In dark matter direct detection experiments, the free nuclear recoil description breaks down as the de Broglie wavelength of dark matter approaches the typical atomic spacing of the target material. In this work, we investigate the particular case of scattering off of crystal targets, whose collective excitations are well understood as phonons. As experimental energy thresholds decrease, it becomes increasingly important to understand the response of targets to energy depositions below the nuclear recoil scale. For dark matter masses lighter than 1 MeV, the scattering rate is dominated by single phonons, while at masses larger than 100 MeV, we expect the scattering to approach the free nuclear recoil result. Starting from the phonon formalism in the harmonic crystal approximation, we perform the first calculations of scattering rates in the intermediate 1-100 MeV mass regime where multiphonon process dominate and demonstrate how the multiphonon response smoothly approaches free nuclear recoil. We then drop the harmonic approximation and calculate possible corrections to the scattering rates due to crystal anharmonicity. We find these anharmonic corrections to be large at small dark matter masses ∼ MeV and large experimental thresholds ∼ 100 MeV, but approach the harmonic result as the DM mass increases.

Applications of quantum computing to high energy physics (HEP) is a relatively new field of research. As such, the relevant literature is not well organized in one place and a clear road-map for people approaching the field is not currently available. Addressing this issue was the main motivation for this article, which is intended a pedagogical introduction to the field and specifically to our research direction, i.e. application of quantum computing to parton shower event generators, with the hope of more people becoming interested in exploring this path. Our paper on the subject, “A quantum algorithm for high energy physics simulations” [8], is the subject of chapter 4. I hope this article can provide a direct path for people familiar with quantum mechanics and quantum field theory to start reading papers or conducting research in this area of quantum computing applications in HEP. In this regard, the quantum algorithm we present in Chapter 4, can serve as an example of development of a novel efficient quantum algorithm to solve a problem in a particle physics model.

The scattering of dark matter (DM) particles to excite collective vibrational modes knownas phonons in crystal targets is a motivated method of observing DM with masses mχ < 1 MeV. This is due to the matching between the typical energy and momentum imparted into the target and those of the phonons. For heavier dark matter particles with masses mχ ≳ 1 GeV, the scattering is instead point-like off of the individual nuclei in the crystal, rather than collective scattering from many atoms. While the single phonon and nuclear recoil responses are understood, the transition between the two is not. An understanding of this intermediate regime requires a consideration of multiphonon processes, in particular as higher-order corrections that increasingly contribute to the total scattering rate as the typical energy depositions increase. We utilize several simplifying approximations to arrive at analytic descriptions for multiphonon excitation, allowing us to fully characterize the crystal’s phonon response across the relevant mass spectrum for incident DM. Our results allow us to identify the dominant signals to look for in experimental DM searches with cubic crystal targets as a function of the detector energy thresholds.