Abstract
We investigate the formation of rashbon bound states and strong-coupling effects in an ultracold Fermi gas with a spherical spin–orbit interaction, \(H_\mathrm{so}=\lambda {\varvec{p}}\cdot \mathbf{\sigma }\) (where \(\mathbf{\sigma }=(\sigma _x,\sigma _y,\sigma _z)\) are Pauli matrices). Extending the strong-coupling theory developed by Nozières and Schmitt-Rink (NSR) to include this spin–orbit coupling, we determine the superfluid phase transition temperature \(T_\mathrm{c}\), as functions of the strength of a pairing interaction \(U_s\), as well as the spin–orbit coupling strength \(\lambda \). Evaluating poles of the NSR particle–particle scattering matrix describing fluctuations in the Cooper channel, we clarify the region where rashbon bound states dominate the superfluid phase transition in the \(U_s\)–\(\lambda \) phase diagram. Since the antisymmetric spin–orbit interaction \(H_\mathrm{so}\) breaks the inversion symmetry of the system, rashbon bound states naturally have not only a spin-singlet and even-parity symmetry, but also a spin-triplet and odd-parity symmetry. Thus, our results would be also useful for the study of this parity-mixing effect in the BCS–BEC crossover regime of a spin–orbit coupled Fermi gas.
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References
S. Giorgini, S. Pitaevskii, Stringari. Rev. Mod. Phys. 80, 1215 (2008)
I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)
C. Chin, R. Grimm, P. Julienne, E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010)
Y. Ohashi, A. Griffin, Phys. Rev. A 67, 063612 (2003)
Y. Ohashi, Phys. Rev. Lett. 94, 050403 (2005)
T.-L. Ho, R.B. Diener, Phys. Rev. Lett. 94, 090402 (2005)
V. Gurarie, L. Radzihovsky, A.V. Andreev, Phys. Rev. Lett. 94, 230403 (2005)
J. Levinsen, N.R. Cooper, V. Gurarie, Phys. Rev. Lett. 99, 210402 (2007)
S.S. Botelho, C.A.R. Sá de Melo, J. Low Temp. Phys. 140, 409 (2005)
M. Iskin, C.A.R. Sá de Melo, Phys. Rev. B 72, 224513 (2005)
E. Grosfeld, N.R. Cooper, A. Stern, R. Ilan, Phys. Rev. B 76, 104516 (2007)
C.-H. Cheng, S.-K. Yip, Phys. Rev. Lett. 95, 070404 (2005)
R.A.W. Maier, C. Marzok, C. Zimmermann, PhW Courteille, Phys. Rev. A 81, 064701 (2010)
R. Watanabe, S. Tsuchiya, Y. Ohashi, Phys. Rev. A 82, 043630 (2010)
A. Perali, P. Pieri, G.C. Strinati, C. Castellani, Phys. Rev. B 66, 024510 (2002)
J. Dalibard, F. Gerbier, G. Juzeliunas, P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011)
Y.-J. Lin, R.L. Compton, A.R. Perry, W.D. Phillips, J.V. Porto, I.B. Spielman, Phys. Rev. Lett. 102, 130401 (2009)
L.W. Cheuk, A.T. Sommer, Z. Hadzibabic, T. Yefsah, W.S. Bakr, M.W. Zwierlein, Phys. Rev. Lett. 109, 095302 (2012)
P. Wang, Z.-Q. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai, J. Zhang, Phys. Rev. Lett. 109, 095301 (2012)
J.P. Vyasanakere, V.B. Shenoy, Phys. Rev. B 83, 094515 (2011)
J.P. Vyasanakere, V.B. Shenoy, Phys. Rev. A 86, 053617 (2012)
J.P. Vyasanakere, V.B. Shenoy, New J. Phys. 14, 043041 (2012)
Z. Zheng, H. Pu, X. Zou, G. Guo, Phys. Rev. A 90, 063623 (2014)
J.P. Vyasanakere, S. Zhang, V.B. Shenoy, Phys. Rev. B 84, 014512 (2011)
Z.-Q. Yu, H. Zhai, Phys. Rev. Lett. 107, 195305 (2011)
L. He, X.-G. Huang, Phys. Rev. B 86, 014511 (2012)
L. Jiang, X. Liu, H. Hu, H. Pu, Phys. Rev. A 84, 063618 (2011)
T. Yamaguchi, Y. Ohashi, Phys. Rev. A 92, 013615 (2015)
C.A. Regal, C. Ticknor, J.L. Bohn, D.S. Jin, Phys. Rev. Lett. 90, 053201 (2003)
C. Ticknor, C.A. Regal, D.S. Jin, J.L. Bohn, Phys. Rev. A 69, 042712 (2004)
J. Zhang, E.G.M. van Kempen, T. Bourdel, L. Khaykovich, J. Cubizolles, F. Chevy, M. Teichmann, L. Tarruell, S.J.J.M.F. Kokkelmans, C. Salomon, Phys. Rev. A 70, 030702(R) (2004)
A.J. Leggett, Rev. Mod. Phys. 47, 331 (1975)
D. Vollhardt, P. Wölfle, The Superfluid Phases of Helium 3 (Taylor and Francis, New York, 2002)
M. Sigrist, K. Ueda, Rev. Mod. Phys. 63, 239 (1991)
G.R. Stewart, Rev. Mod. Phys. 56, 755 (1984)
A.P. Mackenzie, Y. Maeno, Rev. Mod. Phys. 75, 657 (2003)
P. Noziéres, S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985)
C.A.R. Sá de Melo, M. Randeria, J.R. Engelbrecht, Phys. Rev. Lett. 71, 3202 (1993)
J.W. Negele, H. Orland, Quantum Many-Particle Systems, Chapter 2 (Addison-Wesley, New York, 1988)
M. Randeria, in Bose-Einstein Condensation, ed. by A. Griffin, D.W. Snoke, S. Stringari (Cambridge University Press, New York, 1995), p. 355
K. Maki, in Superconductivity, ed. by R.D. Parks (Marcel Dekker, New York, 1969), p. 1035
H. Shiba, Prog. Theor. Phys. 40, 435 (1968)
J.T. Stewart, J.P. Gaebler, D.S. Jin, Nature 454, 744 (2008)
J.P. Gaebler, J.T. Stewart, T.E. Drake, D.S. Jin, A. Perali, P. Pieri, G.C. Strinati, Nat. Phys. 6, 569 (2010)
J.P. Vyasanakere, V.B. Shenoy, Phys. Rev. B 92, 121111 (2015)
Acknowledgments
We thank R. Hanai, H. Tajima, M. Matsumoto, and P. van Wyk, for discussions. This work was supported by the KiPAS project in Keio university. H.T. and R.H. were supported by the Japan Society for the Promotion of Science. Y.O. was supported by Grant-in-Aid for Scientific Research from MEXT and JSPS in Japan (Nos. 25400418, 15H00840, 15K00178).
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Yamaguchi, T., Inotani, D. & Ohashi, Y. Rashbon Bound States Associated with a Spherical Spin–Orbit Coupling in an Ultracold Fermi Gas with an s-Wave Interaction. J Low Temp Phys 183, 161–168 (2016). https://doi.org/10.1007/s10909-016-1558-0
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DOI: https://doi.org/10.1007/s10909-016-1558-0