Hidden curved spaces in Bosonic Kitaev model

TL;DR

This paper demonstrates that hyperbolic surfaces naturally emerge in the bosonic Kitaev model, enabling exploration of curved space quantum phenomena and highly sensitive quantum sensors without physical distortions.

Contribution

It reveals the spontaneous emergence of hyperbolic geometries in the bosonic Kitaev model and proposes their use for advanced quantum sensing and exploration of curved space physics.

Findings

Existence of hyperbolic surfaces in the bosonic Kitaev model without distortions

Coupling of hyperbolic surfaces via chemical potential enables exponential sensitivity

Potential for experimental exploration of curved space quantum phenomena

Abstract

Quantum matter in curved spaces exhibits remarkable properties unattainable in flat spaces. To access curved spaces in laboratories, the conventional wisdom is that physical distortions need to be implemented into a system. In contrast to this belief, here, we show that two hyperbolic surfaces readily exist in bosonic Kitaev model in the absence of any physical distortions and give rise to a range of intriguing phenomena, such as chiral quantum transport or chiral reaction-diffusion. A finite chemical potential couples these two hyperbolic surfaces, delivering a quantum sensor whose sensitivity grows exponentially with the size of the system. Our results provide experimentalists with an unprecedented opportunity to explore intriguing quantum phenomena in curve spaces without distortion or access non-Hermitian phenomena without dissipation. Our work also suggests a new class of quantum sensors in which geometry amplifies small signals.