Supersymmetry, entanglement, and dynamics of polar paramagnetic molecules subject to combined electric, magnetic, and optical fields

• Applicants: Professor Dr. Bretislav Friedrich; Privatdozent Dr. Burkhard Schmidt
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2014 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 247815525

• Final Report Year: 2018

Final Report Abstract

Perhaps the greatest enrichment of the literature on analytic solvability and supersymmetry is the connection that we have established between the conditions of analytic solvability and the topology of the eigenenergy surfaces. Much of our effort went into explaining this unexpected and far-reaching connection as well as into making use of it. Another general result – obtained for the example of a quantum pendulum (both planar and spherical) – is the connection that we have established between the symmetry of the physical problem and the classes of quasianalytic solutions. Our work on analytic solvability has so far culminated in a generalization that relies on the quantum Hamilton-Jacobi theory and that provides a systematic way of identifying a plethora of novel quasi-analytic solutions. Our work on entanglement, another topic of the proposal, has led to novel schemes for quantum computing with arrays of trapped polar paramagnetic molecules. This work relied on a detailed quantum-mechanical analysis of a pair of polar paramagnetic rotors coupled by the electric-dipole interaction. Our work on the dynamics of molecules subject to time-varying fields concentrated on unipolar pulses interacting with polar and polarizable molecular rotors. For short pulses, many of the dynamical features have been rendered in analytic form, providing valuable insights into the workings of kicked-rotor dynamics.

Publications

• Supersymmetry and topology of the planar quantum pendulum. Frontiers in Physics | Physical Chemistry and Chemical Physics 2, 37 (2014)
  B. Schmidt and B. Friedrich
  
• Directional properties of polar paramagnetic molecules subject to congruent electric, magnetic and optical fields. New J. Phys. 17, 045017 (2015)
  K. Sharma and B. Friedrich
  
• Supersymmetry and eigensurface topology of the spherical quantum pendulum. Phys. Rev. A 91, 022111 (2015)
  B. Schmidt and B. Friedrich
  
• Effect of rotational-state-dependent molecular alignment on the optical dipole force. Phys. Rev. A 94, 013428 (2016)
  Lee Yeong Kim, Ju Hyeon Lee, Hye Ah Kim, Sang-Kyu Kwak, Bretislav Friedrich, Bum Suk Zhao
  
• Pair-eigenstates and mutual alignment of coupled molecular rotors in a magnetic field. Phys. Chem. Chem. Phys. 18, 13467 (2016)
  K. Sharma and B. Friedrich
  
• Prospects for Quantum Computing with an Array of Ultracold Polar Paramagnetic Molecules. J. Chem. Phys. 144, 094301 (2016)
  M. Karra, K. Sharma, B. Friedrich, S. Kais, and D. Herschbach
  
• Conditional quasi-exact solvability of the quantum planar pendulum and of its anti-isospectral hyperbolic counterpart. Eur. Phys. J. D 71, 149 (2017)
  S. Becker, M. Mirahmadi, B. Schmidt, K. Schatz, and B. Friedrich
  
• Dynamics of polar polarizable rotors acted upon by unipolar electromagnetic pulses: From the sudden to the adiabatic regime
  M. Mirahmadi, B. Schmidt, M. Karra, and B. Friedrich
  
• Symmetric tops in combined electric fields: Conditional quasisolvability via the quantum Hamilton-Jacobi theory. Phys. Rev. A 97, 053417 (2018)
  K. Schatz, B. Friedrich, S. Becker, and Burkhard Schmidt