quantum chaos and its potential for robust quantum control in ...
quantum chaos and its potential for robust quantum control in ...
quantum chaos and its potential for robust quantum control in ...
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Kicked HO: phase space structure <strong>and</strong> level dynamics<br />
φ<br />
6<br />
4<br />
2<br />
v<br />
−360 −180 0 180 360<br />
360<br />
180<br />
0<br />
−180<br />
−360<br />
u<br />
H = p2<br />
2m + mν2 x 2<br />
2<br />
+ Acos(kx) ∑ n<br />
δ(t − nτ)<br />
• e.g., cold ions/atoms <strong>in</strong> harmonic<br />
trap<br />
φ<br />
0<br />
0.2 0.3 0.4 0.5<br />
6<br />
4<br />
2<br />
η<br />
v<br />
−40 −20 0 20 40<br />
40<br />
20<br />
0<br />
−20<br />
−40<br />
u<br />
• Eigenphases φ of one-cycle √ Floquet<br />
<br />
propagator vs. η = k<br />
2mν ∼ √ <br />
• q = 2π<br />
ντ<br />
= 5 (top), q = 6 (bottom),<br />
K = Ak2<br />
mν = 2.0<br />
• <strong>in</strong>sets: classical trajectory after 40000<br />
kicks – note the web!<br />
0<br />
0.2 0.3<br />
η<br />
0.4 0.5
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