2 In this approach, an additional state is coupled to the ex- cited state | 3 〉 of the TLS to form a Λ-shaped three-level system [see Fig. 1(b)]. The two lower-energy states in this three-level system are tuned to be degenerate. Due to dis- sipation of the excited state, the atom will eventually ar- rive at a particular superposition of the two lower-energy states which is orthogonal to the excited state. This phe- nomenon results from the destructive quantum interfer- ence between the two transitions | 1 〉 → | 3 〉 and | 2 〉 → | 3 〉 and the superposition state is called the dark state [34]. When atomic motion is also considered, the carrier tran- sition ( | 1 , n 〉 → | 3 , n 〉 ) and thus the heating process of the atomic motion in the sideband cooling scheme is hence suppressed. It was shown that atomic motion can be cooled to its ground state in the non-resolved sideband regime [33]. In the present work, we propose a new scheme to cool a MR via capacitive coupling to a triple quantum dot (TQD) schematically displayed in Fig. 1(a). We consider the strong Coulomb-blockade regime so that at most one electron is allowed to present at one time in the TQD. The TQD acts as a three-level system in Λ configura- tion, in which the two dot states | 1 〉 and | 2 〉 (i.e., the single-electron orbital states in dots 1 and 2) are cou- pled to a third (excited) state | 3 〉 via two tunnel barri- ers [see Fig. 1(a)]. Here, the degrees of freedom of the MR is analogous to the motional degrees of freedom of the atoms discussed above and the TQD is an electronic analog of a three-level atom. We will show that by prop- erly tuning the gate voltages, one can degenerate the two lower-energy states and obtain a dark state in the TQD. By capacitively coupling to the TQD, the MR can be cooled to its ground state, in full analogy to the slowing down of the atoms via quantum interference. Compar- ing with the cooling of atoms [33], our approach has the following potential advantages: (i) Our cooling system is completely electronic and can be conveniently fabricated on a chip. (ii) Simply by adjusting the gate voltages, it is easy to achieve the two degenerate lower-energy states required for realizing destructive quantum interference in the TQD. Moreover, in contrast to the cooling of a MR by coupling it to a superconducting qubit [35], the decay rate Γ of the higher-energy state of the TQD, which is equal to the rate of electrons tunneling from the TQD to the electrode, is tunable in our case by varying the gate voltage. Moreover, we also propose a method to verify whether the MR is successfully cooled by coupling it to a double quantum dot (DQD). This DQD can be reduced from the TQD by applying appropriate gate voltages. When the DQD and the MR is tuned into a strongly disper- sive regime in which the transition frequency difference between the two subsystems is much larger than the This paper is organized as follows. Section II intro- duces a microscopic model for the coupled MR-TQD system. We show that the TQD is an electronic ana- log of a three-level atom driven by two electromagnetic fields. Also, we show how the TQD evolves into the dark state. In Sec. III, we derive a master equation to describe the quantum dynamics of the coupled MR-TQD system. With this master equation, we further derive in Sec. IV the master equation of the MR by eliminating the TQD degrees of freedom. Moreover, we calculate the steady- state average phonon occupancy of the MR and show that the MR can indeed be cooled to its ground state by using the quantum interference in the TQD. In Sec. V, we propose a method to verify if the MR is successfully cooled by measuring the full-frequency current spectrum of a charge detector. Section VI summarizes our results. In the appendix, we give a detailed derivation of the mas- ter equation for the reduced density matrix of the MR. coupling strength between them, the coupling between the MR and the DQD only yields a phonon-number- dependent Stark shift to the transition frequency of the DQD. This Stark shift corresponds to the shift of the resonant peak in the current spectrum of a charge detec- tor. Thus, by measuring the shift of the resonant peak, one can readout the phonon-number state and examine whether the MR is successfully cooled or not. FIG. 1: (color online) Schematic diagram of a TQD system. Dots 1 and 2 are both tunnel-coupled to dot 3 (with interdot coupling strengths Ω 1 and Ω 2 , respectively) while they are only capacitively coupled to each other. A MR is capacitively coupled to dots 1 and 3 of the TQD. (b) A three-level system in Λ configuration. The energy detunings between the two lower-energy states and the third excited state are respectively Δ 1 and Δ 2 . The coupling strength between the state | 1 〉 ( | 2 〉 ) and the state | 3 〉 is Ω 1 (Ω 2 ). C. Cooling a MR via quantum interference in a triple quantum dot