Phase-space reconstruction of an atomic chaotic system

We consider the dynamics of a single atom submitted to periodic pulses of a far-detuned standing wave generated by a high-finesse optical cavity, which is an atomic version of the well-known “kicked rotor.” We show that the classical phase-space map can be “reconstructed” by monitoring the transmission of the cavity. We also studied the effect of spontaneous emission on the reconstruction and put limits to the maximum acceptable spontaneous emission rate.

Figure 1

Schematic view of the proposed setup. If the atom is at a crest (a) or at a node (b) of the cavity electromagnetic field, the Kerr nonlinear refractive index produced is different, the resonance condition of the cavity is modified, and the transmitted intensity changes, allowing detection of the longitudinal position of the atom.

Figure 2

First return map $S_n\times S_{n+1}$ for the cavity-transmission signal, with $F={10}^6$. Structures are clearly visible, but no direct relation to the topology of the phase space of the KR [Fig. 4a, below] can be drawn.

Figure 3

Correspondence between the transmission signal and the atom longitudinal position inside the cavity.

Figure 4

Comparison between the original (a) and reconstructed (b) KR phase-space map. Parameters are $K=0.8$ and $F={10}^6$. Larger structures are easier to reconstruct than smaller ones.

Figure 5

Influence of the spontaneous emission in the phase-space reconstruction. Parameters are $K=0.8$ and $F={10}^6$.