Unlike the Rydberg blockade regime, the Rydberg antiblockade regime (RABR) allows more than one Rydberg atom to be excited, which can bring other interesting phenomena and applications. We propose an alternative scheme to quickly achieve the RABR. The proposed RABR can be implemented by adjusting the detuning of the classical driving field, which is, in turn, based on the former numbers of the excited Rydberg atoms. In contrast to the former schemes, the current one enables more than two atoms to be excited to Rydberg states in a short period of time and thus is useful for large-scale quantum information processing. The proposed RABR can be used to construct two- and multiqubit quantum logic gates. In addition, a Rydberg excitation superatom, which can decrease the blockade error and enlarge the blockade radius for Rydberg blockade-based schemes, is constructed based on the suggested RABR and used to realize a more robust quantum logic gate. The mechanical effect and the ionization are discussed, and the performance is investigated using the master-equation method. Finally, other possible applications of the present RABR are also given.

We propose several schemes for implementing a two-qubit quantum phase gate between two Rydberg atoms. The schemes could be realized in one step without adiabatic passage which depends on the specifical shapes and tailored pulse sequences of the laser fields. When the Rydberg-Rydberg-interaction (RRI) strength and the parameters of the driving fields satisfy some certain conditions, the effective Rabi oscillation between the two-excitation Rydberg state and the ground state would be generated, which is out of the Rydberg blockade regime and essential for our scheme. In addition, the individual addressing of the atoms is not required. And the schemes can work under strong or weak RRI strength. The imperfections induced by the variation of RRI strength and spontaneous emission are discussed through solving the master equation numerically.

Although the three-body Rydberg antiblockade regime (RABR) can produce Rabi oscillation between the Rydberg collective excited state and the collective ground state, it is still hard to use the RABR to construct the three-qubit quantum logic gate in one step since the effective Hamiltonian is always accompanied by undesired Stark shifts. In order to overcome this difficulty, an additional laser is introduced to eliminate the Stark shifts in the ground-state subspace. And the initial RABR condition is modified to eliminate the remaining undesired Stark shifts in the collective-excitation subspace. The modified RABR is then generalized to the $n (n>3)$-qubit case. Based on the proposed regime, one-step schemes to construct three- and $n$-qubit quantum controlled-PHASE gates are proposed without the requirement of atomic addressability. The asymmetric Rydberg-Rydberg interaction, which is more practical for Rydberg atoms, is also discussed and proven to be feasible for the modified RABR and quantum controlled-PHASE gate in theory. A full-Hamiltonian-based master equation is used to evaluate the performance and some experimental parameters are also considered.

Through analyzing the effective dynamics of two Rydberg atoms under the dispersive coupling process, we give a method to modify the traditional antiblockade regime with simultaneous driving without adding any extra controls and resources. The modified regime can be used to construct controlled-PHASE and controlled-NOT gates in one step without manipulating the shape and amplitude, and tailoring sequences of the driving pulses. For the controlled-PHASE gate, only one pumping process from the ground state to the Rydberg state of each atom is required thus the resource is minimal. And the atomic addressability is not necessary. The scheme can be improved a lot after adding single-qubit operations since arbitrary phases can be achieved accurately with a short period of evolution time. For one-step construction of controlled-NOT gate, two schemes with high fidelities are given and discussed. Besides, the modified regime can also be used to improve the performance of the dissipation-based quantum entanglement preparation scheme. The optimal value of the modified condition for entanglement preparation is discussed for a wide range of parameters. Our study enriches the physics and applications of the simultaneous-driving-based Rydberg antiblockade regime without adding any operation complexity.

Nonadiabatic geometric quantum computation (NGQC) has been developed to realize fast and robust geometric gate. However, the conventional NGQC is that all of the gates are performed with exactly the same amount of time, whether the geometric rotation angle is large or small, due to the limitation of cyclic condition. Here, we propose an unconventional scheme, called nonadiabatic noncyclic geometric quantum computation (NNGQC), that arbitrary single- and two-qubit geometric gate can be constructed via noncyclic non-Abelian geometric phase. Consequently, this scheme makes it possible to accelerate the implemented geometric gates against the effects from the environmental decoherence. Furthermore, this extensible scheme can be applied in various quantum platforms, such as superconducting qubit and Rydberg atoms. Specifically, for single-qubit gate, we make simulations with practical parameters in neutral atom system to show the robustness of NNGQC and also compare with NGQC using the recent experimental parameters to show that the NNGQC can significantly suppress the decoherence error. In addition, we also demonstrate that nontrivial two-qubit geometric gate can be realized via unconventional Rydberg blockade regime within current experimental technologies. Therefore, our scheme provides a promising way for fast and robust neutral-atom-based quantum computation.

Dense atom ensembles with Rydberg excitations display intriguing collective effects mediated by their strong, long-range dipole–dipole interactions. These collective effects, often modeled using Rydberg superatoms, have gained significant attention across various fields due to their potential applications in quantum information processing and quantum optics. In this review article, we delve into the theoretical foundations of Rydberg interactions and explore experimental techniques for their manipulation and detection. We also discuss the latest advancements in harnessing Rydberg collective effects for quantum computation and optical quantum technologies. By synthesizing insights from theoretical studies and experimental demonstrations, we aim to provide a comprehensive overview of this rapidly evolving field and its potential impact on the future of quantum technologies.