Manifestations of Physics beyond the Standard Model in Atomic and Molecular Phenomena

The Standard Model of elementary particles comprises the fundamental building blocks of observable matter. To date, it is one of the most successful theories in physics. Despite this, it is not complete. There remains a list of fundamental physical phenomena which go unexplained by the Standard Model. Most notably, it is unable to explain the observed matter-antimatter asymmetry in the universe, fails to supply an adequate candidate dark matter particle and is unable to explain the origin of dark energy. Efforts to extend the Standard Model in order to account for these phenomena have become a focus of contemporary physics. The use of atomic and molecular systems to probe dark matter interactions and test the stability of fundamental constants is a central focus of this thesis. Interactions with ultralight scalar and pseudoscalar fields can induce variations in these constants, altering the hyperfine structure of atoms and molecules. To exploit this, a new mechanism is proposed in which scalar field dark matter may be detected through its effect on hyperfine transitions in alkali atoms. It is further shown that comparing the variation of the electric quadrupole hyperfine constant with that of the magnetic dipole hyperfine constant offers enhanced sensitivity to the dark matter interaction. Atomic clock comparisons provide an additional and complementary avenue, and data from these experiments are used to constrain the variation of hadronic parameters, ultralight dark matter models, possible violations of the Einstein Equivalence Principle, and the existence of long-range forces beyond gravity. In parallel, constraints are obtained on the variation of the QCD interaction scale, ΛQCD, within a framework where a dark matter or dark energy field couples to it through a sole gluonic channel, and its prospective sensitivity to the anticipated 229Th nuclear clock is examined. A complementary focus of this work is the study of enhanced nuclear moments that violate the fundamental symmetries of parity (P) and time reversal (T). Such moments provide sensitive tests of theories predicting CP violation and are directly relevant to explaining the observed matter-antimatter asymmetry of the universe. In octupole-deformed nuclei, near-degenerate states of opposite parity are mixed by Tand P-violating nuclear forces, aligning the nuclear axis with the spin and allowing the otherwise forbidden intrinsic Schiff, electric dipole, and magnetic quadrupole moments to manifest in the laboratory frame with large amplification. Calculations of these moments are presented for isotopes predicted to exhibit octupole deformation, showing that Schiff and magnetic quadrupole moments are significantly enhanced compared with those in spherical nuclei. When coupled to electrons, these moments induce T, P-violating atomic and molecular electric dipole moments, greatly increasing the sensitivity of EDM searches. The implications of these enhancements are explored for atoms, molecules, and solids containing such nuclei, highlighting their potential utility in tests of unification theories and in the search for axion dark matter.