Molecular rotations in matter-wave interferometry

We extend the theory of matter-wave interferometry of pointlike particles to nonspherical objects by taking the orientational degrees of freedom into account. In particular, we derive the grating transformation operator, which maps the impinging state onto the outgoing state, for a general, orientation-dependent interaction potential between the grating and the molecule. The grating operator is then worked out for the diffraction of symmetric top molecules from standing light waves, and the resulting interference pattern is calculated in the near field. This allows us to identify a signature of the orientational degrees of freedom in near-field matter-wave experiments.

Figure 1

The thermal distribution $p_{\mathrm{th}}\left(q\right)$, Eq. (22), of the temporal average $q$ of ${sin}^2\theta \left(t\right)$ for the free symmetric rotor with different moments of inertia, $I/I_3=1/2$ (solid line), $I/I_3=10$ (dashed line), and $I/I_3\to \infty$ (dot-dashed line).

Figure 2

Quantum (upper curves) and classical (lower curves) absolute sinusoidal fringe visibility as a function of relative separation $L/L_T$ for a linear molecule in the KDTLI for three different values of $\mathrm{\Delta }\alpha /{\alpha }_{\parallel }$.

Figure 3

Absolute value of the sinusoidal quantum fringe visibility (21) as a function of laser power for a linear rigid molecule in the KDTLI for three different values of $\mathrm{\Delta }\alpha /{\alpha }_{\parallel }$.

Figure 4

Absolute value of the sinusoidal quantum fringe visibility (23) as a function of laser power for the prolate symmetric top in the KDTLI for different values of $I/I_3$ $\left(\mathrm{\Delta }\alpha /{\alpha }_{\parallel }=0.9\right)$.