Qubit-Coupled Mechanics - IFSC

The Dispersive Coupling Limit
Typically ħλ ≪ ΔE − ħω
Full Hamiltonian
H = E ee V g σ z + E J B σ x + ħω a † a + 1 2 + ħλ(a† + a) ∙ σ z
Some typical parameters
λ ~ 1 − 10 ′ s MHz
ΔE ~ 1 − 10 ′ s GHz
Coupling Strength
CPB Energy Scale
Interaction results in
simple shifts in energies of
the two systems
(Dispersive or non-resonant
Coupling limit)
where
ΔE =
ω ~ 10 ′ s − 100 ′ s MHz
E 2 2
ee + E J
Mechanical Frequency
The dispersive shift of each
system depends on the
state of the other system
*See: Irish & Schwab, PRB 68, 155311 (2003); Haroche & Raimond, Exploring the Quantum: Atoms, Cavities & Photons*