Fermions in Synthetic Non-Abelian Gauge Fields

Sambuddha Sanyal, Sudeep Kumar Ghosh, Jayantha P Vyasanakere


Quantum emulation property of the cold atoms has generated alot of interest in studying systems with synthetic gauge fields. In this article,we describe the physics of two component Fermi gas in the presence ofsynthetic non-Abelian SU(2) gauge fields. Even for the non-interacting systemwith the gauge fields, there is an interesting change in the topology ofthe Fermi surface by tuning only the gauge field strength. When a trapping potential is used in conjunction with the gauge fields, the non-interactingsystem has the ability to produce novel Hamiltonians and show characteristic change in the density profile of the cloud. Without trap, the gauge fields act as an attractive interaction amplifier and for special kinds of gaugefield configurations, there are two-body bound states for any attraction even in three dimensions. For a many body system, the gauge fields can induce a cross over from a weak superfluid to a strong superfluid with transition temperature as high as the Fermi temperature. The superfluid state obtained for a very large gauge field strength is a superfluid of new kindof bosons, called “rashbons”, the properties of which are independent ofits constituent two component fermions and are solely determined by thegauge field strength. We also discuss the collective excitations over the superfluid ground states and the experimental relevance of the physics.

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W. D. Phillips, Rev. Mod. Phys. 70, 721 (1998).

S. Chu, Rev. Mod. Phys. 70, 685 (1998).

C. N. Cohen-Tannoudji, Rev. Mod. Phys. 70, 707 (1998).

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995).

R. Feynman, International Journal of eoretical Physics

, 467 (1982).

N. R. Cooper, Advances in Physics 57, 539 (2008).

J. Dalibard, F. Gerbier, G. Juzeli¯unas, and P. ¨ Ohberg, Rev. Mod. Phys. 83, 1523 (2011).

Y.-J. Lin, R. L. Compton, K. Jimenez-Garcia, J. V. Porto,

and I. B. Spielman, Nature 462, 628 (2009).

Y.-J. Lin, R. L. Compton, A. R. Perry, W. D. Phillips, J.

V. Porto, and I. B. Spielman, Phys. Rev. Lett. 102, 130401


Y.-J. Lin, K. Jimenez-Garcia, and I. B. Spielman, Nature

, 83 (2011).

R. A. Williams, L. J. LeBlanc, K. Jimenez-Garcia, M. C.

Beeler, A. R. Perry, W. D. Phillips, and I. B. Spielman, Science

, 314 (2012).

J.-Y. Zhang, S.-C. Ji, L. Zhang, Z.-D. Du, W. Zheng, Y.-

J. Deng, H. Zhai, S. Chen, and J.-W. Pan, ArXiv e-prints

(2013), arXiv:1305.7054.

P. Wang, Z.-Q. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H.

Zhai, and J. Zhang, Phys. Rev. Lett. 109, 095301 (2012).

L. W. Cheuk, A. T. Sommer, Z. Hadzibabic, T. Yefsah, W.

S. Bakr, and M. W. Zwierlein, Phys. Rev. Lett. 109, 095302


D. Jaksch and P. Zoller, New J. Phys. 5, 56 (2003).

K. Osterloh, M. Baig, L. Santos, P. Zoller, and M. Lewenstein, Phys. Rev. Lett. 95, 010403 (2005).

J. Ruseckas, G. Juzeli¯unas, P. ¨Ohberg, and M. Fleischhauer, Phys. Rev. Lett. 95, 010404 (2005).

F. Gerbier and J. Dalibard, New J. Phys. 12, 033007 (2010).

Z.-F. Xu, L. You, and M. Ueda, Phys. Rev. A 87, 063634


B. M. Anderson, I. B. Spielman, and G. Juzeli¯unas, Phys.

Rev. Lett. 111, 125301 (2013).

T. D. Stanescu, B. Anderson, and V. Galitski, Phys. Rev. A

, 023616 (2008).

T.-L. Ho and S. Zhang, Phys. Rev. Lett. 107, 150403


C. Wang, C. Gao, C.-M. Jian, and H. Zhai, Phys. Rev. Lett.

, 160403 (2010).

W. Cong-Jun, I. Mondragon-Shem, and Z. Xiang-Fa, Chinese Physics Letters 28, 097102 (2011).

R. Sachdeva and S. Ghosh, Phys. Rev. A 85, 013642 (2012).

J. P. Vyasanakere and V. B. Shenoy, Phys. Rev. B 83, 094515 (2011).

J. P. Vyasanakere, S. Zhang, and V. B. Shenoy, Phys. Rev. B 84, 014512 (2011).

J. P. Vyasanakere and V. B. Shenoy, New J. Phys. 14, 043041 (2012).

S. K. Ghosh, J. P. Vyasanakere, and V. B. Shenoy, Phys. Rev. A 84, 053629 (2011).

J. P. Vyasanakere and V. B. Shenoy, Phys. Rev. A 86, 053617 (2012).

R. Winkler, Spin Orbit Coupling Ects in Two-Dimensional

Electron and Hole Systems (Springer, Berlin, 2003).

J. K. Jain, Composite Fermions (Cambridge University

Press, Cambridge, UK, 2007).

C. J. Pethick and H. Smith, Bose-Einstein Condensation in

Dilute Gases (Cambridge University Press, 2004).

E. Braaten, M. Kusunoki, and D. Zhang, Ann. Phys. 323,


J. R. Taylor, Scattering eory (Dover Publications, New

York, 2006).

A. J. Leggett, Quantum Liquids: Bose Condensation and

Cooper Pairing in Condensed-Matter Systems (Oxford

University Press, 2006).

M. Sigrist and K. Ueda, Rev. Mod. Phys. 63, 239 (1991).

M. Randeria, in Bose-Einstein Condensation, edited by A.

Griffin, D. Snoke, and S. Stringari (Cambridge University

Press, 1995) Chap. 15.

Z.-Q. Yu and H. Zhai, Phys. Rev. Lett. 107, 195305 (2011).

A. A. Abrikosov, L. P. Gor’kov, and I. Y. Dzyaloshinskii,

Quantum field theoretical methods in statistical physics

(Pergamon, 1965).

J. P. Vyasanakere and V. B. Shenoy, Manuscript under


V. B. Shenoy and J. P. Vyasanakere, J. Phys. B: At. Mol. Opt. Phys. 46, 134009 (2013).

V. B. Shenoy, Phys. Rev. A 88, 033609 (2013).

V. B. Shenoy, Phys. Rev. A 89, 043618 (2014).


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