### Abstract

Bose-Einstein condensates (BECs) are a macroscopic state of quantum matter at temperatures nine orders of magnitude colder than outer space. BECs can be trapped in crystals of light: when the crystal takes the form of a honeycomb optical lattice, Dirac physics arises at the Brillouin zone edges, just like in graphene. The weakly interacting quantum gas comprising the BEC generates an effective nonlinearity, giving rise to the nonlinear Dirac equation (NLDE) [1], as we will show. This equation, together with the relativistic linear stability equations (RLSE) [2], comprise a relativistic generalization of the famous nonlinear Schrodinger equation and Boguliubov-de Gennes equations familiar from, for example, propagation of light in Kerr nonlinear media. We present a zoo of exotic vortex [3], skyrmion, and soliton [4,5] solutions to the NLDE+RLSE system, and explain the practical realization of these concepts in present experiments on BECs in the optical equivalent of 2D graphene and 1D armchair and zigzag graphene nanoribbons.

Original language | English (US) |
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Title of host publication | Laser Science, LS 2014 |

Publisher | Optical Society of America (OSA) |

ISBN (Electronic) | 1557522863 |

State | Published - Oct 14 2014 |

Event | Laser Science, LS 2014 - Tucson, United States Duration: Oct 19 2014 → Oct 23 2014 |

### Other

Other | Laser Science, LS 2014 |
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Country | United States |

City | Tucson |

Period | 10/19/14 → 10/23/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering
- Electronic, Optical and Magnetic Materials

### Cite this

*Laser Science, LS 2014*Optical Society of America (OSA).

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*Laser Science, LS 2014.*Optical Society of America (OSA), Laser Science, LS 2014, Tucson, United States, 10/19/14.

**Lightspeed at a snail's pace : Relativity meets ultracold physics.** / Carr, Lincoln D.; Haddad, Laith H.; Weaver, Christopher M.; O'Hara, Kenneth.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Lightspeed at a snail's pace

T2 - Relativity meets ultracold physics

AU - Carr, Lincoln D.

AU - Haddad, Laith H.

AU - Weaver, Christopher M.

AU - O'Hara, Kenneth

PY - 2014/10/14

Y1 - 2014/10/14

N2 - Bose-Einstein condensates (BECs) are a macroscopic state of quantum matter at temperatures nine orders of magnitude colder than outer space. BECs can be trapped in crystals of light: when the crystal takes the form of a honeycomb optical lattice, Dirac physics arises at the Brillouin zone edges, just like in graphene. The weakly interacting quantum gas comprising the BEC generates an effective nonlinearity, giving rise to the nonlinear Dirac equation (NLDE) [1], as we will show. This equation, together with the relativistic linear stability equations (RLSE) [2], comprise a relativistic generalization of the famous nonlinear Schrodinger equation and Boguliubov-de Gennes equations familiar from, for example, propagation of light in Kerr nonlinear media. We present a zoo of exotic vortex [3], skyrmion, and soliton [4,5] solutions to the NLDE+RLSE system, and explain the practical realization of these concepts in present experiments on BECs in the optical equivalent of 2D graphene and 1D armchair and zigzag graphene nanoribbons.

AB - Bose-Einstein condensates (BECs) are a macroscopic state of quantum matter at temperatures nine orders of magnitude colder than outer space. BECs can be trapped in crystals of light: when the crystal takes the form of a honeycomb optical lattice, Dirac physics arises at the Brillouin zone edges, just like in graphene. The weakly interacting quantum gas comprising the BEC generates an effective nonlinearity, giving rise to the nonlinear Dirac equation (NLDE) [1], as we will show. This equation, together with the relativistic linear stability equations (RLSE) [2], comprise a relativistic generalization of the famous nonlinear Schrodinger equation and Boguliubov-de Gennes equations familiar from, for example, propagation of light in Kerr nonlinear media. We present a zoo of exotic vortex [3], skyrmion, and soliton [4,5] solutions to the NLDE+RLSE system, and explain the practical realization of these concepts in present experiments on BECs in the optical equivalent of 2D graphene and 1D armchair and zigzag graphene nanoribbons.

UR - http://www.scopus.com/inward/record.url?scp=84919776095&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84919776095&partnerID=8YFLogxK

M3 - Conference contribution

BT - Laser Science, LS 2014

PB - Optical Society of America (OSA)

ER -