Quantum Magnetomechanics with Levitating Superconducting Microspheres

We show that by magnetically trapping a superconducting microsphere close to a quantum circuit, it is possible to perform ground-state cooling and prepare quantum superpositions of the center-of-mass motion of the microsphere. Due to the absence of clamping losses and time-dependent electromagnetic fields, the mechanical motion of micrometer-sized metallic spheres in the Meissner state is predicted to be very well isolated from the environment. Hence, we propose to combine the technology of magnetic microtraps and superconducting qubits to bring relatively large objects to the quantum regime.

Figure 1

(a) Scheme of the AHC with a pickup coil. (b) Quadrupole field created by the AHC. (c) Field expelled by the sphere in the Meissner state.

Figure 2

The (a) steady-state phonon number occupation $⟨\widehat{n}{⟩}_{\mathrm{ss}}$ (assuming ${\Gamma }_{\mathrm{ext}}=0$) and (b) the cooling rate $\Gamma$ over $\tilde{\Gamma }={\tilde{g}}^2{cos}^2(\alpha )/{\Gamma }_0$ are plotted as a function of $\beta$ for ${\Gamma }_{\phi }/{\Gamma }_0=0$ (solid blue line), ${\Gamma }_{\phi }/{\Gamma }_0=0.1$ (dashed red line), and ${\Gamma }_{\phi }/{\Gamma }_0=1$ (dotted orange line).

Figure 3

Scheme of the protocol to prepare quantum superpositions of a mechanical oscillator using the parametric coupling to a qubit. (a) The state $|+⟩|0⟩$ that is prepared at $t=0$ and recovered at $t=2t^{\star }$. (b) The superposition state Eq. (4) that is created at $t=t^{\star }$.