Abstract
We investigate the dynamics of a population-imbalanced two-species fermionic system trapped in an optical lattice. The paired fermions here can form bosonic molecules via Feshbach coupling in the presence of an external magnetic field. It is shown that the natural fluctuations of the condensate fraction are periodic beyond a threshold Feshbach detuning; below this threshold value, the condensate fraction shows no oscillation at all. The oscillation frequency vs. detuning curve is linear in nature. The slope and intercept of this line are shown to carry important information about the amount of imbalance present in the system, and the momentum-space structure of the exotic phases.
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All the data obtained from analytical/numerical calculations have been presented in the forms of graphical plots. Some additional data are presented as tables in the Appendix.
References
A.O. Koetsier, D.B.M. Dickerscheid, H.T.C. Stoof, Phys. Rev. A 74, 033621 (2006)
E. Zhao, A. Paramekanti, Phys. Rev. Lett 97, 230404 (2006)
A. Amaricci, A. Privitera, M. Capone, Phys. Rev. A 89, 053604 (2014)
Z. Shen, L. Radzihovsky, V. Gurarie, Phys. Rev. Lett. 109, 245302 (2012)
J.K. Chin, D.E. Miller, Y. Liu, C. Stan, W. Setiawan, C. Sanner, K. Xu, W. Ketterle, Nature 443, 961 (2006)
W.V. Liu, F. Wilczek, Phys. Rev. Lett. 90, 047002 (2003)
P.F. Bedaque, H. Caldas, G. Rupak, Phys. Rev. Lett. 91, 247002 (2003)
S.-T. Wu, S. Yip, Phys. Rev. A 67, 053603 (2003)
H. Caldas, C.W. Morais, A.L. Mota, Phys. Rev. D 72, 045008 (2005)
R. Dasgupta, Phys. Rev. A 80, 063623 (2009)
B. Deb, A. Mishra, H. Mishra, P.K. Panigrahi, Phys. Rev. A 70, 011604 (2004)
P. Zou, L. He, X.-J. Liu, H. Hu, Phys. Rev. A 97, 043616 (2018)
M. Karmakar, S. Roy, S. Mukherjee, R. Narayanan, Phys. Rev. Res. 4, 043159 (2022)
W.V. Liu, arXiv:2109.02208v2 (2022)
D.E. Sheehy, L. Radzihovsky, Ann. Phys. 322, 1790 (2007)
D.E. Sheehy, L. Radzihovsky, Phys. Rev. Lett. 96, 060401 (2006)
Y. Shin, M.W. Zwierlein, C.H. Schunck, A. Schirotzek, W. Ketterle, Phys. Rev. Lett. 97, 030401 (2006)
P. Fulde, R.A. Ferrel, Phys. Rev. A 135, 550 (1964)
A.I. Larkin, Yu.N. Ovchinnikov, Sov. Phys. JETP 20, 25 (1965)
T. Mizushima, K. Machida, M. Ichioka, Phys. Rev. Lett. 94, 060404 (2005)
O. K. Diessel, J. Von Milezewski, A. Christianen, R. Schmidt, arXiv:2209.11758 (2022)
E. Vitali, P. Rosenberg, S. Zhang, Phys. Rev. Lett 128, 203201 (2022)
T. Kawamura, R. Hanai, D. Kagamihara, D. Inotani, Y. Ohashi, Phys. Rev. A 101, 013602 (2020)
D.C.W. Foo, G.J. Conduit, Phys. Rev. A 100, 063602 (2019)
C. Gross, I. Bloch, Science 357, 995 (2017)
S. Schmid, G. Thalhammer, K. Winkler, F. Lang, J.H. Denschlag, New J. Phys. 8, 159 (2006)
M. Aidelsburger, M. Atala, M. Lohse, J.T. Barreiro, B. Paredes, I. Bloch, Phys. Rev. Lett. 111, 185301 (2013)
S. Rosi, A. Bernard, N. Fabbri, L. Fallani, C. Fort, M. Inguscio, T. Calarco, S. Montangero, Phys. Rev. A 88, 021601 (2013)
A. Rosch, D. Rasch, B. Binz, M. Vojta, Phys. Rev. Lett. 101, 265301 (2008)
W. Hofstetter, J.I. Cirac, P. Zoller, E. Demler, M.D. Lukin, Phys. Rev. Lett 89, 220407 (2002)
T. Paananen, T.K. Koponen, P. Törmä, J.P. Martikainen, Phys. Rev. A 77, 053602 (2008)
A. Kujawa, R. Micnas, Acta Phys. Pol. A 114, 43 (2008)
T.K. Koponen, T. Paananen, J.-P. Martikainen, P. Törmä, PRL 99, 120403 (2007)
M. Karmakar, P. Majumdar, Phys. Rev. A 93, 053609 (2016)
T. Koponen, J. Kinnunen, J.-P. Martikainen, L.M. Jensen, P. Törmä, New J. Phys. 8, 179 (2006)
I. Zapata, B. Wunsch, N.T. Zinner, E. Demler, Phys. Rev. Lett 105, 095301 (2010)
A. Cichy, K.J. Kapcia, A. Ptok, Sci. Rep. 9, 6719 (2019)
N. DeSilvaTheja, Phys. Rev. A 91, 053627 (2015)
J. Wang, L. Zhang, Y. Yu, C. Lee, Q. Chen, Phys. Rev. A 101, 053617 (2020)
J. Wang, L. Sun, Q. Zhang, L. Zhang, Y. Yu, C. Lee, Q. Chen, Phys. Rev. A 101, 053618 (2020)
M.O.J. Heikkinen, P. Törmä, Phys. Rev. A 83, 053630 (2011)
J.P.A. Devreese, S.N. Klimin, J. Tempere, Phys. Rev. A 83, 013606 (2011)
J.P.A. Devreese, M. Wouters, J. Tempere, Phys. Rev. A 84, 043623 (2011)
J.P.A. Devreese, S. Klimin, M. Wouters, J. Tempere, Mod. Phys. Lett. B 26, 1230014 (2012)
E. Altman, E. Demler, M.D. Lukin, Phys. Rev. A 70, 013603 (2004)
A. Lüscher, R.M. Noack, A.M. Läuchli, Phys. Rev. A 78, 013637 (2008)
D. Pęcak and T. Sowiański, Phys. Rev. Research, 2, 012077 (2020)
A. Korolyuk, F. Massel, P. Törmä, Phys. Rev. Lett. 104, 236402 (2010)
M. Singh, G. Orso, Phys. Rev. Res. 2, 023148 (2020)
W. Yi, L.-M. Duan, Phys. Rev. Lett. 97, 120401 (2006)
J. Kajala, F. Massel, P. Törmä, Phys. Rev. A 84, 041601(R) (2011)
L. Zhou, K. Zhang, B. Zhu, Y. Li, W. Zhang, Phys. Lett. A 376, 25 (2012)
R. Dasgupta, J.K. Bhattacharjee, Eur. Phys. J. B 94(2), 1–14 (2021)
S. Trotzky, P. Cheinet, S. Fölling, M. Feld, U. Schnorrberger, A.M. Rey, A. Polkovnikov, E.A. Demler, M.D. Lukin, I. Bloch, Science 319, 295–299 (2008)
D. Hu, L. Niu, B. Yang, X. Chen, B. Wu, H. Xiong, X. Zhou, Phys. Rev. A 92, 043614 (2015)
Z. Wang, B. Yang, D. Hu, X. Chen, H. Xiong, B. Wu, X. Zhou, Phys. Rev. A 94, 033624 (2016)
P. Kettmann, S. Hannibal, M.D. Croitoru, V.M. Axt, T. Kuhn, Phys. Rev. A 96, 033618 (2017)
A. Recati, F. Piazza, Phys. Rev. B 99, 064505 (2019)
E.A. Yuzbashyan, M.D. Zero, V. Gurarie, M.S. Foster, Phys. Rev. A 91, 033628 (2015)
J. Tokimoto, S. Tsuchiya, T. Nikuni, J. Phys. Soc. Jpn. 88, 023601 (2019)
L. Salasnich, Condens. Matter 2, 22 (2017)
G. Lyu, K.-T. Xi, S. Yoon, Q. Chen, G. Watanabe, Phys. Rev. A. 107, 02332 (2023)
D. Phan, A.V. Chubukov, Phys. Rev. B 107, 134519 (2023)
S.M. Garot, G. Pettini, M. Modugno, Phys. Rev. A 98, 043624 (2018)
B. Sun, M.S. Pindzola, J. Phys. B At. Mol. Opt. Phys. 43, 055301 (2010)
R. Combescot, MYu. Kagon, S. Stringari, Phys. Rev. A 74, 042717 (2006)
F.S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, M. Inguscio, Science 293, 843 (2001)
Y.-A. Chen, S. Nascimbéne, M. Aidelsburger, M. Atala, S. Trotzky, I. Bloch, Phys. Rev. Lett 107, 210405 (2011)
G. Kordas, D. Witthaut, S. Wimberger, Ann. Phys. (Berlin) 527, 619 (2015)
F. Trimborn, D. Witthaut, S. Wimberger, J. Phys. B At. Mol. Opt. Phys. 41, 171001 (2008)
F. Trimborn, D. Witthaut, H. Hennig, G. Kordas, T. Geisel, S. Wimberger, Eur. Phys. J. D 63, 63 (2011)
A. Vardi, V. A. Yurovsky, J. R. Anglin, Phys. Rev. A. 64, 063611 (2001)
A. Vardi and J. R. Anglin, Phys. Rev. Lett. 86, 568 (2001)
G. Kordas, D. Witthaut, P. Buonsante, A. Vezzani, R. Burioni, A.I. Karanikas, S. Wimberger, Eur. Phys. J. Spec. Top. 224, 2127 (2015)
F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 3 (1999)
T. Rom, Th. Best, D. Van Oosten, U. Schneider, S. Folling, B. Parades, I. Bloch, Nature 444, 733–736 (2006)
M. Kohl, H. Moritz, T. Stoferle, K. Gunter, T. Esslinger, Phys. Rev. Lett. 94, 080403 (2005)
S. Ramanan, T. Mishra, M.S. Luthra, R.V. Pai, B.P. Das, Phys. Rev. A 79, 013625 (2009)
T. Stoferle, H. Moritz, C. Schori, M. Kohl, T. Esslinger, Phys. Rev. Lett. 92, 130403 (2004)
I. Jimenz-Garcia, R.L. Compton, Y.-J. Lin, W.D. Phillips, J.V. Porto, I.B. Spielman, Phys. Rev. Lett 105, 110401 (2010)
A. Isacsson, S.M. Girvin, Phys. Rev. A 72, 053604 (2005)
Y. Matsunda, H. Shimahara, J. Phys. Soc. Jph 76, 051005 (2007)
A.R. Carlos, Sa de Melo Phys. Today 61, 10 (2008)
C. Kollath, A. Iucci, T. Giamarchi, W. Hofstetter, U. Schollwock, Phys. Rev. Lett. 97, 050402 (2006)
A.-M. Dare, L. Raymond, G. Albinet, A.-M.S. Tremblay, Phys. Rev. B 76, 064402 (2007)
R. Sensarma, D. Pekker, M.D. Lukin, E. Demler, Phys. Rev. Lett. 103, 035303 (2009)
H. Pichler, J. Schachenmayer, A.J. Daley, P. Zoller, Phys. Rev. A 87, 033606 (2013)
M. Lubasch, F. Mintert, S. Wimberger, Phys. Rev. A 84, 063615 (2011)
J.-W. Huo, F.-C. Zhang, W. Chen, M. Troyler, U. Schollwock, Phys. Rev. A 84, 043608 (2011)
F. Illuminati, A. Albus, Phys. Rev. Lett. 93, 090406 (2004)
Z. Xu, S. Chiesa, S. Yang, S.-Q. Su, D.E. Sheenhy, J. Moreno, R.T. Scalettar, M. Jarrell, Phys. Rev. A 84, 021607 (2011)
K. Chartkunchand, Ultracold Atoms in Optical Lattices (Doctoral dissertation, University of Nevada, Reno) (2006)
J.A. Scaramazza, B. Kain, H.Y. Ling, Eur. Phys. J. D 70, 147 (2016)
T. Kohler, K. Goral, P.S. Julienne, Rev. Mod. Phys. 78, 1311 (2006)
I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)
M. Holland, S.J.J.M.F. Kokkelmans, M.L. Chiofalo, R. Walser, Phys. Rev. Lett 87, 120406 (2001)
C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases, 2nd edn. (Cambridge University Press, New York, 2008)
L. Pitaevskii, S. Stringari, Bose-Einstein Condensation and Superfluidity. International Series of Monographs on Physics, vol. 164 (Oxford Science Publications, Oxford, 2015)
Acknowledgements
AM would like to acknowledge University Grants Commission (UGC), Govt. of India for financial support (Student ID: 201610064840). RD would like to acknowledge Science and Engineering Research Board (SERB), Department of Science and Technology, Govt. of India for providing support under the CRG scheme (CRG/2022/007312).
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Appendix: Calculation of parameters for \(^6\text{ Li }\) and \(^{40}\text{ K }\)
Appendix: Calculation of parameters for \(^6\text{ Li }\) and \(^{40}\text{ K }\)
In this section, we compute the \(g_1\) and \(g_2\) values for \(^6\text{ Li }\) and \(^{40}\text{ K }\) corresponding to different amounts of fractional imbalance and dimension for \(^6\text{ Li }\) and \(^{40}\text{ K }\) sample. Building elements of \(g_1\) and \(g_2\) for both \(^6\text{ Li }\) and \(^{40}\text{ K }\) is shown in Table 1 in the page of tables. Tables 2, 3, and 4 contain the relevant system parameters in different dimensions.
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Mukherjee, A., Dasgupta, R. Periodic dynamics of population-imbalanced fermionic condensates in optical lattices. Eur. Phys. J. B 97, 15 (2024). https://doi.org/10.1140/epjb/s10051-024-00649-9
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DOI: https://doi.org/10.1140/epjb/s10051-024-00649-9