Decoherence measurement of two coupled micromasers

We present a setup of two coupled micromaser cavities for studying decoherence. The system is prepared in a state where, initially, one photon is contained in one of the two cavities. The coupling of the two resonators allows the photon to tunnel into the other cavity with a certain probability. The system thus oscillates between the two states $\mid 1{⟩}_L\mid 0{⟩}_R$ and $\mid 0{⟩}_L\mid 1{⟩}_R$. It is shown how to map these states onto the states $\mid g⟩$ and $\mid e⟩$ of probe atoms used to investigate the status of the cavity system. It is an important result that the symmetry of our special setup allows decoherence to be monitored by measuring just the diagonal elements of the atomic density matrix. This property relies on the fact that only $\mid 0⟩$ and $\mid 1⟩$ states are relevant. To our knowledge, this is the first proposal that tries to exploit this particular property.

Figure 1

Schematic layout showing the atoms that can pass through the two coupled micromasers and are detected state-selectively at the detectors by field ionization. For the experimental realization the double cavity consists of two cavities of our standard micromaser. The degree of coupling of the two cavities depends on the size of the coupling hole and on the tuning of the eigenfrequencies of the two cavities with respect to each other. The entrance and exit holes of the double cavities are the same as in the standard micromaser.

Figure 2

Plot of the space curve (black line) described by the tip of the Bloch vector spiraling inward in a plane motion from the surface of the Bloch sphere. Parameters are $t_{tun}=1\mathrm{ms}$, cavity decay time $t_{cav}=100\mathrm{ms}$, and temperature $T=200\mathrm{mK}$.

Figure 3

(Color) Plot of $P\left(t\right)={\rho }_{10,10}-{\rho }_{01,01}$ (black dashed curve) and twice the off-diagonal element $2\mathrm{Im}\left({\rho }_{10,01}\right)$ (red curve) of the density matrix for $t_{tun}=1\mathrm{ms}$, cavity decay time $t_{cav}=100\mathrm{ms}$, and temperature $T=200\mathrm{mK}$.

Figure 4

(Color) Plot of the atomic population probabilities $P_{eg}\left(t\right)$ (blue curve) and $P_{ee}\left(t\right)$ (green curve) when the field is probed with atoms in the excited state $\mid e⟩$ and interaction time $\tau$ (see text).