double excitations of the system, which is further exploited to speed up the stabilization of an entangled state with a single Rydberg state excitation. The corresponding feedback operations are greatly simplified, since only one regular atom needs to be controlled during the whole process, irrespective of the number of particles. The form of the entangled state is also adjustable via regulating the Rabi frequencies of driving fields. Moreover, a relatively long lifetime of the high-lying Rydberg level guarantees a high fidelity in a realistic situation.
A scheme is proposed for dissipative generation of maximally entanglement between two Rydberg atoms in the context of cavity QED. The spontaneous emission of atoms combined with quantum Zeno dynamics and the Rydberg antiblockade guarantees a unique steady solution of the master equation of the system, which just corresponds to the antisymmetric Bell state $|S\ensuremath{\rangle}$. The convergence rate can be accelerated by the ground-state blockade mechanism of Rydberg atoms. Meanwhile the effect of cavity decay is suppressed by the Zeno requirement, leading to a steady-state fidelity about 9090%90 as the single-atom cooperativity parameter $C\ensuremath{\equiv}{g}^{2}/(\ensuremath{\kappa}\ensuremath{\gamma})=10$, and this restriction is further relaxed to C=5.2C=5.2C=5.2 once the quantum-jump-based feedback control is exploited.
Based on Lyapunov control, a scheme is proposed to accelerate dissipation dynamics for the generation of high-fidelity entanglement between two Rydberg atoms in the context of cavity QED. We first use quantum Zeno dynamics and the Rydberg antiblockade to find a unique steady state (two-atom singlet state) for the system. Then, we apply additional coherent control (ACC) fields to improve the evolution speed of the dissipative system. The ACC fields are designed based on the target state and they vanish gradually along with increasing of the fidelity; thus, the system is guaranteed to be finally stable. Additionally, the current accelerated scheme is checked to be robust against systematic and amplitude-noise errors.
A time-dependent periodical field can be utilized to efficiently modify the Rabi coupling of system, exhibiting nontrivial dynamics. We propose a scheme to show that this feature can be utilized for speeding up the formation of dissipative steady entanglement based on the Rydberg antiblockade mechanism. When the modulation frequency is exactly equal to the central frequency of the driving field, a sufficient residence time of the two-excitation Rydberg state is allowed for an irreversible spontaneous decay onto the target state, leading to a steady entanglement with a high fidelity $\ensuremath{\sim}0.98$ and a shorter generation time $<400\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$. We show that a global maximal fidelity benefits from a consistence of microwave-field coupling and spontaneous decay strengths. The scheme manifests robust insensitivities towards the imperfect initialization, the fluctuations of van der Waals interaction, and the modulation frequency. This simple approach to facilitate the generation of dissipative entangled two-qubit states may guide an experimental direction in Rydberg quantum technology and quantum information.
Integrating Rydberg-state control of atom-atom interactions with cavity control of atom-light interactions enables the combination of local entangling operations with photon-mediated long-range coupling, measurement, and communication. Such integration is challenging because electric fields generated by charges on cavity optics and by cavity-stabilizing actuators may disturb Rydberg-state coherence. Here, we couple a Rydberg tweezer array to a high-cooperativity optical cavity, suppressing the electric fields produced by cavity length actuation so that the residual field variation of about 3 mV/cm3~\mathrm{mV/cm}3 mV/cm rms does not limit Rydberg coherence. We demonstrate two capabilities that neither system provides alone. First, we use Purcell-enhanced fluorescence to read out atoms directly in the ground-Rydberg basis within 7.5 μs7.5~μ\mathrm{s}7.5 μs, well within the Rydberg-state lifetime, with ground- and Rydberg-state detection infidelities of 3%3\%3% and 5%5\%5%, respectively, and with low atom loss. Second, we use Rydberg-Rydberg interactions to control collective light-atom scattering into the cavity mode. Specifically, we drive blockaded Rabi oscillations between a state with two ground-state atoms, which scatter collectively with a superradiant or subradiant rate controlled by the atomic positions, and an entangled state with a single Rydberg excitation, which scatters like a single atom. These capabilities open routes toward networked Rydberg processors, mid-circuit measurements in analog quantum simulators, and many-body quantum optics with entangled emitters coupled collectively to light.
We investigate the generation of a multibody Dicke state in a coupled cavity system subject to environmental noise. Based on quantum feedback control, cavity decay may play a constructive role in obtaining the intended state. The required interaction time need not be accurately controlled. In addition, the feedback operations are only applied to a single atom in one cavity during the whole evolution process, and it is not necessary to change the control strategy as the number of atoms increases. Thus, our proposal can exploit the core advantage of coupled cavities to implement a scalable control scheme for preparing multibody entanglement.
We propose a scheme for rapid generation of high fidelity steady-state entanglement between a pair of atoms. A two-photon excitation process toward long-lived Rydberg states with finite pairwise interaction, a dark-state interference effect in the individual atoms, and spontaneous emission from their short-lived excited states lead to rapid, dissipative formation of an entangled steady state. We show that for a wide range of physical parameters, this entangled state is formed on a time scale given by the strengths of coherent Raman and Rabi fields applied to the atoms, while it is only weakly dependent on the Rydberg interaction strength.