Topological Casimir effect in a quantum LC circuit: real-time dynamics

Abstract

We study novel contributions to the partition function of the Maxwell system defined on a small compact manifold $\mathbb{M}$ with nontrivial mappings ${\pi }_1[U(1)]\cong \mathbb{Z}$. These contributions cannot be described in terms of conventional physical propagating photons with two transverse polarizations, and instead emerge as a result of tunneling transitions between topologically different but physically identical vacuum winding states.\exclude{These new terms give an extra contribution to the Casimir pressure, yet to be measured.} We argue that if the same system is considered in the background of a small external time-dependent E\&M field, then real physical photons will be emitted from the vacuum, similar to the dynamical Casimir effect (DCE) where photons are radiated from the vacuum due to time-dependent boundary conditions. The fundamental technical difficulty for such an analysis is that the radiation of physical photons on mass shell is inherently a real-time Minkowskian phenomenon while the vacuum fluctuations interpolating between topological $|k⟩$ sectors rest upon a Euclidean instanton formulation. We overcome this obstacle by introducing auxiliary topological fields which allows for a simple analytical continuation between Minkowski and Euclidean descriptions, and develop a quantum mechanical technique to compute these effects. We also propose an experimental realization of such small effects using a microwave cavity with appropriate boundary conditions. Finally, we comment on the possible cosmological implications of this effect.

matches the published version, title changed, appendices added to clarify the relation between the Hamiltonian description in Minkowski space and the path integral description in Euclidean formulation

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Cited by in corpus (4)

• Axion detection via Topological Casimir Effect
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• Cosmological Magnetic Field and Dark Energy as two sides of the same coin
• A few thoughts on $\theta$ and the electric dipole moments