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The interaction between light and matter can be enhanced by trapping the light in an optical cavity. In a short Google research I didn't find an experiment trying to enhance neutrino-matter interaction in this way. Is it just impractical? If yes, why? The situation with light and neutrinos should be quite similar: Light coming from a distant source of photons arrives with plane wavefronts on earth. If we want to enhance the interaction of let's say some molecules with light of a specific wavelength $\color{#ff0000}{\lambda}$ we send it into a Fabry-Pérot cavity of length $m/2 \cdot \color{#ff0000}{\lambda}$ with $m \in \mathbb{N}$. The mirrors are distributed Bragg reflectors (DBRs) consisting of alternating layers with high $\color{#0050ff}{n_h}$ and low refractive index $\color{#00b8ff}{n_l}$, each with an optical thickness of a quarter wavelength $\color{#0084ff}{n} d = \color{#ff0000}{\lambda} / 4$. The reflection at a single refractive index boundary is small (given by Fresnel equations), but the interference between the partial reflections allows reflectivities of > 99.999%. The light is then concentrated between the mirrors and can interact efficiently with material which by itself would have a small interaction cross-section.

In the case of neutrinos the DBRs would be made of alternating layers of high $\color{#00415b}{\rho_h}$ and low density $\color{#aeb8df}{\rho_l}$ material. One can even define an equivalent refractive index $${\color{#577c9d}{n_i}}^2 = \left( \color{#51ff00}{\lambda} / \color{#51ff00}{\lambda}_\color{#577c9d}{i} \right)^2$$ (see Eq. 5.1 in [1]) with the de Broglie wavelength $\color{#51ff00}{\lambda}$ in free space and $\color{#51ff00}{\lambda}_\color{#577c9d}{i}$ in medium $\color{#577c9d}{i}$. Similar to when light hits a refractive index boundary, a part of the neutrino wavefunction is coherently scattered into the backwards direction at each interface. Adding up the amplitudes of all partial reflections increases the reflectivity of such a DBR. [2] proposes a lock-in measurement to detect the momentum transfer from reflecting a stream of neutrinos off a DBR. In that paper, they specifically talk about neutrinos with particularly long de Broglie wavelengths using DBRs with layer thicknesses around $a \approx 30\,\text{cm}$, but the thin film technology has substantially improved since then, so that one could work with layer thicknesses of tens of nanometers.

Where does the idea of cavity-enhanced neutrino detection go wrong? Or is it simply that a cavity would constrain the wavevector of the neutrinos too much, since they need to come from the right direction with the right wavelength?

A. P.
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  • Neutrinos interact with matter with the weak coupling constant in first order. Look at the difference between the electromagnetic coupling and the weak coupling here http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/couple.html – anna v Dec 24 '22 at 10:59
  • @annav For the neutrino DBR to work, only a change in the de Broglie wavelength $\lambda_i$ is required. This is achieved by the interaction potential $U$ between matter and neutrinos (see around Eq. 5.1 in [1]). As far as I understood it, this should be independent of the type of interaction. – A. P. Dec 24 '22 at 11:15
  • The coupling constant controls the probability of interaction It is much more probable that a photon will interact with matter than a neutrino, To get reflections there have to be interactions – anna v Dec 24 '22 at 11:57
  • look for a plan for low energy neutrino detection, https://arxiv.org/abs/2104.14352 they are talkin of 10 events per year. – anna v Dec 24 '22 at 12:01
  • Thanks for the comments, @annav. I understand that a localized interaction is very unlikely. Like those creating a phonon at an impurity, as in the arXiv paper, are measured in events/year. But isn't the ensemble scattering on a DBR different here? If you consider a photon being scattered by a mirror, each atom in the mirror only contributes a small partial wave (≙ small probability of the photon interacting with this particular atom), but the overall reflection probability is close to 1. – A. P. Dec 24 '22 at 13:02
  • the probability is still controlled by the size of the coupling constant of the interaction. "Neutrinos are abundant subatomic particles that are famous for passing through anything and everything, only very rarely interacting with matter. About 100 trillion neutrinos pass through your body every second." https://icecube.wisc.edu/news/press-releases/2017/11/first-look-at-how-earth-stops-high-energy-neutrinos-in-their-tracks/ no photons pass through your body, they are stopped by interacting with the atoms of your body because em coupling constant is very much larger than the weak . – anna v Dec 24 '22 at 16:01
  • What's bad about the paper [1] is that one hardly gets any numbers out. But in Fig. 2 they plot the reflectivity for a $N=8$ layer DBR, which is around $10^{-4.5}$. If I extrapolate, a $N=800$ layer DBR would amount to 25% reflectivity. That would certainly be a challenge for conventional thin film deposition methods. – A. P. Dec 24 '22 at 17:43
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    I think this is a fun idea tbh! I haven't thought it through, but I think the main issue with this will be absorption. The special thing about the materials which you use in optical cavities is that they can have rather different refractivity (real part of the refractive index) while still having low absorption (imaginary part). I don't know how this works out for neutrinos, but I suspect that both will scale similarly with the density. That would mean that if you add more layers, your enhancement by refraction from the layers is eventually cancelled by absorption in the layers. – Wolpertinger Jan 04 '23 at 14:11

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