The spin Hall effect in a quantum gas
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Abstract
Electronic properties such as current flow are generally independent of the electron's spin angular momentum, an internal degree of freedom possessed by quantum particles. The spin Hall effect, first proposed 40 years ago1, is an unusual class of phenomena in which flowing particles experience orthogonally directed, spin-dependent forces-analogous to the conventional Lorentz force that gives the Hall effect, but opposite in sign for two spin states. Spin Hall effects have been observed for electrons flowing in spin-orbit-coupled materials such as GaAs and InGaAs (refs 2, 3) and for laser light traversing dielectric junctions4. Here we observe the spin Hall effect in a quantum-degenerate Bose gas, and use the resulting spin-dependent Lorentz forces to realize a cold-atom spin transistor. By engineering a spatially inhomogeneous spin-orbit coupling field for our quantum gas, we explicitly introduce and measure the requisite spin-dependent Lorentz forces, finding them to be in excellent agreement with our calculations. This 'atomtronic' transistor behaves as a type of velocity-insensitive adiabatic spin selector, with potential application in devices such as magnetic5 or inertial6 sensors. In addition, such techniques for creating and measuring the spin Hall effect are clear prerequisites for engineering topological insulators7,8 and detecting their associated quantized spin Hall effects in quantum gases. As implemented, our system realizes a laser-actuated analogue to the archetypal semiconductor spintronic device, the Datta-Das spin transistor9,10.
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" level="a">The spin Hall effect in a quantum gas</title><author><name sortKey="Beeler, M C" uniqKey="Beeler M">M. C. Beeler</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland</s1><s2>Gaithersburg, Maryland 20899</s2><s3>USA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>6 aut.</sZ></inist:fA14><country>États-Unis</country><wicri:noRegion>Gaithersburg, Maryland 20899</wicri:noRegion></affiliation><affiliation wicri:level="1"><inist:fA14 i1="03"><s1>The Johns Hopkins Applied Physics Laboratory</s1><s2>Laurel, Maryland 20723</s2><s3>USA</s3><sZ>1 aut.</sZ></inist:fA14><country>États-Unis</country><wicri:noRegion>The Johns Hopkins Applied Physics Laboratory</wicri:noRegion></affiliation></author><author><name sortKey="Williams, R A" uniqKey="Williams R">R. A. Williams</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland</s1><s2>Gaithersburg, Maryland 20899</s2><s3>USA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>6 aut.</sZ></inist:fA14><country>États-Unis</country><wicri:noRegion>Gaithersburg, Maryland 20899</wicri:noRegion></affiliation><affiliation wicri:level="1"><inist:fA14 i1="04"><s1>National Physical Laboratory</s1><s2>Teddington TW11 0LW</s2><s3>GBR</s3><sZ>2 aut.</sZ></inist:fA14><country>Royaume-Uni</country><wicri:noRegion>National Physical Laboratory</wicri:noRegion></affiliation></author><author><name sortKey="Jimenez Garcia, K" uniqKey="Jimenez Garcia K">K. Jimenez-Garcia</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland</s1><s2>Gaithersburg, Maryland 20899</s2><s3>USA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>6 aut.</sZ></inist:fA14><country>États-Unis</country><wicri:noRegion>Gaithersburg, Maryland 20899</wicri:noRegion></affiliation><affiliation wicri:level="1"><inist:fA14 i1="02"><s1>Departamento de Física, Centro de Investigación y Estudios Avanzados del Instituto Politécnico Nacional</s1><s2>Mexico D.F. 07360</s2><s3>MEX</s3><sZ>3 aut.</sZ></inist:fA14><country>Mexique</country><wicri:noRegion>Mexico D.F. 07360</wicri:noRegion></affiliation><affiliation wicri:level="1"><inist:fA14 i1="05"><s1>The James Franck Institute and Department of Physics, The University of Chicago</s1><s2>Chicago, Illinois 60637</s2><s3>USA</s3><sZ>3 aut.</sZ></inist:fA14><country>États-Unis</country><wicri:noRegion>Chicago, Illinois 60637</wicri:noRegion></affiliation></author><author><name sortKey="Leblanc, L J" uniqKey="Leblanc L">L. J. Leblanc</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland</s1><s2>Gaithersburg, Maryland 20899</s2><s3>USA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>6 aut.</sZ></inist:fA14><country>États-Unis</country><wicri:noRegion>Gaithersburg, Maryland 20899</wicri:noRegion></affiliation></author><author><name sortKey="Perry, A R" uniqKey="Perry A">A. R. Perry</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland</s1><s2>Gaithersburg, Maryland 20899</s2><s3>USA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>6 aut.</sZ></inist:fA14><country>États-Unis</country><wicri:noRegion>Gaithersburg, Maryland 20899</wicri:noRegion></affiliation></author><author><name sortKey="Spielman, I B" uniqKey="Spielman I">I. B. Spielman</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland</s1><s2>Gaithersburg, Maryland 20899</s2><s3>USA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>6 aut.</sZ></inist:fA14><country>États-Unis</country><wicri:noRegion>Gaithersburg, Maryland 20899</wicri:noRegion></affiliation></author></titleStmt><publicationStmt><idno type="inist">13-0289397</idno><date when="2013">2013</date><idno type="stanalyst">PASCAL 13-0289397 INIST</idno><idno type="RBID">Pascal:13-0289397</idno><idno type="wicri:Area/Main/Corpus">000788</idno><idno type="wicri:Area/Main/Repository">000337</idno></publicationStmt><seriesStmt><idno type="ISSN">0028-0836</idno><title level="j" type="abbreviated">Nature : (Lond.)</title><title level="j" type="main">Nature : (London)</title></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Angular momentum</term><term>Bose-Einstein condensation</term><term>Bose-Einstein gas</term><term>Degrees of freedom</term><term>Equations of motion</term><term>Gallium arsenides</term><term>Gallium selenides</term><term>Indium arsenides</term><term>Lorentz force</term><term>Polarized spin</term><term>Semiconductor materials</term><term>Spin Hall effect</term><term>Spin transistor</term><term>Spin-orbit interactions</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Effet Hall de spin</term><term>Spin polarisé</term><term>Equation mouvement</term><term>Moment cinétique</term><term>Degré liberté</term><term>Force Lorentz</term><term>Condensation Bose Einstein</term><term>Gaz Bose Einstein</term><term>Interaction spin orbite</term><term>Arséniure de gallium</term><term>Arséniure d'indium</term><term>Séléniure de gallium</term><term>Semiconducteur</term><term>GaAs</term><term>InGaAs</term><term>Transistor à spin</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Electronic properties such as current flow are generally independent of the electron's spin angular momentum, an internal degree of freedom possessed by quantum particles. The spin Hall effect, first proposed 40 years ago<sup>1</sup>, is an unusual class of phenomena in which flowing particles experience orthogonally directed, spin-dependent forces-analogous to the conventional Lorentz force that gives the Hall effect, but opposite in sign for two spin states. Spin Hall effects have been observed for electrons flowing in spin-orbit-coupled materials such as GaAs and InGaAs (refs 2, 3) and for laser light traversing dielectric junctions<sup>4</sup>. Here we observe the spin Hall effect in a quantum-degenerate Bose gas, and use the resulting spin-dependent Lorentz forces to realize a cold-atom spin transistor. By engineering a spatially inhomogeneous spin-orbit coupling field for our quantum gas, we explicitly introduce and measure the requisite spin-dependent Lorentz forces, finding them to be in excellent agreement with our calculations. This 'atomtronic' transistor behaves as a type of velocity-insensitive adiabatic spin selector, with potential application in devices such as magnetic<sup>5</sup> or inertial<sup>6</sup> sensors. In addition, such techniques for creating and measuring the spin Hall effect are clear prerequisites for engineering topological insulators<sup>7,8</sup> and detecting their associated quantized spin Hall effects in quantum gases. As implemented, our system realizes a laser-actuated analogue to the archetypal semiconductor spintronic device, the Datta-Das spin transistor<sup>9,10</sup>.</div></front></TEI><inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>0028-0836</s0></fA01><fA02 i1="01"><s0>NATUAS</s0></fA02><fA03 i2="1"><s0>Nature : (Lond.)</s0></fA03><fA05><s2>498</s2></fA05><fA06><s2>7453</s2></fA06><fA08 i1="01" i2="1" l="ENG"><s1>The spin Hall effect in a quantum gas</s1></fA08><fA11 i1="01" i2="1"><s1>BEELER (M. C.)</s1></fA11><fA11 i1="02" i2="1"><s1>WILLIAMS (R. A.)</s1></fA11><fA11 i1="03" i2="1"><s1>JIMENEZ-GARCIA (K.)</s1></fA11><fA11 i1="04" i2="1"><s1>LEBLANC (L. J.)</s1></fA11><fA11 i1="05" i2="1"><s1>PERRY (A. R.)</s1></fA11><fA11 i1="06" i2="1"><s1>SPIELMAN (I. B.)</s1></fA11><fA14 i1="01"><s1>Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland</s1><s2>Gaithersburg, Maryland 20899</s2><s3>USA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>6 aut.</sZ></fA14><fA14 i1="02"><s1>Departamento de Física, Centro de Investigación y Estudios Avanzados del Instituto Politécnico Nacional</s1><s2>Mexico D.F. 07360</s2><s3>MEX</s3><sZ>3 aut.</sZ></fA14><fA14 i1="03"><s1>The Johns Hopkins Applied Physics Laboratory</s1><s2>Laurel, Maryland 20723</s2><s3>USA</s3><sZ>1 aut.</sZ></fA14><fA14 i1="04"><s1>National Physical Laboratory</s1><s2>Teddington TW11 0LW</s2><s3>GBR</s3><sZ>2 aut.</sZ></fA14><fA14 i1="05"><s1>The James Franck Institute and Department of Physics, The University of Chicago</s1><s2>Chicago, Illinois 60637</s2><s3>USA</s3><sZ>3 aut.</sZ></fA14><fA20><s1>201-204</s1></fA20><fA21><s1>2013</s1></fA21><fA23 i1="01"><s0>ENG</s0></fA23><fA43 i1="01"><s1>INIST</s1><s2>142</s2><s5>354000504185250200</s5></fA43><fA44><s0>0000</s0><s1>© 2013 INIST-CNRS. All rights reserved.</s1></fA44><fA45><s0>30 ref.</s0></fA45><fA47 i1="01" i2="1"><s0>13-0289397</s0></fA47><fA60><s1>P</s1><s3>CR</s3></fA60><fA61><s0>A</s0></fA61><fA64 i1="01" i2="1"><s0>Nature : (London)</s0></fA64><fA66 i1="01"><s0>GBR</s0></fA66><fC01 i1="01" l="ENG"><s0>Electronic properties such as current flow are generally independent of the electron's spin angular momentum, an internal degree of freedom possessed by quantum particles. The spin Hall effect, first proposed 40 years ago<sup>1</sup>, is an unusual class of phenomena in which flowing particles experience orthogonally directed, spin-dependent forces-analogous to the conventional Lorentz force that gives the Hall effect, but opposite in sign for two spin states. Spin Hall effects have been observed for electrons flowing in spin-orbit-coupled materials such as GaAs and InGaAs (refs 2, 3) and for laser light traversing dielectric junctions<sup>4</sup>. Here we observe the spin Hall effect in a quantum-degenerate Bose gas, and use the resulting spin-dependent Lorentz forces to realize a cold-atom spin transistor. By engineering a spatially inhomogeneous spin-orbit coupling field for our quantum gas, we explicitly introduce and measure the requisite spin-dependent Lorentz forces, finding them to be in excellent agreement with our calculations. This 'atomtronic' transistor behaves as a type of velocity-insensitive adiabatic spin selector, with potential application in devices such as magnetic<sup>5</sup> or inertial<sup>6</sup> sensors. In addition, such techniques for creating and measuring the spin Hall effect are clear prerequisites for engineering topological insulators<sup>7,8</sup> and detecting their associated quantized spin Hall effects in quantum gases. 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