Magnetic Resonance in an Atomic Vapor Excited by a Mechanical Resonator

We demonstrate a direct resonant interaction between the mechanical motion of a mesoscopic resonator and the spin degrees of freedom of a sample of neutral atoms in the gas phase. This coupling, mediated by a magnetic particle attached to the tip of the miniature mechanical resonator, excites a coherent precession of the atomic spins about a static magnetic field. The novel coupled atom-resonator system may enable development of low-power, high-performance sensors, and enhance research efforts connected with the manipulation of cold atoms, quantum control, and high-resolution microscopy.

Figure 1

The cantilever tip has a magnetic moment ${\overrightarrow{M}}_{\mathrm{tip}}$. The motion ($\Delta x_{\mathrm{tip}}$) of the tip of a microfabricated cantilever creates an oscillatory magnetic field ($\Delta {\overrightarrow{B}}_{\mathrm{tip}}$) at the location of the atomic sample, which excites a coherent precession of the atomic spin about a static magnetic field ${\overrightarrow{B}}_0$. The resulting time-varying precession is detected through the intensity modulation it creates on a resonant, circularly polarized optical field. The total static magnetic field is a combination of the dc field produced by the cantilever tip and an applied field (${\overrightarrow{B}}_{\mathrm{ext}}$).

Figure 2

The magnetic cantilever. A small magnetic particle of NdFeNbB is attached to the tip of the cantilever to produce a magnetic field.

Figure 3

A two-dimensional contour plot of ${\overrightarrow{B}}_0$ and $\Delta {\overrightarrow{B}}_{\mathrm{tip}}$, slicing through the cell center plane. The model assumes that the magnetic dipole (the tip) is $3.25\times {10}^{-9}\mathrm{A}·{\mathrm{m}}^2$ at $(x,z)=(-0.5\mathrm{mm},-1.0\mathrm{mm})$, $B_{\mathrm{ext}}=1.8\mu \mathrm{T}$, and the cell center is at the origin. The tip displacement used to calculate the rf field $\Delta {\overrightarrow{B}}_{\mathrm{tip}}$ is assumed to be $200\mu \mathrm{m}$ and is estimated from the PZT displacement enhanced by the $Q$ factor of the cantilever.

Figure 4

The magnetic resonances. (a) $|{\overrightarrow{B}}_{\mathrm{ext}}|=1.8\mu \mathrm{T}$: the center frequency of the broad resonance is at the vibrational frequency of the cantilever. (b) $|{\overrightarrow{B}}_{\mathrm{ext}}|=2.8\mu \mathrm{T}$: the center frequency of the broad resonance is offset from the vibrational frequency of the cantilever. The insets show the narrow resonances at a reduced span and sweep rate of the driving frequency.

Figure 5

The amplitude of the magnetic resonance driven by the cantilever as a function of the external magnetic field.