Thermal limitation of far-field matter-wave interference

We assess the effect of the heat radiation emitted by mesoscopic particles on their ability to show interference in a double-slit arrangement. The analysis is based on a stationary, phase-space-based description of matter-wave interference in the presence of momentum-exchange-mediated decoherence.

Figure 1

Thermal decoherence time for double-slit interference as a function of the initial particle temperature. The curves correspond to a slit separation $d$ of 50, 100, and $500\mathrm{nm}$, and $1\mu \mathrm{m}$ (top to bottom). The solid lines incorporate the effect of cooling as described by (23, 24), while the dashed lines show the result (26) for an asymptotically large heat capacity (they are indistinguishable for $d=500\mathrm{nm}$ and $1\mu \mathrm{m}$). The particle parameters ${\mathcal{A}}_{\epsilon }=5\times {10}^{-18}{\mathrm{m}}^2$ and $C_V=12000k_{\mathrm{B}}$ correspond to ultrafine carbonaceous aerosols, as discussed in the text.

Figure 2

Thermal decoherence time for double-slit interference with fullerene molecules. The solid lines were calculated from Eq. (23) using the full frequency- and cooling-dependent emission rate. Compared to Fig. 1, similar decoherence times are found only at considerably larger temperatures. The comparison with the dotted lines shows that for fullerenes the mesoscopic result (26) is not yet applicable, not even for a qualitative description of the temperature dependence of the interference contrast (${\mathcal{A}}_{\epsilon }={10}^{-22}{\mathrm{m}}^2$ [31]).