Influence of conformational molecular dynamics on matter wave interferometry

We investigate the influence of thermally activated internal molecular dynamics on the phase shifts of matter waves inside a molecule interferometer. While de Broglie physics generally describes only the center-of-mass motion of a quantum object, our experiment demonstrates that the translational quantum phase is sensitive to dynamic conformational state changes inside the diffracted molecules. The structural flexibility of tailor-made organic particles is sufficient to admit a mixture of strongly fluctuating dipole moments. These modify the electric susceptibility and through this the quantum interference pattern in the presence of an external electric field. Detailed molecular dynamics simulations combined with density-functional theory allow us to quantify the time-dependent structural reconfigurations and to predict the ensemble-averaged square of the dipole moment which is found to be in good agreement with the interferometric result. The experiment thus opens a different perspective on matter wave interferometry, as we demonstrate here that it is possible to collect structural information about molecules even if they are delocalized over more than 100 times their own diameter.

Figure 1

(a) Snapshots of the MDS of perfluoroalkylated azobenzenes at $10$ ns ($1$), $35$ ns ($2$), and $40$ ns ($3$). One can clearly recognize the varying exposure of different side chains toward external fields. Although the molecule has no permanent static electric dipole moment in the thermal ground state, excitation at 500 K is associated with a rapid evolution and the expression of temporary dipole moments  (in debye, D). (b) Static scalar polarizability, ${\alpha }_{\mathrm{stat}}$, and electric dipole moment along the MDS trajectory. While ${\alpha }_{\mathrm{stat}}$ is essentially constant, $d$ varies by as much as $300\%$.

Figure 2

(a) Two typical interference patterns at $U=1$ kV (solid circles) and $U=6$ kV (open circles). (b) Interference fringe shift (right scale) and visibility (left scale) as a function of the deflection voltage. Open circles: measured shift. Continuous line: quantum fit (see text) from which we extract the molecular susceptibility. Solid circles: experimental fringe visibility. Dashed line: expected decrease of the fringe visibility for the experimentally determined velocity distribution and susceptibility. Error bars: $1\sigma$ uncertainty of the fit to the raw data.

Figure 3

Fringe visibility as a function of the diffracting laser power. Solid circles: Average of three consecutive measurements. Error bars: standard deviation. Solid line: calculated quantum curve with the optical polarizability ${\alpha }_{\mathrm{opt}}$ as the only free parameter. Dashed lines: Same fit for ${\alpha }_{\mathrm{opt}}\pm 10\%$. The measured velocity distribution ($v_{\mathrm{mean}}=140$ m/s, $\Delta v_{\mathrm{FWHM}}=28$ m/s) is included in the simulation of the fringe visibility.