SU(3) spin–orbit-coupled Bose–Einstein condensate confined in a harmonic plus quartic trap
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摘要
We consider a SU(3) spin–orbit coupled Bose–Einstein condensate confined in a harmonic plus quartic trap.The ground-state wave functions of such a system are obtained by minimizing the Gross–Pitaevskii energy functional, and the effects of the spin-dependent interaction and spin–orbit coupling are investigated in detail.For the case of ferromagnetic spin interaction, the SU(3) spin–orbit coupling induces a threefold-degenerate plane wave ground state with nontrivial spin texture.For the case of antiferromagnetic spin interaction, the system shows phase separation for weak SU(3) spin–orbit coupling, where three discrete minima with unequal weights in momentum space are selected, while hexagonal honeycomb lattice structure for strong SU(3) SOC, where three discrete minima with equal weights are selected.
We consider a SU(3) spin–orbit coupled Bose–Einstein condensate confined in a harmonic plus quartic trap.The ground-state wave functions of such a system are obtained by minimizing the Gross–Pitaevskii energy functional, and the effects of the spin-dependent interaction and spin–orbit coupling are investigated in detail.For the case of ferromagnetic spin interaction, the SU(3) spin–orbit coupling induces a threefold-degenerate plane wave ground state with nontrivial spin texture.For the case of antiferromagnetic spin interaction, the system shows phase separation for weak SU(3) spin–orbit coupling, where three discrete minima with unequal weights in momentum space are selected, while hexagonal honeycomb lattice structure for strong SU(3) SOC, where three discrete minima with equal weights are selected.
We consider a SU(3) spin–orbit coupled Bose–Einstein condensate confined in a harmonic plus quartic trap.The ground-state wave functions of such a system are obtained by minimizing the Gross–Pitaevskii energy functional, and the effects of the spin-dependent interaction and spin–orbit coupling are investigated in detail.For the case of ferromagnetic spin interaction, the SU(3) spin–orbit coupling induces a threefold-degenerate plane wave ground state with nontrivial spin texture.For the case of antiferromagnetic spin interaction, the system shows phase separation for weak SU(3) spin–orbit coupling, where three discrete minima with unequal weights in momentum space are selected, while hexagonal honeycomb lattice structure for strong SU(3) SOC, where three discrete minima with equal weights are selected.
引文
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[9]Wang P, Yu Z Q, Fu Z, Miao J, Huang L, Chai S, Zhai H and Zhang J2012 Phys.Rev.Lett.109 095301
[10]Anderson B M, Juzeliūnas G, Galitski V M and Spielman I B 2012Phys.Rev.Lett.108 235301
[11]Huang L, Meng Z, Wang P, Peng P, Zhang S L, Chen L, Li D, Zhou Q and Zhang J 2016 Nat.Phys.12 540
[12]Meng Z M, Huang L H, Peng P, Li D H, Chen L C, Xu Y, Zhang C,Wang P and Zhang J 2016 Phys.Rev.Lett.117 235304
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[17]Yu Z Q and He L 2017 Acta Phys.Sin.66 220301(in Chinese)
[18]Zhang H, Chen F, Yu C, Sun L and Xu D 2017 Chin.Phys.B 26 080304
[19]Wen L, Sun Q, Chen Y, Wang D S, Hu J, Chen H, Liu W M, Juzeliūnas G, Malomed B A and Ji A C 2016 Phys.Rev.A 94 061602
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[22]Goldman N, Juzeliūnas G,?hberg P and Spielman I B 2014 Rep.Prog.Phys.77 126401
[23]Zhai H 2015 Rep.Prog.Phys.78 026001
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[25]Zhang X F, Dong D F, Liu T, Liu W M and Zhang S G 2012 Phys.Rev.A 86 063628
[26]Zhang X F, Kato M, Han W, Zhang S G and Saito H 2017 Phys.Rev.A95 033620
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[30]Huang C C, Liu C H and Wu W C 2010 Phys.Rev.A 81 043605
[31]Hsueh C H, Horng T L, Gou S C and Wu W C 2011 Phys.Rev.A 84023610
[32]Chen G P, Zhang Z Y, Dong B, Wang L X, Zhang X F and Zhang S G2015 Phys.Lett.A 379 2193
[33]Chen G P, Chen S L, Xie Z W, Zhang X F and Zhang S G 2016 Commun.Theor.Phys.66 53
[34]Wu C, Mondragon-Shem I and Zhou X F 2011 Chin.Phys.Lett.28097102
[35]Sinha S, Nath R and Santos L 2011 Phys.Rev.Lett.107 270401
[36]Kawakami T, Mizushima T, Nitta M and Machida K 2012 Phys.Rev.Lett.109 015301
[37]Achilleos V, Frantzeskakis D J, Kevrekidis P G and Pelinovsky D E2013 Phys.Rev.Lett.110 264101
[38]Lobanov V E, Kartashov Y V and Konotop V V 2014 Phys.Rev.Lett.112 180403
[39]Zhang Y, Zhou Z, Malomed B A and Pu H 2015 Phys.Rev.Lett.115253902
[40]Sakaguchi H and Malomed B A 2014 Phys.Rev.E 90 062922
[41]Sakaguchi H and Malomed B A 2016 New J.Phys.18 025020
[42]Kartashov Y V and Konotop V V 2017 Phys.Rev.Lett.118 190401
[43]Gra? T, Chhajlany R W, Muschik C A and Lewenstein M 2014 Phys.Rev.B 90 195127
[44]Barnett R, Boyd G R and Galitski V 2012 Phys.Rev.Lett.109 235308
[45]Bornheimer U, Miniatura C and Grémaud B 2018 Phys.Rev.A 98043614
[46]Han W, Zhang X F, Song S W, Saito H, Zhang W, Liu W M and Zhang S G 2016 Phys.Rev.A 94 033629
[47]Kawaguchi Y and Ueda M 2012 Phys.Rep.520 253
[48]Stamper-Kurn D M and Ueda M 2013 Rev.Mod.Phys.85 1191
[49]Arfken G B, Weber H J and Harris F E 2000 Mathematical Methods for Physicists(Elsevier:Academic Press)
[50]Press W H, Teukolsky S A, Vetterling W T and Flannery B P 1992Numerical Recipes in Fortran 77(Cambridge:Cambridge University Press)
[51]Bao W Z, Jaksch D and Markowich P 2003 J.Comput.Phys.187 318
[52]Zhang Y, Mao L and Zhang C 2012 Phys.Rev.Lett.108 035302
[53]Wen L, Sun Q, Wang H Q, Ji A C and Liu W M 2012 Phys.Rev.A 86043602
[2]Ueda M 2010 Fundamentals and New Frontiers of Bose-Einstein Condensation(Singapore:World Scientific Press)
[3]Lin Y J, Compton R L, Jiménez-García K, Porto J V, and Spielman I B2009 Nature 462 628
[4]Fu Z, Huang L, Meng Z, Wang P, Zhang L, Zhang S, Zhai H, Zhang P and Zhang J 2014 Nat.Phys.10 110
[5]Lin Y J, Jiménez-García K and Spielman I B 2011 Nature 471 83
[6]Lin Y J, Compton R L, Jiménez-García K, Phillips W D, Porto J V and Spielman I B 2011 Nat.Phys.7 531
[7]Wang C, Gao C, Jian C M and Zhai H 2010 Phys.Rev.Lett.105 160403
[8]Ho T L and Zhang S 2011 Phys.Rev.Lett.107 150403
[9]Wang P, Yu Z Q, Fu Z, Miao J, Huang L, Chai S, Zhai H and Zhang J2012 Phys.Rev.Lett.109 095301
[10]Anderson B M, Juzeliūnas G, Galitski V M and Spielman I B 2012Phys.Rev.Lett.108 235301
[11]Huang L, Meng Z, Wang P, Peng P, Zhang S L, Chen L, Li D, Zhou Q and Zhang J 2016 Nat.Phys.12 540
[12]Meng Z M, Huang L H, Peng P, Li D H, Chen L C, Xu Y, Zhang C,Wang P and Zhang J 2016 Phys.Rev.Lett.117 235304
[13]Ji S C, Zhang J Y, Zhang L, Du Z D, Zheng W, Deng Y J, Zhai H, Chen S and Pan J W 2014 Nat.Phys.10 314
[14]Wu Z, Zhang L, Sun W, Xu X T, Wang B Z, Ji S C, Deng Y, Chen S,Liu X J and Pan J W 2016 Science 354 83
[15]Li Y E and Xue J K 2016 Chin.Phys.Lett.33 100502
[16]Li J and Liu W M 2018 Acta Phys.Sin.67 110302(in Chinese)
[17]Yu Z Q and He L 2017 Acta Phys.Sin.66 220301(in Chinese)
[18]Zhang H, Chen F, Yu C, Sun L and Xu D 2017 Chin.Phys.B 26 080304
[19]Wen L, Sun Q, Chen Y, Wang D S, Hu J, Chen H, Liu W M, Juzeliūnas G, Malomed B A and Ji A C 2016 Phys.Rev.A 94 061602
[20]Wen L, Zhang X F, Hu A Y, Zhou J, Yu P, Xia L, Sun Q and Ji A C2018 Anns.Phys.390 181
[21]Dalibard J, Gerbier F, Juzeliūnas F and?hberg P 2011 Rev.Mod.Phys.83 1523
[22]Goldman N, Juzeliūnas G,?hberg P and Spielman I B 2014 Rep.Prog.Phys.77 126401
[23]Zhai H 2015 Rep.Prog.Phys.78 026001
[24]Hu H, Ramachandhran B, Pu H and Liu X J 2012 Phys.Rev.Lett.108010402
[25]Zhang X F, Dong D F, Liu T, Liu W M and Zhang S G 2012 Phys.Rev.A 86 063628
[26]Zhang X F, Kato M, Han W, Zhang S G and Saito H 2017 Phys.Rev.A95 033620
[27]Sinha S and Shlyapnikov G V 2005 Phys.Rev.Lett.94 150401
[28]Sánchez-Lotero P and Palacios J J 2005 Phys.Rev.A 72 043613
[29]Matveenko S I, Kovrizhin D, Ouvry S and Shlyapnikov G V 2009 Phys.Rev.A 80 063621
[30]Huang C C, Liu C H and Wu W C 2010 Phys.Rev.A 81 043605
[31]Hsueh C H, Horng T L, Gou S C and Wu W C 2011 Phys.Rev.A 84023610
[32]Chen G P, Zhang Z Y, Dong B, Wang L X, Zhang X F and Zhang S G2015 Phys.Lett.A 379 2193
[33]Chen G P, Chen S L, Xie Z W, Zhang X F and Zhang S G 2016 Commun.Theor.Phys.66 53
[34]Wu C, Mondragon-Shem I and Zhou X F 2011 Chin.Phys.Lett.28097102
[35]Sinha S, Nath R and Santos L 2011 Phys.Rev.Lett.107 270401
[36]Kawakami T, Mizushima T, Nitta M and Machida K 2012 Phys.Rev.Lett.109 015301
[37]Achilleos V, Frantzeskakis D J, Kevrekidis P G and Pelinovsky D E2013 Phys.Rev.Lett.110 264101
[38]Lobanov V E, Kartashov Y V and Konotop V V 2014 Phys.Rev.Lett.112 180403
[39]Zhang Y, Zhou Z, Malomed B A and Pu H 2015 Phys.Rev.Lett.115253902
[40]Sakaguchi H and Malomed B A 2014 Phys.Rev.E 90 062922
[41]Sakaguchi H and Malomed B A 2016 New J.Phys.18 025020
[42]Kartashov Y V and Konotop V V 2017 Phys.Rev.Lett.118 190401
[43]Gra? T, Chhajlany R W, Muschik C A and Lewenstein M 2014 Phys.Rev.B 90 195127
[44]Barnett R, Boyd G R and Galitski V 2012 Phys.Rev.Lett.109 235308
[45]Bornheimer U, Miniatura C and Grémaud B 2018 Phys.Rev.A 98043614
[46]Han W, Zhang X F, Song S W, Saito H, Zhang W, Liu W M and Zhang S G 2016 Phys.Rev.A 94 033629
[47]Kawaguchi Y and Ueda M 2012 Phys.Rep.520 253
[48]Stamper-Kurn D M and Ueda M 2013 Rev.Mod.Phys.85 1191
[49]Arfken G B, Weber H J and Harris F E 2000 Mathematical Methods for Physicists(Elsevier:Academic Press)
[50]Press W H, Teukolsky S A, Vetterling W T and Flannery B P 1992Numerical Recipes in Fortran 77(Cambridge:Cambridge University Press)
[51]Bao W Z, Jaksch D and Markowich P 2003 J.Comput.Phys.187 318
[52]Zhang Y, Mao L and Zhang C 2012 Phys.Rev.Lett.108 035302
[53]Wen L, Sun Q, Wang H Q, Ji A C and Liu W M 2012 Phys.Rev.A 86043602