Probing two Higgs oscillations in a one-dimensional Fermi superfluid with Raman-type spin–orbit coupling

Abstract

We theoretically investigate the Higgs oscillation in a one-dimensional Raman-type spin–orbit-coupled Fermi superfluid with the time-dependent Bogoliubov–de Gennes equations. By linearly ramping or abruptly changing the effective Zeeman field in both the Bardeen–Cooper–Schrieffer state and the topological superfluid state, we find the amplitude of the order parameter exhibits an oscillating behaviour over time with two different frequencies (i.e., two Higgs oscillations) in contrast to the single one in a conventional Fermi superfluid. The observed period of oscillations has a great agreement with the one calculated using the previous prediction [Volkov and Kogan, J. Exp. Theor. Phys. 38, 1018 (1974)], where the oscillating periods are now determined by the minimums of two quasi-particle spectrum in this system. We further verify the existence of two Higgs oscillations using a periodic ramp strategy with theoretically calculated driving frequency. Our predictions would be useful for further theoretical and experimental studies of these Higgs oscillations in spin–orbit-coupled systems.

Graphical abstract

Keywords

Higgs mode / spin–orbit coupled Fermi superfluid

References

[1] P. B. Littlewood and C. M. Varma, Gauge-invariant theory of the dynamical interaction of charge density waves and superconductivity, Phys. Rev. Lett. 47, 811 (1981)

[2] P. B. Littlewood and C. M. Varma, Amplitude collective modes in superconductors and their coupling to chargedensity waves, Phys. Rev. B 26, 4883 (1982)

[3] R. Sooryakumar and M. V. Klein, Raman scattering by superconducting-gap excitations and their coupling to charge-density waves, Phys. Rev. Lett. 45, 660 (1980)

[4] R. Sooryakumar and M. V. Klein, Raman scattering from superconducting gap excitations in the presence of a magnetic field, Phys. Rev. B 23, 3213 (1981)

[5] M. Matsumoto, B. Normand, T. M. Rice, and M. Sigrist, Field- and pressure-induced magnetic quantum phase transitions in TlCuCl₃, Phys. Rev. B 69, 054423 (2004)

[6] C. Rüegg, B. Normand, M. Matsumoto, A. Furrer, D. F. McMorrow, K. W. Krämer, H. U. Güdel, S. N. Gvasaliya, H. Mutka, and M. Boehm, Quantum magnets under ressure: Controlling elementary excitations in TlCuCl₃, Phys. Rev. Lett. 100, 205701 (2008)

[7] R. G. Scott, F. Dalfovo, L. P. Pitaevskii, and S. Stringari, Rapid ramps across the BEC–BCS crossover: A route to measuring the superfluid gap, Phys. Rev. A 86, 053604 (2012)

[8] E. Altman and A. Auerbach, Oscillating superfluidity of bosons in optical lattices, Phys. Rev. Lett. 89, 250404 (2002)

[9] L. Pollet and N. Prokof’ev, Higgs mode in a two dimensional superfluid, Phys. Rev. Lett. 109, 010401 (2012)

[10] U. Bissbort, S. Götze, Y. Li, J. Heinze, J. S. Krauser, M. Weinberg, C. Becker, K. Sengstock, and W. Hofstetter, Detecting the amplitude mode of strongly interacting lattice bosons by Bragg scattering, Phys. Rev. Lett. 106, 205303 (2011)

[11] M. Endres, T. Fukuhara, D. Pekker, M. Cheneau, P. Schauβ, C. Gross, E. Demler, S. Kuhr, and I. Bloch, The “Higgs” amplitude mode at the two-dimensional superfluid/Mott insulator transition, Nature 487, 454 (2012)

[12] D. Pekker and C. Varma, Amplitude/Higgs modes in condensed matter physics, Annual Review of Condensed Matter Physics 6, 269 (2015)

[13] R. Matsunaga, Y. I. Hamada, K. Makise, Y. Uzawa, H. Terai, Z. Wang, and R. Shimano, Higgs amplitude mode in the BCS superconductors Nb_1-xTi_xN induced by terahertz pulse excitation, Phys. Rev. Lett. 111, 057002 (2013)

[14] D. Sherman, U. S. Pracht, B. Gorshunov, S. Poran, J. Jesudasan, M. Chand, P. Raychaudhuri, M. Swanson, N. Trivedi, A. Auerbach, et al., The Higgs mode in disordered superconductors close to a quantum phase transition, Nature Phys. 11, 188 (2015)

[15] E. A. Yuzbashyan and M. Dzero, Dynamical vanishing of the order parameter in a fermionic condensate, Phys. Rev. Lett. 96, 230404 (2006)

[16] S. Hannibal, P. Kettmann, M. D. Croitoru, A. Vagov, V. M. Axt, and T. Kuhn, Quench dynamics of an ultracold Fermi gas in the BCS regime: Spectral properties and confinement-induced breakdown of the Higgs mode, Phys. Rev. A 91, 043630 (2015)

[17] E. Altman and A. Vishwanath, Dynamic projection on feshbach molecules: A probe of pairing and phase fluctuations, Phys. Rev. Lett. 95, 110404 (2005)

[18] A. Perali, P. Pieri, and G. C. Strinati, Extracting the condensate density from projection experiments with Fermi gases, Phys. Rev. Lett. 95, 010407 (2005)

[19] S. Matyjaśkiewicz, M. H. Szymańska, and K. Góral, Probing fermionic condensates by fast-sweep projection onto Feshbach molecules, Phys. Rev. Lett. 101, 150410 (2008)

[20] A. Behrle, T. Harrison, J. Kombe, K. Gao, M. Link, J.- S. Bernier, C. Kollath, and M. Köhl, Higgs mode in a strongly interacting fermionic superfluid, Nature Phys. 14, 781 (2018)

[21] B. Liu, H. Zhai, and S. Zhang, Evolution of the Higgs mode in a fermion superfluid with tunable interactions, Phys. Rev. A 93, 033641 (2016)

[22] X. Han, B. Liu, and J. Hu, Observability of Higgs mode in a system without Lorentz invariance, Phys. Rev. A 94, 033608 (2016)

[23] H. Kurkjian, S. N. Klimin, J. Tempere, and Y. Castin, Pair-breaking collective branch in BCS superconductors and superfluid Fermi gases, Phys. Rev. Lett. 122, 093403 (2019)

[24] A. Volkov and S. M. Kogan, Collisionless relaxation of the energy gap in superconductors, Soviet J. Exp. Theor. Phys. 38, 1018 (1974)

[25] P. Wang, Z.-Q. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai, and J. Zhang, Spin–orbit coupled degenerate Fermi gases, Phys. Rev. Lett. 109, 095301 (2012)

[26] L. W. Cheuk, A. T. Sommer, Z. Hadzibabic, T. Yefsah, W. S. Bakr, and M. W. Zwierlein, Spin-injection spectroscopy of a spin–orbit coupled Fermi gas, Phys. Rev. Lett. 109, 095302 (2012)

[27] P. Wang, W. Yi, and G. Xianlong, Topological phase transition in the quench dynamics of a one-dimensional fermi gas with spin–orbit coupling, New J. Phys. 17, 013029 (2015)

[28] Y. Dong, L. Dong, M. Gong, and H. Pu, Dynamical phases in quenched spin–orbit-coupled degenerate Fermi gas, Nature Commun. 6, 6103 (2015)

[29] L. Kong, G. Fan, S.-G. Peng, X.-L. Chen, H. Zhao, and P. Zou, Dynamical generation of solitons in one dimensional Fermi superfluids with and without spin–orbit coupling, Phys. Rev. A 103, 063318 (2021)

[30] R. Wei and E. J. Mueller, Majorana fermions in onedimensional spin–orbit-coupled Fermi gases, Phys. Rev. A 86, 063604 (2012)

[31] M. A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, and M. Rigol, One dimensional bosons: From condensed matter systems to ultracold gases, Rev. Mod. Phys. 83, 1405 (2011)

[32] X.-W. Guan, M. T. Batchelor, and C. Lee, Fermi gases in one dimension: From Bethe ansatz to experiments, Rev. Mod. Phys. 85, 1633 (2013)

[33] M. Olshanii, Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons, Phys. Rev. Lett. 81, 938 (1998)

[34] E. Haller, M. Gustavsson, M. J. Mark, J. G. Danzl, R. Hart, G. Pupillo, and H.-C. Nägerl, Nägerl, Realization of an excited, strongly correlated quantum gas phase, Science 325, 1224 (2009)

[35] E. Haller, M. J. Mark, R. Hart, J. G. Danzl, L. Reichsöllner, V. Melezhik, P. Schmelcher, and H.-C. Nägerl, Confinement-induced resonances in low dimensional quantum systems, Phys. Rev. Lett. 104, 153203 (2010)

[36] S.-G. Peng, S. S. Bohloul, X.-J. Liu, H. Hu, and P. D. Drummond, Confinement-induced resonance in quasionedimensional systems under transversely anisotropic confinement, Phys. Rev. A 82, 063633 (2010)

[37] S.-G. Peng, H. Hu, X.-J. Liu, and P. D. Drummond, Confinement-induced resonances in anharmonic waveguides, Phys. Rev. A 84, 043619 (2011)

[38] S.-G. Peng, S. Tan, and K. Jiang, Manipulation of p-wave scattering of cold atoms in low dimensions using the magnetic field vector, Phys. Rev. Lett. 112, 250401 (2014)

[39] Y.-J. Lin, K. Jiménez-García, and I. B. Spielman, Spin–orbit-coupled Bose–Einstein condensates, Nature 471, 83 (2011)

[40] J.-Y. Zhang, S.-C. Ji, Z. Chen, L. Zhang, Z.-D. Du, B. Yan, G.-S. Pan, B. Zhao, Y.-J. Deng, H. Zhai, S. Chen, and J.-W. Pan, Collective dipole oscillations of a spin–orbit coupled Bose–Einstein condensate, Phys. Rev. Lett. 109, 115301 (2012)

[41] R. A. Williams, M. C. Beeler, L. J. LeBlanc, K. JiménezGarcía, and I. B. Spielman, Raman-induced interactions in a single-component Fermi gas near an s-wave Feshbach resonance, Phys. Rev. Lett. 111, 095301 (2013)

[42] C. Qu, C. Hamner, M. Gong, C. Zhang, and P. Engels, Observation of Zitterbewegung in a spin–orbit coupled Bose–Einstein condensate, Phys. Rev. A 88, 021604 (2013)

RIGHTS & PERMISSIONS

2022 Higher Education Press