Coupling an Inverted Spin Ensemble to a Microwave Resonator

Using an ensemble of nitrogen (P1) centers in diamond placed inside a 3-D loop-gap resonator, we observe population inversion of a satellite P1 transition when a microwave pump tone is applied to the central P1 transition. This inversion is manifested by amplification of the probe tone applied to the satellite transition. A mechanism for generating this inversion is proposed, involving higher-order cross relaxations within the P1 centers [1] and spin flip-flops with nearby nitrogen-vacancy (NV) centers that are also present in the diamond sample.

We also observe a splitting of this amplifying peak due to coupling with the microwave resonator. The polariton modes created by this coupling differ qualitatively from the standard, non-inverted case, in particular lacking an avoided crossing [2]. We modeled this “abnormal” anticrossing by assuming a “negative ensemble coupling constant,” and find that the model is consistent with the observed experimental data.

[1] P. P. Sorokin, G. J. Geller, and I. L. Gelles. Phys. Rev. 118(4), 939-945 (1960).
[2] B. Julsgaard and K. Mølmer. Phys. Rev. A. 86, 063810 (2012).