Abstract
In Chapter 9 I described a protocol to efficiently generate small clusters of fractional quantum Hall states at sites of a deep optical lattice, in the limit where particles were unable to tunnel between sites on experimentally relevant timescales. One motivation for this chapter is to construct a theory of deep lattices that are nevertheless weak enough to allow particle tunneling between sites (analogous to the Bose-Hubbard limit of bosons in an optical lattice introduced in Chapter 2.). I construct a theory—specifically an effective lattice model—that captures the dominant behavior for bosons, and essentially identical techniques lead to a description of fermions. In the bosonic case, I construct an analog of the Gutzwiller mean field theory (introduced in Chapter 2) for this generalized model. I show that the resulting model has a phase diagram topologically the same as the Bose-Hubbard model: there are globally insulating phases with fractional quantum Hall puddles at each site and no coherence between them occupying “Mott lobes” in the chemical potential-lattice depth phase diagram, and a superfluid phase with coherence between the fractional quantum Halls states at each site.
This chapter was adapted from “On-site correlations in optical lattices: Band mixing to coupled quantum Hall puddles" by Kaden R.A. Hazzard and Erich J. Mueller, published in Physical Review A 81, 031602(R) (2010).
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References
S.M. Girvin, A.H. MacDonald, Phys. Rev. Lett. 58, 1252 (1987)
N. Read, Phys. Rev. Lett. 62, 8689 (1989)
E. Shimshoni, A. Auerbach, A. Kapitulnik, Phys. Rev. Lett. 80, 3352 (1998)
S. Will, T. Best, U. Schneider, L. Hackermüler, D. Lühmann, I. Bloch, Nature 465, 197 (2010)
I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)
D. Jaksch, C. Bruder, J.I. Cirac, C.W. Gardiner, P. Zoller, Phys. Rev. Lett. 81, 3108 (1998)
G. Mazzarella, S.M. Giampaolo, F. Illuminati, Phys. Rev. A 73, 013625 (2006)
A. Smerzi, A. Trombettoni, Phys. Rev. A 68, 023613 (2003)
L. Li, J. Checkelsky, Y. Hor, C. Uher, A. Hebard, R. Cava, N. Ong, Science 321, 547 (2008)
J. Larson, A. Collin, J. Martikainen, Phys. Rev. A 79, 033603 (2009)
O.E. Alon, A.I. Streltsov, L.S. Cederbaum, Phys. Rev. Lett. 95, 030405 (2005)
P.R. Johnson, E. Tiesinga, J.V. Porto, C.J. Williams, New J. Phys. 11, 093022 (2009)
C. Chin, private communication.
M. Popp, B. Paredes, J.I. Cirac, Phys. Rev. A 70, 053612 (2004)
S.K. Baur, K.R.A. Hazzard, E.J. Mueller, Phys. Rev. A 78, 061608 (2008)
P. Barmettler, A.M. Rey, E. Demler, M.D. Lukin, I. Bloch, V. Gritsev, Phys. Rev. A 78, 012330 (2008)
L. Jiang, A.M. Rey, O. Romero-Isart, J.J. Garcá-Ripoll, A. Sanpera, M.D. Lukin, Phys. Rev. A 79, 022309 (2009)
G.K. Campbell, J. Mun, M. Boyd, P. Medley, A.E. Leanhardt, L.G. Marcassa, D.E. Pritchard, W. Ketterle, Science 313, 649 (2006)
A.J. Daley, J.M. Taylor, S. Diehl, M. Baranov, P. Zoller, Phys. Rev. Lett. 102, 040402 (2009)
D.B.M. Dickerscheid, U.A. Khawaja, van D. Oosten, H.T.C. Stoof, Phys. Rev. A 71, 043604 (2005)
T. Busch, B. Englert, K. Rzazewski, M. Wilkens, Found. Phys. 28, 549 (1998)
M.P.A. Fisher, P.B. Weichman, G. Grinstein, D.S. Fisher, Phys. Rev. B 40, 546570 (1989)
B. Capogrosso-Sansone, N.V. Prokof’ev, B.V. Svistunov, Phys. Rev. B 75, 134302 (2007)
R.B. Diener, T. Ho, Phys. Rev. Lett. 96, 010402 (2006)
H. Zhai, T. Ho, Phys. Rev. Lett. 99, 100402 (2007)
M. Köhl, H. Moritz, T. Stöferle, K. Günter, T. Esslinger, Phys. Rev. Lett. 94, 080403 (2005)
L. Duan, Phys. Rev. Lett. 95, 243202 (2005)
C. Mathy, D.A. Huse, Phys. Rev. A 79, 063412 (2009)
This material is based upon work supported by the National Science Foundation through grant No. PHY-0758104. We thank Stefan Baur, John Shumway, and Mukund Vengalattore for useful conversations.
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Hazzard, K.R.A. (2011). Incorporating Arbitrarily Strong On-Site Correlations into Lattice Models. In: Quantum Phase Transitions in Cold Atoms and Low Temperature Solids. Springer Theses. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8179-0_10
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