Josephson Quantum Mechanics at Odd Parity
Julia S. Meyer1, Manuel Houzet1, and Yuli V. Nazarov2
1 Univ. Grenoble Alpes, CEA, INAC-Pheliqs, F-38000 Grenoble, France
2 Kavli Institute of Nanoscience, Delft University of Technology, 2628 CJ Delft, The Netherlands
Embedding a Josephson junction into an electromagnetic environment results in quantum fluctuations of the superconducting phase. This opened up the field of Josephson Quantum Mechanics with its numerous opportunities to engineer and fabricate the practical quantum devices[1].
We concentrate on the tunnel junctions with few conduction channels. Such junction may be in a stable odd parity state when a single quasiparticle is trapped in the lowermost Andreev bound state.[2] This is called quasiparticle poisoning and completely cancels supercurrent in the corresponding channel.
Despite such cancellation, embedding the odd parity junction into an electromagnetic environment gives rise to a special quantum mechanics of superconducting phase, very distinct from the conventional one [3] as far as the underlying theoretical structure is concerned. We investigate it theoretically covering several most representative cases and predict a set of spectacular experimentally observable effects. We show that the poisoning is incomplete in low-impedance environment. We demonstrate four-fold degeneracy of the odd-parity ground state in high-impedance environment. For a Coulomb island, the odd parity junction provides overlap and hybridization of the charging states of different parities. We study how this affects phase slips in the junction.
[1] Y. Makhlin, G. Schön, and A. Shnirman, Quantum-state engineering with josephson-junction devices, Rev. Mod. Phys. 73, 357 (2001).
[2] N. M. Chtchelkatchev and Y. V. Nazarov, Andreev quantum dots for spin manipulation, Phys. Rev. Lett. 90, 226806 (2003).
[3] G. Schön and A. Zaikin, Quantum coherent effects, phase transitions, and the dissipative dynamics of ultra small tunnel junctions, Physics Reports 198, 237 (1990).