Dissipatively driven entanglement of two macroscopic atomic ensembles

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 83, Issue 5, 2011, Pages

  Muschik, Christine A ^a   Polzik, Eugene S ^b   Cirac, J Ignacio ^a  

^a MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC ENSEMBLE; ATOMIC SYSTEM; DECOHERENCE; DIPOLE DIPOLE INTERACTIONS; ENGINEERED ENVIRONMENTS; ENTANGLED STATE; ENTANGLEMENT GENERATION; ROBUST METHODS; THEORETICAL FRAMEWORK; TWO-LEVEL SYSTEM; VACUUM MODES;

ATOMS; ELECTROMAGNETIC FIELDS;

QUANTUM ENTANGLEMENT;

EID: 79961061736     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.83.052312     Document Type: Article

References (88)

1. H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.5932 81, 5932 (1998).
2. L.-M. Duan, J. I. Cirac, M. Lukin, and P. Zoller, Nature (London) NATUAS 0028-0836 10.1038/35106500 414, 413 (2001). (Pubitemid 34173718)
3. P. Zoller, Eur. Phys. J. D EPJDF6 1434-6060 10.1140/epjd/e2005-00251-1 36, 203 (2005). (Pubitemid 41442672)
4. T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S.-Y. Lan, T.A. B. Kennedy, and A. Kuzmich, Nature (London) NATUAS 0028-0836 10.1038/nature04315 438, 833 (2005). (Pubitemid 41753062)
5. C. W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, Nature (London) NATUAS 0028-0836 10.1038/nature04353 438, 828 (2005). (Pubitemid 41753061)
6. M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, Nature (London) NATUAS 0028-0836 10.1038/nature04327 438, 837 (2005). (Pubitemid 41753063)
7. H. J. Kimble, Nature (London) NATUAS 0028-0836 10.1038/nature07127 453, 1023 (2008). (Pubitemid 351871745)
8. Z. Yuan, Nature (London) NATUAS 0028-0836 10.1038/nature07241 454, 1098 (2008).
9. K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, Nature (London) NATUAS 0028-0836 10.1038/nature06670 452, 67 (2008). (Pubitemid 351356101)
10. Y.-A. Chen, S. Chen, Z.-S. Yuan, B. Zhao, C.-S. Chuu, Jörg Schmiedmayer, and J.-W. Pan, Nat. Phys. NATUAS 1745-2473 10.1038/nphys832 4, 103 (2008).
11. K. Hammerer, A. S. Sørensen, and E. S. Polzik, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.82.1041 82, 1041 (2010).
12. J. F. Poyatos, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.4728 77, 4728 (1996).
13. M. B. Plenio, S. F. Huelga, A. Beige, and P. L. Knight, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.2468 59, 2468 (1999). (Pubitemid 40648397)
14. A. Beige, D. Braun, and P. L. Knight, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/2/1/322 2, 22 (2000).
15. A. Beige, S. Bose, D. Braun, S. F. Huelga, P. L. Knight, M. B. Plenio, and V. Vedral, J. Mod. Opt. 10.1080/09500340008232183 47, 2583 (2000).
16. A. Beige, D. Braun, B. Tregenna, and P. L. Knight, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.1762 85, 1762 (2000).
17. C. Myatt, Nature (London) NATUAS 0028-0836 10.1038/35002001 403, 269 (2000). (Pubitemid 30062375)
18. M. B. Plenio and S. F. Huelga, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.197901 88, 197901 (2002).
19. X. X. Yi, C. S. Yu, L. Zhou, and H. S. Song, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.052304 68, 052304 (2003).
20. B. Kraus and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.013602 92, 013602 (2004).
21. S. Mancini and J. Wang, Eur. Phys. J. D EPJDF6 1434-6060 10.1140/epjd/e2004-00187-x 32, 257 (2004).
22. B. Baumgartner, H. Narnhofer, and W. Thirring, J. Phys. A EPJDF6 1751-8113 10.1088/1751-8113/41/6/065201 41, 065201 (2007).
23. R. Doll, M. Wubs, P. Hänggi, and S. Kohler, Phys. Rev. B EPJDF6 1098-0121 10.1103/PhysRevB.76.045317 76, 045317 (2007).
24. B. Kraus, H. P. Büchler, S. Diehl, A. Kantian, A. Micheli, and P. Zoller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.042307 78, 042307 (2008).
25. M. Branderhorst, Science SCIEAS 0036-8075 10.1126/science.1154576 320, 638 (2008). (Pubitemid 351934118)
26. N. Syassen, Science SCIEAS 0036-8075 10.1126/science.1155309 320, 1329 (2008). (Pubitemid 351929467)
27. S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. P. Büchler, and P. Zoller, Nat. Phys. SCIEAS 1745-2473 10.1038/nphys1073 4, 878 (2008).
28. R. Doll, P. Hänggi, S. Kohler, and M. Wubs, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2009-00115-6 68, 1434 (2009).
29. F. Verstraete, M. M. Wolf, and J. I. Cirac, Nat. Phys. EPJBFY 1745-2473 10.1038/nphys1342 5, 633 (2009).
30. M. Hor-Meyll, A. Auyuanet, C. V. S. Borges, A. Aragao, J. A. O. Huguenin, A. Z. Khoury, and L. Davidovich, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.042327 80, 042327 (2009).
31. G. Vacanti and A. Beige, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/11/8/083008 11, 083008 (2009).
32. A. Isar, Open Sys. Inf. Dynam. NJOPFM 1230-1612 10.1142/S1230161209000153 16, 205 (2009).
33. M. Ludwig, K. Hammerer, and F. Marquart, Phys. Rev. A 1050-2947 10.1103/PhysRevA.82.012333 82, 012333 (2010).
34. D. G. Angelakis, S. Mancini, and S. Bose, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/85/20007 85, 20007 (2009).
35. D. G. Angelakis, L. Dai, and L.-C. Kwek, Europhys. Lett. 0295-5075 10.1209/0295-5075/91/10003 91, 10003 (2010).
36. H. Weimer, M. Müller, I. Lesanovsky, P. Zoller, and H. P. Büchler, Nature Phys. 1745-2473 10.1038/nphys1614 6, 382 (2010).
37. F. Benatti, R. Floreanini, and U. Marzolino, Phys. Rev. A 1050-2947 10.1103/PhysRevA.81.012105 81, 012105 (2010).
38. K. Temme, M. M. Wolf, and F. Verstraete, e-print arXiv: 0912.0858.
39. S. Pielawa, L. Davidovich, D. Vitaly, and G. Morigi, Phys. Rev. A 1050-2947 10.1103/PhysRevA.81.043802 81, 043802 (2010).
40. G. Goldstein, P. Cappellaro, J. R. Maze, J. S. Hodges, L. Jiang, A. S. Sorensen, and M. D. Lukin, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.106. 140502 106, 140502 (2011).
41. X. Wang and S. G. Schirmer, e-print arXiv: 1005.2114.
42. E. de Valle, JOSA B 10.1364/JOSAB.28.000228 28, 228 (2011).
43. M. Kiffner and M. J. Hartmann, Phys. Rev. A 1050-2947 10.1103/PhysRevA.82.033813 82, 033813 (2010).
44. M. Kiffner and M. J. Hartmann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.021806 81, 021806 (R) (2010).
45. S. Pielawa, L. Davidovich, D. Vitali, and G. Morigi, Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.043802 81, 043802 (2010).
46. J. T. Barreiro, P. Schindler, O. Gühne, T. Monz, M. Chwalla, C. F. Roos, M. Hennrich, and R. Blatt, Nature Phys. 1745-2473 10.1038/nphys1781 6, 943 (2010).
47. A. S. Parkins, E. Solano, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.053602 96, 053602 (2006). (Pubitemid 43270955)
48. If the dissipatively generated entanglement is to be used in standard schemes, the driving fields which stabilize the state are switched off and the entangled atomic state can either be used directly (for example, for teleportation) or read out on demand.
49. K. G. H. Vollbrecht, C. A. Muschik, and J. I. Cirac, e-print arXiv: 1011.4115.
50. L. M. Duan, J. I. Cirac, P. Zoller, and E. S. Polzik, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.5643 85, 5643 (2000). (Pubitemid 32090285)
51. B. Julsgaard, A. Kozhekin, and E. S. Polzik, Nature (London) NATUAS 0028-0836 10.1038/35096524 413, 400 (2001). (Pubitemid 32928590)
52. W. Wasilewski, T. Fernholz, K. Jensen, L. S. Madsen, H. Krauter, C. Muschik, and E. S. Polzik, Opt. Express 10.1364/OE.17.014444 17, 14444 (2009).
53. We use operators A, B labeled with a tilde for bosonic modes. Later in the text, operators A, B without a tilde are used to denote linear combinations of spins.
54. M. G. Raymer, A. C. Funk, B. C. Sanders, and H. de Guise, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.052104 67, 052104 (2003).
55. x = 12.
56. For large, strongly polarized atomic ensembles, collective spins can be described by bosonic modes J I - a, J II - b using the Holstein-Primakoff approximation. The results derived here are based on related approximations and are valid for N 1 (compare Appendix).
57. 2) / √ 2 if a photon is detected at one of the two output ports.
58. H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, e-print arXiv: 1006.4344.
59. †] = 1.
60. m = ± 1.
61. Undesired radiative transitions | → | and | → | involve the emission of a photon but no change of the internal atomic state. These processes are not explicitly shown in Fig..
62. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley, New York, 1998).
63. atomic.
64. R. H. Lehmberg, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.2.883 2, 883 (1970).
65. D. Porras and J. I. Cirac, e-print arXiv: 0704.0641.
66. D. Porras and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.053816 78, 053816 (2008).
67. L.-M. Duan, J. I. Cirac, and P. Zoller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.023818 66, 023818 (2002).
68. An analysis of the generation of entanglement between two atomic ensembles in the opposite limit of fixed atomic positions can be found in O. Mishina, D. Kupriyanov, and E. S. Polzik, in Proceedings of the NATO Advanced Research Workshop, Crete 2005: Quantum Communication and Security, NATO Sciences Series, III: Computer and Systems, Vol. 199, pp. 346.
69. In the two-level model shown in Fig., Γ d rad, probe = 2 (Γ cool probe + Γ heat probe), due to the ratio of Clebsch-Gordan coefficients | 1 2, ± 1 2; 1, 1 | 1 2, 1 2 | 2 / | 1 2, ± 1 2; 1, 0 | 1 2, ± 1 2 | 2 = 2.
70. LW.
71. B is the Boltzmann constant, T is the temperature, and m is the atomic mass.
72. T. J. Kippenberg and K. Vahala, Science 0036-8075 10.1126/science.1156032 321, 1172 (2008).
73. F. Marquart and S. M. Girvin, Physics 1943-2879 10.1103/Physics.2.40 2, 40 (2009).
74. M. Aspelmeyer, S. Gröblacher, K. Hammerer, and N. Kiesel, J. Opt. Soc. Am. B JOBPDE 0740-3224 10.1364/JOSAB.27.00A189 27, A189 (2010)
75. (JOSA B Feature Issue on Quantum Optical Information Technologies, edited by, P. Grangier, A. Jordan, and, G. Morigi,).
76. I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.093901 99, 093901 (2007). (Pubitemid 47331119)
77. F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.093902 99, 093902 (2007). (Pubitemid 47331118)
78. C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.033804 77, 033804 (2008). (Pubitemid 351393428)
79. † b = 0 in the steady state.
80. L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.2722 84, 2722 (2000).
81. R. Simon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.2726 84, 2726 (2000).
82. T. Holstein and H. Primakoff, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.58.1098 58, 1098 (1940).
83. ij, A as discussed in Appendix 2.
84. x . The decorrelation approximation is justified as long as only a small number of collective (coherent) excitations is created in the atomic sample. In practice, the degree of squeezing, which can be produced in atomic samples, is small, such that the decorrelation approximation is a reasonable assumption for the settings considered in this article.
85. x [compare Eq.] in the steady state and the error is by a factor N smaller than J x 2 for all times.
86. M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.5094 84, 5094 (2000).
87. M. D. Lukin, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.75.457 75, 457 (2003). (Pubitemid 36719928)
88. A. V. Gorshkov, A. André, M. D. Lukin, and A. S. Sø rensen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.033804 76, 033804 (2007). (Pubitemid 47429392)