Dynamic fragmentation in a quenched two-mode Bose–Einstein condensate

doi:10.1007/s11467-015-0530-9

Frontiers of Physics

2016, Vol. 11

Issue (3): 101204 https://doi.org/10.1007/s11467-015-0530-9

本期目录

Dynamic fragmentation in a quenched two-mode Bose–Einstein condensate

Shu-Yuan Wu (吴淑媛)^1,²,Hong-Hua Zhong (钟宏华)^1,^2,³,Jia-Hao Huang (黄嘉豪)^1,²,Xi-Zhou Qin (秦锡洲)^1,²,Chao-Hong Lee (李朝红)^1,^2,^*(

)

¹. School of Physics and Astronomy, Sun Yat-Sen University, Guangzhou 510275, China
². State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-Sen University, Guangzhou 510275, China
³. Department of Physics, Jishou University, Jishou 416000, China

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Abstract：

We investigate the fragmentation in a two-mode Bose–Einstein condensate with Josephson coupling. We explore how the fragmentation and entropy of the ground state depend on the intermode asymmetry and interparticle interactions. Owing to the interplay between the asymmetry and the interactions, a sequence of notches and plateaus in the fragmentation appears with the single-atom tunneling and interaction blockade, respectively. We then analyze the dynamical properties of the fragmentation in three typical quenches of the asymmetry: linear, sudden, and periodic quenches. In a linear quench, the final state is a fragmented state due to the sequential Landau–Zener tunneling, which can be analytically explained by applying the two-level Landau–Zener formula for each avoided level crossing. In a sudden quench, the fragmentation exhibits persistent fluctuations that sensitively depend on the interparticle interactions and intermode coupling. In a periodic quench, the fragmentation is modulated by the periodic driving, and a suitable modulation may allow one to control the fragmentation.

Key words： fragmentation two-mode BEC quantum quench

收稿日期: 2015-09-10 出版日期: 2016-06-08

Corresponding Author(s): Chao-Hong Lee (李朝红)

引用本文:

. [J]. Frontiers of Physics, 2016, 11(3): 101204.
Shu-Yuan Wu (吴淑媛),Hong-Hua Zhong (钟宏华),Jia-Hao Huang (黄嘉豪),Xi-Zhou Qin (秦锡洲),Chao-Hong Lee (李朝红). Dynamic fragmentation in a quenched two-mode Bose–Einstein condensate. Front. Phys. , 2016, 11(3): 101204.

链接本文:

https://academic.hep.com.cn/fop/CN/10.1007/s11467-015-0530-9
https://academic.hep.com.cn/fop/CN/Y2016/V11/I3/101204

1	O. Penrose and L. Onsager, Bose˗Einstein condensation and liquid helium, Phys. Rev. 104(3), 576 (1956) https://doi.org/10.1103/PhysRev.104.576
2	A. J. Leggett, Bose˗Einstein condensation in the alkali gases: Some fundamental concepts, Rev. Mod. Phys. 73(2), 307 (2001) https://doi.org/10.1103/RevModPhys.73.307
3	P. Bader and U. R. Fischer, Fragmented many-body ground states for scalar Bosons in a single trap, Phys. Rev. Lett. 103(6), 060402 (2009) https://doi.org/10.1103/PhysRevLett.103.060402
4	U. R. Fischer and B. Xiong, Robustness of fragmented condensate many-body states for continuous distribution amplitudes in Fock space, Phys. Rev. A 88(5), 053602 (2013) https://doi.org/10.1103/PhysRevA.88.053602
5	A. I. Streltsov, L. S. Cederbaum, and N. Moiseyev, Ground-state fragmentation of repulsive Bose˗Einstein condensates in double-trap potentials, Phys. Rev. A 70(5), 053607 (2004) https://doi.org/10.1103/PhysRevA.70.053607
6	R. Kanamoto, H. Saito, and M. Ueda, Quantum phase transition in one-dimensional Bose˗Einstein condensates with attractive interactions, Phys. Rev. A 67(1), 013608 (2003) https://doi.org/10.1103/PhysRevA.67.013608
7	C. J. Myatt, E. A. Burt, R. W. Ghrist, E. A. Cornell, and C. E. Wieman, Production of two overlapping Bose˗Einstein condensates by sympathetic cooling, Phys. Rev. Lett. 78(4), 586 (1997) https://doi.org/10.1103/PhysRevLett.78.586
8	D. M. Stamper-Kurn, M. R. Andrews, A. P. Chikkatur, S. Inouye, H. J. Miesner, J. Stenger, and W. Ketterle, Optical confinement of a Bose˗Einstein condensate, Phys. Rev. Lett. 80(10), 2027 (1998) https://doi.org/10.1103/PhysRevLett.80.2027
9	T. L. Ho and S. K. Yip, Fragmented and single condensate ground states of spin-1 Bose gas, Phys. Rev. Lett. 84(18), 4031 (2000) https://doi.org/10.1103/PhysRevLett.84.4031
10	O. E. Müstecaplıoğlu, M. Zhang, S. Yi, L. You, and C. P. Sun, Dynamic fragmentation of a spinor Bose˗Einstein condensate, Phys. Rev. A 68(6), 063616 (2003) https://doi.org/10.1103/PhysRevA.68.063616
11	A. Görlitz, T. L. Gustavson, A. E. Leanhardt, R. Löw, A. P. Chikkatur, S. Gupta, S. Inouye, D. E. Pritchard, and W. Ketterle, Sodium Bose˗Einstein condensates in the in the F= 2 state in a large-volume optical trap, Phys. Rev. Lett. 90(9), 090401 (2003) https://doi.org/10.1103/PhysRevLett.90.090401
12	H. Schmaljohann, M. Erhard, J. Kronjäger, M. Kottke, S. van Staa, L. Cacciapuoti, J. J. Arlt, K. Bongs, and K. Sengstock, Dynamics of F= 2 spinor Bose˗Einstein condensates, Phys. Rev. Lett. 92(4), 040402 (2004) https://doi.org/10.1103/PhysRevLett.92.040402
13	T. Kuwamoto, K. Araki, T. Eno, and T. Hirano, Magnetic field dependence of the dynamics of 87Rb spin-2 Bose˗Einstein condensates, Phys. Rev. A 69(6), 063604 (2004) https://doi.org/10.1103/PhysRevA.69.063604
14	S. Levy, E. Lahoud, I. Shomroni, and J. Steinhauer, The a.c. and d.c. Josephson effects in a Bose˗Einstein condensate, Nature 449(7162), 579 (2007) https://doi.org/10.1038/nature06186
15	R. W. Spekkens and J. E. Sipe, Spatial fragmentation of a Bose˗Einstein condensate in a double-well potential, Phys. Rev. A 59(5), 3868 (1999) https://doi.org/10.1103/PhysRevA.59.3868
16	L. Cederbaum and A. Streltsov, Best mean-field for condensates, Phys. Lett. A 318(6), 564 (2003) https://doi.org/10.1016/j.physleta.2003.09.058
17	E. J. Mueller, T. L. Ho, M. Ueda, and G. Baym, Fragmentation of Bose˗Einstein condensates, Phys. Rev. A 74(3), 033612 (2006) https://doi.org/10.1103/PhysRevA.74.033612
18	T. L. Ho and C. Ciobanu, The Schrödinger cat family in attractive Bose gases, J. Low Temp. Phys. 135(3-4), 257 (2004) https://doi.org/10.1023/B:JOLT.0000024552.87247.eb
19	Q. Zhu, Q. Zhang, and B. Wu, Extended two-site Bose–Hubbard model with pair tunneling: Spontaneous symmetry breaking, effective ground state and fragmentation, J. Phys. At. Mol. Opt. Phys. 48(4), 045301 (2015) https://doi.org/10.1088/0953-4075/48/4/045301
20	K. Sakmann, A. I. Streltsov, O. E. Alon, and L. S. Cederbaum, Universality of fragmentation in the Schrödinger dynamics of bosonic Josephson junctions, Phys. Rev. A 89(2), 023602 (2014) https://doi.org/10.1103/PhysRevA.89.023602
21	L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose˗Einstein condensate, Nature 443(7109), 312 (2006) https://doi.org/10.1038/nature05094
22	S. Hofferberth, I. Lesanovsky, B. Fischer, T. Schumm, and J. Schmiedmayer, Non-equilibrium coherence dynamics in one-dimensional Bose gases, Nature 449(7160), 324 (2007) https://doi.org/10.1038/nature06149
23	Y. A. Chen, S. D. Huber, S. Trotzky, I. Bloch, and E. Altman, Many-body Landau˗Zener dynamics in coupled one-dimensional Bose liquids, Nat. Phys. 7(1), 61 (2011) https://doi.org/10.1038/nphys1801
24	D. Chen, M. White, C. Borries, and B. DeMarco, Quantum quench of an atomic Mott insulator, Phys. Rev. Lett. 106(23), 235304 (2011) https://doi.org/10.1103/PhysRevLett.106.235304
25	F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Grobner, A. J. Daley, and H. C. Nägerl, Observation of many-body dynamics in long-range tunneling after a quantum quench, Science 344(6189), 1259 (2014) https://doi.org/10.1126/science.1248402
26	C. Lee, W. Hai, L. Shi, X. Zhu, and K. Gao, Chaotic and frequency-locked atomic population oscillations between two coupled Bose˗Einstein condensates, Phys. Rev. A 64(5), 053604 (2001) https://doi.org/10.1103/PhysRevA.64.053604
27	K. Sengupta, S. Powell, and S. Sachdev, Quench dynamics across quantum critical points, Phys. Rev. A 69(5), 053616 (2004) https://doi.org/10.1103/PhysRevA.69.053616
28	P. Calabrese and J. Cardy, Time dependence of correlation functions following a quantum quench, Phys. Rev. Lett. 96(13), 136801 (2006) https://doi.org/10.1103/PhysRevLett.96.136801
29	C. Kollath, A. M. Läuchli, and E. Altman, Quench dynamics and nonequilibrium phase diagram of the Bose-Hubbard model, Phys. Rev. Lett. 98(18), 180601 (2007) https://doi.org/10.1103/PhysRevLett.98.180601
30	G. Roux, Quenches in quantum many-body systems: One-dimensional Bose˗Hubbard model reexamined, Phys. Rev. A 79(2), 021608 (2009) https://doi.org/10.1103/PhysRevA.79.021608
31	B. Sciolla and G. Biroli, Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose˗Hubbard model, Phys. Rev. Lett. 105(22), 220401 (2010) https://doi.org/10.1103/PhysRevLett.105.220401
32	J. Dziarmaga and M. Tylutki, Excitation energy after a smooth quench in a Luttinger liquid, Phys. Rev. B 84(21), 214522 (2011) https://doi.org/10.1103/PhysRevB.84.214522
33	D. Poletti and C. Kollath, Slow quench dynamics of periodically driven quantum gases, Phys. Rev. A 84(1), 013615 (2011) https://doi.org/10.1103/PhysRevA.84.013615
34	F. H. L. Essler, S. Evangelisti, and M. Fagotti, Dynamical correlations after a quantum quench, Phys. Rev. Lett. 109(24), 247206 (2012) https://doi.org/10.1103/PhysRevLett.109.247206
35	X. Yin and L. Radzihovsky, Quench dynamics of a strongly interacting resonant Bose gas, Phys. Rev. A 88(6), 063611 (2013) https://doi.org/10.1103/PhysRevA.88.063611
36	J. S. Bernier, R. Citro, C. Kollath, and E. Orignac, Correlation dynamics during a slow interaction quench in a one-dimensional Bose gas, Phys. Rev. Lett. 112(6), 065301 (2014) https://doi.org/10.1103/PhysRevLett.112.065301
37	E. J. Torres-Herrera and L. F. Santos, Quench dynamics of isolated many-body quantum systems, Phys. Rev. A 89(4), 043620 (2014) https://doi.org/10.1103/PhysRevA.89.043620
38	M. Eckstein, M. Kollar, and P. Werner, Thermalization after an interaction quench in the Hubbard model, Phys. Rev. Lett. 103(5), 056403 (2009) https://doi.org/10.1103/PhysRevLett.103.056403
39	M. Rigol, Breakdown of thermalization in finite one-dimensional systems, Phys. Rev. Lett. 103(10), 100403 (2009) https://doi.org/10.1103/PhysRevLett.103.100403
40	M. Cazalilla and M. Rigol, Focus on dynamics and thermalization in isolated quantum many-body systems, New J. Phys. 12(5), 055006 (2010) https://doi.org/10.1088/1367-2630/12/5/055006
41	A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83(3), 863 (2011) https://doi.org/10.1103/RevModPhys.83.863
42	A. C. Cassidy, C. W. Clark, and M. Rigol, Generalized thermalization in an integrable lattice system, Phys. Rev. Lett. 106(14), 140405 (2011) https://doi.org/10.1103/PhysRevLett.106.140405
43	C. A. Parra-Murillo, J. Madroñero, and S. Wimberger, Quantum diffusion and thermalization at resonant tunneling, Phys. Rev. A 89(5), 053610 (2014) https://doi.org/10.1103/PhysRevA.89.053610
44	W. H. Zurek, U. Dorner, and P. Zoller, Dynamics of a quantum phase transition, Phys. Rev. Lett. 95(10), 105701 (2005) https://doi.org/10.1103/PhysRevLett.95.105701
45	C. Lee, Universality and anomalous mean-field breakdown of symmetry-breaking transitions in a coupled two-component Bose˗Einstein condensate, Phys. Rev. Lett. 102(7), 070401 (2009) https://doi.org/10.1103/PhysRevLett.102.070401
46	J. Dziarmaga and M. M. Rams, Dynamics of an inhomogeneous quantum phase transition, New J. Phys. 12(5), 055007 (2010) https://doi.org/10.1088/1367-2630/12/5/055007
47	J. Dziarmaga, M. Tylutki, and W. H. Zurek, Quench from Mott insulator to superfluid, Phys. Rev. B 86(14), 144521 (2012) https://doi.org/10.1103/PhysRevB.86.144521
48	F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, A. J. Daley, and H. C. Nägerl, Quantum quench in an atomic one-dimensional Ising chain, Phys. Rev. Lett. 111(5), 053003 (2013) https://doi.org/10.1103/PhysRevLett.111.053003
49	U. Schneider, L. Hackermuller, J. P. Ronzheimer, S. Will, S. Braun, T. Best, I. Bloch, E. Demler, S. Mandt, D. Rasch, and A. Rosch, Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms, Nat. Phys. 8(3), 213 (2012) https://doi.org/10.1038/nphys2205
50	M. Cheneau, P. Barmettler, D. Poletti, M. Endres, P. Schausz, T. Fukuhara, C. Gross, I. Bloch, C. Kollath, and S. Kuhr, Light-cone-like spreading of correlations in a quantum many-body system, Nature 481(7382), 484 (2012) https://doi.org/10.1038/nature10748
51	J. P. Ronzheimer, M. Schreiber, S. Braun, S. S. Hodgman, S. Langer, I. P. McCulloch, F. Heidrich-Meisner, I. Bloch, and U. Schneider, Expansion dynamics of interacting Bosons in homogeneous lattices in one and two dimensions, Phys. Rev. Lett. 110(20), 205301 (2013) https://doi.org/10.1103/PhysRevLett.110.205301
52	P. Jurcevic, B. P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, and C. F. Roos, Quasiparticle engineering and entanglement propagation in a quantum many-body system, Nature 511(7508), 202 (2014) https://doi.org/10.1038/nature13461
53	G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, Quantum dynamics of an atomic Bose˗Einstein condensate in a double-well potential, Phys. Rev. A 55(6), 4318 (1997) https://doi.org/10.1103/PhysRevA.55.4318
54	X. X. Yang and Y. Wu, SU(2) coherent state description of two-mode Bose–Einstein condensates, Commum. Theor. Phys. 37(5), 539 (2002) https://doi.org/10.1088/0253-6102/37/5/539
55	L. M. Kuang, J. H. Li, and B. Hu, Polarization and decoherence in a two-component Bose–Einstein condensate, J. Opt. B 4(5), 295 (2002) https://doi.org/10.1088/1464-4266/4/5/311
56	A. H. Zeng and L. M. Kuang, Influence of quantum entanglement on quantum tunnelling between two atomic Bose˗Einstein condensates, Phys. Lett. A 338(3˗5), 323 (2005)
57	C. Lee, Adiabatic Mach˗Zehnder interferometry on a quantized Bose˗Josephson junction, Phys. Rev. Lett. 97(15), 150402 (2006) https://doi.org/10.1103/PhysRevLett.97.150402
58	D. Witthaut, F. Trimborn, and S. Wimberger, Dissipation induced coherence of a two-mode Bose˗Einstein condensate, Phys. Rev. Lett. 101(20), 200402 (2008) https://doi.org/10.1103/PhysRevLett.101.200402
59	X. X. Yang and Y. Wu, Effective two-state model and NOON states for double-well Bose˗Einstein condensates in strong-interaction regime, Commum. Theor. Phys. 52(2), 244 (2009) https://doi.org/10.1088/0253-6102/52/2/10
60	F. Trimborn, D. Witthaut, V. Kegel, and H. Korsch, Nonlinear Landau˗Zener tunneling in quantum phase space, New J. Phys. 12(5), 053010 (2010) https://doi.org/10.1088/1367-2630/12/5/053010
61	C. Lee, J. Huang, H. Deng, H. Dai, and J. Xu, Nonlinear quantum interferometry with Bose condensed atoms, Front. Phys. 7(1), 109 (2012) https://doi.org/10.1007/s11467-011-0228-6
62	S. S. Li, J. B. Yuan, and L. M. Kuang, Coherent manipulation of spin squeezing in atomic Bose˗Einstein condensate via electromagnetically induced transparency, Front. Phys. 8(1), 27 (2013) https://doi.org/10.1007/s11467-013-0288-x
63	A. Sinatra, J. C. Dornstetter, and Y. Castin, Spin squeezing in Bose˗Einstein condensates: Limits imposed by decoherence and non-zero temperature, Front. Phys. 7(1), 86 (2012) https://doi.org/10.1007/s11467-011-0219-7
64	R. Gati and M. K. Oberthaler, A bosonic Josephson junction, J. Phys. At. Mol. Opt. Phys. 40(10), R61 (2007) https://doi.org/10.1088/0953-4075/40/10/R01
65	W. D. Li, Y. Zhang, and J. Q. Liang, Energy-band structure and intrinsic coherent properties in two weakly linked Bose˗Einstein condensates, Phys. Rev. A 67(6), 065601 (2003) https://doi.org/10.1103/PhysRevA.67.065601
66	C. Lee, L. B. Fu, and Y. S. Kivshar, Many-body quantum coherence and interaction blockade in Josephson-linked Bose˗Einstein condensates, Europhys. Lett. 81(6), 60006 (2008) https://doi.org/10.1209/0295-5075/81/60006
67	D. Raventós, T. Graß, and B. Juliá-Díaz, Cold bosons in optical lattices: Correlations, localization, and fragmentation, arXiv: 1410.7280
68	B. Juli’a-Diaz, D. Dagnino, M. Lewenstein, J. Martorell, and A. Polls, Macroscopic self-trapping in Bose˗Einstein condensates: Analysis of a dynamical quantum phase transition, Phys. Rev. A 81(2), 023615 (2010) https://doi.org/10.1103/PhysRevA.81.023615
69	C. Zener, Non-Adiabatic crossing of energy levels, Proceedings of the Royal Society of London Series A 137, 696 (1932) https://doi.org/10.1098/rspa.1932.0165
70	H. Zhong, Q. Xie, J. Huang, X. Qin, H. Deng, J. Xu, and C. Lee, Photon-induced sideband transitions in a manybody Landau˗Zener process, Phys. Rev. A 90(2), 023635 (2014) https://doi.org/10.1103/PhysRevA.90.023635
71	E. J. Torres-Herrera and L. F. Santos, Non-exponential fidelity decay in isolated interacting quantum systems, Phys. Rev. A 90(3), 033623 (2014) https://doi.org/10.1103/PhysRevA.90.033623
72	A. Eckardt, T. Jinasundera, C. Weiss, and M. Holthaus, Analog of photon-assisted tunneling in a Bose˗Einstein condensate, Phys. Rev. Lett. 95(20), 200401 (2005) https://doi.org/10.1103/PhysRevLett.95.200401
73	T. Jinasundera, C. Weiss, and M. Holthaus, Manyparticle tunnelling in a driven Bosonic Josephson junction, Chem. Phys. 322(1˗2), 118 (2006)
74	M. Grifoni and P. Hänggi, Driven quantum tunneling, Phys. Rep. 304(5˗6), 229 (1998)
75	G. Liu, N. Hao, S. L. Zhu, and W. M. Liu, Topological superfluid transition induced by a periodically driven optical lattice, Phys. Rev. A 86(1), 013639 (2012) https://doi.org/10.1103/PhysRevA.86.013639

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