We present designs of all-optical reversible gates, namely, Feynman, Toffoli, Peres, and Feynman double gates, with optically controlled microresonators. To demonstrate the applicability, a bacteriorhodopsin protein-coated silica microcavity in contact between two tapered single-mode fibers has been used as an all-optical switch. Low-power control signals (<200？μW) at 532？nm and at 405？nm control the conformational states of the protein to switch a near infrared signal laser beam at 1310 or 1550？nm. This configuration has been used as a template to design four-port tunable resonant coupler logic gates. The proposed designs are general and can be implemented in both fiber-optic and integrated-optic formats and with any other coated photosensitive material. Advantages of directed logic, high Q-factor, tunability, compactness, low-power control signals, high fan-out, and flexibility of cascading switches in 2D/3D architectures to form circuits make the designs promising for practical applications. 1. Introduction There is tremendous research effort to achieve all-optical information processing for ultrafast and ultrahigh bandwidth communication and computing. The natural parallelism of optics along with advances in fabricating micro- and nanostructures has opened up exciting possibilities to generate, manipulate, and detect light and to tailor the optical molecular response for low-power all-optical computing [1–5]. A switch is the basic building block of information processing systems and optical logic gates are integral components of higher optical computing circuits. Conventional classical computing is based on Boolean logic that is irreversible, that is, the inputs cannot be inferred from the output, as the number of output bits is less than the inputs. This leads to destruction of information and hence to the dissipation of a large amount of energy [6–9]. Conservative and reversible logic circumvents this problem by having equal number of inputs and outputs and opening up the possibility of ultra-low power computing [6–9]. It is also compatible with revolutionary optical and quantum computing paradigms. Quantum arithmetic has to be built from reversible logical components, as unitary operations are reversible and hence quantum networks effecting elementary arithmetic operations such as addition, multiplication, and exponentiation cannot be directly deduced from their classical Boolean counterparts [10]. Several reversible logic gates have been proposed that include Fredkin gate (FG), Feynman gate, Toffoli gate (TG), Peres gate, and Feynman double gate
References
[1]
S. Roy, Ed., “Special issue on optical computing, circuits, devices and systems,” IET Circuits, Devices & Systems, vol. 5, no. 2, pp. 73–75, 2011.
[2]
H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nature Photonics, vol. 4, no. 5, pp. 261–263, 2010.
[3]
D. A. B. Miller, “Are optical transistors the logical next step?” Nature Photonics, vol. 4, no. 1, pp. 3–5, 2010.
[4]
J. L. O'Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nature Photonics, vol. 3, no. 12, pp. 687–695, 2009.
[5]
Q. Xu and R. Soref, “Reconfigurable optical directed-logic circuits using microresonator-based optical switches,” Optics Express, vol. 19, no. 6, pp. 5244–5259, 2011.
[6]
R. Landauer, “Irreversibility and heat generation in the computing process,” IBM Journal of Research and Development, vol. 5, no. 3, pp. 183–191, 1961.
[7]
C. H. Bennett, “Logical reversibility of computation,” IBM Journal of Research and Development, vol. 17, no. 6, pp. 525–532, 1973.
[8]
K. Maruyama, F. Nori, and V. Vedral, “The physics of Maxwell's demon and information,” Reviews of Modern Physics, vol. 81, no. 1, pp. 1–22, 2009.
[9]
H. J. Caulfield, L. Qian, C. S. Vikram et al., “Conservative optical logic devices: COLD,” Advances in Imaging and Electron Physics, vol. 142, pp. 1–52, 2006.
[10]
A. Peres, “Reversible logic and quantum computers,” Physical Review A, vol. 32, no. 6, pp. 3266–3276, 1985.
[11]
E. Fredkin and T. Toffoli, “Conservative logic,” International Journal of Theoretical Physics, vol. 21, no. 3-4, pp. 219–253, 1982.
[12]
A. Barenco, C. H. Bennett, R. Cleve et al., “Elementary gates for quantum computation,” Physical Review A, vol. 52, no. 5, pp. 3457–3467, 1995.
[13]
J. Shamir, H. J. Caulfield, W. Miceli, and R. J. Seymour, “Optical computing and the Fredkin Gates,” Applied Optics, vol. 25, no. 10, pp. 1604–1607, 1986.
[14]
G. J. Milburn, “Quantum optical Fredkin gate,” Physical Review Letters, vol. 62, no. 18, pp. 2124–2127, 1989.
[15]
L. Qian and H. J. Caulfield, “Abstract passive interferometers with applications to conservative logic,” Optik, vol. 116, no. 8, pp. 404–408, 2005.
[16]
E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature, vol. 409, no. 6816, pp. 46–52, 2001.
[17]
J. Fiurá？ek, “Linear-optics quantum Toffoli and Fredkin gates,” Physical Review A, vol. 73, no. 6, Article ID 062313, 7 pages, 2006.
[18]
K. Morita, “Reversible computing and cellular automata—a survey,” Theoretical Computer Science, vol. 395, no. 1, pp. 101–131, 2008.
[19]
H. J. Caulfield, R. A. Soref, and C. S. Vikram, “Universal reconfigurable optical logic with silicon-on-insulator resonant structures,” Photonics and Nanostructures, vol. 5, no. 1, pp. 14–20, 2007.
[20]
X. Q. Shao, J. J. Wen, X. R. Jin, A. D. Zhu, S. Zhang, and K. H. Yeon, “Efficient scheme for implementing a Fredkin gate via resonant interaction with two-mode cavity quantum electrodynamics,” Chinese Physics Letters, vol. 24, no. 10, pp. 2730–2732, 2007.
[21]
A. R. Trivedi and S. Bandyopadhyay, “Single spin Toffoli-Fredkin logic gate,” Journal of Applied Physics, vol. 103, no. 10, Article ID 104311, 5 pages, 2008.
[22]
D. H. Wood and J. Chen, “Fredkin gate circuits via recombination enzymes,” Proceedings of the IEEE Congress on Evolutionary Computation (CEC '04), vol. 2, pp. 1896–1900, 2004.
[23]
A. J. Poustie and K. J. Blow, “Demonstration of an all-optical Fredkin gate,” Optics Communications, vol. 174, no. 1–4, pp. 317–320, 2000.
[24]
N. Kostinski, M. P. Fok, and P. R. Prucnal, “Experimental demonstration of an all-optical fiber-based Fredkin gate,” Optics Letters, vol. 34, no. 18, pp. 2766–2768, 2009.
[25]
P. Remón, R. Ferreira, J. M. Montenegro, R. Suau, E. Pérez-Inestrosa, and U. Pischel, “Reversible molecular logic: a photophysical example of a Feynman Gate,” ChemPhysChem, vol. 10, no. 12, pp. 2004–2007, 2009.
[26]
T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Physical Review A, vol. 75, no. 2, Article ID 022313, 5 pages, 2007.
[27]
S. X. Qiang, C. Li, and Z. Shou, “Two simple schemes for implementing Toffoli gate via atom-cavity field interaction in cavity quantum electrodynamics,” Chinese Physics B, vol. 18, no. 2, pp. 440–445, 2009.
[28]
T. Monz, K. Kim, W. H？nsel et al., “Realization of the quantum Toffoli gate with trapped ions,” Physical Review Letters, vol. 102, no. 4, Article ID 040501, 2009.
[29]
K. J. Vahala, “Optical microcavities,” Nature, vol. 424, no. 6950, pp. 839–846, 2003.
[30]
S. J. B. Yoo, “Future prospects of silicon photonics in next generation communication and computing systems,” Electronics Letters, vol. 45, no. 12, pp. 584–588, 2009.
[31]
L. D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Optics Express, vol. 17, no. 23, pp. 21108–21117, 2009.
[32]
T. A. Ibrahim, R. Grover, L. C. Kuo, S. Kanakaraju, L. C. Calhoun, and P. T. Ho, “All-optical AND/NAND logic gates using semiconductor microresonators,” IEEE Photonics Technology Letters, vol. 15, no. 10, pp. 1422–1424, 2003.
[33]
T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, “Optical circuits based on polariton neurons in semiconductor microcavities,” Physical Review Letters, vol. 101, no. 1, Article ID 016402, 4 pages, 2008.
[34]
M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nature Photonics, vol. 2, no. 12, pp. 741–747, 2008.
[35]
M. Trupke, J. Goldwin, B. Darquié et al., “Atom detection and photon production in a scalable, open, optical microcavity,” Physical Review Letters, vol. 99, no. 6, Article ID 063601, 2007.
[36]
D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature, vol. 421, no. 6926, pp. 925–928, 2003.
[37]
M. P？llinger, D. O'Shea, F. Warken, and A. Rauschenbeutel, “Ultrahigh-Q tunable whispering-gallery-mode microresonator,” Physical Review Letters, vol. 103, no. 5, Article ID 053901, 2009.
[38]
F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nature Methods, vol. 5, no. 7, pp. 591–596, 2008.
[39]
H. C. Tapalian, J. P. Laine, and P. A. Lane, “Thermooptical switches using coated microsphere resonators,” IEEE Photonics Technology Letters, vol. 14, no. 8, pp. 1118–1120, 2002.
[40]
A. Tewary, M. J. F. Digonnet, J. Y. Sung, J. H. Shin, and M. L. Brongersma, “Silicon-nanocrystal-coated silica microsphere thermooptical switch,” IEEE Journal on Selected Topics in Quantum Electronics, vol. 12, no. 6, pp. 1476–1479, 2006.
[41]
D. Oesterhelt and W. Stoeckenius, “Rhodopsin-like protein from the purple membrane of Halobacterium halobium,” Nature, vol. 233, no. 39, pp. 149–152, 1979.
[42]
R. R. Birge, “Photophysics and molecular electronic applications of the rhodopsins,” Annual Review of Physical Chemistry, vol. 41, no. 1, pp. 683–733, 1990.
[43]
D. Oesterhelt, C. Brauchle, and N. Hampp, “Bacteriorhodopsin: a biological material for information processing,” Quarterly Reviews of Biophysics, vol. 24, no. 4, pp. 425–478, 1991.
[44]
N. Hampp, “Bacteriorhodopsin as a photochromic retinal protein for optical memories,” Chemical Reviews, vol. 100, no. 5, pp. 1755–1776, 2000.
[45]
S. Roy, C. P. Singh, and K. P. J. Reddy, “Generalized model for all-optical light modulation in bacteriorhodopsin,” Journal of Applied Physics, vol. 90, no. 8, pp. 3679–3688, 2001.
[46]
N. Hampp and D. Oesterhelt, “Nanobiotechnology: concepts, applications and perspectives,” in Nanobiotechnology, C. Niemeyer and C. Mirkin, Eds., pp. 146–167, Wiley-VCH Verlag GmbH & Co., Weinheim, Germany, 2004.
[47]
J. Topolancik and F. Vollmer, “All-optical switching in the near infrared with bacteriorhodopsin-coated microcavities,” Applied Physics Letters, vol. 89, no. 18, Article ID 184103, pp. 1–3, 2006.
[48]
J. Topolancik and F. Vollmer, “Photoinduced transformations in bacteriorhodopsin membrane monitored with optical microcavities,” Biophysical Journal, vol. 92, no. 6, pp. 2223–2229, 2007.
[49]
S. Roy, M. Prasad, J. Topolancik, and F. Vollmer, “All-optical switching with bacteriorhodopsin protein coated microcavities and its application to low power computing circuits,” Journal of Applied Physics, vol. 107, no. 5, Article ID 053115, 9 pages, 2010.
[50]
S. Roy and M. Prasad, “Novel proposal for all-optical Fredkin logic gate with bacteriorhodopsin coated microcavity and its applications,” Optical Engineering, vol. 49, no. 6, Article ID 065201, 11 pages, 2010.
[51]
C. P. Singh and S. Roy, “All-optical switching in bacteriorhodopsin based on M state dynamics and its application to photonic logic gates,” Optics Communications, vol. 218, no. 1–3, pp. 55–66, 2003.
[52]
S. Shim, J. Dasgupta, and R. A. Mathies, “Femtosecond time-resolved stimulated raman reveals the birth of bacteriorhodopsin's J and K intermediates,” Journal of the American Chemical Society, vol. 131, no. 22, pp. 7592–7597, 2009.
[53]
L. Fabian, E. K. Wolff, L. Oroszi, P. Ormos, and A. Der, “Fast integrated optical switching by the protein bacteriorhodopsin,” Applied Physics Letters, vol. 97, no. 2, Article ID 023305, 7 pages, 2010.
[54]
M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Physical Review Letters, vol. 85, no. 1, pp. 74–77, 2000.
[55]
D. Sridharan, E. Waks, G. Solomon, and J. T. Fourkas, “Reversible tuning of photonic crystal cavities using photochromic thin films,” Applied Physics Letters, vol. 96, no. 15, Article ID 153303, pp. 1–3, 2010.
[56]
J. Nag, J. D. Ryckman, M. T. Hertkorn, B. K. Choi, R. F. Haglund, and S. M. Weiss, “Ultrafast compact silicon-based ring resonator modulators using metal-insulator switching of vanadium dioxide,” in Physics and Simulation of Optoelectronic Devices 18, vol. 7597 of Proceedings of SPIE, pp. 0–9, 2010.
