JMP  Vol.2 No.9 , September 2011
Proposal for a Loophole-Free Bell Test with Electron Spins of Donors in Silicon
ABSTRACT
So far, all experimental tests of Bell inequalities which must be satisfied by all local realistic hidden-variable theories and are violated by quantum mechanical predictions have left at least one loophole open. We propose a feasible setup allowing for a loophole-free test of the Bell inequalities. Two electron spin qubits of donors31P in a nanoscale silicon host in different cavities 300 m apart are entangled through a bright coherent light and postselections using homodyne measurements. The electron spins are then read out randomly and independently by Alice and Bob, respectively, with unity efficiency in less than 0.7 µs by using optically induced spin to charge transduction detected by radio-frequency single electron transistor. A violation of Bell inequality larger than 37% and 18% is achievable provided that the detection accuracy is 0.99 and 0.95, respectively.

Cite this paper
nullF. Hong, S. Xiong, Y. Xiang and W. Tang, "Proposal for a Loophole-Free Bell Test with Electron Spins of Donors in Silicon," Journal of Modern Physics, Vol. 2 No. 9, 2011, pp. 1056-1061. doi: 10.4236/jmp.2011.29128.
References
[1]   J. F. Clauser and A. Shimony, “Bell’s Theorem. Experi-mental Tests and Implications,” Reports on Progress in Physics, Vol. 41, No. 12, 1978, pp. 1863-1883. doi:10.1088/0034-4885/41/12/002

[2]   A. Einstein, B. Podolsky and N. Rosen, “Can Quantum Mechanical Description of Physical Reality Be Considered Complete?” Physical Reviews, Vol. 47, No. 10, 1935, pp. 777-780. doi:10.1103/PhysRev.47.777

[3]   J. S. Bell, “On the Einstein Podolsky Rosen Paradox,” Physics, Vol. 1, No. 3, 1964, pp. 195-200.

[4]   J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Physical Review Letters, Vol. 23, No. 15, 1969, pp. 880-884. doi:10.1103/PhysRevLett.23.880

[5]   S. J. Freedman and J. F. Clauser, “Experimental Test of Local Hidden-Variable Theories,” Physical Review Letters, Vol. 28, No. 14, 1972, pp. 938-941. doi:10.1103/PhysRevLett.28.938

[6]   E. S. Fry and R. C. Thompson, “Experimental Test of Local Hidden-Variable Theories,” Physical Review Letters, Vol. 37, No. 8, 1976, pp. 465-468. doi:10.1103/PhysRevLett.37.465

[7]   A. Aspect, P. Grangier and G. Roger, “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedanken Experiment: A New Violation of Bell’s Inequalities,” Physical Review Letters, Vol. 49, 1982, p. 91. doi:10.1103/PhysRevLett.49.91

[8]   Z. Y. Ou and L. Mandel, “Violation of Bell’s Inequality and Classical Probability in a Two-Photon Correlation Experiment,” Physical Review Letters, Vol. 61, No. 1, 1988, pp. 50-53. doi:10.1103/PhysRevLett.61.50

[9]   P. R. Tapster, J. G. Rarity and P. C. M. Owens, “Violation of Bell’s Inequality over 4 km of Optical Fiber,” Physical Review Letters, Vol. 73, No. 14, 1994, pp. 1923-1926. doi:10.1103/PhysRevLett.73.1923

[10]   P. G. Kwiat, K. Mattle, H. Weinfurter and A. Zeilinger, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Physical Review Letters, Vol. 75, No. 24, 1995, pp. 4337-4341. doi:10.1103/PhysRevLett.75.4337

[11]   W. Tittel, J. Brendel, H. Zbinden and N. Gisin, “Violation of Bell Inequalities by Photons More Than 10 km Apart,” Physical Review Letters, Vol. 81, No. 17, 1998, pp. 3563-3566. doi:10.1103/PhysRevLett.81.3563

[12]   M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe and D. J. Wineland, “Experimental Violation of a Bell’s Inequality with Efficient Detection,” Nature, Vol. 409, 2001, pp. 791-794.

[13]   P. M. Pearle. “Hidden-Variable Example Based upon Data Rejection,” Physics Review D, Vol. 2, No. 8, 970, pp. 1418-1425.

[14]   E. Santos, “Critical Analysis of the Empirical Tests of Local Hidden-Variable Theories,” Physical Review A, Vol. 46, No.7, 1992, pp. 3646-3656. doi:10.1103/PhysRevA.46.3646

[15]   J. S. Bell, “Speakable and Unspeakable in Quantum Me-chanics,” Cambridge University Press, Cambridge, 1988.

[16]   E. Santos, “Constraints for the Violation of the Bell In-equality in Einstein-Podolsky-Rosen -Bohm Experiments,” Physical Review A, Vol. 200, 1995, p. 1.

[17]   S. F. Huelga, M. Ferrero and E. Santos, “Atomic-Cascade Experiment with Detection of the Recoil Atom,” Euro-physics Letters, Vol. 27, No. 3, 1994, p. 181.

[18]   E. S. Fry, T. Walther and S. Li, “Proposal for a Loophole Free Test of the Bell Inequalities,” Physical Review A, Vol. 52, no. 6, 1995, pp. 4381-4395. doi:10.1103/PhysRevA.52.4381

[19]   M. Freyberger, et al., “Proposed Test of Bells Inequality without a Detection Loophole by Using Entangled Ryd-berg Atoms,” Physical Review A, Vol. 53, No. 3, 1996, pp. 1232-1244. doi:10.1103/PhysRevA.53.1232

[20]   C. Simon and W. T. M. Irvine, “Robust Long-Distance Entanglement and a Loophole-Free Bell Test with Ions and Photons,” Physical Review Letters, Vol. 91, No. 11, 2003, pp. 1-4. doi:10.1103/PhysRevLett.91.110405

[21]   H. Nha and H. J. Carmichael, “Proposed Test of Quantum Nonlocality for Continuous Variables,” Physical Review Letters, Vol. 93, No. 2, 2004, Article ID: 020401. doi:10.1103/PhysRevLett.93.020401

[22]   R. Garcia-Patron, J. Fiurasek, N. J. Cerf, J. Wenger, R. Tualle-Brouri and P. Grangier, “Proposal for a Loo-phole-Free Bell Test Using Homodyne Detection,” Phys-ical Review Letters, Vol. 93, No. 13, 2004, Article ID: 130409.

[23]   B. E. Kane, “A Silicon-Based Nuclear Spin Quantum Computer,” Nature, Vol. 393, No. 6681, 1998, pp. 133- 137.

[24]   P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W. J. Munro and Y. Yamamoto, “Hybrid Quan-tum Repeater Using Bright Coherent Light,” Physical Review Letters, Vol. 96, 2006, Article ID: 240501. doi:10.1103/PhysRevLett.96.240501

[25]   R. J. Schoelkopf, P. Wahlgren, A. A. Kozhevnikov, P. Delsing and D. E. Prober, “The Radio-Frequency Sin-gle-Electron Transistor (RF-SET): A Fast and Ultrasensi-tive Electrometer,” Science, Vol. 280, No. 5367, 1998, pp. 1238-1242.

[26]   T. M. Buehler, D. J. Reilly, R. P. Starrett, A. D. Greentree, A. R. Hamilton, A. S. Dzurak and R. G. Clark, “Sin-gle-Shot Readout with the Radio-Frequency Sin-gle-Electron Transistor in the Presence of Charge Noise,” Applied Physics Letters, Vol. 86, No. 14, 2005, Article ID: 143117. doi:10.1063/1.1897423

[27]   M. J. Testolin, A. D. Greentree, C. J. Wellard and L. C. L. Hollenberg, “Optically Induced Spin-to-Charge Trans-duction in Donor-Spin Readout,” Physical Review B, Vol. 72, No. 19, 2005, Article ID: 195325. doi:10.1103/PhysRevB.72.195325

[28]   M. Leong, B. Doris, J. Kedzierski, K. Rim and M. Yang, “Silicon Device Scaling to the Sub-10-nm Regime,” Science, Vol. 306, No. 5704, 2004, pp. 2057-2060.

[29]   M. K?nig, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi and S.-C. Zhang, “Quantum Spin Hall Insulator State in HgTe Quantum Wells,” Science, Vol. 318, No. 5851, 2007, pp. 766-770.

[30]   L. C. L Hollenberg, C. J. Wellard, C. I. Pakes and A. G. Fowler, “Single-Spin Readout for Buried Dopant Semi-conductor Qubits,” Physical Review B, Vol. 69, No. 23, 2004, Article ID: 233301. doi:10.1103/PhysRevB.69.233301

[31]   T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro and Y. Yamamoto, “Hybrid Quantum Repeater Based on Dispersive CQED Interactions between Matter Qubits and Bright Coherent Light,” New Journal of Physics, Vol. 8, 2006, p. 184. doi:10.1088/1367-2630/8/9/184

[32]   M. O. Scully and M. S. Zubairy, “Quantum Optics,” Cambridge, 1997.

[33]   C. D. Hill, L. C. L. Hollenberg, A. G. Fowler, C. J. Wel-lard, A. D. Greentree and H.-S. Goan, “Global Control and Fast Solid-State Donor Electron Spin Quantum Computing,” Physical Review B, Vol. 72, No. 4, 2005, Article ID: 045350. doi:10.1103/PhysRevB.72.045350

[34]   N. Gisin, G. Ribordy, W. Tittel and H. Zbinden, “Quan-tum Cryptography,” Reviews of Modern Physics, Vol. 74, 2002, pp. 145-195. doi:10.1103/RevModPhys.74.145

[35]   O. Guise, J. T. Yates Jr. and J. Levy, “Patterning of Sub-10-nm Ge islands on Si(100) by Directed Self-Assembly,” Applied Physics Letters, Vol. 87, No. 17, 2005, Article ID: 171902. doi:10.1063/1.2112198

[36]   D. Karaiskaj, M. L. W. Thewalt, T. Ruf, M. Cardona, H. -J. Pohl, G. G. Deviaych, P. G. Sennikov and H. Riemann, “Photoluminescence of Isotopically Purified Silicon: How Sharp Are Bound Exciton Transitions?” Physical Review Letters, Vol. 86, No. 26, 2001, pp. 6010-6013. doi:10.1103/PhysRevLett.86.6010

 
 
Top