Speakers
Description
A cloud of trapped ions, represented here by a four level atomic system $\mid S_{1/2}>,\mid P_{1/2}>,\mid D_{3/2}>$ and $\mid D_{5/2}>$, is probed by the collection of photons from the transition $\mid P_{1/2}>$ to $\mid S_{1/2}>$.
Figure : Four level atomic system of Ca+ ions
The lambda configuration with lasers at 866nm and 397nm allows for a two-photon dark state to take place. If the $ \mid S_{1/2}>$ state is coupled with the $\mid D_{5/2}>$ state (which we are going to refer to as $\mid S>$ and $\mid Q>$) a three photon dark state is to be expected 1. Indeed the transition at 729nm is weakly coupled and the sub-system is diagonalizable:
\begin{equation}
\mid S_{Q}>=N_{1}(\mid S> + \alpha\mid Q>) and \mid Q_{S}>=N(\mid D> - \alpha \mid S>)
\end{equation}
with a normalisation factor $N_{1}$, and $\alpha =\Omega_{C}/2\Delta C $, we achieve a new lambda-shaped system with a dark state written as:
\begin{equation}
\mid \Psi_{dark}> = N_{2} (\varepsilon \mid D> + \mid Q_{S}>)
\end{equation}
With $ \varepsilon = \alpha \Omega_{B}/\Omega_{R}$ and a normalisation factor $N_{2}$. The condition for this state not to be coupled to the rest of the system is:
\begin{equation}
\Delta R + \Delta C - \Delta B + \alpha \Omega _{C} /2 =0
\end{equation}
To achieve a stable 3-photon coherent population trapping experimentally, one has to reduce the relative phase fluctuations of the three lasers. In order to do so, two lasers are phase-locked onto a frequency comb which is himself locked onto the 729nm laser. This 729nm ultra-stable Ti:Sa laser was built within the laboratory and has a frequency stability of better than $5\times10^{-14}$ for one second. For this 3-photon resonance, the phase matching condition: $ \vec K_{R}+ \vec K_{C}- \vec K_{B}= \vec 0$ cancels out the first order Doppler Effect.
Recent experimental results will be presented.
1 C. Champenois, G. Hagel, M. Houssin, M. Knoop, C. Zumsteg, and F. Vedel, "Terahertz frequency standard based on three-photon coherent population trapping", Phys. Rev. Lett., vol.99, no. 1, p.013001, 2007.
