Theory for Molecular Tests of Fundamental Physics

Even today, fundamental difficulties remain in the understanding of our universe. Among those are inexplicable phenomena like the enormous excess of matter over anti-matter (baryon asymmetry) — connected to the question why is there matter at all — or dark matter (DM) and dark energy which are invoked to explain the structure and evolution of our universe, and problems like the unification of quantum theory with gravity. In order to take a step closer to resolving such issues, it is important to test the known laws of physics, summarized in the standard models of particle physics (SM) and cosmology (ΛCDM model), as accurately as possible. Direct experimental tests of the SM can be carried out with high energies at large colliders like the LHC at CERN, and direct tests of the ΛCDM model are usually performed at large observatories like LIGO. In contrast, the theoretical foundations of chemistry are mostly well understood. Hence, molecules are theoretically and experimentally well controllable. Thus, measurements in standard-sized laboratories with ultra-high precision are possible, so that the less well understood laws of physics can be tested. Such low-energy experiments provide indirect tests of the standard models in the realm of chemistry by probing the fundamental symmetries of nature. Therewith, these tests are complementary to direct tests of the laws of physics in cosmology or high-energy physics. In this cumulative thesis quantum chemical methods are developed and applied to design new experiments and improve existing experiments that employ molecules for tests of fundamental symmetries and, therewith, search for new physics beyond the standard models (BSM). A simultaneous violation of parity and time-reversal symmetry (P,T) is closely connected to baryon asymmetry. P,T-violation appears in a larger amount in unifying BSM theories than in the SM itself. P,T-violation on the elementary particle level is relativistically enhanced in heavy atoms and heavy-elemental molecules and results in permanent electric dipole moments (EDMs) of atoms and molecules which are non-vanishing in the limit of vanishing electric fields. In the first part of this thesis, P,T-violations in diatomic and small polyatomic molecules are studied in order to find well-suited candidates for a first measurement of a permanent EDM. Within this study relativistic effects as well as effects due to the chemical environment of the heavy atom are systematically analyzed. Furthermore, the effects of various fundamental sources of P,T-violation that contribute to the P,T-odd EDM of a molecule are studied. It is discussed, how these sources can be disentangled from experiments that aim to measure the permanent EDMs of different molecules. Among this research one of the first calculations of P,T-odd effects in polyatomic molecules is presented. In the second part of this thesis, the applicability of chiral molecules as sensitive probes for P-violating cosmic fields is demonstrated. P-violating cosmic fields are predicted in several cold DM (CDM) models as well as in the standard model extension (SME) that allows for local Lorentz invariance violation (LLIV). LLIV appears in several theories that aim to unify quantum theory and gravity. It is shown that well-chosen chiral molecules containing heavy elements can improve present limits on P-odd interactions of electrons with cosmic fields by at least two orders of magnitude. This renders chiral molecules particularly interesting for searches for BSM physics. In order to guide future searches for candidate molecules, challenges that may appear in the theoretical description or the design of experiments are discussed. In the last part of this thesis, the possibilities to use a clock transition in the iodine molecule to limit LLIV are explored in cooperation with the BOOST collaboration. Quantum chemical studies of such effects in iodine are presented. These calculations are essential for an estimate of the expected sensitivity of the BOOST satellite mission, which employs the iodine molecular clock as probe for LLIV

Quasi-relativistic approach to analytical gradients of parity violating potentials

An analytic gradient approach for the computation of derivatives of parity-violating (PV) potentials with respect to displacements of the nuclei in chiral molecules is described and implemented within a quasirelativistic mean-field framework. Calculated PV potential gradients are utilised for estimating PV frequency splittings between enantiomers in rotational and vibrational spectra of four chiral polyhalomethanes, i.e. CHBrClF, CHClFI, CHBrFI and CHAtFI. Values calculated within the single-mode approximation for the frequency shifts agree well with previously reported theoretical values. The influence of non-separable anharmonic effects (multi-mode effects) on the vibrational frequency shifts, which are readily accessible with the present analytic derivative approach, are estimated for the C--F stretching fundamental of all four molecules and computed for each of the fundamentals in CHBrClF and CHAtFI. Multi-mode effects are found to be significant, in particular for the C--F stretching modes, being for some modes and cases of similar size as the single-mode contribution.Comment: 20 p/8 fig/4 tab/suppl: 26 tab; minor text changes/corr, eqs 2/27 corr; Numer. vals changed slightly per: more consist. use of fin. nucl; same numer. grid for zora/pv oper. matrix elem. and derivs; improved acc. in assem. of DFT grad; tighter conv. crit. in HF at CHClFI(eq); fewer digits; Tab I/II vals from fin. suppl. of ref 40, as prev. earlier version was linked on publ.'s webpag

BOOST -- A Satellite Mission to Test Lorentz Invariance Using High-Performance Optical Frequency References

BOOST (BOOst Symmetry Test) is a proposed satellite mission to search for violations of Lorentz invariance by comparing two optical frequency references. One is based on a long-term stable optical resonator and the other on a hyperfine transition in molecular iodine. This mission will allow to determine several parameters of the standard model extension in the electron sector up to two orders of magnitude better than with the current best experiments. Here, we will give an overview of the mission, the science case and the payload.Comment: 11 pages, 2 figures, accepted for publication in Phys. Rev.

Toward Clinically Compatible Phase-Contrast Mammography

Phase-contrast mammography using laboratory X-ray sources is a promising approach to overcome the relatively low sensitivity and specificity of clinical, absorption-based screening. Current research is mostly centered on identifying potential diagnostic benefits arising from phase-contrast and dark-field mammography and benchmarking the latter with conventional state-of-the-art imaging methods. So far, little effort has been made to adjust this novel imaging technique to clinical needs. In this article, we address the key points for a successful implementation to a clinical routine in the near future and present the very first dose-compatible and rapid scan-time phase-contrast mammograms of both a freshly dissected, cancer-bearing mastectomy specimen and a mammographic accreditation phantom