Spectroscopic characteristics of a microwave cavity at - TU-MRS

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SPECTROSCOPIC CHARACTERISTICS OF A MICROWAVE CAVITY AT

NONZERO TEMPERATURE

E.I. Baibekov

Kazan Federal University, 420008, Kazan, Russian Federation [email protected]

We consider an ensemble of a large number

N

of non-interacting spins

s

1 2 coupled to a single mode of electromagnetic field in an ideal microwave cavity. The system is described by Tavis-Cummings Hamiltonian [1],

H

p

s

S z

bS

b S

, where

b

(

b

) is photon creation (annihilation) operator,

S z

and

S

are collective spin operators. Supposing that the photon number is <<

N

, one can obtain the corresponding energy spectra either numerically (for

N

~ 10

) or analytically. In the latter case, the spin ensemble must be very close to its highest polarization state, i.e.

S z

 

N

2 . If the spins are under thermal equilibrium, this corresponds to zero temperature. It is known [2] that emission spectrum of the cavity at resonance (

p

s

) consists of a single line at frequency

p

split by a gap of 2

N

(Rabi splitting).

If the spins belong to paramagnetic atoms distributed in a solid, the zero-temperature approximation is inadequate even for

T

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

2

S z

, where

N



S z

denotes temperature average. We show that the splitting remains under condition

N

2 , i.e. for a wide temperature range when

N



1

. At higher

T

, the lines gradually merge into one. The obtained results corroborate recent observations of Rabi splitting in magnetically coupled spin-photon system [3].

This work was supported by RFBR (Grant no. 12-02-31336) and by Dynasty

Foundation.

References

1. M. Tavis, F.W. Cummings, Phys. Rev.

170

, 379 (1968).

2. J.J. Sanchez-Mondragon, N.B. Narozhny, J.H. Eberly, Phys. Rev. Lett.

51

, 550 (1983).

3. I. Chiorescu, N. Groll, S. Bertaina, T. Mori, S. Miyashita, Phys. Rev. B

82

, 024413 (2010).

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