How to Measure the Phase Diffusion Dynamics in the Micromaser

We propose a realistic scheme for measuring the micromaser linewidth by monitoring the phase diffusion dynamics of the cavity field. Our strategy consists of exciting an initial coherent state with the same photon number distribution as the micromaser steady-state field, singling out a purely diffusive process in the system dynamics. After the injection of a counterfield, measurements of the population statistics of a probe atom allow us to derive the micromaser linewidth in all ranges of the relevant parameters, establishing experimentally the distinctive features of the micromaser spectrum due to the discreteness of the electromagnetic field.

Figure 1

Density matrix ${\rho }_{n,m}$ of the micromaser cavity field: (a) initial coherent state $|\alpha ⟩$; (b) diagonal steady-state field after the phase diffusion process. Dimensionless parameters: $\alpha =3.0654$, $g\tau =0.494$, $g/\gamma =12.300$, $r/\gamma =10$, and ${\overline{n}}_b=0.03$.

Figure 2

Exponential decay of the expectation value of the cavity field due to phase diffusion $\mathrm{R}\mathrm{e}⟨\widehat{a}⟩$ vs dimensionless time $\gamma t$ from the MME (same parameters as in Fig. 1).

Figure 3

Solid line: probability ${\tilde{p}}_{\mathrm{e}}$, Eq. (8), that an excited probe atom leaves the cavity excited. Dashed line: fit from Eq. (9) for $t>D^{-1}$, with $K_{{\tau }_{\mathrm{p}}}=-0.283$, ${\tilde{p}}_{\mathrm{e}}(\infty ,{\tau }_{\mathrm{p}})=0.551$, and $D/\gamma =0.047$. Same parameters as in previous figures.