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Ground-state cooling of a mechanical resonator by single- and two-phonon processes
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View: Figures


Image of FIG. 1.
FIG. 1.

Schematic diagram of a Λ-type three-level system that consists of the ground state |l⟩ in the left dot, and the ground state |r⟩ and the first excited state |e⟩ in the right dot in a double quantum dot device. The right dot is driven by a light field of the Rabi frequency Ω2 (with frequency ω2) and a light field of the Rabi frequency Ω1 (with frequency ω1) is applied to drive the transition between |l⟩ and |e⟩. The chemical potential μ L is well above the level |l⟩ and μ R between the levels |r⟩ and |e⟩, i.e. μ L  ≫ E l and E r  ≪ μ R  ≪ E e . The excited state of the left dot is far-off-resonance with the excited state of the right one, thus electrons are allowed to transfer from left dot to right dot through the transition |l⟩↔|e⟩ and the tunneling between the two ground states.

Image of FIG. 2.
FIG. 2.

The population occupations ρ BB and ρ DD in steady state are plotted as a function of Ω in different dephasings and as a function of β (inset) under different light strengths. For simplicity, we set β i  = β, I = 1, 2, 3, and Ω1 = Ω2 = Ω. The other parameters are T = 50Γ, δ = 0, Γ L  = 10Γ, Γ R  = 3Γ, and γ1 = γ2 = 0.1Γ. All parameters are scaled in unit of Γ.

Image of FIG. 3.
FIG. 3.

The total cooling rate γ tot and the mean phonon number of the resonator ⟨n st as functions of dephasings and Ω (a) or ω m (b). In (a) (including inset), the resonator frequency ω m  = 100.2Γ; in (b) (including inset), Ω = 4.48Γ. We set Ω1 = Ω2 = Ω and β i  = β, I = 1, 2, 3. Here α = Γ, , and γ p  = 1 × 10−5Γ. The other parameters are same with that in Fig. 2.

Image of FIG. 4.
FIG. 4.

Similar to Figs. 3(a) and 3(b) except ω m  = 120Γ in (a) and Ω = 53Γ in (b) (including inset). In (b), the symbol star is plotted for the case β = 10−4Γ and the solid line for the case β = 0.

Image of FIG. 5.
FIG. 5.

(a) and (b) illustrate the mean phonon number of the resonator and the Mandel’s parameter Q as the function of Ω, respectively, when 2ω m  = E + − E D . The other parameters are Γ L  = 10Γ, Γ R  = 0.5Γ, T = 50Γ, γ1 = γ2 = 0.1Γ, γ p  = 10−5Γ, α = 10Γ and n p  = 400.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Ground-state cooling of a mechanical resonator by single- and two-phonon processes