Preparing ground states and squeezed states of nanomechanical cantilevers by fast dissipation

We propose a protocol that enables strong coupling between a flux qubit and the quantized motion of a magnetized nanomechanical cantilever. The flux qubit is driven by microwave fields with suitable parameters to induce sidebands, which will lead to the desired coupling. We show that the nanomechanical modes can be cooled to the ground states and the single-mode squeezed vacuum states can be generated via fast dissipation of the flux qubit. In our scheme, the qubit decay plays a positive role and can help drive the system to the target states.

Figure 1

The magnetic tip attached to the end of a nanomechanical cantilever with dimensions (l, w, t) is positioned above a flux qubit, thereby a strong coupling is achieved. The area of flux through the qubit can be considered as the same as the tip's size.

Figure 2

Schematic of sideband cooling by the dissipation of a flux qubit. To select the JC terms in Eq. (6), the flux qubit is driven by a red sideband with frequency ${\omega }_d=\nu -\omega .$

Figure 3

The mean phonon number of the nanomechanical cantilever versus time $gt/2\pi$. Here $T=0.1$ K, $n_{th}\simeq 41$, and $\omega =50$ MHZ.

Figure 4

The average phonon number changes with $\Gamma$ when the cooling and heating rate reach the balance. The parameters are in the regime of $A^{+}\ll n_{th}\gamma$ and $2g^2/\Gamma \ll \Gamma$.

Figure 5

Setup of preparing the single-mode squeezed states by the dissipation of the flux qubit. To select the desired coupling, the flux qubit is driven by two fluxes with different frequencies, ${\omega }^{+}$ being the blue sideband driving frequency, while ${\omega }^{-}$ being the red sideband driving frequency.

Figure 6

Coherent variance V of the the nanomechanical mode and population P of the flux qubit in the excited states changes with dimensionless variable ${\Theta }_1$t/2$\pi$. We choose $\Gamma =2\pi \times 4$ MHz, $g=2\pi \times 5$ MHz, ${\Theta }_1=2\pi \times 1$ MHz, ${\Theta }_2=2\pi \times 0.7$ MHz (corresponding ${\eta }^{-}=0.2$ and ${\eta }^{+}=0.14)$, and $\gamma =5$ KHz (corresponding to $Q=1.2\times {10}^4)$.

Figure 7

The coherent variance as a function of the temperature. The parameters are the same as that in Fig. 6.