Kazan Federal University, 420008, Kazan, Russian Federation [email protected]
We consider an ensemble of a large number
of non-interacting spins
1 2 coupled to a single mode of electromagnetic field in an ideal microwave cavity. The system is described by Tavis-Cummings Hamiltonian ,
) is photon creation (annihilation) operator,
are collective spin operators. Supposing that the photon number is <<
, one can obtain the corresponding energy spectra either numerically (for
) or analytically. In the latter case, the spin ensemble must be very close to its highest polarization state, i.e.
2 . If the spins are under thermal equilibrium, this corresponds to zero temperature. It is known  that emission spectrum of the cavity at resonance (
) consists of a single line at frequency
split by a gap of 2
If the spins belong to paramagnetic atoms distributed in a solid, the zero-temperature approximation is inadequate even for
of a few Kelvin. In the present work we develop a generalized calculation scheme and obtain the cavity emission spectrum for low polarization states. We calculate the lineshapes and obtain the generalized Rabi splitting of 2
denotes temperature average. We show that the splitting remains under condition
2 , i.e. for a wide temperature range when
. At higher
, the lines gradually merge into one. The obtained results corroborate recent observations of Rabi splitting in magnetically coupled spin-photon system .
This work was supported by RFBR (Grant no. 12-02-31336) and by Dynasty
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