# Project A5:

Fractional Josephson vortices in the quantum limit

## Summary

In conventional long Josephson junctions a magnetic field applied parallel to the barrier penetrates the junction in the form of quantized vortices (fluxons) carrying a single quantum of magnetic flux each. From a mathematical point of view a fluxon is a soliton which can freely move along the junction. Classical and quantum information processing devices based on fluxons were proposed and are presently investigated. Recently it became possible to fabricate and study so-called Josephson pi-junctions. The most interesting phenomena take place when one considers a long Josephson junction one part of which behaves as a conventional 0-junction and another part as a pi-junction. There are several available technologies to fabricate such devices. At the boundary between 0 and pi regions a new type of vortex (a semifluxon) carrying only half of a flux quantum can form spontaneously. Each semifluxon is pinned at the 0-pi-boundary and may have positive or negative polarity that makes it similar to a spin 1/2 system with degenerate energies of up and down states. Further, using special current injectors, even more general boundaries can be created that allow for the formation of vortices carrying any fractional value kappa of a flux quantum (kappa-vortices). Semifluxons and kappa-vortices, being pinned at the boundaries but being able to deform, are objects that interpolate between the immobile magnetic flux quanta stored in a superconducting ring and the free moving integer fluxons in a conventional long Josephson junction. For these limiting cases quantum behaviour (quantum superpositions of immobile flux quanta, tunnelling of fluxons) has been demonstrated experimentally by several groups. We thus expect that also kappa-vortices will behave as quantum objects at sufficiently low temperatures (at some 10 mK). Within this project we would like to develop a quantum mechanical description of fractional vortices and perform experiments which will demonstrate their quantum nature. Since fractional flux quanta can represent the ground state of the system (which, in fact, is a new state of matter) they are robust objects more resistant to decoherence than single particles. One can control the states of a fractional vortex (e.g. set or read-out) using external currents and magnetic fields. Within this project we start from the investigation of a single fractional vortex and move towards more complex systems such as two- or three-vortex molecules and, ultimately, 1D arrays ("crystals") of vortices. There are many degrees of freedom that can be controlled (kappa, vortex distance, polarity, size of the vortex, etc.) allowing to tailor cooperative quantum states of these systems in a wide parameter range and to understand the scaling behaviour of their properties when going from a small group of kappa-vortices to larger systems like 1D or, in a future stage, even 2D arrays of such objects.

## Project leaders

Dr. Edward Goldobin, Physikalisches Institut II, Universität Tübingen

Prof. Dr. Reinhold Kleiner, Physikalisches Institut II, Universität Tübingen

Prof. Dr. Wolfgang P. Schleich, Institut für Quantenphysik, Universität Ulm

## Refs & Publications

R. Menditto, H. Sickinger, M. Weides, H. Kohlstedt, D. Koelle, R. Kleiner, E. Goldobin*"Tunable φ Josephson junction ratchet"*

*Phys. Rev. E*

**94**, 0422002 (2016)*;*doi: 10.1103/PhysRevE.94.042202

E. Goldobin, R. Menditto, D. Koelle, R. Kleiner

*"Model I-V curves and figures of merit of underdamped deterministic Josephson ratchets"*

*Phys. Rev. E*

**94**, 032203 (2016)*;*doi: 10.1103/PhysRevE.94.032203

R. Menditto, H. Sickinger, M. Weides, H. Kohlstedt, M. Zonda, T. Novotný, D. Koelle, R. Kleiner, E. Goldobin

*"Phase retrapping in a φ Josephson junction: Onset of the butterfly effect"*

*Phys. Rev. B*

**93**, 174506 (2016)*;*doi: 10.1103/PhysRevB.93.174506

E. Goldobin, S. Mironov, A. Buzdin, R. G. Mints, D. Koelle, R. Kleiner

*"Effective model for a short Josephson junction with a phase discontinuity"*

*Phys. Rev. B*

**93**, 134514 (2016)*;*doi: 10.1103/PhysRevB.93.134514

E. Goldobin, D. Koelle, R. Kleiner

*"Tunable ±φ, φ0 and φ0 ± φ Josephson junction"*

*Phys. Rev. B ,*; arXiv: 1504.05858

**91**, 214511 (2015)*;*doi: 10.1103/PhysRevB.91.214511

D. M. Heim, N. G. Pugach, M. Yu. Kupriyanov, E. Goldobin, D. Koelle, R. Kleiner, N. Ruppelt, M. Weides, H. Kohlstedt

*"The effect of normal and insulating layers on 0-π transitions in Josephson junctions with ferromagnetic barriers"*

*New J. Phys. ,*;

**17**, 113022 (2015)*;*doi: 10.1088/1367-2630/17/11/113022

A. Lipman, R. G. Mints, D. Koelle, R. Kleiner, E. Goldobin

*"Josephson junctions with tunable current-phase relation"*

*Phys. Rev. B*

**90**, 184502 (2014)*;*doi: 10.1103/PhysRevB.90.184502

E. Goldobin, R. Kleiner, D. Koelle, and R. G. Mints

*"Phase Retrapping in a Pointlike φ Josephson Junction: The Butterfly Effect"*

*Phys. Rev. Lett.*

**111**, 057004 (2013)*;*doi: 10.1103/PhysRevLett.111.057004

E. Goldobin, H. Sickinger, M. Weides, N. Ruppelt, H. Kohlstedt, R. Kleiner, and D. Koelle

*"Memory cell based on a φ Josephson junction"*

*Appl. Phys. Lett.*

**102**, 242602 (2013)*;*doi: 10.1063/1.4811752

D. M. Heim, K. Vogel, W. P. Schleich, D. Kölle, R. Kleiner, and E. Goldobin

*"A tunable macroscopic quantum system based on two fractional vortices"*

*New Journal of Physics*

**15**, 053020 (2013)*;*doi: 10.1088/1367-2630/15/5/053020

D. M. Heim, W. P. Schleich, P. M. Alsing, J. P. Dahl, and S. Varro

*"Tunneling of an energy eigenstate through a parabolic barrier viewed from Wigner phase space"*

*Phys. Lett. A*

**377**, 1822-1825 (2013)*;*doi: 10.1016/j.physleta.2013.05.017

D. M. Heim, N. G. Pugach, M. Y. Kupriyanov, E. Goldobin, D. Kölle, and R. Kleiner

*"Ferromagnetic planar Josephson junction with transparent interfaces: a φ junction proposal"*

*J. Phys.: Condens. Matter*

**25**, 215701 (2013)*;*doi: 10.1088/0953-8984/25/21/215701

M. Grupp, W. P. Schleich, E. Goldobin, D. Kölle, R. Kleiner, and R. Walser

*"Emergence of atomic semifluxons in optical Josephson junctions"*

*Phys. Rev. A*

**87**, 021602 (2013)*;*doi: 10.1103/PhysRevA.87.021602

J. M. Meckbach, M. Merker, S. J. Bühler, K. Ilin, B. Neumeier, U. Kienzle, E. Goldobin, R. Kleiner, D. Kölle, and M. Siegel

*"Sub-μm Josephson Junctions for Superconducting Quantum Devices"*

*IEEE Trans. Appl. Supercond.*;

**23**, 1100504 (2013)*arXiv:1210.1012 [cond-mat.supr-con]*

*;*doi: 10.1109/TASC.2012.2231719

H. Sickinger, A. Lipman, M. Weides, R. G. Mints, H. Kohlstedt, D. Kölle, R. Kleiner, and E. Goldobin

*"Experimental Evidence of φ Josephson Junction"*

*Phys. Rev. Lett.*

**109**, 107002 (2012)*;*doi: 10.1103/PhysRevLett.109.107002

U. Kienzle, J. M. Meckbach, K. Buckenmaier, T. Gaber, H. Sickinger, Ch. Kaiser, K. Ilin, M. Siegel, D. Kölle, R. Kleiner, and E. Goldobin

*"Spectroscopy of a fractional Josephson vortex molecule"*

*Phys. Rev. B*

**85**, 014521 (2012)*;*doi: 10.1103/PhysRevB.85.014521

N. G. Pugach, M. Yu. Kupriyanov, E. Goldobin, R. Kleiner, and D. Kölle

*"Superconductor-insulator-ferromagnet-superconductor Josephson junction: from the dirty to the clean limit"*

*Phys. Rev. B*

**84**, 144513 (2011)*;*doi: 10.1103/PhysRevB.84.144513

M. Weides, U. Peralagu, H. Kohlstedt, J. Pfeiffer, M. Kemmler, C. Gürlich, E. Goldobin, D. Kölle, and R. Kleiner

*"Critical current diffraction pattern of SIFS Josephson junctions with step-like F-layer"*

*Supercond. Sci. Technol.*;

**23**, 095007 (2010)*arXiv:1006.5109v2 [cond-mat.supr-con]*

S. Scharinger, C. Gürlich, R. G. Mints, M. Weides, H. Kohlstedt, E. Goldobin, D. Kölle, and R. Kleiner

*"Interference patterns of multifacet 20 x ( 0-π) Josephson junctions with ferromagnetic barrier"*

*Phys. Rev. B*

**81**, 174535 (2010)N. G. Pugach, E. Goldobin, R. Kleiner, and D. Kölle

*"Method for reliable realization of a φ Josephson Junction"*

*Phys. Rev. B*

**81**, 104513 (2010)*;*doi: 10.1103/PhysRevB.81.104513

C. Gürlich, S. Scharinger, M. Weides, H. Kohlstedt, R. G. Mints, E. Goldobin, D. Kölle, and R. Kleiner

*"Visualizing supercurrents in ferromagnetic Josephson junctions with various arrangements of 0 and π segments"*

*Phys. Rev. B*

**81**, 094502 (2010)M. Kemmler, M. Weides, M. Weiler, M. Opel, S. T. B. Gönnenwein, A. S. Vasenko, A. A. Golubov, H. Kohlstedt, D. Kölle, R. Kleiner, and E. Goldobin

*"Magnetic interference patterns in 0-π SIFS Josephson junctions: Effects of asymmetry between 0 and π regions"*

*Phys. Rev. B*

**81**, 054522 (2010)E. Goldobin, K. Vogel, W.P. Schleich, D. Kölle, and R. Kleiner

*"Coherent superpositions of single semifluxon states in a 0−π Josephson Junction"*

*Phys. Rev. B*;

**81**, 054514 (2010)*arXiv:0812.2394v1 [cond-mat.supr-con]*

*;*doi: 10.1103/PhysRevB.81.054514

K. Vogel, W.P. Schleich, T. Kato, D. Kölle, R. Kleiner, and E. Goldobin

*"Theory of fractional vortex escape in a long Josephson junction"*

*Phys. Rev. B*;

**80**, 134515 (2009)*arXiv:0812.3587v1 [cond-mat.supr-con]*

U. Kienzle, T. Gaber, K. Buckenmaier, K. Ilin, M. Siegel, D. Kölle, R. Kleiner, and E. Goldobin

*"Thermal Escape of Fractional Vortices in Long Josephson Junctions"*

*Phys. Rev. B*

**80**, 014504 (2009)N. G. Pugach, A. V. Vedyayev, M. Yu. Kupriyanov, C. Lacroix, E. Goldobin, D. Kölle, R. Kleiner, and A. S. Sidorenko

*"Ferromagnetic Josephson Junctions with Step-Like Interface Transparency"*

*Phys. Rev. B*

**80**, 134516 (2009)A. Dewes, T. Gaber, D. Kölle, R. Kleiner, and E. Goldobin

*"Semifluxon molecule under control"*

*Phys. Rev. Lett.*

**101**, 247001 (2008)J. Pfeiffer, M. Kemmler, D. Kölle, R. Kleiner, E. Goldobin, M. Weides, A. K. Feofanov, J. Lisenfeld, and A. V. Ustinov

*"Static and dynamic properties of 0, π, and 0-π ferromagnetic tunnel Josephson Junctions"*

*Phys. Rev. B*

**77**, 214506 (2008)*;*doi: 10.1103/PhysRevB.77.214506

R. Walser, E. Goldobin, O. Crasser, D. Kölle, R. Kleiner, and W. P. Schleich

*"Semifluxons in Superconductivity and Cold Atomic Gases"*

New. J. Phys.

*, 045020 (2008)*

**10***;*doi: 10.1088/1367-2630/10/4/045020

E. Goldobin, D. Kölle, R. Kleiner, and A. Buzdin

*"Josephson junctions with second harmonic in the current-phase relation: properties of φ junctions"*

*Phys. Rev. B*

**76**, 224523 (2007)M. Weides, H. Kohlstedt, R. Waser, M. Kemmler, J. Pfeiffer, D. Kölle, R. Kleiner, and E. Goldobin

*"Ferromagnetic 0-π Josephson junctions"*

*Appl. Phys. A*

**89**, 613-617 (2007)*;*doi: 10.1007/s00339-007-4206-3

T. Gaber, K. Buckenmaier, D. Kölle, R. Kleiner, and E. Goldobin

*"Fractional Josephson vortices: oscillating macroscopic spins"*

*Appl. Phys. A*

**89**, 587-592 (2007)K. Buckenmaier, T. Gaber, M. Siegel, D. Kölle, R. Kleiner, and E. Goldobin

*"Spectroscopy of the Fractional Vortex Eigenfrequency in a Long Josephson 0−κ Junction"*

*Phys. Rev. Lett.*

**98**, 117006 (2007)M. Weides, M. Kemmler, E. Goldobin, H. Kohlstedt, R. Waser, D. Kölle, and R. Kleiner

*"0-π Josephson tunnel junctions with ferromagnetic barrier"*

*Phys. Rev. Lett.*

**97**, 247001 (2006)M. Weides, M. Kemmler, E. Goldobin, D. Kölle, R. Kleiner, H. Kohlstedt, and A. Buzdin

*"High Quality Ferromagnetic 0 and π Josephson Tunnel Junctions"*

*Appl. Phys. Lett.*

**89**, 122511 (2006)E. Goldobin, K. Vogel, O. Crasser, R. Walser, W. P. Schleich, D. Kölle, and R. Kleiner

*"Quantum Tunneling of Semifluxons in a 0-π-0 long Josephson junction"*

*Phys. Rev. B*

**72**, 054527 (2005)