Cyclotron dynamics of a Bose–Einstein condensate in a quadruple-well potential with synthetic gauge fields

Abstract

We investigate the cyclotron dynamics of Bose–Einstein condensate (BEC) in a quadruple-well potential with synthetic gauge fields. We use laser-assisted tunneling to generate large tunable effective magnetic fields for BEC. The mean position of BEC follows an orbit that simulated the cyclotron orbits of charged particles in a magnetic field. In the absence of atomic interaction, atom dynamics may exhibit periodic or quasi-periodic cyclotron orbits. In the presence of atomic interaction, the system may exhibit self-trapping, which depends on synthetic gauge fields and atomic interaction strength. In particular, the competition between synthetic gauge fields and atomic interaction leads to the generation of several discontinuous parameter windows for the transition to self-trapping, which is obviously different from that without synthetic gauge fields.

Graphical abstract

Keywords

cyclotron dynamics / Bose–Einstein condensate / quadruple-well potential / synthetic gauge fields

References

[1] I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80(3), 885 (2008)

[2] M. Z. Hasan and C. L. Kane, Topological insulators, Rev. Mod. Phys. 82(4), 3045 (2010)

[3] Q. Niu, Advances on topological materials, Front. Phys. 15(4), 43601 (2020)

[4] M. Yang, X. L. Zhang, and W. M. Liu, Tunable topological quantum statesin three- and two-dimensional materials, Front. Phys. 10(2), 161 (2015)

[5] K. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45(6), 494 (1980)

[6] D. C. Tsui, H. L. Stormer, and A. C. Gossard, Twodimensional magnetotransport in the extreme quantum limit, Phys. Rev. Lett. 48(22), 1559 (1982)

[7] R. B. Laughlin, Anomalous quantum hall effect: An incompressible quantum fluid with fractionally charged excitations, Phys. Rev. Lett. 50(18), 1395 (1983)

[8] D. Jaksch and P. Zoller, Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms, New J. Phys. 5, 56 (2003)

[9] N. Goldman, G. Juzeliūnas, P. Öhberg, and I. B. Spielman, Light-induced gauge fields for ultracold atoms, Rep. Prog. Phys. 77(12), 126401 (2014)

[10] F. Schäfer, T. Fukuhara, S. Sugawa, Y. Takasu, and Y. Takahashi, Tools for quantum simulation with ultracold atoms in optical lattices, Nat. Rev. Phys. 2(8), 411 (2020)

[11] D. W. Zhang, Z. D. Wang, and S. L. Zhu, Relativistic quantum effects of Dirac particles simulated by ultracold atoms, Front. Phys. 7(1), 31 (2012)

[12] A. L. Fetter, Rotating trapped Bose–Einstein condensates, Rev. Mod. Phys. 81(2), 647 (2009)

[13] J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Artificial gauge potentials for neutral atoms, Rev. Mod. Phys. 83(4), 1523 (2011)

[14] I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86(1), 153 (2014)

[15] N. R. Cooper, J. Dalibard, and I. B. Spielman, Topological bands for ultracold atoms, Rev. Mod. Phys. 91(1), 015005 (2019)

[16] K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, Vortex formation in a stirred Bose–Einstein condensate, Phys. Rev. Lett. 84(5), 806 (2000)

[17] J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, Observation of vortex lattices in Bose–Einstein condensates, Science 292(5516), 476 (2001)

[18] S. Tung, V. Schweikhard, and E. A. Cornell, Observation of vortex pinning in Bose–Einstein condensates, Phys. Rev. Lett. 97(24), 240402 (2006)

[19] R. A. Williams, S. Al-Assam, and C. J. Foot, Observation of vortex nucleation in a rotating two-dimensional lattice of Bose–Einstein condensates, Phys. Rev. Lett. 104(5), 050404 (2010)

[20] N. R. Cooper, Rapidly rotating atomic gases, Adv. Phys. 57(6), 539 (2008)

[21] M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y. A. Chen, and I. Bloch, Experimental realization of strong effective magnetic fields in an optical lattice, Phys. Rev. Lett. 107(25), 255301 (2011)

[22] H. Miyake, G. A. Siviloglou, C. J. Kennedy, W. C. Burton, and W. Ketterle, Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices, Phys. Rev. Lett. 111(18), 185302 (2013)

[23] M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices, Phys. Rev. Lett. 111(18), 185301 (2013)

[24] M. Aidelsburger, M. Atala, S. Nascimbene, S. Trotzky, Y. A. Chen, and I. Bloch, Experimental realization of strong effective magnetic fields inoptical superlattice potentials, Appl. Phys. B 113(1), 1 (2013)

[25] M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, Observation of chiral edge states with neutral fermions in synthetic Hall ribbons, Science 349(6255), 1510 (2015)

[26] B. K. Stuhl, H. I. Lu, L. M. Aycock, D. Genkina, and I. B. Spielman, Visualizing edge states with an atomic Bose gas in the quantum Hall regime, Science 349(6255), 1514 (2015)

[27] A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, Optical atomic clocks, Rev. Mod. Phys. 87(2), 637 (2015)

[28] A. R. Kolovsky, Creating artificial magnetic fields for cold atoms by photon-assisted tunneling, Europhys. Lett. 93(2), 20003 (2011)

[29] J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Windpassinger, Tunable gauge potential for neutral and spinless particles in driven optical lattices, Phys. Rev. Lett. 108(22), 225304 (2012)

[30] G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, Experimental realization of the topological Haldane model with ultracold fermions, Nature 515(7526), 237 (2014)

[31] L. W. Clark, B. M. Anderson, L. Feng, A. Gaj, K. Levin, and C. Chin, Observation of density-dependent gauge fields in a Bose–Einstein condensate based on micromotion control in a shaken two-dimensional lattice, Phys. Rev. Lett. 121(3), 030402 (2018)

[32] C. Schweizer, F. Grusdt, M. Berngruber, L. Barbiero, E. Demler, N. Goldman, I. Bloch, and M. Aidelsburger, Floquet approach to Z₂ lattice gauge theories with ultracold atoms in optical lattices, Nat. Phys. 15(11), 1168 (2019)

[33] F. Görg, K. Sandholzer, J. Minguzzi, R. Desbuquois, M. Messer, and T. Esslinger, Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter, Nat. Phys. 15(11), 1161 (2019)

[34] V. Lienhard, P. Scholl, S. Weber, D. Barredo, S. de Léséleuc, R. Bai, N. Lang, M. Fleischhauer, H. P. Büchler, T. Lahaye, and A. Browaeys, Realization of a densitydependent Peierls phase in a synthetic, spin–orbit coupled Rydberg system, Phys. Rev. X 10(2), 021031 (2020)

[35] C. J. Kennedy, W. C. Burton, W. C. Chung, and W. Ketterle, Observation of Bose–Einstein condensation in a strong synthetic magnetic field, Nat. Phys. 11(10), 859 (2015)

[36] G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, Quantum dynamics of an atomic Bose–Einstein condensate in a double-well potential, Phys. Rev. A 55(6), 4318 (1997)

[37] A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, Quantum coherent atomic tunneling between two trapped Bose–Einstein condensates, Phys. Rev. Lett. 79(25), 4950 (1997)

[38] M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction, Phys. Rev. Lett. 95(1), 010402 (2005)

[39] B. Wang, P. Fu, J. Liu, and B. Wu, Self-trapping of Bose–Einstein condensates in optical lattices, Phys. Rev. A 74(6), 063610 (2006)

[40] L. J. LeBlanc, A. B. Bardon, J. McKeever, M. H. T. Extavour, D. Jervis, J. H. Thywissen, F. Piazza, and A. Smerzi, Dynamics of a tunable superfluid junction, Phys. Rev. Lett. 106(2), 025302 (2011)

[41] P. G. Harper, Single band motion of conduction electronsin a uniform magnetic field, Proc. Phys. Soc. A 68(10), 874 (1955)

[42] D. R. Hofstadter, Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev. B 14(6), 2239 (1976)

[43] A. X. Zhang, Y. Zhang, Y. F. Jiang, Z. F. Yu, L. X. Cai, and J. K. Xue, Cyclotron dynamics of neutral atoms in optical lattices with additional magnetic field and harmonic trap potential, Chin. Phys. B 29(1), 010307 (2020)

[44] J. Liu, L. Fu, B. Y. Ou, S. G. Chen, D. I. Choi, B. Wu, and Q. Niu, Theory of nonlinear Landau–Zener tunneling, Phys. Rev. A 66(2), 023404 (2002)

[45] D. F. Ye, L. B. Fu, and J. Liu, Rosen–Zener transition in a nonlinear two-level system, Phys. Rev. A 77(1), 013402 (2008)

[46] G. F. Wang, L. B. Fu, and J. Liu, Periodic modulation effect on self-trapping of two weakly coupled Bose–Einstein condensates, Phys. Rev. A 73(1), 013619 (2006)

[47] J. Liu, L. B. Fu, B. Liu, and B. Wu, Role of particle interactions in the Feshbach conversion of fermionic atoms to bosonic molecules, New J. Phys. 10(12), 123018 (2008)

[48] J. Liu, B. Liu, and L. B. Fu, Many-body effects on nonadiabatic Feshbach conversion in bosonic systems, Phys. Rev. A 78(1), 013618 (2008)

[49] S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, Coherent oscillations between two weakly coupled Bose–Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping, Phys. Rev. A 59(1), 620 (1999)

[50] L. Fu and J. Liu, Quantum entanglement manifestation of transition to nonlinear self-trapping for Bose–Einstein condensates in a symmetric double well, Phys. Rev. A 74(6), 063614 (2006)

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