Influence of molecular temperature on the coherence of fullerenes in a near-field interferometer

We study ${\mathrm{C}}_{70}$ fullerene matter waves in a Talbot-Lau interferometer as a function of their temperature. While the ideal fringe visibility is observed at moderate molecular temperatures, we find a gradual degradation of the interference contrast if the molecules are heated before entering the interferometer. A method is developed to assess the distribution of the microcanonical temperatures of the molecules in free flight. This way the heating-dependent reduction of interference contrast can be compared with the predictions of quantum theory. We find that the observed loss of coherence agrees quantitatively with the expected decoherence rate due to the thermal radiation emitted by the hot molecules.

Figure 1

The Talbot-Lau interferometer consists of three equal gratings with a slit separation of $d=0.99\mu \mathrm{m}$ spaced by a distance of $L=38\mathrm{cm}$. The interference contrast can be reduced by heating the fullerenes in front of the interferometer via multiple laser beams.

Figure 2

High-contrast Talbot-Lau interference fringes are observed for fullerenes at temperatures below 1000 K. The fringe visibility of 47% corresponds to the quantum mechanical expectation, indicating coherent molecular evolution.

Figure 3

Electronic excitation energies of ${\mathrm{C}}_{70}$ [20]. The first photon excites the $S_1$ state followed by a rapid nonradiative conversion to the relatively long-lived triplet state $T_1$. All further photon absorption takes place in the electronic triplet configuration.

Figure 4

The calculated spectral photon emission rate for (microcanonical) molecular temperatures between 2000 and 3000 K; cf. Eq. (1). It involves a measured frequency-dependent absorption cross section [28]. The data imply that about three visible photons are emitted during a transit time of 4 ms.

Figure 5

Ion yield at the heating stage; experimental data (symbols) compared to the model calculation (solid lines). Top: Arrangement with ten heating beams and laser powers of $P=2$, 3, 4, 5, 6, 8, 10 W. Curves with higher count rates are associated with higher laser powers. Bottom: Arrangement with four heating beams and laser powers of $P=4$, 6, 8, 10 W.

Figure 6

Relative change of the molecular detection rate at $D_2$ as a function of the heating laser power. Experimental data (symbols) vs model calculation (solid lines). Top: Fullerenes with $100\mathrm{m}∕\mathrm{s}$. The number of heating beams was (a) one, (b) two, (c) four, and (d) ten. Bottom: Faster fullerenes with a velocity of $190\mathrm{m}∕\mathrm{s}$ and (a) two, (b) four, (c) ten, and (d) 16 heating beams.

Figure 7

Temperature distributions in the beam implied by our model calculation directly after the heating stage (a),(b) and at the position of the first grating (c),(d). The shading is proportional to the probability density of the temperature. The data are shown for a fullerene velocity of $100\mathrm{m}∕\mathrm{s}$ (a),(c) and of $190\mathrm{m}∕\mathrm{s}$ (b),(d), respectively. The stripes in (a) and (b) correspond to the temperature increase $\Delta T=139\mathrm{K}$ due to a single photon absorption. The stripes are somewhat closer in (c) and (d) due to cooling.

Figure 8

Fullerene interference fringes corresponding to the first-order Talbot-Lau effect at different powers of the heating laser. The stronger the heating in front of the interferometer the more thermal radiation is emitted within the interferometer, leading to a monotonic reduction of fringe contrast. The variation of the mean absolute count rate is caused by the thermal ionization detection scheme. While it is irrelevant for the assessment of the degree of coherence, it provides us with a second method for the evaluation of the molecular temperature, as discussed in the text and indicated in Fig. 6. The solid curves are sinusoidal fits used to extract the fringe visibility.

Figure 9

Reduction of the interference visibility due to heating with laser power $P$. The circles give the experimental visibility extracted from fringe patterns such as shown in Fig. 8; the solid lines are the theoretical expectation given by Eq. (16). The fullerenes in the top graph have a velocity of $190\mathrm{m}∕\mathrm{s}$ corresponding to the first Talbot order, while in the bottom graph the fullerene velocity is $100\mathrm{m}∕\mathrm{s}$ corresponding to the second Talbot order. The upper scale gives the mean fullerene temperature at the entrance of the interferometer.