1970

1. 400 K Transient RTS in YBCO 200 Photo-excited YBCO 164 K@30GPa 1994 135 K Tc (K) HgBaCaCuO 1988 2014 TlBaCaCuO 1993 100 YBaCuO 1987 LaBaCuO 1986 0 1970 1980 1990 2000 2010 Year

2. Resonant excitation of 20THz apical-O phonon in underdoped YBCO S. Kaiser, A.Cavalleri et al., PRB 89, 184516 (2014). 20 THz ~ 80 meV pulses of ~300 fs duration

3. Optically Induced “SC” for UD-YBCO c-axis polarized pump light tuned to the frequency of the apical-O phonon mode (~ 20 THz) resonantly create the interlayer coherence. S. Kaiser, A.Cavalleri et al., Phys. Rev. B 89, 184516 (2014).

4. Transient “RTS” (Tc’ > 300 K) in YBCO Excitation (pumping) of large amplitude c-axis apical-O phonon Emergence of a Josephson plasma in the c-axis (probe) reflection spectrum in several picoseconds duration at temperatures far above Tc YBa2Cu3O6.45 Tc = 35 K 350 K Tc’ Josephson Plasma Tc S. Kaiser et al., PRB 89, 184516 (2014). C.R. Hunt et al., arXiv: 1607.08655.

5. Consequence of Broken Gauge Symmetry: SC Yoichiro Nambu Emergence： 1.“Stiffness”: Zero resistance & Meissner effect 2.Topological defects: Vortex 3. Collective mode: Anderson-Higgs(Plasmon)

6. Broken Gauge Symmetry：”Collective mode” Phase fluctuation mode of SC order parameter w Plasma mode E2 = (mc2)2 + p2c2 wp (charged particles) Anderson-Higgs mechanismLong-range Coulomb Dq ~ 0 and consequently DN ~ ∞. Nambu-Goldstone (neutral particles) Fluctuation of N charge-density fluctuation plasma mode m = 0 q 0 wp2= ne2/m*e P.W. Anderson: Phys. Rev. 130, 439 (1963). P.W. Higgs: Phys. Rev. Lett. 13, 508 (1964).

7. Broken Gauge Symmetry：”Collective mode” Phase fluctuation mode of SC order parameter w Reflectivity spectrum of a conventional superconductor Plasma mode E2 = (mc2)2 + p2c2 wp 1.0 Anderson-Higgs mechanismLong-range Coulomb A tiny change associated with opening of a SC gap Nambu-Goldstone Reflectivity q 0 wp2= ne2/m*e Phase (Anderson-Higgs) mode at frequency wp wp 0 2.0 4.0 Photon energy ħw (eV) cf. Amplitude fluctuation mode which is not optical-active  next page Indistiguishable from the spectrum in the normal state (T > Tc)

8. Amplitude ”Higgs”mode in superconductors P.B. Littlewood & C.M. Varma, PRL 47, 811 (1981); PRB 26, 4883 (1982). The observation of the amplitude mode has been limited to the specific cases. Amplitude mode is not optical-active and is hard to see. CDW amplitude mode w 2(q)=(2D)2+(1/3)vF2q2 without CDW R. Sooryakumar & M.V. Klein, PRL 45, 660 (1980); PRB 23, 3213 (1981). M.-A. Measson, A. Sacuto et al., PRB 89, 060503(R) (2014).

9. ”Higgs amplitude mode” under strong THz excitation R. Matsunaga, R. Shimano et al., Phys. Rev. Lett. 111, 057002 (2013). R. Matsunaga, H. Aoki, R. Shimano et al., Science 345, 1145 (2014). T. Cea, C. Castellani, L. Benfatto, PRL 115, 157002 (2015); PRB 93, 180507 (R) (2016). objections from: NbN on MgO

10. Josephson Plasma Mode: c-axis high-Tc cuprates Interlayer phase coherence is established at Tcbyforming a Josephson-junction array along the c-axis c wp: Josephson plasma frequency CuO2 ħwp< 2D0 CuO2 CuO2 K. Tamasaku, Y. Nakamura & S. Uchida, Phys. Rev. Lett. 69, 1455 (1992). O.K.S. Tsui, N.P. Ong et al., Phys. Rev. Lett. 73, 724 (1994).

11. Josephson Plasma Mode: c-axis high-Tc cuprates Weakly coupled Josephson-junction array  Very small condensate spectral weight Very low-frequency of the Anderson-Higgs mode along the c-axis wp: Josephson plasma frequency ħwp< 2D0 “Appearance of Josephson plasma mode in the c-axis R-spectrum is a strong evidence of SC, as zero-R and Meissner are.” wp2= ne2/mc*e n/mc*→ 0 K. Tamasaku, Y. Nakamura & S. Uchida, Phys. Rev. Lett. 69, 1455 (1992). O.K.S. Tsui, N.P. Ong et al., Phys. Rev. Lett. 73, 724 (1994).

12. No plausible explanation other than JP Emergence of a sharp plasma edge from incoherent c-axis charge dynamics YBa2Cu3O6.45Tc = 35 K S. Kaiser, A.Cavalleri et al., PRB 89, 184516 (2014). r c(mW cm) ra rc 0 r a(mW cm) Josephson Plasma

13. Presence of inter- and intra-bilayer Josephson plasma modes in bilayer cuprates wp wpo intrabilayer mode wp wpo interbilayer mode Josephson coupling within a bilayer is much stronger, and persists above Tc. Intra-bilayerwpo wpo ~ 50 meV >> wp Inter-bilayerwp D. van der Marel & A. Tsvetkov, Czech. J. Phys. 46, 3165 (1996).

14. Inter-bilayer coherence from intra-bilayer coherence ? Inter-bilayer phase coherence (T > Tc, after pumping) Intra-bilayer coherence without inter-bilayer phase coherence (T >Tc, before pumping) Josephson coupled CuO2 CuO2

15. Coherent (w=0) SW from high-energy region ? W. Hu et al., Nat. Phys. 13, 705 (2014). Specific to bilayer/multilayer cuprates ? ‘schematic’

16. Signatures of Pair Formation above Tc 1)Josephson (intra-bilayer) plasma above Tc 1) A. Dubroka, C. Bernhard, PRL 106, 047006 (2011). 2) Diamagnetic signal above Tc / Vortex Nernst effect Ton Z.A. Xu, N.P. Ong, SU, Nature 406, 486 (2000). 3) Bogoliubov QP interference above Tc 2) Jhinhwang Lee et al., Science 325, 1099 (2009). 3)

17. Signature of Preformed Pairs: SC Fluctuations 400 PG T* 300 TN SC fluctuations TemperatureT (K) 200 Ton 100 Tc FL AF d-SC 0 0 0.1 0.2 0.3 Hole dopingp QCP ?

18. Signature of Preformed Pairs above Tc in equilibrium 400 PG T* 300 Pairs without interlayer phase coherence TN TemperatureT (K) 200 Ton Establishment of interlayer phase coherence 100 Tc FL AF d-SC 0 0 0.1 0.2 0.3 Hole dopingp QCP ?

19. Charge and SC fluctuations are of the same order of magnitude. 400 300 PG T* TemperatureT (K) 200 TSCon TCDWon 100 Tc FL AF d-SC 0 0.3 0 0.1 0.2 Hole dopingp QCP ?

20. Melting of Charge Order (CDW) ? M. Först et al., PRB 90, 184514 (2014). R. Mankowsky et al., Nature 516, 71(2014).

21. ‘Temporal’ Tc’ follows T*(PG) > Ton 400 Tc’ 300 PG T* TN TemperatureT (K) 200 Ton 100 Tc FL AF d-SC 0 0.3 0 0.1 0.2 Hole dopingp QCP ?

22. More than establishment of interlayer coherence 400 Tc’ T* 300 in equilibrium PG ‘preformed pairs’ in the plane TN TemperatureT (K) 200 Tcon Establishment of interlayer phase coherence 100 Tc FL AF d-SC 0 0.3 0 0.1 0.2 Hole dopingp The emergence of a plasma edge at T where no signature of ‘preformed pairs’ is observed in equilibrium QCP ?

23. d-SC and d-CDW (SDW) are born from PG (?) 400 Strange Metal Strange Metal TN 300 cooling cooling PG T* PG Temperature (K) 200 cooling cooling CDW & d-SCfluctuations AF 100 Tc SDW FL d-SC CDW FL 0 d-SC 0 0.3 0.1 0.2 Hole dopingp

24. Resonant excitation of 20THz apical-O phonon in underdoped YBCO S. Kaiser, A.Cavalleri et al., PRB 89, 184516 (2014). 20 THz ~ 80 meV pulses of ~300 fs duration

25. Open question: What is the mechanism of driving pair formation and enhancing the interlayer coherence ? ● Excitation of large amplitude apical-O displacement: Transiently creates a displaced crystal structure with atomic positions more favorable for higher Tc ? ●Reduction of the interbilayer fluctuations by a LASER (parametric) cooling ? Dynamically stabilized SC state within the PG phase Like a Kapitza pendulum (?) N. Peter Armitage, Nature Mater. 13, 665 (2014).

26. Nonlinear lattice excitation causes a simultaneous displacement of relevant atomic positions. R. Mankowsky, A. Cavalleri et al., Nature 516, 71(2014). THz optical pulses can resonantly drive selected vibrational modes and deform the crystal structure which is inaccessible in equillibrium.

27. Non-Equilibrium Lattice Distortions Resonant excitation of apical-O vibrations by c-axis polarized 20THZ light pulse→transient lattice distortions R. Först et al., PRB 90, 184514 (2014). R. Mankowsky et al., Nature 516, 71(2014). Reduced intra-bilayer coupling and enhanced inter-bilayerr coupling(?) CuO2 Y longer(?) Increase of the O-Cu-O buckling CuO2 apical- O Ba shorter(?) Modulation of apical-O distance CuO2 CuO2

28. Evidence for apical-O displacement (?) Emergence of double plasma modes and associated optical mode in the intermediate relaxation process in YBCO C.R.Hunt, A. Cavalleri, unpublished. arXiv: 1607.08655. YBCO6.45 Im[-1/e (w)]

29. Double JP modes emerging under B// K.M. Kojima, S. Uchida, Y. Fudamoto, and S. Tajima, Phys. Rev. Lett. 89, 247001 (2002).

30. Double JP modes in modulated structure Double Josephsson plasma modes in T* cuprate T.Kakeshita et al., PRL 86, 4140 (2001). H. Shibata and T. Yamada, PRL 81, 3519 (1998). D. Dulic et al., PRL 86, 4144 (2001). Cu La (Sr) Cu Sm Cu

31. Double JP modes in modulated structure A possible explanation for the double plasma modes probed at 1.8 ps after excitation apical-O Cu Cu Y Y Ba Ba Cu Cu YBa2Cu3O7-d

32. Supplementary Information

33. Double JP modes in strongly excited LSCO K. Tomari, H. Eisaki, R. Shimano; LEES Workshop 2016 1.5 eV excitation for both Epump // c &  c

34. Why 1.5 eV in LSCO ? d-d excitations involving dz2 orbital 1.5 eV 1.5 eV S. Uchida et al., Phys. Rev. B 43, 7942 (1991). S. Uchida, K. Tamasaku & S. Tajima, Phys. Rev. B 53, 14558 (1996).

35. A possible explanation strong dz2excitation  modulation of Cu dz2 – O2pzhybridization  modulation of apical-O position apical-O Cu Cu La (Sr) La (Sr) Cu Cu Cu Cu La2-xSrxCuO4