Fast multicomponent cat-state generation under resonant or strong-dressing Rydberg-Kerr interaction

Abstract

Cat states are maximally entangled states with applications in metrology and fault-tolerant quantum computation. The experiments have revealed that Rydberg collective avalanche decoherence acts as the bottleneck for cat creation with Rydberg atoms. This process initiates after the black body radiation (BBR-)induced decay of Rydberg atoms and sets a strong limit on the cat creation time. These findings necessitate the exploration of new ideas to accelerate current Rydberg cat schemes. To enhance the interaction-to-loss ratio, this paper delves into cat state formation in the strong Rydberg dressing regime, uncovering the emergence of cat states despite the presence of complex orders of nonlinearities. This unexplored regime demonstrates the potential for rapid cat state formation, particularly beneficial for operation in typical 2D lattices in Rydberg Labs. In an extreme case, this article demonstrates that second-order nonlinearity could be isolated under resonant Rydberg driving if a large number of atoms are accommodated inside the blockade volume. The resonant model significantly enhances the interaction-to-loss ratio while circumventing the adiabaticity condition, allowing fast switching of lasers. In addition, the paper presents a method for generating multi-component cat states, which are superpositions of $m$ coherent spin states ($|m-\text{CSS}\rangle$). The maximum value of $m$ is determined by the number of atoms within the blockade radius, where $m=\sqrt{N}$. The states with larger $m$ are more robust against the presence of multiple orders of nonlinearity in the strong dressing Hamiltonian and are accessible in a much shorter time compared to traditional 2-component cat states.