Quantum Field Theory of Nematic Transitions in Spin-Orbit-Coupled Spin-1 Polar Bosons

König, E. J.; Pixley, J. H.

doi:10.1103/PhysRevLett.121.083402

Title: Quantum Field Theory of Nematic Transitions in Spin-Orbit-Coupled Spin-1 Polar Bosons

Journal Article · Wed Aug 22 00:00:00 EDT 2018 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.121.083402· OSTI ID:1509948

^[1];

^[1]

Rutgers Univ., Piscataway, NJ (United States). Dept. of Physics and Astronomy, Center for Materials Theory

We theoretically study an ultracold gas of spin-1 polar bosons in a one-dimensional continuum, which are subject to linear and quadratic Zeeman fields and a Raman induced spin orbit coupling. Concentrating on the regime in which the background fields can be treated perturbatively, we analytically solve the model in its low-energy sector; i.e., we characterize the relevant phases and the quantum phase transitions between them. Depending on the sign of the effective quadratic Zeeman field ε, two superfluid phases with distinct nematic order appear. In addition, we uncover a spin-disordered superfluid phase at strong coupling. We employ a combination of renormalization group calculations and duality transformations to access the nature of the phase transitions. At ε=0, a line of spin-charge separated pairs of Luttinger liquids divides the two nematic phases, and the transition to the spin-disordered state at strong coupling is of the Berezinskii-Kosterlitz-Thouless type. In contrast, at ε≠0, the quantum critical theory separating nematic and strong coupling spin-disordered phases contains a Luttinger liquid in the charge sector that is coupled to a Majorana fermion in the spin sector (i.e., the critical theory at finite ε maps to a quantum critical Ising model that is coupled to the charge Luttinger liquid). Because of an emergent Lorentz symmetry, both have the same logarithmically diverging velocity. We discuss the experimental signatures of our findings that are relevant to ongoing experiments in ultracold atomic gases of ²³Na.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Rutgers Univ., Piscataway, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: FG02-99ER45790

OSTI ID:: 1509948

Alternate ID(s):: OSTI ID: 1465910

Journal Information:: Physical Review Letters, Vol. 121, Issue 8; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 10 works

Citation information provided by
Web of Science

References (65)

Spinor Bose Condensates in Optical Traps Ho, Tin-Lun Physical Review Letters, Vol. 81, Issue 4 https://doi.org/10.1103/PhysRevLett.81.742	journal	July 1998
Spinor Bose–Einstein condensates Kawaguchi, Yuki; Ueda, Masahito Physics Reports, Vol. 520, Issue 5 https://doi.org/10.1016/j.physrep.2012.07.005	journal	November 2012
Observation of symmetry-protected topological band with ultracold fermions Song, Bo; Zhang, Long; He, Chengdong Science Advances, Vol. 4, Issue 2 https://doi.org/10.1126/sciadv.aao4748	journal	February 2018
Spin–orbit coupling in quantum gases Galitski, Victor; Spielman, Ian B. Nature, Vol. 494, Issue 7435 https://doi.org/10.1038/nature11841	journal	February 2013
Spin-dependent Bragg spectroscopy of a spinor Bose gas Baillie, D.; Blakie, P. B. Physical Review A, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevA.93.033607	journal	March 2016
Phase diagram of spin-1 antiferromagnetic Bose-Einstein condensates Jacob, David; Shao, Lingxuan; Corre, Vincent Physical Review A, Vol. 86, Issue 6 https://doi.org/10.1103/PhysRevA.86.061601	journal	December 2012
Phase transitions and elementary excitations in spin-1 Bose gases with Raman-induced spin-orbit coupling Yu, Zeng-Qiang Physical Review A, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevA.93.033648	journal	March 2016
Phase transitions of $S = 1$ spinor condensates in an optical lattice Podolsky, Daniel; Chandrasekharan, Shailesh; Vishwanath, Ashvin Physical Review B, Vol. 80, Issue 21 https://doi.org/10.1103/PhysRevB.80.214513	journal	December 2009
Thermal Phase Transitions of Strongly Correlated Bosons with Spin-Orbit Coupling Hickey, Ciarán; Paramekanti, Arun Physical Review Letters, Vol. 113, Issue 26 https://doi.org/10.1103/PhysRevLett.113.265302	journal	December 2014
Resonant control of spin dynamics in ultracold quantum gases by microwave dressing Gerbier, Fabrice; Widera, Artur; Fölling, Simon Physical Review A, Vol. 73, Issue 4 https://doi.org/10.1103/PhysRevA.73.041602	journal	April 2006
Magnetic phases of spin-1 spin–orbit-coupled Bose gases Campbell, D. L.; Price, R. M.; Putra, A. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms10897	journal	March 2016
Spinor Bose gases: Symmetries, magnetism, and quantum dynamics Stamper-Kurn, Dan M.; Ueda, Masahito Reviews of Modern Physics, Vol. 85, Issue 3 https://doi.org/10.1103/RevModPhys.85.1191	journal	July 2013
Nesting-driven multipolar order in CeB6 from photoemission tomography Koitzsch, A.; Heming, N.; Knupfer, M. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms10876	journal	March 2016
Symmetry classification of spin-orbit-coupled spinor Bose-Einstein condensates Xu, Z. F.; Kawaguchi, Y.; You, L. Physical Review A, Vol. 86, Issue 3 https://doi.org/10.1103/PhysRevA.86.033628	journal	September 2012
Interaction-driven exotic quantum phases in spin-orbit-coupled spin-1 bosons Pixley, J. H.; Natu, Stefan S.; Spielman, I. B. Physical Review B, Vol. 93, Issue 8 https://doi.org/10.1103/PhysRevB.93.081101	journal	February 2016
Experimental realization of two-dimensional synthetic spin–orbit coupling in ultracold Fermi gases Huang, Lianghui; Meng, Zengming; Wang, Pengjun Nature Physics, Vol. 12, Issue 6 https://doi.org/10.1038/nphys3672	journal	February 2016
Stepwise Bose-Einstein Condensation in a Spinor Gas Frapolli, C.; Zibold, T.; Invernizzi, A. Physical Review Letters, Vol. 119, Issue 5 https://doi.org/10.1103/PhysRevLett.119.050404	journal	August 2017
Phase Diagram of Two-Dimensional Polar Condensates in a Magnetic Field James, A. J. A.; Lamacraft, A. Physical Review Letters, Vol. 106, Issue 14 https://doi.org/10.1103/PhysRevLett.106.140402	journal	April 2011
Fate of the one-dimensional Ising quantum critical point coupled to a gapless boson Alberton, Ori; Ruhman, Jonathan; Berg, Erez Physical Review B, Vol. 95, Issue 7 https://doi.org/10.1103/PhysRevB.95.075132	journal	February 2017
Striped ferronematic ground states in a spin-orbit-coupled $S = 1$ Bose gas Natu, Stefan S.; Li, Xiaopeng; Cole, William S. Physical Review A, Vol. 91, Issue 2 https://doi.org/10.1103/PhysRevA.91.023608	journal	February 2015
Tricriticalities and Quantum Phases in Spin-Orbit-Coupled Spin-1 Bose Gases Martone, Giovanni I.; Pepe, Francesco V.; Facchi, Paolo Physical Review Letters, Vol. 117, Issue 12 https://doi.org/10.1103/PhysRevLett.117.125301	journal	September 2016
Nonuniversal Ordering of Spin and Charge in Stripe Phases Krüger, Frank; Scheidl, Stefan Physical Review Letters, Vol. 89, Issue 9 https://doi.org/10.1103/PhysRevLett.89.095701	journal	August 2002
Half-Quantum Vortices in an Antiferromagnetic Spinor Bose-Einstein Condensate Seo, Sang Won; Kang, Seji; Kwon, Woo Jin Physical Review Letters, Vol. 115, Issue 1 https://doi.org/10.1103/PhysRevLett.115.015301	journal	July 2015
Interacting spin-orbit-coupled spin-1 Bose-Einstein condensates Sun, Kuei; Qu, Chunlei; Xu, Yong Physical Review A, Vol. 93, Issue 2 https://doi.org/10.1103/PhysRevA.93.023615	journal	February 2016
Spin-nematic order in antiferromagnetic spinor condensates Zibold, T.; Corre, V.; Frapolli, C. Physical Review A, Vol. 93, Issue 2 https://doi.org/10.1103/PhysRevA.93.023614	journal	February 2016
Synthetic magnetic fields for ultracold neutral atoms Lin, Y. -J.; Compton, R. L.; Jiménez-García, K. Nature, Vol. 462, Issue 7273 https://doi.org/10.1038/nature08609	journal	December 2009
Emergent Lorentz Symmetry with Vanishing Velocity in a Critical Two-Subband Quantum Wire Sitte, M.; Rosch, A.; Meyer, J. S. Physical Review Letters, Vol. 102, Issue 17 https://doi.org/10.1103/PhysRevLett.102.176404	journal	April 2009
Spin waves, vortices, fermions, and duality in the Ising and Baxter models Ogilvie, Michael C. Annals of Physics, Vol. 136, Issue 2 https://doi.org/10.1016/0003-4916(81)90099-3	journal	October 1981
Strong-coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: Odd-integer Mott lobes and helical magnetic phases Pixley, J. H.; Cole, William S.; Spielman, I. B. Physical Review A, Vol. 96, Issue 4 https://doi.org/10.1103/PhysRevA.96.043622	journal	October 2017
Coherent Magnon Optics in a Ferromagnetic Spinor Bose-Einstein Condensate Marti, G. Edward; MacRae, Andrew; Olf, Ryan Physical Review Letters, Vol. 113, Issue 15 https://doi.org/10.1103/PhysRevLett.113.155302	journal	October 2014
Quantum Tricriticality and Phase Transitions in Spin-Orbit Coupled Bose-Einstein Condensates Li, Yun; Pitaevskii, Lev P.; Stringari, Sandro Physical Review Letters, Vol. 108, Issue 22 https://doi.org/10.1103/PhysRevLett.108.225301	journal	May 2012
Topological Defects and the Superfluid Transition of the $s = 1$ Spinor Condensate in Two Dimensions Mukerjee, Subroto; Xu, Cenke; Moore, J. E. Physical Review Letters, Vol. 97, Issue 12 https://doi.org/10.1103/PhysRevLett.97.120406	journal	September 2006
Spin-Orbit Coupled Degenerate Fermi Gases Wang, Pengjun; Yu, Zeng-Qiang; Fu, Zhengkun Physical Review Letters, Vol. 109, Issue 9 https://doi.org/10.1103/PhysRevLett.109.095301	journal	August 2012
Raman-dressed spin-1 spin-orbit-coupled quantum gas Lan, Zhihao; Öhberg, Patrik Physical Review A, Vol. 89, Issue 2 https://doi.org/10.1103/PhysRevA.89.023630	journal	February 2014
Fourier transform spectroscopy of a spin–orbit coupled Bose gas Valdés-Curiel, A.; Trypogeorgos, D.; Marshall, E. E. New Journal of Physics, Vol. 19, Issue 3 https://doi.org/10.1088/1367-2630/aa6279	journal	March 2017
Approach for making visible and stable stripes in a spin-orbit-coupled Bose-Einstein superfluid Martone, Giovanni I.; Li, Yun; Stringari, Sandro Physical Review A, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevA.90.041604	journal	October 2014
On the spin-liquid phase of one-dimensional spin-1 bosons Essler, F. H. L.; Shlyapnikov, G. V.; Tsvelik, A. M. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2009, Issue 02 https://doi.org/10.1088/1742-5468/2009/02/P02027	journal	February 2009
Visualizing edge states with an atomic Bose gas in the quantum Hall regime Stuhl, B. K.; Lu, H. - I.; Aycock, L. M. Science, Vol. 349, Issue 6255 https://doi.org/10.1126/science.aaa8515	journal	September 2015
Realization of two-dimensional spin-orbit coupling for Bose-Einstein condensates Wu, Z.; Zhang, L.; Sun, W. Science, Vol. 354, Issue 6308 https://doi.org/10.1126/science.aaf6689	journal	October 2016
Spin Correlation and Discrete Symmetry in Spinor Bose-Einstein Condensates Zhou, Fei Physical Review Letters, Vol. 87, Issue 8 https://doi.org/10.1103/PhysRevLett.87.080401	journal	August 2001
Real-space mean-field theory of a spin-1 Bose gas in synthetic dimensions Hurst, Hilary M.; Wilson, Justin H.; Pixley, J. H. Physical Review A, Vol. 94, Issue 6 https://doi.org/10.1103/PhysRevA.94.063613	journal	December 2016
Emergent rank-5 nematic order in URu2Si2 Ikeda, Hiroaki; Suzuki, Michi-To; Arita, Ryotaro Nature Physics, Vol. 8, Issue 7 https://doi.org/10.1038/nphys2330	journal	June 2012
Superstripes and the Excitation Spectrum of a Spin-Orbit-Coupled Bose-Einstein Condensate Li, Yun; Martone, Giovanni I.; Pitaevskii, Lev P. Physical Review Letters, Vol. 110, Issue 23 https://doi.org/10.1103/PhysRevLett.110.235302	journal	June 2013
Spin–orbit-coupled Bose–Einstein condensates Lin, Y. -J.; Jiménez-García, K.; Spielman, I. B. Nature, Vol. 471, Issue 7336 https://doi.org/10.1038/nature09887	journal	March 2011
Magnetically stabilized nematic order. II. Critical states and algebraically ordered nematic spin liquids in one-dimensional optical lattices Zhai, Hui; Zhou, Fei Physical Review B, Vol. 72, Issue 1 https://doi.org/10.1103/PhysRevB.72.014422	journal	July 2005
Pairing in Luttinger Liquids and Quantum Hall States Kane, Charles L.; Stern, Ady; Halperin, Bertrand I. Physical Review X, Vol. 7, Issue 3 https://doi.org/10.1103/PhysRevX.7.031009	journal	July 2017
Bose-Einstein Condensation with Internal Degrees of Freedom in Alkali Atom Gases Ohmi, Tetsuo; Machida, Kazushige Journal of the Physical Society of Japan, Vol. 67, Issue 6 https://doi.org/10.1143/JPSJ.67.1822	journal	June 1998
On the spin-liquid phase of one dimensional spin-1 bosons Essler, F. H. L.; Shlyapnikov, G. V.; Tsvelik, A. M. arXiv https://doi.org/10.48550/arxiv.0811.0844	text	January 2008
The Raman dressed spin-1 spin-orbit coupled quantum gas Lan, Zhihao; Ohberg, Patrik arXiv https://doi.org/10.48550/arxiv.1311.6177	text	January 2013
Coherent magnon optics in a ferromagnetic spinor Bose-Einstein condensate Marti, G. Edward; MacRae, Andrew; Olf, Ryan arXiv https://doi.org/10.48550/arxiv.1404.5631	text	January 2014
Approach for making visible and stable stripes in a spin-orbit-coupled Bose-Einstein superfluid Martone, Giovanni I.; Li, Yun; Stringari, Sandro arXiv https://doi.org/10.48550/arxiv.1409.3149	text	January 2014
Visualizing edge states with an atomic Bose gas in the quantum Hall regime Stuhl, B. K.; Lu, H. -I; Aycock, L. M. arXiv https://doi.org/10.48550/arxiv.1502.02496	text	January 2015
Half-Quantum Vortices in an Antiferromagnetic Spinor Bose-Einstein Condensate Seo, Sang Won; Kang, Seji; Kwon, Woo Jin arXiv https://doi.org/10.48550/arxiv.1503.05648	text	January 2015
Experimental realization of a two-dimensional synthetic spin-orbit coupling in ultracold Fermi gases Huang, Lianghui; Meng, Zengming; Wang, Pengjun arXiv https://doi.org/10.48550/arxiv.1506.02861	text	January 2015
Spin nematic order in antiferromagnetic spinor condensates Zibold, Tilman; Corre, Vincent; Frapolli, Camille arXiv https://doi.org/10.48550/arxiv.1506.06176	text	January 2015
Tricriticalities and Quantum Phases in Spin-Orbit-Coupled Spin-$1$ Bose Gases Martone, Giovanni I.; Pepe, Francesco V.; Facchi, Paolo arXiv https://doi.org/10.48550/arxiv.1511.09225	text	January 2015
Spin-dependent Bragg spectroscopy of a spinor Bose gas Baillie, D.; Blakie, P. B. arXiv https://doi.org/10.48550/arxiv.1601.02716	text	January 2016
Fate of the one-dimensional Ising quantum critical point coupled to a gapless boson Alberton, Ori; Ruhman, Jonathan; Berg, Erez arXiv https://doi.org/10.48550/arxiv.1609.02599	text	January 2016
Fourier transform spectroscopy of a spin-orbit coupled Bose gas Valdés-Curiel, A.; Trypogeorgos, D.; Marshall, E. E. arXiv https://doi.org/10.48550/arxiv.1612.00819	text	January 2016
Pairing in Luttinger Liquids and Quantum Hall States Kane, Charles L.; Stern, Ady; Halperin, Bertrand I. arXiv https://doi.org/10.48550/arxiv.1701.06200	text	January 2017
Observation of symmetry-protected topological band with ultracold fermions Song, Bo; Zhang, Long; He, Chengdong arXiv https://doi.org/10.48550/arxiv.1706.00768	text	January 2017
Spin correlation and Discrete symmetry in Spinor Bose-Einstein Condensates Zhou, Fei arXiv https://doi.org/10.48550/arxiv.cond-mat/0102372	text	January 2001
Magnetically Stabilized Order. II: Critical states and algebraically ordered nematic spin liquids in one-dimensional optical lattices Zhai, Hui; Zhou, Fei arXiv https://doi.org/10.48550/arxiv.cond-mat/0501490	text	January 2005
Topological defects and the superfluid transition of the $s=1$ spinor condensate in two dimensions Mukerjee, Subroto; Xu, Cenke; Moore, J. E. arXiv https://doi.org/10.48550/arxiv.cond-mat/0605102	text	January 2006
Bose-Einstein condensation with internal degrees of freedom in alkali atom gases Ohmi, Tetsuo; Machida, Kazushige arXiv https://doi.org/10.48550/arxiv.cond-mat/9803160	text	January 1998

Similar Records

Superfluid density and Berezinskii-Kosterlitz-Thouless transition of a spin-orbit-coupled Fulde-Ferrell superfluid

Journal Article · Mon Feb 09 00:00:00 EST 2015 · Physical Review A - Atomic, Molecular, and Optical Physics · OSTI ID:1509948

Cao, Ye; Liu, Xia -Ji; He, Lianyi; +2 more

SU(N) magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations

Journal Article · Sat Oct 15 00:00:00 EDT 2011 · Physical Review. A · OSTI ID:1509948

Manmana, Salvatore R.; Hazzard, Kaden R. A.; Gang, Chen; +2 more

Magnetically stabilized nematic order. II. Critical states and algebraically ordered nematic spin liquids in one-dimensional optical lattices

Journal Article · Fri Jul 01 00:00:00 EDT 2005 · Physical Review. B, Condensed Matter and Materials Physics · OSTI ID:1509948

Hui, Zhai; Fei, Zhou

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
74 ATOMIC AND MOLECULAR PHYSICS

Title: Quantum Field Theory of Nematic Transitions in Spin-Orbit-Coupled Spin-1 Polar Bosons

Citation Formats

References (65)

Similar Records

Related Subjects