Testing macroscopic realism through high-mass interferometry

We define a quantum witness for high-mass matter-wave interferometers that allows us to test fundamental assumptions of macroscopic realism. We propose an experimental realization using absorptive laser gratings and show that such systems can strongly violate a macrorealistic quantum-witness equality. The measurement of the witness can therefore provide clear evidence of physics beyond macrorealism for macromolecules and nanoparticles.

Figure 1

Talbot-Lau interferometer configurations for a quantum-witness test. (a) The interferometer consists of three absorptive standing-wave gratings, $G_0^{\left(i\right)},i=1,2,3$, formed with lasers of wavelength ${\lambda }_{\mathrm{L}}$. (b) The middle grating is replaced by a combination of one laser beam with wavelength ${\lambda }_{\mathrm{L}}$ followed immediately, in position or time, by another with wavelength $2{\lambda }_{\mathrm{L}}$. The second beam serves as a mask that blocks particles passing through the “even” nodes of the original $G_0^{\left(2\right)}$ grating. We denote this combination $G_{+}^{\left(2\right)}$. (c) The second beam is shifted by ${\lambda }_{\mathrm{L}}$ such that the “odd” nodes are blocked. We denote this combination $G_{-}^{\left(2\right)}$.

Figure 2

(a) Mean number of photons $n\left(x\right)$ absorbed by a particle at position $x$ in the one-color grating $G_0^{\left(2\right)}$. (b) The same for the two-color grating $G_{+}^{\left(2\right)}$. Here, the total photon number (black solid line) has contributions with period ${\lambda }_{\mathrm{L}}/2$ (green dashed line) and ${\lambda }_{\mathrm{L}}$ (blue dot-dashed line). (c),(d) The corresponding transmission probabilities. With intensities chosen such that $n_0^{\left(2b\right)}=\frac{4}{3}{n}_0^{\left(2a\right)}=n_0^{\left(2\right)}\gg 1$, Eq. (3) is satisfied and grating $G_{+}^{\left(2\right)}$ has a transmission like that of $G_0^{\left(2\right)}$ but with every other “hole” closed.

Figure 3

The expectation values $\langle Q\rangle ,{\langle Q\rangle }_{\mathrm{m}}$ and quantum witness $W$ as a function of the ratio between grating separation $\xi$ and Talbot length ${\xi }_{\mathrm{T}}={\lambda }_{\mathrm{L}}^2/4{\lambda }_{\mathrm{dB}}$. The peaks in $\langle Q\rangle$ and ${\langle Q\rangle }_{\mathrm{m}}$ are a consequence of Talbot revivals. It is the wave nature of this phenomenon that results in differences between $\langle Q\rangle$ and ${\langle Q\rangle }_{\mathrm{m}}$. As a consequence, the witness develops strong peaks at $\xi \approx (2q-1){\xi }_{\mathrm{T}}$, which become sharper and taller with increasing $n_0^{\left(2\right)}$. The parameters used here are $n_0^{\left(3\right)}=2,\beta \left({\lambda }_{\mathrm{L}}\right)=\beta \left(2{\lambda }_{\mathrm{L}}\right)=1$, and $n_0^{\left(2\right)}=10,50$.

Figure 4

(a) Maximum value of the quantum witness, $W_{\max }$, and the revised upper bound, $W_{\delta }$, as a function of $n_0^{\left(2\right)}$ for $n_0^{\left(3\right)}=1,5,10$. (b) The bound $W_{\delta }$ (log scale). For $n_0^{\left(2\right)}\gtrsim 10$, this is smaller by several orders of magnitude than the predicted violations. The parameters here are the same as in Fig. 3.