Quantum simulators for unconventional superconductors and deformable solids

1. Quantum simulators for unconventional superconductors and deformable solids Jim Hague and Calum MacCormick Department of Physical Sciences The Open University arXiv:1109.1225 In Press, New J. Phys (Deformable solids) arXiv:1111.5594 (Unconventional superconductors)

2. Coming up... • Importance of electron-phonon interactions in unconventional superconductors and other condensed matter systems • Rydberg atoms, dressing schemes, bilayers. • Proposed cold atoms simulator, mapping to standard Hamiltonians • Efficacy and numerical simulation • Readout

3. Electron-phonon interactions in condensed matter • Essential to understand conventional superconductivity, polyacetylene, Peierles distortion, resistance (and others) • Isotope effects / other electron-phonon effects found in contemporary condensed matter problems: Colossal magnetoresistance, high Tc, other unconventional superconductors.

4. Part I: Unconventional superconductors J.P.Hague, C.MacCormick, arXiv:1111.5594

5. Isotope effects in cuprate high Tc • Significant isotope effects in cuprates • Susceptibility, Meissner fraction, penetration depth and others Anom. G.M.Zhao et al. J. Phys.: Condens. Matter, 13 (2001) R569 J.P.Hague, C.MacCormick, arXiv:1111.5594

6. Other unconventional superconductors • Fulleride A3C60 compounds, Tc ~ 40K [1-3] • Bismuthates (Tc > 30K) [4-7] • Borocarbides and chloronitrides (Tc > 20K) [8-10] • Magnesium diboride, Tc ~ 40K (layered) • Intercalated graphite compounds ~ 10K (layered) (see the nice review ‘The Other High Temperature Superconductors’ by Warren Pickett) J.P.Hague, C.MacCormick, arXiv:1111.5594

7. Rydberg atoms, dressing and bilayers • We consider only Rydberg states with s symmetry. • In the high dipole limit and in the Foerster regime, the interaction has 1/R3 form [1]. For s-symmetry, there is no angular dependence. • To enhance Rydberg lifetime, dressed states are used where laser detuned D from transition - excite virtual Rydberg state. • [1] PHYSICAL REVIEW A 77, 032723 2008. T.G.Walker and M.Saffman. J.P.Hague, C.MacCormick, arXiv:1111.5594

8. Itinerant layer filling changes. Require shallow well so atoms hop. • Phonon layer must be half-filled – require deep well, but shallow base for adabatic phonons. Achieve this with painted potentials. J.P.Hague, C.MacCormick, arXiv:1111.5594

9. J.P.Hague, C.MacCormick, arXiv:1111.5594

10. C-axis phonons • Extend phonon potential perpendicular to planes to obtain: W is Rabi frequency, D is tuning, m dipole moment, b interplane spacing, r distance in plane, n fermion number operator in itinerant plane, d annihilates phonons. J.P.Hague, C.MacCormick, arXiv:1111.5594

11. Tunability • Change lattice spacing: Modify hopping. • Increase interplane distance / change Rydberg quantum numbers: modify interaction. • Modify potentials in phonon layer: change phonon frequency / no. of modes J.P.Hague, C.MacCormick, arXiv:1111.5594

12. Good agreement with effective interaction F(x) is effective interaction, b is interplane dist, a intraplane dist, r=iax J.P.Hague, C.MacCormick, arXiv:1111.5594

13. Quantum Monte Carlo simulations show excellent agreement. Here U=4t, l is fermion-phonon coupling. b is interplane distance, a is interatomic dist, Rs Froehlich screening radius (see JPH+P.Kornilovitch, PRB for Frohlich bipolaron in 2D) J.P.Hague and C.MacCormick, arXiv:1111.5594

14. Readout • Turn off potential in itinerant layer to obtain dispersions and correlation functions • Phonon occupation numbers can be resolved using spectroscopically. • May also be able to ‘shake’ optical lattice to probe phonon and electron states. J.P.Hague, C.MacCormick, arXiv:1111.5594

15. Part II: Polyacetylene and other strongly deformable solids J.P.Hague, C.MacCormick, arXiv:1109.1225 (In Press, New J. Phys.)

16. Rydberg dressing schemes and ‘electron’ transport • Calculate hopping from van Vleck perturbation theory • a = W / D, where W is Rabi frequency and D is detuning • N is no. of atoms in system • V is m2/R3 See S. Wuester, C. Ates, A. Eisfeld, and J. Rost, New J. Phys 13, 073044 (2011). J.P.Hague, C.MacCormick, arXiv:1109.1225 (In Press, New J. Phys.)

17. A proposal for a cold atom/ion ‘electron’-phonon simulator J.P.Hague, C.MacCormick, arXiv:1109.1225 (In Press, New J. Phys.)

18. Mapping on to a Su-Schrieffer-Heeger interaction J.P.Hague, C.MacCormick, arXiv:1109.1225 (In Press, New J. Phys.)

19. Mapping on to a Su-Schrieffer-Heeger interaction For momentum independent phonons (i.e. cold atoms) J.P.Hague, C.MacCormick, arXiv:1109.1225 (In Press, New J. Phys.)

20. Perturbation theory J.P.Hague, C.MacCormick, arXiv:1109.1225 (In Press, New J. Phys.)

21. Experimental considerations J.P.Hague, C.MacCormick, arXiv:1109.1225 (In Press, New J. Phys.)

22. Summary • Summarised the importance of electron-phonon interactions in condensed matter. • Demonstrated that bilayers of Rydberg atoms can be mapped onto fermionic Hubbard-Holstein model (i.e. correlation in the presence of electron-phonon interactions). • Used numerics to examine similarity with similar problems in cuprate (and other) unconventional superconductors. J.P.Hague and C.MacCormick, arXiv:1111.5594, arXiv:1109.1225 J.P.Hague, C.MacCormick, arXiv:1111.5594