Abstract
We study the quantum dynamics of spin-orbit (SO) coupled Bose-Einstein condensates (BECs) in a double-well potential inspired by the recent experiment developed by NIST group. We focus on the regime where the number of atoms is very large and perform a two-mode approximation. An analytical solution of the two-site Bose-Hubbard-like Hamiltonian is found for weak nonlinear interactions by a rotating wave approximation (RWA). The quantum dynamics of several observables, ranging from the population and pseudospin imbalance, to the atomic and spin current are explicitly computed. We show a spin Josephson effect which could be detected in experiments and employed in realistic devices.
Similar content being viewed by others
References
X.L. Qi, S.C. Zhang, Physics Today 63, 33 (2010)
M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)
C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 146802 (2005)
B.A. Bernevig, T.L. Hughes, S.C. Zhang, Science 314, 1757 (2006)
J.D. Sau, R.M. Lutchyn, S. Tewari, S. Das Sarma, Phys. Rev. Lett. 104, 040502 (2010)
I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)
F. Gerbier, J. Dalibard, Nature 12, 033007 (2010)
J. Dalibard, F. Gerbier, G. Juzeliunas, P. Ohberg, Rev. Mod. Phys. 83, 1523 (2011)
N. Goldman, G. Juzeliunas, P. Ohberg, I. B. Spielman [arXiv:1308.6533v1]
Y.J. Lin, R.L. Compton, A.R. Perry, W.D. Phillips, J.V. Porto, I.B. Spielman, Phys. Rev. Lett. 102, 130401 (2009)
Y.J. Lin, R.L. Compton, K. Jimenez-Garcia, J.V. Porto, I.B. Spielman, Nature 462, 628 (2009)
Y.J. Lin, R.L. Compton, K. Jimenez-Garcia, W.D. Phillips, J.V. Porto, I.B. Spielman, Nat. Phys. 7, 531 (2011)
Y.J. Lin, K. Jimenez-Garcia, I.B. Spielman, Nature 471, 83 (2011)
V. Galitski, I.B. Spielman, Nature 494, 49 (2013)
Y.A. Bychkov, E.I. Rashba, J. Phys. C 17, 6039 (1984)
G. Dresselhaus, Phys. Rev. 100, 580 (1955)
D.L. Campbell, G. Juzeliunas, I.B. Spielman, Phys. Rev. A 84, 025602 (2011)
C. Wang, C. Gao, C.M. Jian, H. Zhai, Phys. Rev. Lett. 105, 160403 (2010)
T.L. Ho, S. Zhang, Phys. Rev. Lett. 107, 150403 (2011)
C.M. Jian, H. Zhai, Phys. Rev. B 84, 060508 (2011)
Y. Li, L.P. Pitaevski, S. Stringari, Phys. Rev. Lett. 108, 225301 (2012)
X.Q. Xu, J.H. Han, Phys. Rev. Lett. 107, 200401 (2011)
X.F. Zhou, J. Zhou, C.J. Wu, Phys. Rev. A 84, 063624 (2011)
J. Radic, T.A. Sedrakyan, I.B. Spielman, V. Galitski, Phys. Rev. A 84, 063604 (2011)
E. van der Bijl, R.A. Duine, Phys. Rev. Lett. 107, 195302 (2011)
Y. Li, G.I. Martone, S. Stringari, Europhys. Lett. 99, 56008 (2012)
T. Grass, K. Saha, K. Sengupta, M. Lewenstein, Phys. Rev. A 84, 053632 (2011)
Y. Li, G.I. Martone, L.P. Pitaevski, S. Stringari, Phys. Rev. Lett. 110, 235302 (2013)
Y. Zhang, L. Mao, C. Zhang, Phys. Rev. Lett. 108, 035302 (2012)
D.W. Zhang, Z.Y. Xue, H. Yan, Z.D. Wang, S.L. Zhu, Phys. Rev. A 85, 013628 (2012)
H. Zhai, Int. J. Mod. Phys. B 26, 1230001 (2012)
A.J. Leggett, Rev. Mod. Phys. 73, 307 (2001)
B.D. Josephson, Phys. Lett. 1, 251 (1962)
B.D. Josephson, Rev. Mod. Phys. 36, 216 (1964)
J. Javanainen, Phys. Rev. Lett. 57, 3164 (1986)
I. Zapata, F. Sols, A.J. Leggett, Phys. Rev. A 57, 1050 (1998)
G.J. Milburn, J. Corney, E.M. Wright, D.F. Walls, Phys. Rev. A 55, 4318 (1997)
D. Ananikian, T. Bergeman, Phys. Rev. A 74, 039905 (2006)
A. Smerzi, S. Fantoni, S. Giovanazzi, S.R. Shenoy, Phys. Rev. Lett. 79, 4950 (1997)
S. Raghavan, A. Smerzi, S. Fantoni, S.R. Shenoy, Phys. Rev. A 59, 620 (1999)
S. Giovanazzi, A. Smerzi, S. Fantoni, Phys. Rev. Lett. 84, 4521 (2000)
F.S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, M. Inguscio, Science 293, 843 (2001)
M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, M.K. Oberthaler, Phys. Rev. Lett. 95, 010402 (2005)
S. Levy, E. Lahoud, I. Shomroni, J. Steinhauer, Nature 449, 579 (2007)
G. Kalosakas, A.R. Bishop, Phys. Rev. A 65, 043616 (2002)
G. Kalosakas, A.R. Bishop, V.M. Kenkre, Phys. Rev. A 68, 023602 (2003)
R. Gati, M.K. Oberthaler, J. Phys. B: At. Mol. Opt. 40, R61 (2007)
G. Ferrini, A. Minguzzi, F.W.J. Hekking, Phys. Rev. A 78, 023606 (2008)
H.J. Lipkin, N. Meshkov, A.J. Glick, Nucl. Phys. 62, 188 (1965)
N. Meshkov, A.J. Glick, H.J. Lipkin, Nucl. Phys. 62, 199 (1965)
A.J. Glick, H.J. Lipkin, N. Meshkov, Nucl. Phys. 62, 211 (1965)
S. Dusuel, J. Vidal, Phys. Rev. B 71, 224420 (2005)
P. Ribeiro, J. Vidal, R. Mosseri, Phys. Rev. Lett. 99, 050402 (2007)
R. Orus, S. Dusuel, J. Vidal, Phys. Rev. Lett. 101, 025701 (2008)
S. Ashhab, C. Lobo, Phys. Rev. A 66, 013609 (2002)
H. Pu, W. Zhang, P. Meystre, Phys. Rev. Lett. 89, 090401 (2002)
K. Molmer, Phys. Rev. Lett. 90, 110403 (2003)
H.T. Ng, P.T. Leung, Phys. Rev. A 71, 013601 (2005)
G. Mazzarella, M. Moratti, L. Salasnich, M. Salerno, F. Toigo, J. Phys. B: At. Mol. Opt. 42, 125301 (2009)
X.Q. Xu, L.H. Lu, Y.Q. Li, Phys. Rev. A 78, 043609 (2008)
I.I. Satija, R. Balakrishnan, P. Naudus, J. Heward, M. Edwards, C.W. Clark, Phys. Rev. A 79, 033616 (2009)
B. Julia-Diaz, M. Guilleumas, M. Lewenstein, A. Polls, A. Sanpera, Phys. Rev. A 80, 023616 (2009)
M. Guilleumas, B. Julia-Diaz, M. Mele-Messeguer, A. Polls, Las. Phys. 20, 1163 (2010)
M. Mele-Messeguer, B. Julia-Diaz, M. Guilleumas, A. Polls, A. Sanpera, New J. Phys. 13, 033012 (2011)
A. Naddeo, R. Citro, J. Phys. B: At. Mol. Opt. 43, 135302 (2010)
R. Citro, A. Naddeo, E. Orignac, J. Phys. B: At. Mol. Opt. 44, 115306 (2011)
B. Sun, M.S. Pindzola, Phys. Rev. A 80, 033616 (2009)
D.W. Zhang, L.B. Fu, Z.D. Wang, S.L. Zhu, Phys. Rev. A 85, 043609 (2012)
M.A. Garcia-March, G. Mazzarella, L. Dell’Anna, B. Julia-Diaz, L. Salasnich, A. Polls, Phys. Rev. A 89, 063607 (2014)
A.P. Alodjanc, S.M. Arakeljan, A.S. Chirkin, JETP 81, 34 (1995)
L.M. Kuang, Z.W. Ouyang, Phys. Rev. A 80, 033616 (2009)
A detailed calculation for the limiting cases of weak and strong Raman coupling can be found in a longer version of this paper [arXiv:1405.5356]
Y.A. Chen, S. Nascimbene, M. Aidelsburger, M. Atala, S. Trotzky, I. Bloch, Phys. Rev. Lett. 107, 210405 (2011)
M. Atala, M. Aidelsburger, M. Lohse, J.T. Barreiro, B. Paredes, I. Bloch [arXiv:1402.0819v1]
I. Zutic, J. Fabian, S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004)
M.C. Beeler, R.A. Williams, K. Jimenez-Garcia, L.J. Le Blanc, A.R. Perry, I.B. Spielman, Nature 498, 201 (2013)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Citro, R., Naddeo, A. Spin-orbit coupled Bose-Einstein condensates in a double well. Eur. Phys. J. Spec. Top. 224, 503–518 (2015). https://doi.org/10.1140/epjst/e2015-02380-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2015-02380-4