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Continuous-time quantum random walk is constructed when photons propagate passing the branches of the waveguide array. It is possible to make quantum simulator, based on the quantum walk in waveguides, on a commercial scale firstly, but there are still some problems such as input state, the structure and boundary of the waveguides that should be treated at present. A nearest-neighbor coupling model is used to deal with the question of coupled waveguides and an explicit analytical solution can be derived. Using the analytical solution, we analyze the effects of input state on particle number probability distribution function and the second-order coherence degree of the quantum walk process in periodic waveguides. The results show that the symmetry properties of the input state would influence the distribution of second-order coherence degree, but have little effect on the probability distribution function.
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Keywords:
- periodic waveguide array /
- quantum walk /
- second-order coherence degree /
- entanglement state
[1] Aharonov Y, Davidovich L, Zagury N 1993 Phys. Rev. A 48 1687
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[16] Guo G C, Zhou Z W 2000 Physics 11 695 (in Chinese) [郭光灿, 周正威 2000 物理 11 695]
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[1] Aharonov Y, Davidovich L, Zagury N 1993 Phys. Rev. A 48 1687
[2] Bacon D, Childs A M, Chuang I L, Kempe J, Leung D W, Zhou X 2001 Phys. Rev. A 64 062302
[3] Childs A M, Goldstone J 2004 Phys. Rev. A 70 042312
[4] Xue P, Sanders B C, Leibfried D 2009 Phys. Rev. Lett. 103 183602
[5] Luo H, Hu X L, Xue P 2011 3 198 (in Chinese) [骆浩, 胡小龙, 薛鹏 2011 量子光学学报 3 198]
[6] Zhang P, Ren X F, Zou X B, Liu B H Y, Huang Y F, Guo G C 2007 Phys. Rev. A 75 052310
[7] Amit Rai, Perk J H H 2008 Phys. Rev. A 78 042304
[8] Perets H B, Lahini Y, Pozzi F, Sorel M, Morandotti R, Silberberg Y 2008 Phys. Rev. Lett. 100 170506
[9] Bromberg Y, Lahini Y, Morandotti R, Silberberg Y 2009 Phys. Rev. Lett. 102 253904
[10] Peruzzo A, Lobino M, Matthews J C, Matsuda N, Politi A, Poulios K, Zhou X Q, Lahini Y, Ismail N, Worhoff K, Bromberg Y, Silberberg Y, Thompson M G 2010 Science 329 1500
[11] Sansoni L, Sciarrino F, Vallone G, Mataloni P, Crespi A, Ramponi R, Osellame R 2012 Phys. Rev. Lett. 108 010502
[12] Matthews J C F, Thompson M G 2012 Nature Photonics 6 45
[13] Solntsev A S, Sukhorukov A A, Neshev D N, Kivshar Y S 2012 Phys. Rev. Lett. 108 023601
[14] Aspuru-Guzik, Alan Walther, Philip 2012 Nature Physics 8 285
[15] Liu K, Li W D, Zhang W Z, Shi P, Ren C N, Gu Y J 2012 Acta Phys. Sin. 61 120301 (in Chinese) [刘凯, 李文东, 张闻钊, 史鹏, 任春年, 顾永建 2012 61 120301]
[16] Guo G C, Zhou Z W 2000 Physics 11 695 (in Chinese) [郭光灿, 周正威 2000 物理 11 695]
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