Qubit-Coupled Mechanics - IFSC
Qubit-Coupled Mechanics - IFSC
Qubit-Coupled Mechanics - IFSC
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The Dispersive Coupling Limit<br />
*See: Irish & Schwab, PRB 68, 155311 (2003)<br />
Interaction Leads to Shift in Energy of CPB and NEMS<br />
Analogous To dispersive shifts in CQED<br />
Two Dispersive Effects Occur<br />
CPB-state-dependent<br />
Frequency<br />
Shift in NR<br />
NR- dependent<br />
shift in CPB<br />
transition energy<br />
N ≡ # Quanta in NR<br />
χ = 2λ 2 /ΔE<br />
Analogous to single-atom<br />
refractive shift in CQED<br />
δω ± ≈ ±ħχ<br />
Analogous<br />
to Lamb Shift<br />
δE ≈ ħχ(2N + 1)<br />
Analogous<br />
to Stark Shift<br />
Energy levels w/o interaction<br />
N = 2<br />
N = 1<br />
N = 0<br />
…<br />
…<br />
…<br />
ħω 0<br />
∆E<br />
|−⟩ |+⟩<br />
Energy levels with interaction<br />
N = 2<br />
N = 1<br />
N = 0<br />
∆E + 3ħχ<br />
…<br />
∆E + ħχ<br />
|−⟩ |+⟩<br />
2<br />
1<br />
1<br />
0<br />
Dispersive interaction is non-destructive: H iii ∝ σ z ⋅ a † a ⇒ H 0 , H iii = 0
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