We theoretically and experimentally study the Rabi splitting induced by photon tunneling modes in a paired structure
composed of a permittivity-negative medium and a permeability-negative medium. It is shown that a tunneling mode
will appear at the frequency where the paired structure is equivalent to a media with effective (near) zero refractive
index. A cavity may be realized with features: subwavelength cavity size and exponentially increasing of the optical
field. Therefore, the photon tunneling mode in a metamaterial with effective (near) zero refractive index may be used as
a cavity with highly localized field and small volume.