in combination with periodic reservoir reloading
from a cold atom source (such as a MOT), could be
used to maintain arrays indefinitely.
Atom-by-atom assembly of defect-free arrays
forms a scalable platform with unique possibilities. It combines features that are typically associated with ion-trapping experiments, such as
single-qubit addressability (32, 33) and fast cycling times, with the flexible optical trapping of
neutral atoms in a scalable fashion. Furthermore,
in contrast to solid-state platforms, such atomic
arrays are highly homogeneous (31) and mostly
decoupled from their environment. The homogeneity of our array should also allow for cooling
of the atomic motion via simultaneous sideband
cooling in all tweezers at once (34, 35).
These features provide an excellent starting
point for multiqubit experiments, for studies of
quantum many-body effects, and for exploring
future applications. The required interactions between the atoms can be engineered using several approaches. Even without sideband cooling,
exciting the atoms into high-lying Rydberg states
would introduce strong dipole interactions that
can be used for fast entangling gates (24, 25, 27).
The parallelism afforded by our flexible atom
rearrangement enables efficient diagnostics of
such Rydberg-mediated entanglement. These interactions may also enable approaches to quantum
simulations that involve both coherent coupling
and engineered dissipation (26, 27), as well as
large-scale entangled quantum states for applications in precision measurements (36).
An alternative approach to engineering interactions involves the integration of atom arrays
with nanophotonic platforms as demonstrated previously (28, 29). These enable photon-mediated interactions that can be employed to
couple the atoms within a local multiqubit register or for efficient communication between the
registers using a modular quantum network architecture (3).
Finally, our platform could enable new bottom-up approaches to studying quantum many-body
physics in Hubbard models (15, 16, 30), where
atomic Mott insulators with fixed atom number
and complex spin patterns could be directly assembled. This requires atom temperatures close
to the ground state, coherent tunneling between
the traps, and sizable on-site interactions. With
side-band cooling, ground-state fractions in excess
of 90% have already been demonstrated (34, 35)
and can likely be improved via additional optical
trapping along the longitudinal tweezer axes,
which would also increase on-site interaction
strengths. Coherent tunneling of Rb atoms between
similarly sized tweezers has been observed before by reducing the tweezer distance (15, 16). The
parametric heating, currently limiting the minimal distance between our traps, could be reduced
by working with shallower traps, as needed for
tunneling, and by employing fewer traps to increase the frequency separation between neighboring traps. Eventually, this approach could be
applied to create ultracold quantum matter composed of exotic atomic species or complex molecules
(37, 38) that are difficult to cool evaporatively.
REFERENCES AND NOTES
1. S. Haroche, Ann. Phys. 525, 753–776 (2013).
2. D. J. Wineland, Rev. Mod. Phys. 85, 1103–1114 (2013).
3. C. Monroe, J. Kim, Science 339, 1164–1169 (2013).
4. M. H. Devoret, R. J. Schoelkopf, Science 339, 1169–1174 (2013).
5. W. S. Bakr et al., Science 329, 547–550 (2010).
6. J. F. Sherson et al., Nature 467, 68–72 (2010).
7. C. Weitenberg et al., Nature 471, 319–324 (2011).
8. D. S. Weiss et al., Phys. Rev. A 70, 040302 (2004).
9. J. Vala et al., Phys. Rev. A 71, 032324 (2005).
10. N. Schlosser, G. Reymond, I. Protsenko, P. Grangier, Nature
411, 1024–1027 (2001).
11. M. Weber, J. Volz, K. Saucke, C. Kurtsiefer, H. Weinfurter,
Phys. Rev. A 73, 043406 (2006).
12. K. D. Nelson, X. Li, D. S. Weiss, Nat. Phys. 3, 556–560
13. M. J. Piotrowicz et al., Phys. Rev. A 88, 013420 (2013).
14. F. Nogrette et al., Phys. Rev. X 4, 021034 (2014).
15. A. M. Kaufman et al., Science 345, 306–309 (2014).
16. A. M. Kaufman et al., Nature 527, 208–211 (2015).
17. Y. Miroshnychenko et al., Nature 442, 151 (2006).
18. J. Beugnon et al., Nat. Phys. 3, 696–699 (2007).
19. M. Schlosser et al., New J. Phys. 14, 123034 (2012).
20. H. Kim, et al., Nat. Commun. 7, 13317 (2016).
21. T. Grünzweig, A. Hilliard, M. McGovern, M. F. Andersen,
Nat. Phys. 6, 951–954 (2010).
22. B. J. Lester, N. Luick, A. M. Kaufman, C. M. Reynolds,
C. A. Regal, Phys. Rev. Lett. 115, 073003 (2015).
23. Y. H. Fung, M. F. Andersen, New J. Phys. 17, 073011 (2015).
24. D. Jaksch et al., Phys. Rev. Lett. 85, 2208–2211 (2000).
25. M. Saffman, T. G. Walker, K. Mølmer, Rev. Mod. Phys. 82,
26. H. Weimer, M. Müller, I. Lesanovsky, P. Zoller, H. P. Büchler,
Nat. Phys. 6, 382–388 (2010).
27. A. Browaeys, D. Barredo, T. Lahaye, J. Phys. B 49, 152001
28. J. D. Thompson et al., Science 340, 1202–1205 (2013).
29. A. Goban et al., Nat. Commun. 5, 3808 (2014).
30. S. Murmann et al., Phys. Rev. Lett. 115, 215301 (2015).
31. See supplementary materials on Science Online.
32. T. Xia et al., Phys. Rev. Lett. 114, 100503 (2015).
33. Y. Wang, X. Zhang, T. A. Corcovilos, A. Kumar, D. S. Weiss,
Phys. Rev. Lett. 115, 043003 (2015).
34. A. M. Kaufman, B. J. Lester, C. A. Regal, Phys. Rev. X 2, 041014
35. J. D. Thompson, T. G. Tiecke, A. S. Zibrov, V. Vuletić,
M. D. Lukin, Phys. Rev. Lett. 110, 133001 (2013).
36. P. Kómár et al., Phys. Rev. Lett. 117, 060506 (2016).
37. J. F. Barry, D. J. McCarron, E. B. Norrgard, M. H. Steinecker,
D. DeMille, Nature 512, 286–289 (2014).
38. N. R. Hutzler, L. R. Liu, Y. Yu, K.-K. Ni,
39. D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye,
A. Browaeys, Science 354, 1021–1023 (2016).
We thank K.-K. Ni, N. Hutzler, A. Mazurenko, and A. Kaufman for
insightful discussion. This work was supported by NSF, Center for
Ultracold Atoms, National Security Science and Engineering
Faculty Fellowship, and Harvard Quantum Optics Center. H.B.
acknowledges support by a Rubicon Grant of the Netherlands
Organization for Scientific Research (NWO). During the completion
of this work, we became aware of a related approach (39).
Materials and Methods
Figs. S1 to S5
Movies S1 to S3
References (40, 41)
17 June 2016; accepted 17 October 2016
Published online 3 November 2016
Quentin Bletery,1 Amanda M. Thomas,1 Alan W. Rempel,1 Leif Karlstrom,1
Anthony Sladen,2 Louis De Barros2
The 2004 Sumatra-Andaman and 2011 Tohoku-Oki earthquakes highlighted gaps in our
understanding of mega-earthquake rupture processes and the factors controlling their global
distribution: A fast convergence rate and young buoyant lithosphere are not required to
produce mega-earthquakes. We calculated the curvature along the major subduction zones
of the world, showing that mega-earthquakes preferentially rupture flat (low-curvature)
interfaces. A simplified analytic model demonstrates that heterogeneity in shear strength
increases with curvature. Shear strength on flat megathrusts is more homogeneous, and hence
more likely to be exceeded simultaneously over large areas, than on highly curved faults.
Past mega-earthquakes, such as the mag- nitude (M) 9.6 Chile earthquake in 1960 and the M 9.3 Alaska earthquake in 1964, occurred in areas where the subducting lithosphere was relatively young (and
buoyant) and the plate convergence rate was
relatively high (1). These observations led some
authors to hypothesize that maximum earthquake
size is controlled by these two geological param-
eters (2, 3). The development of space-based
geodesy enabled refined measurements of plate
motion that challenged the role of convergence
rate (4–6). Additionally, the moment magnitude
(Mw) 9.0 Tohoku-Oki earthquake (7) ruptured
lithosphere that is over 120 million years old (8),
ruling out lithospheric age as the dominant con-
trol. Weak correlations appear in recent data sets
among a variety of parameters, including forearc
structure (9, 10); age, density, and buoyancy of the
slab (6); upper plate motion (11); upper plate strain
(12); long-term trench migration (11); trench sedi-
ment thickness (12); and width of the seismogenic
1Department of Earth Sciences, University of Oregon, 1272
University of Oregon, Eugene, OR 97403, USA. 2Université
Côte d’Azur, CNRS, OCA, IRD, Géoazur, 250 rue Albert
Einstein, Sophia Antipolis, 06560 Valbonne, France.
*Corresponding author. Email: email@example.com