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17 - Quantum Turbulence in Atomic Bose-Einstein Condensates

from Part III - Condensates in Atomic Physics

Published online by Cambridge University Press:  18 May 2017

By
N. G. Parker ,
A. J. Allen ,
C. F. Barenghi  and
N. P. Proukakis
Edited by
Nick P. Proukakis ,
David W. Snoke  and
Peter B. Littlewood
N. G. Parker
Affiliation:
Newcastle University, Newcastle upon Tyne
A. J. Allen
Affiliation:
Newcastle University, Newcastle upon Tyne
C. F. Barenghi
Affiliation:
Newcastle University, Newcastle upon Tyne
N. P. Proukakis
Affiliation:
Newcastle University, Newcastle upon Tyne
Nick P. Proukakis
Affiliation:
Newcastle University
David W. Snoke
Affiliation:
University of Pittsburgh
Peter B. Littlewood
Affiliation:
University of Chicago
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Summary

The past decade has seen atomic Bose-Einstein condensates emerge as a promising prototype system to explore the quantum mechanical form of turbulence, buoyed by a powerful experimental toolbox to control and manipulate the fluid, and the amenity to describe the system from first principles. This chapter presents an overview of this topic, from its history and fundamental motivations, its characteristics and key results to date, and finally to some promising future directions.

A Quantum Storm in a Teacup

A befitting title to this chapter could have been “a quantum storm in a teacup.” The storm refers to a turbulent state of a fluid, teeming with swirls and waves. Quantum refers to the fact that the fluid is not the classical viscous fluid of conventional storms but rather a quantum fluid in which viscosity is absent and the swirls are quantized. The quantum fluid in our story is a quantum-degenerate gas of bosonic atoms, an atomic Bose-Einstein condensate (BEC), formed at less than a millionth of a degree above absolute zero. And finally the teacup refers to the bowl-like potential used to confine the gas; this makes the fluid inherently inhomogeneous and finite-sized. A typical image of our quantum storm in a teacup is shown in Fig. 17.1a.

This chapter reviews quantum turbulence in atomic condensates, tracing its history (Section 17.2), introducing the main theoretical approach (Section 17.3) and the underyling quantum vortices (Section 17.4).We then turn to describing physical characteristics (Section 17.5), the experimental observations to date (Section 17.6), methods of generating turbulence (Section 17.7), and some exciting research directions (Section 17.8) before presenting an outlook (Section 17.9).

Origins

Turbulence refers to a highly agitated, disordered, and nonlinear fluid motion, characterized by the presence of eddies and energy across a range of length and time scales [3]. It occurs ubiquitously in nature, from blood flow and waterways to atmospheres and the interstellar medium, and is of practical importance in many industrial and engineering contexts. Since da Vinci's first scientific study of turbulent flow of water past obstacles, circa 1507, research into turbulence in classical viscous fluids continues with vigor; however, due to its rich complexities, the physical essence and mathematical description of turbulence remain a challenge.

Type
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Universal Themes of Bose-Einstein Condensation , pp. 348 - 370
Publisher: Cambridge University Press
Print publication year: 2017

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References

[1] White, A. C., Barenghi, C. F., Proukakis, N. P., Youd, A. J., and Wacks, D. H. 2010. Nonclassical velocity statistics in a turbulent atomic Bose-Einstein condensate. Phys. Rev. Lett., 104, 075301.Google Scholar
[2] Baggaley, A. W., Laurie, J., and Barenghi, C. F. 2012. Vortex-density fluctuations, energy spectra, and vortical regions in superfluid turbulence. Phys. Rev. Lett., 109, 205304.Google Scholar
[3] Frisch, U. 1995. Turbulence: The Legacy of Kolmogorov. Cambridge, UK: Cambridge University Press.
[4] Feynman, R. P. 1955. Application of quantum mechanics to liquid helium. Progress in Low Temperature Physics, 1, 17–53.Google Scholar
[5] Gorter, C. J. 1949. The two fluid model for helium II. Il Nuovo Cimento Series 9, 245–250.Google Scholar
[6] Donnelly, R. J., and Swanson, C. E. 2006. Quantum turbulence. J. Fluid Mech., 173, 387.Google Scholar
[7] Feynman, R., Leighton, R. B., and Sands, M. 1964. The Feynman Lectures on Physics. Boston, MA: Addison-Wesley.
[8] Vinen, W. F. 1957. Mutual friction in a heat current in liquid helium II. I. Experiments on steady heat currents. Proc. R. Soc. A, 240, 114–127.Google Scholar
[9] Maurer, J., and Tabeling, P. 1998. Local investigation of superfluid turbulence. Europhys. Lett., 43, 29.Google Scholar
[10] Salort, J., Baudet, C., Castaing, B., Chabaud, B., Daviaud, F., Didelot, T., Diribarne, P., Dubrulle, B., Gagne, Y., Gauthier, F., Girard, A., Hbral, B., Rousset, B., Thibault, P., and Roche, P.-E. 2010. Turbulent velocity spectra in superfluid flows. Phys. Fluids, 22, 125102.Google Scholar
[11] Skrbek, L. 2011. Quantum turbulence. J. Phys. Conf. Ser., 318, 012004.Google Scholar
[12] Barenghi, C. F., Skrbek, L., and Sreenivasan, K. R. 2014. Introduction to quantum turbulence. Proc. Nat. Acad. Sci., 111(Supplement 1), 4647–4652.Google Scholar
[13] Kerr, R. M. 2011. Vortex stretching as a mechanism for quantum kinetic energy decay. Phys. Rev. Lett., 106, 224501.Google Scholar
[14] Baggaley, A. W., Barenghi, C. F., and Sergeev, Y. A. 2014. Three-dimensional inverse energy transfer induced by vortex reconnections. Phys. Rev. E, 89, 013002.Google Scholar
[15] Walmsley, P. M., and Golov, A. I. 2008. Quantum and quasiclassical types of superfluid turbulence. Phys. Rev. Lett., 100, 245301.Google Scholar
[16] Baggaley, A. W., Barenghi, C. F., and Sergeev, Y. A. 2012. Quasiclassical and ultraquantum decay of superfluid turbulence. Phys. Rev. B, 85, 060501.Google Scholar
[17] Guo, W., Cahn, S. B., Nikkel, J. A., Vinen, W. F., and McKinsey, D. N. 2010. Visualization study of counterflow in superfluid 4He using metastable helium molecules. Phys. Rev. Lett., 105, 045301.Google Scholar
[18] Bradley, D. I., Fisher, S. N., Guenault, A. M., Haley, R. P., Pickett, G. R., Potts, D., and Tsepelin, V. 2011. Direct measurement of the energy dissipated by quantum turbulence. Nat. Phys., 7, 473.Google Scholar
[19] Hosio, J. J., Eltsov, V. B., Heikkinen, P. J., Hänninen, R., Krusius, M., and L'vov, V. S. 2013. Energy and angular momentum balance in wall-bounded quantum turbulence at very low temperatures. Nat. Comm., 4, 1614.Google Scholar
[20] Krstulovic, G. 2012. Kelvin-wave cascade and dissipation in low-temperature superfluid vortices. Phys. Rev. E, 86, 055301.Google Scholar
[21] Kozik, E., and Svistunov, B. 2004. Kelvin-wave cascade and decay of superfluid turbulence. Phys. Rev. Lett., 92, 035301.Google Scholar
[22] Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E., and Cornell, E. A. 1995. Observation of Bose-Einstein condensation in a dilute atomic vapor. Science, 269, 198.Google Scholar
[23] Davis, K. B., Mewes, M. O., Andrews, M. R., van Druten, N. J., Durfee, D. S., Kurn, D. M., and Ketterle, W. 1995. Bose-Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett., 75, 3969.Google Scholar
[24] Inouye, S., Andrews, M. R., Stenger, J., Miesner, H.-J., Stamper-Kurn, D. M., and Ketterle, W. 1998. Observation of Feshbach resonances in a Bose-Einstein condensate. Nature, 392, 151.Google Scholar
[25] Henderson, K., Ryu, C., MacCormick, C., and Boshier, M. G. 2009. Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates. New J. Phys., 11, 043030.Google Scholar
[26] Görlitz, A., Vogels, J. M., Leanhardt, A. E., Raman, C., Gustavson, T. L., Abo-Shaeer, J. R., Chikkatur, A. P., Gupta, S., Inouye, S., Rosenband, T., and Ketterle, W. 2001. Realization of Bose-Einstein condensates in lower dimensions. Phys. Rev. Lett., 87, 130402.Google Scholar
[27] Kevrekidis, P. G., Frantzeskakis, D. J., and Carretero-Gonzalez, R. (eds). 2008. Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment. Berlin, Germany: Springer.
[28] Tsubota, M., Kobayashi, M., and Takeuchi, H. 2013. Quantum hydrodynamics. Phys. Rep., 522, 192–238.Google Scholar
[29] Allen, A. J., Parker, N. G., Proukakis, N. P., and Barenghi, C. F. 2014. Quantum turbulence in atomic Bose-Einstein condensates. J. Phys.: Conf. Ser., 544, 012023.Google Scholar
[30] White, A. C., Anderson, B. P., and Bagnato, V. S. 2014. Vortices and turbulence in trapped atomic condensates. Proc. Nat. Acad. Sci., 111(Supplement 1), 4719–4726.Google Scholar
[31] Berloff, N. G., and Svistunov, B. V. 2002. Scenario of strongly nonequilibrated Bose- Einstein condensation. Phys. Rev. A, 66, 013603.Google Scholar
[32] Parker, N. G., and Adams, C. S. 2005. Emergence and decay of turbulence in stirred atomic Bose-Einstein condensates. Phys. Rev. Lett., 95, 145301.Google Scholar
[33] Kobayashi, M., and Tsubota, M. 2007. Quantum turbulence in a trapped Bose- Einstein condensate. Phys. Rev. A, 76, 045603.Google Scholar
[34] Tsubota, M., and Kobayashi, M. 2008. Quantum turbulence in trapped atomic Bose- Einstein condensates. J. Low Temp. Phys., 150, 402–409.Google Scholar
[35] Henn, E., Seman, J., Roati, G., Magalhatidle;es, K., and Bagnato, V. 2009. Emergence of turbulence in an oscillating Bose-Einstein condensate. Phys. Rev. Lett., 103, 045301.Google Scholar
[36] Neely, T. W., Samson, E. C., Bradley, A. S., Davis, M. J., and Anderson, B. P. 2010. Observation of vortex dipoles in an oblate Bose-Einstein condensate. Phys. Rev. Lett., 104, 160401.Google Scholar
[37] Kwon, W. J., Moon, G., Choi, J., Seo, S. W., and Shin, Y. 2014. Relaxation of superfluid turbulence in highly oblate Bose-Einstein condensates. Phys. Rev. A, 90, 063627.Google Scholar
[38] Pethick, C. J., and Smith, H. 2002. Bose-Einstein Condensation in Dilute Gases. Cambridge, UK: Cambridge University Press.
[39] Dalfovo, Franco, Giorgini, Stefano, Pitaevskii, Lev P., and Stringari, Sandro. 1999. Theory of Bose-Einstein condensation in trapped gases. Rev. Mod. Phys., 71, 463–512.Google Scholar
[40] Proukakis, Nick P., and Jackson, Brian. 2008. Finite-temperature models of Bose- Einstein condensation. J. Phys. B, 41, 203002.Google Scholar
[41] Blakie, P. B., Bradley, A. S., Davis, M. J., Ballagh, R. J., and Gardiner, C. W. 2008. Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques. Adv. Phys., 57, 363–455.Google Scholar
[42] Proukakis, N. P., Gardiner, S. A., Davis, M. J., and Szymańska, M. H. (eds). 2013. Quantum Gases: Finite Temperature and Non-Equilibrium Dynamics. London, UK: Imperial College Press.
[43] Berloff, N. G., Brachet, M., and Proukakis, N. P. 2014. Modeling quantum fluid dynamics at nonzero temperatures. Proc. Nat. Acad. Sci., 111(Supplement 1), 4675–4682.Google Scholar
[44] Berloff, Natalia G., and Roberts, Paul H. 1999. Motions in a Bose condensate: VI. Vortices in a nonlocal model. J. Phys. A, 32, 5611.Google Scholar
[45] Kuchemann, D. 1965. Report on the I.U.T.A.M symposium on concentrated vortex motions in fluids. J. Fluid Mech., 21, 1–20.Google Scholar
[46] Leanhardt, A. E., Görlitz, A., Chikkatur, A. P., Kielpinski, D., Shin, Y., Pritchard, D. E., and Ketterle, W. 2002. Imprinting vortices in a Bose-Einstein condensate using topological phases. Phys. Rev. Lett., 89, 190403.Google Scholar
[47] Middelkamp, S., Torres, P. J., Kevrekidis, P. G., Frantzeskakis, D. J., Carretero- González, R., Schmelcher, P., Freilich, D. V., and Hall, D. S. 2011. Guiding-center dynamics of vortex dipoles in Bose-Einstein condensates. Phys. Rev. A, 84, 011605.Google Scholar
[48] Aref, H. 2007. Point vortex dynamics: a classical mathematics playground. J. Math. Phys., 48, 065401.Google Scholar
[49] Jackson, B., Proukakis, N. P., Barenghi, C. F., and Zaremba, E. 2009. Finitetemperature vortex dynamics in Bose-Einstein condensates. Phys. Rev. A, 79, 053615.Google Scholar
[50] Rooney, S. J., Bradley, A. S., and Blakie, P. B. 2010. Decay of a quantum vortex: test of nonequilibrium theories for warm Bose-Einstein condensates. Phys. Rev. A, 81, 023630.CrossRefGoogle Scholar
[51] Allen, A. J., Zaremba, E., Barenghi, C. F., and Proukakis, N. P. 2013. Observable vortex properties in finite-temperature Bose gases. Phys. Rev. A, 87, 013630.Google Scholar
[52] Gautam, S., Roy, Arko, and Mukerjee, Subroto. 2014. Finite-temperature dynamics of vortices in Bose-Einstein condensates. Phys. Rev. A, 89, 013612.Google Scholar
[53] Thompson, L., and Stamp, P. C. E. 2012. Quantum dynamics of a Bose superfluid vortex. Phys. Rev. Lett., 108, 184501.Google Scholar
[54] Madison, K. W., Chevy, F., Wohlleben, W., and
Dalibard|J. 2000. Vortex formation in a stirred Bose-Einstein condensate. Phys. Rev. Lett., 84, 806–809.
[55] Freilich, D. V., Bianchi, D.M., Kaufman, A. M., Langin, T. K., and Hall, D. S. 2010. Real-time dynamics of single vortex lines and vortex dipoles in a Bose-Einstein condensate. Science, 329, 1182.Google Scholar
[56] Kwon, W. J., Seo, S. W., and Shin, Y. 2015. Periodic shedding of vortex dipoles from a moving penetrable obstacle in a Bose-Einstein condensate. Phys. Rev. A, 92, 033613.Google Scholar
[57] Anderson, B. P., Haljan, P. C., Regal, C. A., Feder, D. L., Collins, L. A., Clark, C. W., and Cornell, E. A. 2001. Watching dark solitons decay into vortex rings in a Bose-Einstein condensate. Phys. Rev. Lett., 86, 2926–2929.Google Scholar
[58] Hodby, E., Hechenblaikner, G. A., Hopkins, S. M., Marago, O., and Foot, C. J. 2001. Vortex nucleation in Bose-Einstein condensates in an oblate, purely magnetic potential. Phys. Rev. Lett., 88, 010405.Google Scholar
[59] Abo-Shaeer, J. R., Raman, C., Vogels, J. M., and Ketterle, W. 2001. Observation of vortex lattices in Bose-Einstein condensates. Science, 292, 476.Google Scholar
[60] Neely, T. W., Bradley, A. S., Samson, E. C., Rooney, S. J., Wright, E. M., Law, K. J. H., Carretero-González, R., Kevrekidis, P. G., Davis, M. J., and Anderson, B. P. 2013. Characteristics of two-dimensional quantum turbulence in a compressible superfluid. Phys. Rev. Lett., 111, 235301.Google Scholar
[61] Kibble, T. W. B. 1976. Topology of cosmic domains and strings. J. Physics A, 9, 1387.Google Scholar
[62] Zurek, W. H. Cosmological experiments in superfluid helium? Nature, 317.
[63] Weiler, C. N., Neely, T. W., Scherer, D. R., Bradley, A. S., Davis, M. J., and Anderson, B. P. 2008. Spontaneous vortices in the formation of Bose-Einstein condensates. Nature, 455, 948.Google Scholar
[64] Raman, C., Abo-Shaeer, J. R., Vogels, J. M., Xu, K., and Ketterle, W. 2001. Vortex nucleation in a stirred Bose-Einstein condensate. Phys. Rev. Lett., 87, 210402.Google Scholar
[65] Kwon, W. J., Moon, G., Seo, S. W., and Shin, Y. 2015. Critical velocity for vortex shedding in a Bose-Einstein condensate. Phys. Rev. A, 91, 053615.Google Scholar
[66] Powis, A. T., Sammut, S. J., and Simula, T. P. 2014. Vortex gyroscope imaging of planar superfluids. Phys. Rev. Lett., 113, 165303.Google Scholar
[67] Nore, C., Abid, M., and Brachet, M. E. 1997. Decaying Kolmogorov turbulence in a model of superflow. Phys. Fluids, 9, 2644.Google Scholar
[68] Kobayashi, M., and Tsubota, M. 2005. Kolmogorov spectrum of superfluid turbulence: numerical analysis of the Gross-Pitaevskii equation with a small-scale dissipation. Phys. Rev. Lett., 94, 065302.Google Scholar
[69] Yepez, J., Vahala, G., Vahala, L., and Soe, M. 2009. Superfluid turbulence from quantum Kelvin wave to classical Kolmogorov cascades. Phys. Rev. Lett., 103, 084501.Google Scholar
[70] Paoletti, M. S., Fisher, Michael E., Sreenivasan, K. R., and Lathrop, D.P. 2008. Velocity statistics distinguish quantum turbulence from classical turbulence. Phys. Rev. Lett., 101, 154501.Google Scholar
[71] Baggaley, A.W., and Barenghi, C.F. 2011. Quantum turbulent velocity statistics and quasiclassical limit. Phys. Rev. E, 84, 067301.Google Scholar
[72] Mantia, M. La, and Skrbek, L. 2014. Quantum, or classical turbulence? Europhys. Lett., 105, 46002.Google Scholar
[73] Proment, D., Nazarenko, S., and Onorato, M. 2009. Quantum turbulence cascades in the Gross-Pitaevskii model. Phys. Rev. A, 80, 051603.Google Scholar
[74] Gaunt, A. L., Schmidutz, T. F., Gotlibovych, I., Smith, R. P., and Hadzibabic, Z. 2013. Bose-Einstein condensation of atoms in a uniform potential. Phys. Rev. Lett., 110, 200406.Google Scholar
[75] Kraichnan, R. H., and Montgomery, D. 1980. Two-dimensional turbulence. Rep. Prog. Phys., 43, 547.Google Scholar
[76] Boffetta, G., and Ecke, R.E. 2012. Two-dimensional turbulence. Annu. Rev. Fluid Mech., 44, 427–451.Google Scholar
[77] Reeves, M. T., Billam, T. P., Anderson, B. P., and Bradley, A. S. 2013. Inverse energy cascade in forced two-dimensional quantum turbulence. Phys. Rev. Lett., 110, 104501.Google Scholar
[78] Reeves, M. T., Billam, T. P., Anderson, B. P., and Bradley, A. S. 2014. Signatures of coherent vortex structures in a disordered two-dimensional quantum fluid. Phys. Rev. A, 89, 053631.Google Scholar
[79] Bradley, A. S., and Anderson, B. P. 2012. Energy spectra of vortex distributions in two-dimensional quantum turbulence. Phys. Rev. X, 2, 041001.Google Scholar
[80] Nazarenko, Sergey, and Onorato, Miguel. 2006. Wave turbulence and vortices in Bose-Einstein condensation. Physica D, 219, 1–12.Google Scholar
[81] Reeves, M. T., Anderson, B. P., and Bradley, A. S. 2012. Classical and quantum regimes of two-dimensional turbulence in trapped Bose-Einstein condensates. Phys. Rev. A, 8686, 053621.Google Scholar
[82] Barenghi, C. F., Parker, N. G., Proukakis, N. P., and Adams, C. S. 2005. Decay of quantised vorticity by sound emission. J. Low Temp. Phys., 138, 629–634.Google Scholar
[83] Zuccher, S., Caliari, M., Baggaley, A.W., and Barenghi, C. F. 2012. Quantum vortex reconnections. Phys. Fluids, 24, 125108.Google Scholar
[84] Parker, N. G., Proukakis, N. P., Barenghi, C. F., and Adams, C. S. 2004. Controlled vortex-sound interactions in atomic Bose-Einstein condensates. Phys. Rev. Lett., 92, 160403.Google Scholar
[85] Leadbeater, M., Winiecki, T., Samuels, D. C., Barenghi, C. F., and Adams, C. S. 2001. Sound emission due to superfluid vortex reconnections. Phys. Rev. Lett., 86, 1410–1413.Google Scholar
[86] Allen, A. J., Zuccher, S., Caliari, M., Proukakis, N. P., Parker, N. G., and Barenghi, C. F. 2014. Vortex reconnections in atomic condensates at finite temperature. Phys. Rev. A, 90, 013601.Google Scholar
[87] Bewley, G. P., Paoletti, M. S., Sreenivasan, K. R., and Lathrop, D. P. 2008. Characterization of reconnecting vortices in superfluid helium. Proc. Nat. Acad. Sci., 105, 13707–13710.Google Scholar
[88] Vinen, W. F. 2001. Decay of superfluid turbulence at a very low temperature: the radiation of sound from a Kelvin wave on a quantized vortex. Phys. Rev. B, 64, 134520.Google Scholar
[89] Arovas, D. P., and Freire, J. A. 1997. Dynamical vortices in superfluid films. Phys. Rev. B, 55, 1068–1080.Google Scholar
[90] Parker, N. G., Allen, A. J., Barenghi, C. F., and Proukakis, N. P. 2012. Coherent cross talk and parametric driving of matter-wave vortices. Phys. Rev. A, 86, 013631.Google Scholar
[91] Lucas, A., and Surówka, P. 2014. Sound-induced vortex interactions in a zerotemperature two-dimensional superfluid. Phys. Rev. A, 90, 053617.Google Scholar
[92] Parker, N. G., van Bijnen, R. M. W., and Martin, A. M. 2006. Instabilities leading to vortex lattice formation in rotating Bose-Einstein condensates. Phys. Rev. A, 7373, 061603.Google Scholar
[93] Lamporesi, G., Donadello, S., Serafini, S., Dalfovo, F., and Ferrari, G. 2013. Spontaneous creation of Kibble-Zurek solitons in a Bose-Einstein condensate. Nat. Phys., 9, 656.Google Scholar
[94] Caracanhas, M., Fetter, A. L., Muniz, S. R., Magalhes, K. M. F., Roati, G., Bagnato, G., and Bagnato, V. S. 2012. Self-similar expansion of the density profile in a turbulent Bose-Einstein condensate. J. Low Temp. Phys., 166, 49–58.Google Scholar
[95] Thompson, K. J., Bagnato, G. G., Telles, G. D., Caracanhas, M. A., dos Santos, F. E. A., and Bagnato, V. S. 2014. Evidence of power law behavior in the momentum distribution of a turbulent trapped Bose-Einstein condensate. Laser Phys. Lett., 11, 015501.Google Scholar
[96] Frisch, T., Pomeau, Y., and Rica, S. 1992. Transition to dissipation in a model of superflow. Phys. Rev. Lett., 69, 1644–1647.Google Scholar
[97] Stagg, G. W., Allen, A. J., Barenghi, C. F., and Parker, N. G. 2015a. Classical-like wakes past elliptical obstacles in atomic Bose-Einstein condensates. J. Phys. Conf. Ser., 594, 012044.Google Scholar
[98] Stagg, G. W., Allen, A. J., Parker, N. G., and Barenghi, C. F. 2015b. Generation and decay of two-dimensional quantum turbulence in a trapped Bose-Einstein condensate. Phys. Rev. A, 91, 013612.Google Scholar
[99] Allen, A. J., Parker, N. G., Proukakis, N. P., and Barenghi, C. F. 2014. Isotropic vortex tangles in trapped atomic Bose-Einstein condensates via laser stirring. Phys. Rev., 89, 025602.Google Scholar
[100] Stagg, G. W., Parker, N. G., and Barenghi, C. F. 2014. Quantum analogues of classical wakes in Bose-Einstein condensates. J. Phy. B, 47, 095304.Google Scholar
[101] Brachmann, J. F. S., Bakr, W. S., Gillen, J., Peng, A., and Greiner, M. 2011. Inducing vortices in a Bose-Einstein condensate using holographically produced light beams. Opt. Express, 19, 12984–12991.Google Scholar
[102] Horng, T.-L., Hsueh, C.-H., and Gou, S.-C. 2008. Transition to quantum turbulence in a Bose-Einstein condensate through the bending-wave instability of a singlevortex ring. Phys. Rev. A, 77, 063625.Google Scholar
[103] Horng, T.-L., Hsueh, C.-H., Su, S.-W., Kao, Y.-M., and Gou, S.-C. 2009. Two dimensional quantum turbulence in a nonuniform Bose-Einstein condensate. Phys. Rev. A, 80, 023618.Google Scholar
[104] Schweikhard, V., Coddington, I., Engels, P., Tung, S., and Cornell, E. A. 2004. Vortex-lattice dynamics in rotating spinor Bose-Einstein condensates. Phys. Rev. Lett., 93, 210403.Google Scholar
[105] Wright, T. M., Ballagh, R. J., Bradley, A. S., Blakie, P. B., and Gardiner, C. W. 2008. Dynamical thermalization and vortex formation in stirred two-dimensional Bose-Einstein condensates. Phys. Rev. A, 78, 063601.Google Scholar
[106] White, A. C., Barenghi, C. F., and Proukakis, N. P. 2012. Creation and characterization of vortex clusters in atomic Bose-Einstein condensates. Phys. Rev. A, 86, 013635.Google Scholar
[107] Cidrim, A., dos Santos, F. E. A., Galantucci, L., Bagnato, V. S., and Barenghi, C.F. 2016. Controlled polarization of two-dimensional quantum turbulence in atomic Bose-Einstein condensates. Phys. Rev. A, 93, 033651.Google Scholar
[108] Stagg, G. W., Pattinson, R. W., Barenghi, C. F., and Parker, N. G. 2016. Critical velocity for vortex nucleation in a finite-temperature Bose gas. Phys. Rev. A, 93, 023640.Google Scholar
[109] Griesmaier, A., Werner, J., Hensler, S., Stuhler, J., and Pfau, T. 2005. Bose-Einstein condensation of chromium. Phys. Rev. Lett., 94, 160401.Google Scholar
[110] Lu, M., Burdick, N. Q., Youn, S. H., and Lev, B. L. 2011. Strongly dipolar Bose- Einstein condensate of dysprosium. Phys. Rev. Lett., 107, 190401.Google Scholar
[111] Aikawa, K., Frisch, A., Mark, M., Baier, S., Rietzler, A., Grimm, R., and Ferlaino, F. 2012. Bose-Einstein condensation of erbium. Phys. Rev. Lett., 108, 210401.Google Scholar
[112] Lahaye, T., Menotti, C., Santos, L., Lewenstein, M., and Pfau, T. 2009. The physics of dipolar bosonic quantum gases. Rep. Prog. Phys., 72, 126401.Google Scholar
[113] Mulkerin, B. C., van Bijnen, R. M. W., O'Dell, D. H. J., Martin, A. M., and Parker, N. G. 2013. Anisotropic and long-range vortex interactions in two-dimensional dipolar Bose gases. Phys. Rev. Lett., 111, 170402.Google Scholar
[114] Mulkerin, B. C., O'Dell, D. H. J., Martin, A. M., and Parke, N. G. 2014. Vortices in the two-dimensional dipolar Bose gas. J. Phys. Conf. Ser., 497, 012025.Google Scholar
[115] Pattinson, R. W., Proukakis, N. P., and Parker, N. G. In preparation. Quantum turbulence via repeated interspecies interaction quenches of a binary Bose gas at finite temperature.
[116] Eyink, Gregory L., and Sreenivasan, Katepalli R. 2006. Onsager and the theory of hydrodynamic turbulence. Rev. Mod. Phys., 78, 87–135.Google Scholar
[117] Billam, T. P., Reeves, M. T., Anderson, B. P., and Bradley, A. S. 2014. Onsager- Kraichnan condensation in decaying two-dimensional quantum turbulence. Phys. Rev. Lett., 112, 145301.Google Scholar
[118] Simula, T., Davis, M. J., and Helmerson, K. 2014. Emergence of order from turbulence in an isolated planar superfluid. Phys. Rev. Lett., 113, 165302.Google Scholar
[119] Takeuchi, H., Ishino, S., and Tsubota, M. 2010. Binary quantum turbulence arising from countersuperflow instability in two-component Bose-Einstein condensates. Phys. Rev. Lett., 105, 205301.Google Scholar
[120] Kobyakov, D., Bezett, A., Lundh, E., Marklund, M., and Bychkov, V. 2014. Turbulence in binary Bose-Einstein condensates generated by highly nonlinear Rayleigh-Taylor and Kelvin-Helmholtz instabilities. Phys. Rev. A, 89, 013631.Google Scholar
[121] Karl, M., Nowak, B., and Gasenzer, T. 2013. Tuning universality far from equilibrium. Sci. Rep., 3, 2394.Google Scholar
[122] Kasamatsu, K., Tsubota, M., and Ueda, M. 2005. Vortices in multicomponent Bose- Einstein condensates. Int. J. Mod. Phys. B, 19, 1835–1904.Google Scholar
[123] Stamper-Kurn, D. M., and Ueda, M. 2013. Spinor Bose gases: symmetries, magnetism, and quantum dynamics. Rev. Mod. Phys., 85, 1191–1244.Google Scholar
[124] Fujimoto, K., and Tsubota, M. 2012. Counterflow instability and turbulence in a spin-1 spinor Bose-Einstein condensate. Phys. Rev. A, 85, 033642.Google Scholar
[125] Fujimoto, K., and Tsubota, M. 2014. Spin-superflow turbulence in spin-1 ferromagnetic spinor Bose-Einstein condensates. Phys. Rev. A, 90, 013629.Google Scholar
[126] Berloff, N. G. 2010. Turbulence in exciton-polariton condensates. arXiv:1010.5225.

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