Skip to main content Accessibility help
×
Hostname: page-component-7c8c6479df-5xszh Total loading time: 0 Render date: 2024-03-28T18:09:27.508Z Has data issue: false hasContentIssue false

24 - Collective Topological Excitations in 1D Polariton Quantum Fluids

from Part IV - Condensates in Condensed Matter Physics

Published online by Cambridge University Press:  18 May 2017

H. Terças
Affiliation:
University of Innsbruck
D. D. Solnyshkov
Affiliation:
Clermont Université, Blaise Pascal University
G. Malpuech
Affiliation:
Clermont Université, Blaise Pascal University
Nick P. Proukakis
Affiliation:
Newcastle University
David W. Snoke
Affiliation:
University of Pittsburgh
Peter B. Littlewood
Affiliation:
University of Chicago
Get access

Summary

We discuss some recent advances in the spin dynamics in photonic systems and polariton superfluids. In particular, we describe how the spin degree of freedom affects the collective behaviour of the half-soliton gas. First, we demonstrate that the anisotropy in the intra- and interspin interaction leads to the formation of a one-dimensional ordered phase: the topologicalWigner crystal. Second, we show that half-solitons behave as magnetic monopoles in effective magnetic fields. We study the transport properties and demonstrate a deviation from the usual Ohm's law for moderate values of the magnetic field.

Introduction

Photonic systems offer great opportunities for the study of quantum fluids, due to the possibility of creation of macroscopically occupied states with well-controlled properties by coherent excitation with lasers, and the full access to the wavefunction of the quantum fluid by well-established optical methods [1]. The main distinctive feature of quantum fluids as compared with classical ones are the topological defects, which, once created, cannot be removed by a continuous transformation. The most well-known example of such defect is a quantum vortex, which can appear in two-dimensional (2D) and three-dimensional (3D) systems. Its analog in one-dimensional (1D) Bose-Einstein condensates (BECs) is a soliton [2]. In fact, solitons are ubiquitous in systems described by the self-defocussing nonlinear Schrödinger equations. Specifically, for Bose gases, they are associated with the excitations of type II of the Lieb and Liniger theory. Spinor BECs (particularly with two pseudospin projections) offer a plethora of nonlinear spin effects, including half-integer topological defects possible in BECs with spin-anisotropic interactions [3]. Recent experimental work reports on the emergent monopole behaviour of half-solitons in the presence of an effective magnetic field [4]. In this chapter, we highlight some theoretical advances concerning not only the dynamics but also the many-body aspects of the physics of half-solitons.

A Topological Wigner Crystal

It is commonly accepted that the Wigner crystal is one of the most simple yet dramatic many-body effects. In the seminal work published in 1931 [5], Wigner showed that as a result of the competition between the long-ranged potential and kinetic energies, electrons spontaneously form a self-organized crystal at low densities, in a state that strongly differs from the Fermi gas. Experimental observations of this effect have been reported in carbon nanotubes [6].

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Carusotto, I., and Ciuti, C. 2013. Quantum fluids of light. Rev. Mod. Phys., 85, 299.Google Scholar
[2] Pitaevskii, L. P., and Stringari, S. 2003. Bose-Einstein Condensation. Oxford, UK: Clarendon Press.
[3] Salomaa, M. M., and Volovik, G. E. 1987. Quantized vortices in superfluid He3. Rev. Mod. Phys., 59, 533.Google Scholar
[4] Hivet, R., Flayac, H., Solnyshkov, D. D., Tanese, D., Boulier, T., Andreoli, D., Giacobino, E., Bloch, J., Bramati, A., Malpuech, G., and Amo, A. 2012. Half-solitons in a polariton quantum fluid behave like magnetic monopoles. Nat. Phys., 8, 724.Google Scholar
[5] Wigner, E. 1934. On the interaction of electrons in metals. Physical Review, 46, 1002–1011.Google Scholar
[6] Deshpande, V. V., and Bockrath, M. 2007. The one-dimensional wigner crystal in carbon nanotubes. Nat. Phys., 4, 314.Google Scholar
[7] Xu, Zhihao, Li, Linhu, Xianlong, Gao, and Chen, Shu. 2013. Wigner crystal versus Fermionization for one-dimensional Hubbard models with and without long-range interactions. J. Phys: Condens. Matter, 25, 055601.Google Scholar
[8] Łakomy, K., Nath, R., and Santos, L. 2012. Spontaneous crystallization and filamentation of solitons in dipolar condensates. Phys. Rev. A, 85, 033618.Google Scholar
[9] Bloch, I., Dalibard, J., and Zwerger, W. 2008. Many-body physics with ultracold gases. Rev. Mod. Phys., 80, 885–964.Google Scholar
[10] Krive, I. V., Nersesyan, A. A., Jonson, M., and Shekhter, R. I. 1995. Influence of long-range Coulomb interaction on the metal-insulator transition in one-dimensional strongly correlated electron systems. Phys. Rev. B, 52, 10865–10871.Google Scholar
[11] Weber, U., and McGovern, J. A. 1997. A self-consistent approach to the Wigner-Seitz treatment of soliton matter. Phys. Rev. C, 57, 3376.Google Scholar
[12] Shelykh, I. A., Kavokin, A. V., Rubo, Y. G., Liew, T. C. H., and Malpuech, G. 2009. Polarization-sensitive phenomena in planar semiconductor microcavities. Semiconductor Science and Technology, 25, 013001.Google Scholar
[13] Flayac, H., Solnyshkov, D. D., and Malpuech, G. 2011. Oblique half-solitons and their generation in exciton–polariton condensates. Phys. Rev. B, 83, 193305.Google Scholar
[14] Frantzeskakis, D. J. 2010. Dark solitons in atomic Bose-Einstein condensates: from theory to experiments. J. Phys. A, 43, 82.Google Scholar
[15] Öhberg, P., and Santos, L. 2001. Dark solitons in a two-component Bose-Einstein condensate. Phys. Rev. Lett., 86, 2918.Google Scholar
[16] Terças, H., Solnyshkov, D. D., and Malpuech, G. 2013. Topological Wigner crystal of half-solitons in a spinor Bose-Einstein condensate. Phys. Rev. Lett., 110, 035303.Google Scholar
[17] Lieb, E. H., and Liniger, W. 1963. Exact analysis of an interacting Bose gas. I. The general solution and the ground state. Phys. Rev., 130, 1605.Google Scholar
[18] Lieb, E. H. 1963. Exact analysis of an interacting bose gas. II. The excitation spectrum. Phys. Rev., 130, 1616.Google Scholar
[19] Haldane, F. D. M. 2000. ‘Luttinger liquid theory’ of one-dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas. J. Phys. C, 14, 2585.Google Scholar
[20] Schulz, H. 1990. Correlation exponents and the metal-insulator transition in the onedimensional Hubbard model. Phys. Rev. Lett., 64, 2831.Google Scholar
[21] March, N. H. 1988. Comment on melting of the Wigner crystal at finite temperature. Phys. Rev. A, 37, 4526.Google Scholar
[22] Dirac, P. A. M. 1931. Quantised singularities in the electromagnetic field. Proc. Roy. Soc. London Ser. A, 133, 60–72.Google Scholar
[23] Pinfold, James L. 2010. Dirac's dream – the search for the magnetic monopole. AIP Conference Proceedings, 1304, 234.Google Scholar
[24] Castelnovo, C., Moessner, R., and Sondhi, S. L. 2008. Magnetic monopoles in spin ice. Nature, 451, 42.Google Scholar
[25] Bramwell, S. T., Giblin, S. R., Calder, S., Aldus, R., Prabhakaran, D., and Fennell, T. 2009. Measurement of the charge and current of magnetic monopoles in spin ice. Nature, 461, 956.Google Scholar
[26] Jaubert, L. D. C., and Holdsworth, P. C. W. 2009. Signature of magnetic monopole and Dirac string dynamics in spin ice. Nat. Phys., 5, 258–261.Google Scholar
[27] Fennell, T., Deen, P. P., Wildes, A. R., Schmalzl, K., Prabhakaran, D., Boothroyd, A. T., Aldus, R. J., McMorrow, D. F., and Bramwell, S. T. 2009. Magnetic Coulomb phase in the spin ice Ho2Ti2O7. Science, 326, 415.Google Scholar
[28] Morris, D. J. P., Tennant, D. A., Grigera, S. A., Klemke, B., Castelnovo, C., Moessner, R., Czternasty, C., Meissner, M., Rule, K. C., Hoffmann, J. U., Kiefer, K., Gerischer, S., Slobinsky, D., and Perry, R. S. 2009. Dirac strings and magnetic monopoles. Science, 326, 411.Google Scholar
[29] Bramwell, S. T. 2012. Magnetic monopoles: magnetricity near the speed of light. Nat. Phys., 8, 703.Google Scholar
[30] Solnyshkov, D. D., Flayac, H., and Malpuech, G. 2012. Stable magnetic monopoles in spinor polariton condensates. Phys. Rev. B, 85, 073105.Google Scholar
[31] Terças, H., Solnyshkov, D. D., and Malpuech, G. 2014. High-speed DC transport of emergent monopoles in spinor photonic fluids. Phys. Rev. Lett., 113, 036403.Google Scholar
[32] Zakharov, V. E. 1971. Kinetic equation for solitons. Sov. Phys. JETP 33, 538 [Zh. Eksp. Teor. Fiz. 60, 993 (1971)].Google Scholar
[33] El, G. A., and Kamchatnov, A. M. 2005. Kinetic equation for a dense soliton gas. Phys. Rev. Lett., 95, 204101.Google Scholar
[34] Drude, P. 1900. Zur Elektronentheorie der Metalle. Ann. Phys. Ser., 4, 566.Google Scholar
[35] Sommerfeld, A. 1928. Zur elektronentheorie der metalle auf grund der Fermischen Statistik. Zeits. and Physik, 47, 1.Google Scholar
[36] Gantmaker, V. F., and Levinson, Y. B. 1987. Carrier Scattering in Metal and Semiconductors. North-Holland.
[37] Beaulac, T. P., Allen, P. B., and Pinski, F. J. 1982. Electron–phonon effects in copper. II. Electrical and thermal resistivities and Hall coefficient. Phys. Rev. B, 26, 1549.Google Scholar
[38] Onsager, L. 1969. The motion of ions: principles and concepts. Science, 166, 1359.Google Scholar
[39] Parker, N. G., Proukakis, N. P., Barenghi, C. F., and Adams, C. S. 2003. Dynamical instability of a dark soliton in a quasi-one-dimensional Bose-Einstein condensate perturbed by an optical lattice. J. Phys. B, 37, 12.Google Scholar
[40] Malpuech, G., Glazov, M. M., Shelykh, I. A., Bigenwald, P., and Kavokin, K. V. 2006. Electronic control of the polarization of light emitted by polariton lasers. Appl. Phys. Lett., 88, 111118.Google Scholar
[41] Pinsker, F., and Flayac, H. 2014. On-demand dark soliton train manipulation in a spinor polariton condensate. Phys. Rev. Lett., 112, 140405.Google Scholar
[42] Bolotin, K. I., Sikes, K. J., Jiang, Z., Klima, M., Fudenberg, G., Hone, J., Kim, P., and Stormer, H. L. 2008. Ultrahigh electron mobility in suspended graphene. Solid State Communications, 146, 351.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×