Abstract
Light-induced spin-orbit coupling is a flexible tool to study quantum magnetism with ultracold atoms. In this work we show that spin-orbit coupled Bose gases in a one-dimensional optical lattice can be mapped into a two-leg triangular ladder with staggered flux following a lowest-band truncation of the Hamiltonian. The effective flux and the ratio of the tunneling strengths can be independently adjusted to a wide range of values. We identify a certain regime of parameters where a hard-core boson approximation holds and the system realizes a frustrated triangular spin ladder with tunable flux. We study the properties of the effective spin Hamiltonian using the density-matrix renormalization-group method and determine the phase diagram at half-filling. It displays two phases: a uniform superfluid and a bond-ordered insulator. The latter can be stabilized only for low Raman detuning. Finally, we provide experimentally feasible trajectories across the parameter space of the SOC system that cross the predicted phase transition.
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Y.-J. Lin, R.L. Compton, K. Jiménez-García, J.V. Porto, I.B. Spielman, Nature 462, 628 (2009)
Y.-J. Lin, K. Jiménez-García, I.B. Spielman, Nature 471, 83 (2011)
J. Higbie, D.M. Stamper-Kurn, Phys. Rev. Lett. 88, 090401 (2002)
J. Dalibard, F. Gerbier, G. Juzeliūnas, P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011)
N. Goldman, G. Juzeliūnas, P. Öhberg, I.B. Spielman, Rep. Prog. Phys. 77, 126401 (2014)
M.J. Edmonds, M. Valiente, G. Juzeliūnas, L. Santos, P. Öhberg, Phys. Rev. Lett. 110, 085301 (2013)
J.-Y. Zhang, S.-C. Ji, Z. Chen, L. Zhang, Z.-D. Du, B. Yan, G.-S. Pan, B. Zhao, Y.-J. Deng, H. Zhai, S. Chen, J.-W. Pan, Phys. Rev. Lett. 109, 115301 (2012)
S.-C. Ji, L. Zhang, X.-T. Xu, Z. Wu, Y. Deng, S. Chen, J.-W. Pan, Phys. Rev. Lett. 114, 105301 (2015)
Z. Wu, L. Zhang, W. Sun, X.-T. Xu, B.-Z. Wang, S.-C. Ji, Y. Deng, S. Chen, X.-J. Liu, J.-W. Pan, Science 354, 83 (2016)
W. Sun, B.-Z. Wang, X.-T. Xu, C.-R. Yi, L. Zhang, Z. Wu, Y. Deng, X.-J. Liu, S. Chen, J.-W. Pan, Phys. Rev. Lett. 121, 150401 (2018)
Y. Li, L.P. Pitaevskii, S. Stringari, Phys. Rev. Lett. 108, 225301 (2012)
J.-R. Li, J. Lee, W. Huang, S. Burchesky, B. Shteynas, F.Ç. Top, A.O. Jamison, W. Ketterle, Nature 543, 91 (2017)
Y. Li, G.I. Martone, S. Stringari, in Annual Review of Cold Atoms and Molecules (World Scientific, 2015) pp. 201–250
L. Tanzi, E. Lucioni, F. Famà, J. Catani, A. Fioretti, C. Gabbanini, R.N. Bisset, L. Santos, G. Modugno, Phys. Rev. Lett. 122, 130405 (2019)
L. Chomaz, D. Petter, P. Ilzhöfer, G. Natale, A. Trautmann, C. Politi, G. Durastante, R.M.W. van Bijnen, A. Patscheider, M. Sohmen, M.J. Mark, F. Ferlaino, Phys. Rev. X 9, 021012 (2019)
F. Böttcher, J.-N. Schmidt, M. Wenzel, J. Hertkorn, M. Guo, T. Langen, T. Pfau, Phys. Rev. X 9, 011051 (2019)
J. Léonard, A. Morales, P. Zupancic, T. Esslinger, T. Donner, Nature 543, 87 (2017)
J. Cabedo, J. Claramunt, A. Celi, Y. Zhang, V. Ahufinger, J. Mompart, Phys. Rev. A 100, 063633 (2019)
C.R. Cabrera, L. Tanzi, J. Sanz, B. Naylor, P. Thomas, P. Cheiney, L. Tarruell, Science 359, 301 (2018)
P. Cheiney, C.R. Cabrera, J. Sanz, B. Naylor, L. Tanzi, L. Tarruell, Phys. Rev. Lett. 120, 135301 (2018)
G. Semeghini, G. Ferioli, L. Masi, C. Mazzinghi, L. Wolswijk, F. Minardi, M. Modugno, G. Modugno, M. Inguscio, M. Fattori, Phys. Rev. Lett. 120, 235301 (2018)
R.A. Williams, L.J. LeBlanc, K. Jimenez-Garcia, M.C. Beeler, A.R. Perry, W.D. Phillips, I.B. Spielman, Science 335, 314 (2012)
R.P. Anderson, D. Trypogeorgos, A. Valdés-Curiel, Q.-Y. Liang, J. Tao, M. Zhao, T. Andrijauskas, G. Juzeliūnas, I.B. Spielman, Phys. Rev. Res. 2, 013149 (2020)
M. Lewenstein, A. Sanpera, V. Ahufinger, Ultracold Atoms in Optical Lattices: Simulating Quantum Many-body Systems (Oxford University Press, 2012)
O. Boada, A. Celi, J.I. Latorre, M. Lewenstein, Phys. Rev. Lett. 108, 133001 (2012)
T. Ozawa, H.M. Price, Nat. Rev. Phys. 1, 349 (2019)
A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. Spielman, G. Juzeliūnas, M. Lewenstein, Phys. Rev. Lett. 112, 043001 (2014)
B.K. Stuhl, H.-I. Lu, L.M. Aycock, D. Genkina, I.B. Spielman, Science 349, 1514 (2015)
M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, L. Fallani, Science 349, 1510 (2015)
L.F. Livi, G. Cappellini, M. Diem, L. Franchi, C. Clivati, M. Frittelli, F. Levi, D. Calonico, J. Catani, M. Inguscio, L. Fallani, Phys. Rev. Lett. 117, 220401 (2016)
S. Kolkowitz, S.L. Bromley, T. Bothwell, M.L. Wall, G.E. Marti, A. Koller, X. Zhang, A.M. Rey, J. Ye, Nature 542, 66 (2017)
F.A. An, E.J. Meier, B. Gadway, Sci. Adv. 3, e1602685 (2017)
E. Lustig, S. Weimann, Y. Plotnik, Y. Lumer, M.A. Bandres, A. Szameit, M. Segev, Nature 567, 356 (2019)
D.R. Hofstadter, Phys. Rev. B 14, 2239 (1976)
S. Mugel, A. Dauphin, P. Massignan, L. Tarruell, M. Lewenstein, C. Lobo, A. Celi, SciPost Phys. 3, 012 (2017)
D. Genkina, L.M. Aycock, H.-I. Lu, M. Lu, A.M. Pineiro, I. Spielman, New J. Phys. 21, 053021 (2019)
E. Cornfeld, E. Sela, Phys. Rev. B 92, 115446 (2015)
M. Calvanese Strinati, S. Sahoo, K. Shtengel, E. Sela, Phys. Rev. B 99, 245101 (2019)
E. Orignac, T. Giamarchi, Phys. Rev. B 64, 144515 (2001)
E. Granato, Phys. Rev. B 72, 104521 (2005)
A. Tokuno, A. Georges, New J. Phys. 16, 073005 (2014)
M. Atala, M. Aidelsburger, M. Lohse, J.T. Barreiro, B. Paredes, I. Bloch, Nat. Phys. 10, 588 (2014)
A. Petrescu, K. Le Hur, Phys. Rev. Lett. 111, 150601 (2013)
M. Di Dio, S. De Palo, E. Orignac, R. Citro, M.-L. Chiofalo, Phys. Rev. B 92, 060506 (2015)
M. Piraud, F. Heidrich-Meisner, I.P. McCulloch, S. Greschner, T. Vekua, U. Schollwöck, Phys. Rev. B 91, 140406 (2015)
A. Petrescu, K. Le Hur, Phys. Rev. B 91, 054520 (2015)
S. Greschner, M. Piraud, F. Heidrich-Meisner, I.P. McCulloch, U. Schollwöck, T. Vekua, Phys. Rev. A 94, 063628 (2016)
M. Calvanese Strinati, E. Cornfeld, D. Rossini, S. Barbarino, M. Dalmonte, R. Fazio, E. Sela, L. Mazza, Phys. Rev. X 7, 021033 (2017)
A. Petrescu, M. Piraud, G. Roux, I.P. McCulloch, K. Le Hur, Phys. Rev. B 96, 014524 (2017)
R. Citro, S. De Palo, M. Di Dio, E. Orignac, Phys. Rev. B 97, 174523 (2018)
S. Greschner, F. Heidrich-Meisner, Phys. Rev. A 97, 033619 (2018)
S. Greschner, M. Filippone, T. Giamarchi, Phys. Rev. Lett. 122, 083402 (2019)
S. Barbarino, L. Taddia, D. Rossini, L. Mazza, R. Fazio, Nat. Commun. 6, 1 (2015)
S. Barbarino, L. Taddia, D. Rossini, L. Mazza, R. Fazio, New J. Phys. 18, 035010 (2016)
J. Jünemann, A. Piga, S.-J. Ran, M. Lewenstein, M. Rizzi, A. Bermudez, Phys. Rev. X 7, 031057 (2017)
S.K. Ghosh, S. Greschner, U.K. Yadav, T. Mishra, M. Rizzi, V.B. Shenoy, Phys. Rev. A 95, 063612 (2017)
A. Haller, M. Rizzi, M. Burrello, New J. Phys. 20, 053007 (2018)
E. Anisimovas, M. Račiūnas, C. Sträter, A. Eckardt, I.B. Spielman, G. Juzeliūnas, Phys. Rev. A 94, 063632 (2016)
D. Suszalski, J. Zakrzewski, Phys. Rev. A 94, 033602 (2016)
F.A. An, E.J. Meier, B. Gadway, Phys. Rev. X 8, 031045 (2018)
C. Becker, P. Soltan-Panahi, J. Kronjäger, S. Dörscher, K. Bongs, K. Sengstock, New J. Phys. 12, 065025 (2010)
R.G. Melko, A. Paramekanti, A.A. Burkov, A. Vishwanath, D.N. Sheng, L. Balents, Phys. Rev. Lett. 95, 127207 (2005)
S. Wessel, M. Troyer, Phys. Rev. Lett. 95, 127205 (2005)
C. Lacroix, P. Mendels, F. Mila, in Introduction to Frustrated Magnetism: Materials, Experiments, Theory (Springer Science & Business Media, 2011), Vol. 164
J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, L. Mathey, Nat. Phys. 9, 738 (2013)
A. Eckardt, P. Hauke, P. Soltan-Panahi, C. Becker, K. Sengstock, M. Lewenstein, EPL 89, 10010 (2010)
P. Hauke, T. Roscilde, V. Murg, J. Ignacio Cirac, R. Schmied, New J. Phys. 12, 053036 (2010)
A. Celi, T. Grass, A.J. Ferris, B. Padhi, D. Raventós, J. Simonet, K. Sengstock, M. Lewenstein, Phys. Rev. B 94, 075110 (2016)
T. Mishra, R.V. Pai, S. Mukerjee, A. Paramekanti, Phys. Rev. B 87, 174504 (2013)
T. Mishra, R.V. Pai, S. Mukerjee, Phys. Rev. A 89, 013615 (2014)
S. Greschner, T. Mishra, Phys. Rev. B 100, 144405 (2019)
T. Tonegawa, I. Harada, J.-I. Igarashi, Prog. Theor. Phys. Suppl. 101, 513 (1990)
T. Tonegawa, I. Harada, M. Kaburagi, J. Phys. Soc. Jpn. 61, 4665 (1992)
C. Majumdar, D. Ghosh, J. Math. Phys. 10, 1388 (1969)
I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)
L. Barbiero, L. Chomaz, S. Nascimbene, N. Goldman, https://arXiv:1907.10555 [cond-mat.quant-gas] (2019)
J. Sanz, A. Frölian, C.S. Chisholm, C.R. Cabrera, L. Tarruell, https://arXiv:1912.06041 [cond-mat.quant-gas] (2019)
T. Mishra, J. Carrasquilla, M. Rigol, Phys. Rev. B 84, 115135 (2011)
D.L. Campbell, R.M. Price, A. Putra, A. Valdés-Curiel, D. Trypogeorgos, I.B. Spielman, Nat. Commun. 7, 10897 (2016)
D.L. Campbell, I.B. Spielman, New J. Phys. 18, 033035 (2016)
D. Trypogeorgos, A. Valdés-Curiel, N. Lundblad, I.B. Spielman, Phys. Rev. A 97, 013407 (2018)
R.P. Anderson, M.J. Kewming, L.D. Turner, Phys. Rev. A 97, 013408 (2018)
C.K. Majumdar, J. Phys. C: Solid State Phys. 3, 911 (1970)
I. Affleck, F.D.M. Haldane, Phys. Rev. B 36, 5291 (1987)
S. Jiang, O. Motrunich, Phys. Rev. B 99, 075103 (2019)
T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, M.P. Fisher, Science 303, 1490 (2004)
S. Yang, D.-X. Yao, A.W. Sandvik, https://arXiv:2001.02821 [physics.comp-ph] (2020) (2019)
J. Sebby-Strabley, M. Anderlini, P.S. Jessen, J.V. Porto, Phys. Rev. A 73, 033605 (2006)
S. Fölling, S. Trotzky, P. Cheinet, M. Feld, R. Saers, A. Widera, T. Müller, I. Bloch, Nature 448, 1029 (2007)
D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, T. Esslinger, Science 340, 1307 (2013)
K. Loida, J.-S. Bernier, R. Citro, E. Orignac, C. Kollath, Phys. Rev. Lett. 119, 230403 (2017)
T. Graß, C. Muschik, A. Celi, R.W. Chhajlany, M. Lewenstein, Phys. Rev. A 91, 063612 (2015)
T. Graß, A. Celi, G. Pagano, M. Lewenstein, Phys. Rev. A 97, 010302 (2018)
V. Lienhard, P. Scholl, S. Weber, D. Barredo, S. de Léséleuc, R. Bai, N. Lang, M. Fleischhauer, H.P. Büchler, T. Lahaye, A. Browaeys, https://arXiv:2001.10357 [quant-ph] (2020)
C.-L. Hung, A. González-Tudela, J.I. Cirac, H.J. Kimble, Proc. Natl. Acad. Sci. USA 201603777, (2016).
T. Giamarchi, Quantum Physics in One Dimension (Clarendon Press, 2003), Vol. 121
M.A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, M. Rigol, Rev. Mod. Phys. 83, 1405 (2011)
R. Citro, S. De Palo, N. Victorin, A. Minguzzi, E. Orignac, Condens. Matter 5, 15 (2020)
E. Tirrito, M. Rizzi, G. Sierra, M. Lewenstein, A. Bermudez, Phys. Rev. B 99, 125106 (2019)
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Contribution to the Topical Issue “Topological Ultracold Atoms and Photonic Systems”, edited by G. Juzeliūnas, R. Ma, Y.-J. Lin and T. Calarco.
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Cabedo, J., Claramunt, J., Mompart, J. et al. Effective triangular ladders with staggered flux from spin-orbit coupling in 1D optical lattices. Eur. Phys. J. D 74, 123 (2020). https://doi.org/10.1140/epjd/e2020-10129-1
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DOI: https://doi.org/10.1140/epjd/e2020-10129-1