A two-level system resonantly interacting with an ac magnetic or electric field constitutes the physical basis of diverse phenomena and technologies, including nuclear magnetic resonance, stimulated emission, amplification, Rabi oscillations, laser cooling, and quantum information processing.However, despite the seeming simplicity of the problem, Schrodinger's equation for this system can be solved exactly only under the rotating wave approximation, which neglects the counter-rotating field component.When the ac field is sufficiently strong, this approximation fails, leading to a resonance-frequency shift known as the Bloch-Siegert (BS) shift, which is typically minuscule and difficult to analyze.Here, we report the vacuum BS shift, which is induced by the ultrastrong coupling of matter with the counter-rotating component of the vacuum fluctuation field in a cavity.Specifically, an ultrahigh-mobility 2D electron gas inside a high-Q terahertz cavity in a quantizing magnetic field revealed Landau polaritons with a record high value (3513) of the ratio of the vacuum Rabi splitting to the polariton linewidth. Unlike the usual BS shift, we observed an unambiguously large vacuum BS shift up to 40 GHz, which can be exactly analyzed as a consequence of the ultrastrong coupling of counter-rotating circularly polarized radiation and Landau-quantized electrons. This shift, clearly distinguishable from the photon-field self-interaction effect, represents a unique manifestation of a strong-field phenomenon without a strong field.
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Vacuum Bloch-Siegert Shift in Landau Polaritons with Ultrahigh Cooperativity
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