Far-from-equilibrium Quantum Dynamics Group
Violation of discrete symmetries
The symmetry of space reflection was assumed to hold until Lee and Yang discovered the parity(-P)-violation in weak interactions in 1956 . Consecutive experiments connected to P-violation referred to weak decay processes where the involved particles changed their identity . In contrast, possible P-violating interactions in stable atoms must preserve the identity of the involved particles. The first proposals concerning effects of a weak electron-nucleon interaction in atoms with stable nuclei induced by neutral currents were given by Zeldovich in 1958 , but his estimates suggested no obvious possibility to observe these effects.
In the late 1960s the electroweak interactions were introduced by Glashow, Weinberg and Salam. The involved neutral current can couple to matter like a pseudovector particle, i. e. the coupling between the Z-boson and the electron is proportional to the electron helicity which is odd under space reflection.
When M. A. Bouchiat and C. Bouchiat discovered a Z-law for parity mixing amplitudes induced by neutral currents in atoms, with Z being the atomic number, atomic physics became a promising field for the search of P-violation. This Z-effect greatly favours heavy atoms and leads to enhancement effects of the order of -, see  and references therein.
However, theoretical predictions of P-violating effects in heavy atoms have to face the uncertainties given by the models of the electronic and nuclear structure of those heavy atoms. In contrast to these limitations, one finds a well established model of atomic hydrogen which could overcompensate the disadvantage related to the Z-law.
Today, the main motivation for all studies concerning atomic parity-violation (APV) still is - besides P-violation itself - the investigation of one electroweak parameter at low energy, the weak charge of an atomic nucleus, which is closely connected to the weak mixing angle . It was introduced by analogy with the nuclear electric charge indicating a short-range interaction between the nucleus and the electrons of an atom. Hence, the interaction strength is proportional to the electron density near the nucleus times , with being the Fermi constant. In that way, matter exhibits a spatial orientation with acting as the fundamental constant of the electroweak interaction in atomic physics .
Complementary to the high momentum transfers in collider experiments, the interactions between quarks and electrons can be studied in APV experiments in the range of low momentum transfers.
In our group, we investigate the P-violating effects by computing Abelian geometric (Berry-)phases that arise for hydrogen propagating through suitable electromagnetic fields. These Berry phases contain P-violating contributions. We calculate these phases and study the underlying physical properites of P-violation in hydrogen. The magnitudes of the P-violating effects are enhanced under suitable conditions in order to propose experiments that are in principle sensitive to P-violation in hydrogen, see . We are especially interested in longitudinal atomic beam spin echo (lABSE) experiments due to the high precision measurements achievable in interferometry experiments. In addition, we investigate possibilities to enhance the precision of lABSE experiments beyond the standard quantum limit using squeezed many-particle hydrogen states.
Precision measurements of APV in hydrogen by spin echo experiments will have to compete with already established experiments that deal with heavy atoms, and one has to explore which method gives higher precision. Until today, the experimental efforts to observe P-violation in hydrogen and deuterium have not led to satisfying results . For early experimental efforts concerning APV in hydrogen see [7, 8, 9]. We pick two current experiments that engage in the running coupling at low energies: The caesium experiment in Paris around M. A. Bouchiat  as well as the Moller scattering experiments at SLAC [11,12].
Crucial barriers in APV calculations concerning heavy atoms are the uncertainties in the structure of atomic nuclei, e. g. unknown QCD effects or the nature of distorted nuclei, see  and references therein. Here, deviations from the standard model might possibly be traced back to those uncertainties instead of introducing new fundamental physics. These inconveniences can be avoided to the highest degree by investigating hydrogen, the structure of which is theoretically best known among all elements. However, the theoretical models involve the weak charge. Consequently, deviations between experimental results and theoretically predicted values can indicate physics beyond the standard model if the precision of the measurements is raised sufficiently .
- T. Lee and C. Yang, ``Question of Parity Conservation in Weak Interactions'', Phys. Rev. 104 (1956) no. 1, 254-258.
- M. Bouchiat and C. Bouchiat, ``Parity Violation in Atoms'', Rep. Prog. Phys. 60 (1997) 1351-1396.
- Y. B. Zeldovich, ``Parity nonconservation in the first order in the weak-interaction constant in electron scattering and other effects'', Sov. Phys. JETP 9 (1959) 682.
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- T. Bergmann, M. DeKieviet, T. Gasenzer, O. Nachtmann, and M.-I. Trappe, ``Parity Violation in Hydrogen and Longitudinal Atomic Beam Spin Echo I'', Eur. Phys. J. D 54 (2009) no. 3, 551-574.
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- E. G. Adelberger, T. A. Trainor, E. N. Fortson, T. E. Chupp, D. Holmgren, M. Z. Iqbal, and H. E. Swanson, ``A Technique for Measuring Parity Nonconservation in Hydrogenic Atoms'', Nucl. Instru. and Meth. 179 (1981) 181.
- J. Guéna, M. Lintz, and M. A. Bouchiat, ``Measurement of the parity violating 6s-7s transition amplitude in cesium achieved within atomic-unit accuracy by stimulated-emission detection'', Phys. Rev. A 71 (2005) 042108.
- SLAC E158 Collaboration, P. L. Anthony et al., ``Observation of Parity Nonconservation in Mller Scattering'', Phys. Rev. Lett. 92 (2004) 181602.
- SLAC E158 Collaboration, P. L. Anthony et al., ``Precision Measurement of the Weak Mixing Angle in Mller Scattering'', Phys. Rev. Lett. 95 (2005) 081601.
- J. Guena, M. Lintz, and M. Bouchiat, ``Atomic parity violation: Principles, recent results, present motivations'', Mod. Phys. Lett. A 20 (2005) no. 6, 375.