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Chin. Phys. B, 2019, Vol. 28(10): 100501    DOI: 10.1088/1674-1056/ab3dff
SPECIAL TOPIC—110th Anniversary of Lanzhou University Prev   Next  

Enhancing von Neumann entropy by chaos in spin-orbit entanglement

Chen-Rong Liu(刘郴荣)1, Pei Yu(喻佩)1, Xian-Zhang Chen(陈宪章)1, Hong-Ya Xu(徐洪亚)2, Liang Huang(黄亮)1, Ying-Cheng Lai(来颖诚)2,3
1 School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou 730000, China;
2 School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA;
3 Department of Physics, Arizona State University, Tempe, AZ 85287, USA
Abstract  For a quantum system with multiple degrees of freedom or subspaces, loss of coherence in a certain subspace is intimately related to the enhancement of entanglement between this subspace and another one. We investigate intra-particle entanglement in two-dimensional mesoscopic systems, where an electron has both spin and orbital degrees of freedom and the interaction between them is enabled by Rashba type of spin-orbit coupling. The geometric shape of the scattering region can be adjusted to produce a continuous spectrum of classical dynamics with different degree of chaos. Focusing on the spin degree of freedom in the weak spin-orbit coupling regime, we find that classical chaos can significantly enhance spin-orbit entanglement at the expense of spin coherence. Our finding that classical chaos can be beneficial to intra-particle entanglement may have potential applications such as enhancing the bandwidth of quantum communications.
Keywords:  spin-orbit entanglement      chaos      von Neumann entropy      spin decoherence  
Received:  31 July 2019      Revised:  21 August 2019      Published:  05 October 2019
PACS:  05.45.Mt (Quantum chaos; semiclassical methods)  
  71.15.Rf (Relativistic effects)  
  73.23.-b (Electronic transport in mesoscopic systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11775101 and 11422541) and the US Office of Naval Research (Grant No. N00014-16-1-2828).
Corresponding Authors:  Liang Huang     E-mail:  huangl@lzu.edu.cn

Cite this article: 

Chen-Rong Liu(刘郴荣), Pei Yu(喻佩), Xian-Zhang Chen(陈宪章), Hong-Ya Xu(徐洪亚), Liang Huang(黄亮), Ying-Cheng Lai(来颖诚) Enhancing von Neumann entropy by chaos in spin-orbit entanglement 2019 Chin. Phys. B 28 100501

[33] Streltsov A, Adesso G and Plenio M B 2017 Rev. Mod. Phys. 89 041003
[1] Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge Univ. Press)
[34] Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A and Wootters W K 1993 Phys. Rev. Lett. 70 1895
[2] Pattanayak A K and Brumer P 1997 Phys. Rev. Lett. 79 4131
[35] Grover L K 1997 Phys. Rev. Lett. 79 325
[3] Furuya K, Nemes M C and Pellegrino G Q 1998 Phys. Rev. Lett. 80 5524
[36] Boström K and Felbinger T 2002 Phys. Rev. Lett. 89 187902
[4] Loss D and Sukhorukov E V 2000 Phys. Rev. Lett. 84 1035
[37] Hwang W Y 2003 Phys. Rev. Lett. 91 057901
[5] Jalabert R A and Pastawski H M 2001 Phys. Rev. Lett. 86 2490
[38] Feynman R P and Hibbs A R 1965 Quantum Mechanics and Path Integrals (Boston, Massachusetts: McGraw-Hill)
[6] Cucchietti F M, Dalvit D A R, Paz J P and Zurek W H 2003 Phys. Rev. Lett. 91 210403
[39] Cantrell C D and Scully M O 1978 Phys. Rep. 43 499
[7] Samuelsson P, Sukhorukov E V and Büttiker M 2003 Phys. Rev. Lett. 91 157002
[40] Streltsov A, Singh U, Dhar H S, Bera M N and Adesso G 2015 Phys. Rev. Lett. 115 020403
[8] Joos E, Zeh H D, Kiefer C, Giulini D, Kupsch J and Stamatescu I O 2003 Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Berlin Heidelberg, New York)
[41] Chitambar E and Hsieh M H 2016 Phys. Rev. Lett. 117 020402
[9] Wang X, Ghose S, Sanders B C and Hu B 2004 Phys. Rev. E 70 016217
[10] Gorin T, Prosen T, Seligman T H and Znidaric M 2006 Phys. Rep. 435 33 156
[42] Streltsov A, Chitambar E, Rana S, Bera M N, Winter A and Lewenstein M 2016 Phys. Rev. Lett. 116 240405
[11] Schlosshauer M 2007 Decoherence and the Quantum-To-Classical Transition (Springer, Berlin Heidelberg, New York)
[43] Baumgratz T, Cramer M and Plenio M B 2014 Phys. Rev. Lett. 113 140401
[12] Bonança M V S 2011 Phys. Rev. E 83 046214
[44] Xi Z, Li Y and Fan H 2015 Sci. Rep. 5 10922
[13] Zhang H, Liu X, Shen X and Liu J 2013 Int. J. Bifur. Chaos 23 1330014
[14] Wang G, Huang L, Lai Y C and Grebogi C 2014 Phys. Rev. Lett. 112 110406
[45] Cheng S and Hall M J W 2015 Phys. Rev. A 92 042101
[46] Žutić I, Fabian J and Das Sarma S 2004 Rev. Mod. Phys. 76 323
[15] Song L J, Wang X G, LI Y D and Zong Z G 2006 Chin. Phys. Lett. 23 3190
[47] Fert A 2008 Rev. Mod. Phys. 80 1517
[16] Tan J T, Luo Y R, Zhou Z and Hai W H 2016 Chin. Phys. Lett. 33 070302
[48] Baltz V, Manchon A, Tsoi M, Moriyama T, Ono T and Tserkovnyak Y 2018 Rev. Mod. Phys. 90 015005
[17] Song L J, Yan D, Gai Y J and Wang Y B 2010 Acta Phys. Sin. 59 3699 (in Chinese)
[49] Datta S 1995 Electronic Transport in Mesoscopic Systems (Cambridge: Cambridge University Press)
[18] Yang Y B and Wang W G 2015 Chin. Phys. Lett. 32 030301
[50] Lee P A and Stone A D 1985 Phys. Rev. Lett. 55 1622 1625
[19] Stöckmann H J 2006 Quantum Chaos: An Introduction (New York: Cambridge University Press)
[51] Webb R A, Washburn S, Umbach C P and Laibowitz R B 1985 Phys. Rev. Lett. 54 2696
[20] Haake F 2010 Quantum Signatures of Chaos 3rd ed Springer series in synergetics (Berlin: Springer-Verlag)
[52] Stone A D 1985 Phys. Rev. Lett. 54 2692
[21] Huang L, Xu H Y, Grebogi C and Lai Y C 2018 Phys. Rep. 753 1
[53] Jalabert R A, Baranger H U and Stone A D 1990 Phys. Rev. Lett. 65 2442
[22] Hasegawa Y, Loidl R, Badurek G, Baron M and Rauch H 2003 Nature 425 45
[54] Ketzmerick R 1996 Phys. Rev. B 54 10841
[23] Karimi E, Leach J, Slussarenko S, Piccirillo B, Marrucci L, Chen L, She W, Franke-Arnold S, Padgett M J and Santamato E 2010 Phys. Rev. A 82 022115
[55] Sachrajda A S, Ketzmerick R, Gould C, Feng Y, Kelly P J, Delage A and Wasilewski Z 1998 Phys. Rev. Lett. 80 1948
[24] Karimi E and Boyd R W 2015 Science 350 1172
[56] Huckestein B, Ketzmerick R and Lewenkopf C H 2000 Phys. Rev. Lett. 84 5504
[25] Wang X, Cai X, Su Z, Chen M, Wu D, Li L, Liu N, Lu C and Pan J 2015 Nature 518 516
[57] de Moura A P S, Lai Y C, Akis R, Bird J P and Ferry D K 2002 Phys. Rev. Lett. 88 236804
[26] Feng L, Zhang M, Zhou Z, Li M, Xiong X, Yu L, Shi B, Guo G, Dai D and Ren X 2016 Nat. Commun. 7 11985
[58] Yang R, Huang L, Lai Y C and Grebogi C 2011 EuroPhys. Lett. 94 40004
[27] Wang X L, Luo Y H, Huang H L, Chen M C, Su Z E, Liu C, Chen C, Li W, Fang Y Q, Jiang X, Zhang J, Li L, Liu N L, Lu C Y and Pan J W 2018 Phys. Rev. Lett. 120 260502
[59] Yang R, Huang L, Lai Y C and Pecora L M 2012 Appl. Phys. Lett. 100 093105
[28] Einstein A, Podolsky B and Rosen N 1935 Phys. Rev. 47 777
[60] Yang R, Huang L, Lai Y C, Grebogi C and Pecora L M 2013 Chaos 23 013125
[29] Schrödinger E 1935 Math. Proc. Cambridge 31 555
[61] Bao R, Huang L, Lai Y C and Grebogi C 2015 Phys. Rev. E 92 012918
[30] Zurek W H 2003 Rev. Mod. Phys. 75 715
[62] Lai Y C, Xu H Y, Huang L and Grebogi C 2018 Chaos 28 052101
[31] Zeng J Y 2014 Quantum Mechamics. Volume Ⅱ. 5th edn (Beijing: Science Press) (in Chinese)
[63] Liu C R, Chen X Z, Xu H Y, Huang L and Lai Y C 2018 Phys. Rev. B 98 115305
[32] Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
[33] Streltsov A, Adesso G and Plenio M B 2017 Rev. Mod. Phys. 89 041003
[64] Pershin Y V and Privman V 2004 Phys. Rev. B 69 073310
[34] Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A and Wootters W K 1993 Phys. Rev. Lett. 70 1895
[65] Chang C H, Mal'shukov A G and Chao K A 2004 Phys. Rev. B 70 245309
[35] Grover L K 1997 Phys. Rev. Lett. 79 325
[66] Akguc G B and Gong J 2008 Phys. Rev. B 77 205302
[36] Boström K and Felbinger T 2002 Phys. Rev. Lett. 89 187902
[67] Ying L and Lai Y C 2016 Phys. Rev. B 93 085408
[37] Hwang W Y 2003 Phys. Rev. Lett. 91 057901
[68] Frustaglia D, Montangero S and Fazio R 2006 Phys. Rev. B 74 165326
[38] Feynman R P and Hibbs A R 1965 Quantum Mechanics and Path Integrals (Boston, Massachusetts: McGraw-Hill)
[69] Rashba E I 1960 Sov. Phys. Solid. State 2 1109
[39] Cantrell C D and Scully M O 1978 Phys. Rep. 43 499
[70] Dresselhaus G and Dresselhaus M S 1965 Phys. Rev. A 140 A401
[40] Streltsov A, Singh U, Dhar H S, Bera M N and Adesso G 2015 Phys. Rev. Lett. 115 020403
[71] Rashba E I 2000 Phys. Rev. B 62 R16267
[41] Chitambar E and Hsieh M H 2016 Phys. Rev. Lett. 117 020402
[72] Gor'kov L P and Rashba E I 2001 Phys. Rev. Lett. 87 037004
[42] Streltsov A, Chitambar E, Rana S, Bera M N, Winter A and Lewenstein M 2016 Phys. Rev. Lett. 116 240405
[73] Koga T, Nitta J, Takayanagi H and Datta S 2002 Phys. Rev. Lett. 88 126601
[43] Baumgratz T, Cramer M and Plenio M B 2014 Phys. Rev. Lett. 113 140401
[74] Rashba E I and Efros A L 2003 Phys. Rev. Lett. 91 126405
[44] Xi Z, Li Y and Fan H 2015 Sci. Rep. 5 10922
[75] Schliemann J, Egues J C and Loss D 2003 Phys. Rev. Lett. 90 146801
[45] Cheng S and Hall M J W 2015 Phys. Rev. A 92 042101
[46] Žutić I, Fabian J and Das Sarma S 2004 Rev. Mod. Phys. 76 323
[76] Pramanik T, Adhikari S, Majumdar A, Home D and Pan A K 2010 Phys. Lett. A 374 1121
[47] Fert A 2008 Rev. Mod. Phys. 80 1517
[77] Amiri F, Rastgoo S and Golshan M 2014 Phys. Lett. A 378 1985
[48] Baltz V, Manchon A, Tsoi M, Moriyama T, Ono T and Tserkovnyak Y 2018 Rev. Mod. Phys. 90 015005
[78] Luna-Acosta G A, Krokhin A A, Rodríguez M A and Hernández-Tejeda P H 1996 Phys. Rev. B 54 11410
[49] Datta S 1995 Electronic Transport in Mesoscopic Systems (Cambridge: Cambridge University Press)
[79] Mendoza M and Schulz P A 2005 Phys. Stat. Sol. (C) 2 3129
[50] Lee P A and Stone A D 1985 Phys. Rev. Lett. 55 1622 1625
[80] Lin W A and Jensen R V 1997 Phys. Rev. E 56 5251
[51] Webb R A, Washburn S, Umbach C P and Laibowitz R B 1985 Phys. Rev. Lett. 54 2696
[81] Souma S and Nikolić B K 2004 Phys. Rev. B 70 195346
[52] Stone A D 1985 Phys. Rev. Lett. 54 2692
[82] Nikolić B K and Souma S 2005 Phys. Rev. B 71 195328
[53] Jalabert R A, Baranger H U and Stone A D 1990 Phys. Rev. Lett. 65 2442
[83] Dragomirova R L and Nikolić B K 2007 Phys. Rev. B 75 085328
[54] Ketzmerick R 1996 Phys. Rev. B 54 10841
[55] Sachrajda A S, Ketzmerick R, Gould C, Feng Y, Kelly P J, Delage A and Wasilewski Z 1998 Phys. Rev. Lett. 80 1948
[84] Dey M, Maiti S K, Sil S and Karmakar S N 2013 J. Appl. Phys. 114 164318
[56] Huckestein B, Ketzmerick R and Lewenkopf C H 2000 Phys. Rev. Lett. 84 5504
[85] Zhang Y T, Song Z F and Li Y C 2008 Phys. Lett. A 373 144
[57] de Moura A P S, Lai Y C, Akis R, Bird J P and Ferry D K 2002 Phys. Rev. Lett. 88 236804
[86] Safaiee R and Golshan M M 2017 Eur. Phys. J. B 90 121
[58] Yang R, Huang L, Lai Y C and Grebogi C 2011 EuroPhys. Lett. 94 40004
[87] Usuki T, Saito M, Takatsu M, Kiehl R A and Yokoyama N 1995 Phys. Rev. B 52 8244
[59] Yang R, Huang L, Lai Y C and Pecora L M 2012 Appl. Phys. Lett. 100 093105
[88] Akis R, Ferry D K, Bird J P and Vasileska D 1999 Phys. Rev. B 60 2680
[60] Yang R, Huang L, Lai Y C, Grebogi C and Pecora L M 2013 Chaos 23 013125
[89] Xiao X, Chen Z, Nie W, Zhou G and Li F 2014 J. Appl. Phys. 115 223709
[61] Bao R, Huang L, Lai Y C and Grebogi C 2015 Phys. Rev. E 92 012918
[90] Datta S and Biswajit D 1990 Appl. Phys. Lett. 56 665
[62] Lai Y C, Xu H Y, Huang L and Grebogi C 2018 Chaos 28 052101
[91] Mireles F and Kirczenow G 2001 Phys. Rev. B 64 024426
[63] Liu C R, Chen X Z, Xu H Y, Huang L and Lai Y C 2018 Phys. Rev. B 98 115305
[92] Wang J, Sun H B and Xing D Y 2004 Phys. Rev. B 69 085304
[64] Pershin Y V and Privman V 2004 Phys. Rev. B 69 073310
[93] Sun Y, Wen Q Y and Yuan Z 2011 Opt. Commun. 284 527
[65] Chang C H, Mal'shukov A G and Chao K A 2004 Phys. Rev. B 70 245309
[94] Heo J, Hong C H, Lim J I and Yang H J 2013 Chin. Phys. Lett. 30 040301
[66] Akguc G B and Gong J 2008 Phys. Rev. B 77 205302
[67] Ying L and Lai Y C 2016 Phys. Rev. B 93 085408
[68] Frustaglia D, Montangero S and Fazio R 2006 Phys. Rev. B 74 165326
[69] Rashba E I 1960 Sov. Phys. Solid. State 2 1109
[70] Dresselhaus G and Dresselhaus M S 1965 Phys. Rev. A 140 A401
[71] Rashba E I 2000 Phys. Rev. B 62 R16267
[72] Gor'kov L P and Rashba E I 2001 Phys. Rev. Lett. 87 037004
[73] Koga T, Nitta J, Takayanagi H and Datta S 2002 Phys. Rev. Lett. 88 126601
[74] Rashba E I and Efros A L 2003 Phys. Rev. Lett. 91 126405
[75] Schliemann J, Egues J C and Loss D 2003 Phys. Rev. Lett. 90 146801
[76] Pramanik T, Adhikari S, Majumdar A, Home D and Pan A K 2010 Phys. Lett. A 374 1121
[77] Amiri F, Rastgoo S and Golshan M 2014 Phys. Lett. A 378 1985
[78] Luna-Acosta G A, Krokhin A A, Rodríguez M A and Hernández-Tejeda P H 1996 Phys. Rev. B 54 11410
[79] Mendoza M and Schulz P A 2005 Phys. Stat. Sol. (C) 2 3129
[80] Lin W A and Jensen R V 1997 Phys. Rev. E 56 5251
[81] Souma S and Nikolić B K 2004 Phys. Rev. B 70 195346
[82] Nikolić B K and Souma S 2005 Phys. Rev. B 71 195328
[83] Dragomirova R L and Nikolić B K 2007 Phys. Rev. B 75 085328
[84] Dey M, Maiti S K, Sil S and Karmakar S N 2013 J. Appl. Phys. 114 164318
[85] Zhang Y T, Song Z F and Li Y C 2008 Phys. Lett. A 373 144
[86] Safaiee R and Golshan M M 2017 Eur. Phys. J. B 90 121
[87] Usuki T, Saito M, Takatsu M, Kiehl R A and Yokoyama N 1995 Phys. Rev. B 52 8244
[88] Akis R, Ferry D K, Bird J P and Vasileska D 1999 Phys. Rev. B 60 2680
[89] Xiao X, Chen Z, Nie W, Zhou G and Li F 2014 J. Appl. Phys. 115 223709
[90] Datta S and Biswajit D 1990 Appl. Phys. Lett. 56 665
[91] Mireles F and Kirczenow G 2001 Phys. Rev. B 64 024426
[92] Wang J, Sun H B and Xing D Y 2004 Phys. Rev. B 69 085304
[93] Sun Y, Wen Q Y and Yuan Z 2011 Opt. Commun. 284 527
[94] Heo J, Hong C H, Lim J I and Yang H J 2013 Chin. Phys. Lett. 30 040301
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