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arXiv:2408.15523 · Physics Open

Rabi oscillations and entanglement between two atoms interacting by the Rydberg blockade studied by the Jaynes–Cummings Model

Francisco D. Santillan, Andreas Hanke

Published Jul 24, 2025• 2 citations
arXivHTMLPDF

Abstract

The interaction between atoms and a quantized radiation field is fundamentally important in quantum optics and quantum information science. Due to their unusual properties, Rydberg atoms are promising building blocks for two-qubit gates and atom-light quantum interfaces, exploiting the Rydberg blockade interaction which prevents two atoms at close distance ( < 10 μ m ) from being simultaneously excited to Rydberg states. Recently, this effect was used to engineer quantum processors based on arrays of interacting Rydberg atoms illuminated by Raman lasers. Motivated by these experiments, we extend the Jaynes–Cummings model to study the interaction between two Rydberg atoms interacting by the Rydberg blockade and a quantized radiation field. We consider both number (Fock) states of the field and single-mode quantum coherent states. In particular, we discuss different types of entanglements between various components of the total system consisting of the two Rydberg-interacting atoms and coherent states of the field, and show that the behavior is significantly different compared to a system with non-interacting atoms corresponding to the two-atom Tavis-Cummings model. Our results are relevant in view of atom-light quantum interfaces as components for future long-distance quantum communication.

DOI
10.1016/j.physo.2025.100292

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The interaction between atoms and a quantized radiation field is fundamentally important in quantum optics and quantum information science. Due to their unusual properties, Rydberg atoms are promising building blocks for two-qubit gates and atom-light quantum interfaces, exploiting the Rydberg blockade interaction which prevents two atoms at close distance ( < 10 μ m ) from being simultaneously excited to Rydberg states. Recently, this effect was used to engineer quantum processors based on arrays of interacting Rydberg atoms illuminated by Raman lasers. Motivated by these experiments, we extend the Jaynes–Cummings model to study the interaction between two Rydberg atoms interacting by the Rydberg blockade and a quantized radiation field. We consider both number (Fock) states of the field and single-mode quantum coherent states. In particular, we discuss different types of entanglements between various components of the total system consisting of the two Rydberg-interacting atoms and coherent states of the field, and show that the behavior is significantly different compared to a system with non-interacting atoms corresponding to the two-atom Tavis-Cummings model. Our results are relevant in view of atom-light quantum interfaces as components for future long-distance quantum communication.
Quantum information is a rapidly developing field that merges the principles of quantum mechanics with information theory to explore new ways of processing and transmitting information. Qubits, which utilize superposition and entanglement, offer the potential for exponentially faster computation and secure communication methods that are fundamentally different from classical systems. This thesis contributes to the future of quantum information by studying two key platforms using neutral atoms: atomic arrays and atomic ensembles. It summarizes essential theoretical and experimental methods in the field and discusses key findings. To achieve entanglement among atomic qubits, Rydberg interactions are utilized, with two main effects discussed in this thesis. The Rydberg blockade effect is introduced where atoms trapped in an ensemble can form a two-level superatom. A state-insensitive optical lattice is used to achieve long coherence time for both the ground and Rydberg states. Long-lived Rabi oscillations and Ramsey interference are reported to demonstrate the collective enhancement of √N in a superatom. Furthermore, Rydberg dephasing is separated from Rydberg blockade and is investigated as a method to generate single photons from multiply excited states. This thesis presents both theoretical models and temporal evolution measurements of Rydberg dephasing from an initially unentangled Rydberg spinwave into an entangled single photon state. Additionally, this thesis examines the collective atomic dipole moment of a superatom, ⟨E⟩. Theoretical and experimental work are conducted to study the dipole moment when the phase-matched emission is combined with a coherent field in a homodyne detection method. This work advances our understanding of Rydberg interactions and collective dipole moments, contributing to the rapidly developing field of quantum information. The goal is to pave the way for the next era of quantum information through collaborative efforts and innovative research.
We study the atom-photon quantum interface with intracavity Rydberg-blocked atomic ensemble where the ground-Rydberg transition is realized by two-photon transition. Via theoretical analysis, we report our recent findings of the Jaynes-Cummings model on optical domain and robust atom-photon quantum gate enabled by this platform. The requirement on the implementation is mild which includes an optical cavity of moderately high finesse, typical alkali atoms such as Rb or Cs and the condition that cold atomic ensemble is well within the Rydberg blockade radius. The analysis focuses on the atomic ensemble's collective coupling to the quantized optical field in the cavity mode. We demonstrate its capability to serve as a controlled-PHASE gate between photonic qubits and matter qubits. The detrimental effects associated with several major decoherence factors of this system are also considered in the analysis.
We show that Jaynes-Cummings dynamics can be observed in mesoscopic atomic ensembles interacting with a classical electromagnetic field in the regime of a Rydberg blockade where the time dynamics of the average number of Rydberg excitations in mesoscopic ensembles displays collapses and revivals typical of this model. As the frequency of Rabi oscillations between collective states of Rydberg-blockaded ensembles depends on the number of interacting atoms, for randomly loaded optical dipole traps, we predict collapses and revivals of Rabi oscillations. We have studied the effects of finite interaction strengths and a finite laser linewidth on the visibility of the revivals. We have shown that observation of collapses and revivals of Rabi oscillations can be used as a signature of the Rydberg blockade without the need to measure the exact number of Rydberg atoms.
We demonstrate a Rydberg-dressed ground-state blockade that provides a strong tunable interaction energy (~1 MHz), nearly 4 orders of magnitude larger than that in ultra cold collisions, between spins of individually trapped cesium atoms.With this interaction we directly produce Bell-state entanglement between two atoms with a fidelity ≥ 81(2)%, excluding atom loss events, and ≥ 60(3)% when loss is included [1].Our method is based on a Rydberg-dressed spin-flip blockade which allows single-step, direct entanglement of long-lived ground (clock) states.For the Bell-state entanglement generation, the probability remains entirely in the Rydbergdressed ground state, freeing the approach from the experimental burden of coherently exciting optical transitions to and from the Rydberg states.In principle Rydberg-dressed atoms are more insensitive to various decoherence mechanisms and lead to a better quantum control fidelity [2].In addition, we observed Jaynes-Cummings (JC) ladder and its nonlinearity of a Rydbergdressed atomic system.This nonlinearity induced by the Rydberg-dressed spin-flip blockade and the symmetric coupling between a Rydberg atom and atomic ensembles in the ground state, and this differentiates single and two microwave photon excitations from Rydberg-dressed state atoms.
The realization of a Jaynes-Cummings model in the optical domain is proposed for an atomic ensemble. The scheme exploits the collective coupling of the atoms to a quantized cavity mode and the nonlinearity introduced by coupling to high-lying Rydberg states. A two-photon transition resonantly couples the single-atom ground state $|g\ensuremath{\rangle}$ to a Rydberg state $|e\ensuremath{\rangle}$ via a nonresonant intermediate state $|i\ensuremath{\rangle}$, but due to the interaction between Rydberg atoms only a single atom can be resonantly excited in the ensemble. This restricts the state space of the ensemble to the collective ground state $|G\ensuremath{\rangle}$ and the collectively excited state $|E\ensuremath{\rangle}$ with a single Rydberg excitation distributed evenly on all atoms. The collectively enhanced coupling of all atoms to the cavity field with coherent coupling strengths which are much larger than the decay rates in the system leads to the strong coupling regime of the resulting effective Jaynes-Cummings model. We use numerical simulations to show that the cavity transmission can be used to reveal detailed properties of the Jaynes-Cummings ladder of excited states and that the atomic nonlinearity gives rise to highly nontrivial photon emission from the cavity. Finally, we suggest that the absence of interactions between remote Rydberg atoms may, due to a combinatorial effect, induce a cavity-assisted excitation blockade whose range is larger than the typical Rydberg dipole-dipole interaction length.
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.