Spectral tuning of optical coupling between air-mode nanobeam cavities and individual carbon nanotubes

Air-mode nanobeam cavities allow for high efficiency coupling to air-suspended carbon nanotubes due to their unique mode profile that has large electric fields in air\footnote{R. Miura, S. Imamura, R. Ohta, A. Ishii, X. Liu, T. Shimada, S. Iwamoto, Y. Arakawa, and Y. K. Kato, {\it Nature Commun.} {\bf 5}, 5580 (2014).}. Here we utilize heating-induced energy shift of carbon nanotube emission\footnote{P. Finnie, Y. Homma, and J. Lefebvre, {\it Phys. Rev. Lett.} {\bf 94}, 247401 (2005).} to investigate the cavity quantum electrodynamics effects. In particular, we use laser-induced heating which causes a large blue-shift of the nanotube photoluminescence as the excitation power is increased. Combined with a slight red-shift of the cavity mode at high powers, detuning of nanotube emission from the cavity can be controlled. We estimate the spontaneous emission coupling factor $\beta$ at different spectral overlaps and find an increase of $\beta$ factor at small detunings, which is consistent with Purcell enhancement of nanotube emission.