The ‘rotating wave’ approximation is ubiquitously applied in several problems involving coupled light and matter in order to simplify calculations. It states that, in the approximate picture given by quantum theory, matter can be excited into a higher energy level by absorbing a photon but never by emitting a photon. However, theoretical physicists in the 1940s predicted that this approximation broke down under certain circumstances where the light intensity is high enough to couple with matter very strongly. In such cases, the result is a shift in the resonance frequency of matter: the Bloch–Siegert shift.
Our study marks the first time the vacuum Bloch–Siegert shift, which appears even in the limit of zero light intensity, was measured experimentally in a cavity embedding a solid-state system. We used a two-dimensional electron gas contained in solid gallium arsenide and applied a strong, alternating magnetic field, which forced the electrons to move in a circular motion in a particular direction (cyclotron motion). The electrons hybridized with the ‘vacuum’ cavity field into quasiparticles called polaritons. In this setup, we managed to accurately measure a signature of the breakdown of the rotating wave approximation, which is only possible for very strongly coupled light and matter in a cavity of quite high quality. As a result of our experiments, we observed an unexpected shift in the resonance frequency of the polaritons.
Our subsequent theoretical analyses indicated that this frequency shift was a vacuum Bloch–Siegert shift caused by the coupling between the electrons and the vacuum cavity field beyond the rotating wave approximation. More specifically, the shift manifested in the optical spectra of circularly polarized light rotating in the direction opposite to that of the electrons. This shift was hard to observe compared with the signature of coupling between light and electrons circling in the same direction, which is easily observed and has been widely studied.
The vacuum Bloch–Siegert shift caused by the above-described process involves a spontaneous excitation of matter into higher energy states accompanied by the emission of a photon. Thus, our results provided indirect evidence for the existence of ‘virtual photons,’ even for systems in their lowest-energy state—the ground state. Most importantly, such a process suppresses the quantum fluctuations of photons, also known as ‘quantum squeezing.’ In the present case, the quantum fluctuations of the ‘virtual photons’ are squeezed stably even in the ground state, which is a remarkable feat.
Therefore, we believe our work might revolutionize current technology related to quantum computing and quantum sensing. This will hopefully lead to breakthroughs in quantum chemistry, medicine, materials science, electronics, and many other fields.
Xinwei Li, Motoaki Bamba , Qi Zhang, Saeed Fallahi, Geoff C. Gardner, Weilu Gao , Minhan Lou, Katsumasa Yoshioka, Michael J. Manfra, and Junichiro Kono
“Vacuum Bloch–Siegert shift in Landau polaritons with ultra-high cooperativity”
Nature Photonics 12, 324 (2018)