Resolving Vacuum Fluctuations in an Electrical Circuit by Measuring the Lamb Shift

TLDR

Quantum theory predicts that empty space is not truly empty, with virtual particles constantly created and annihilated, and in an electromagnetic field these virtual photons cause a small renormalization of energy known as the Lamb shift. The study experimentally observes the Lamb shift in a solid‑state system. The experiment uses a superconducting qubit strongly dispersively coupled to the vacuum field of a transmission‑line resonator, producing Lamb shifts up to 1.4 % of the qubit transition frequency. The experiment confirms a measurable Lamb shift and shows that the qubit couples more strongly to the vacuum field than to a single cavity photon, an effect attributed to the limited anharmonicity of higher excited states.

Abstract

Quantum theory predicts that empty space is not truly empty. Even in the absence of any particles or radiation, in pure vacuum, virtual particles are constantly created and annihilated. In an electromagnetic field, the presence of virtual photons manifests itself as a small renormalization of the energy of a quantum system, known as the Lamb shift. We present an experimental observation of the Lamb shift in a solid-state system. The strong dispersive coupling of a superconducting electronic circuit acting as a quantum bit (qubit) to the vacuum field in a transmission-line resonator leads to measurable Lamb shifts of up to 1.4% of the qubit transition frequency. The qubit is also observed to couple more strongly to the vacuum field than to a single photon inside the cavity, an effect that is explained by taking into account the limited anharmonicity of the higher excited qubit states.