Abstract

Photonic-crystal-based integrated optical systems have been used for a broad range of sensing applications with great success. This has been motivated by several advantages such as high sensitivity, miniaturization, remote sensing, selectivity and stability. Many photonic crystal sensors have been proposed with various fabrication designs that result in improved optical properties. In parallel, integrated optical systems are being pursued as a platform for photonic quantum information processing using linear optics and Fock states. Here we propose a novel integrated Fock state optical sensor architecture that can be used for force, refractive index and possibly local temperature detection. In this scheme, two coupled cavities behave as an “effective beam splitter”. The sensor works based on fourth order interference (the Hong-Ou-Mandel effect) and requires a sequence of single photon pulses and consequently has low pulse power. Changes in the parameter to be measured induce variations in the effective beam splitter reflectivity and result in changes to the visibility of interference. We demonstrate this generic scheme in coupled L3 photonic crystal cavities as an example and find that this system, which only relies on photon coincidence detection and does not need any spectral resolution, can estimate forces as small as 10−7 Newtons and can measure one part per million change in refractive index using a very low input power of 10−10W. Thus linear optical quantum photonic architectures can achieve comparable sensor performance to semiclassical devices.

© 2015 Optical Society of America

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2014 (2)

S. Chakravarty, A. Hosseini, X. Xu, L. Zhu, Y. Zou, and R. T. Chen, “Analysis of ultra-high sensitivity configuration in chip-integrated photonic crystal microcavity bio-sensors,” Appl. Phys. Lett. 104(19), 191109 (2014).
[Crossref] [PubMed]

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[Crossref] [PubMed]

2013 (9)

J. D. Cohen, S. M. Meenehan, and O. Painter, “Optical coupling to nanoscale optomechanical cavities for near quantum-limited motion transduction,” Opt. Express 21(9), 11227–11236 (2013).
[Crossref] [PubMed]

M. J. Collins, C. Xiong, I.H. Rey, T.D. Vo, J. He, S. Shahnia, C. Reardon, T.F. Krauss, M.J. Steel, A.S. Clark, and B.J. Eggleton, “Integrated spatial multiplexing of heralded single-photon sources,” Nat. Commun. 4, 3582 (2013).
[Crossref]

C. Lang, C. Eichler, L. Steffen, J. M. Fink, M. J. Woolley, A. Blais, and A. Wallraff, “Correlations, indistinguishability and entanglement in Hong-Ou-Mandel experiments at microwave frequencies,” Nature Phys. 9(6), 345–348 (2013).
[Crossref]

Y. Yang, D. Yang, H. Tian, and Y. Ji, “Photonic crystal stress sensor with high sensitivity in double directions based on shoulder-coupled aslant nanocavity,” Sens. Actuators A 193, 149–154 (2013).
[Crossref]

D. Yang, H. Tian, N. Wu, Y. Yang, and Y. Ji, “Nanoscale torsion-free photonic crystal pressure sensor with ultra-high sensitivity based on side-coupled piston-type microcavity,” Sens. Actuators A 199, 30–36 (2013).
[Crossref]

D. K. Wu, K. J. Lee, V. Pureur, and B. T. Kuhlmey, “Performance of refractive index sensors based on directional couplers in photonic crystal fibers,” J. Lightwave Technol. 31(22), 3500–3510 (2013).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H. A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

M. G. Scullion, T. F. Krauss, and A. Di Falco, “Slotted photonic crystal sensors,” Sensors 13(3), 3675–3710 (2013).
[Crossref] [PubMed]

S. Haddadi, A. M. Yacomotti, I. Sagnes, F. Raineri, G. Beaudoin, L. Le Gratiet, and J. A. Levenson, “Photonic crystal coupled cavities with increased beaming and free space coupling efficiency,” Appl. Phys. Lett. 102(1), 011107 (2013).
[Crossref]

2012 (5)

A. M. R. Pinto, J. M. Baptista, J. L. Santos, M. Lopez-Amo, and O. Frazão, “Micro-displacement sensor based on a hollow-core photonic crystal fiber,” Sensors 12(12), 17497–17503 (2012).
[Crossref]

S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335(6076), 1603–1606 (2012).
[Crossref] [PubMed]

E. Gavartin, P. Verlot, and T. J. A. Kippenberg, “Hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7(8), 509–514 (2012).
[Crossref] [PubMed]

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6(11), 768–772 (2012).
[Crossref]

S. Buckley, K. Rivoire, and J. Vuckovic, “Engineered quantum dot single-photon sources,” Rep. Prog. Phys. 75(12), 126503 (2012).
[Crossref] [PubMed]

2011 (8)

M. Jääskeläinen, M. Lombard, and U. Zülicke, “Refraction in spacetime,” Am. J. Phys. 79(6), 672–677 (2011).
[Crossref]

A. Faraon, A. Majumdar, D. Englund, E. Kim, M. Bajcsy, and J. Vuckovi, “Integrated quantum optical networks based on quantum dots and photonic crystals,” New J. Phys. 13(5), 055025 (2011).
[Crossref]

A Datta, L. Zhang, N. Thomas-Peter, U. Dorner, B. J. Smith, and I. A. Walmsley, “Quantum metrology with imperfect states and detectors,” Phys. Rev. A 83(6), 063836 (2011).
[Crossref]

E. Stock, W. Unrau, A. Lochmann, J. A. Töfflinger, M. Öztürk, A. I. Toropov, A. K. Bakarov, V. A. Haisler, and D. Bimberg, “High-speed single-photon source based on self-organized quantum dots,” Semicond. Sci. Technol. 26(1), 014003 (2011).
[Crossref]

J. T. Heeres and P. J. Hergenrother, “High-throughput screening for modulators of protein-protein interactions: use of photonic crystal biosensors and complementary technologies,” Chem. Soc. Rev. 40(8), 4398–4410 (2011).
[Crossref]

J. T. Zhang, L. Wang, J. Luo, A. Tikhonov, N. Kornienko, and S. A. Asher, “2-D array photonic crystal sensing motif,” J. Am. Chem. Soc. 133(24), 9152–9155 (2011).
[Crossref] [PubMed]

K. A. Atlasov, R. Rudra, B. Dwir, and E. Kapon, “Large mode splitting and lasing in optimally coupled photonic-crystal microcavities,” Opt. Express 19(3), 2619–2625 (2011).
[Crossref] [PubMed]

A. R. A. Chalcraft, S. Lam, B. D. Jones, D. Szymanski, R. Oulton, A. C. T. Thijssen, M. S. Skolnick, D. M. Whittaker, T. F. Krauss, and A. M. Fox, “Mode structure of coupled L3 photonic crystal cavities,” Opt. Express 19(6), 5670–5675 (2011).
[Crossref] [PubMed]

2010 (1)

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nature Photon. 4(7), 477–483 (2010).
[Crossref]

2009 (3)

D. K. C. Wu, B. T. Kuhlmey, and B. J. Eggleton, “Ultrasensitive photonic crystal fiber refractive index sensor,” Opt. Express 34(3), 322–324 (2009).

R. Maiwald, D. Leibfried, J. Britton, J. C. Bergquist, G. Leuchs, and D. J. Wineland, “Stylus ion trap for enhanced access and sensing,” Nat. Phys. 5(8), 551–554 (2009).
[Crossref]

A. Di Falco, L. O’Faolain, and T. F. Krauss, “Chemical sensing in slotted photonic crystal heterostructure cavities,” Appl. Phys. Lett. 94(6), 063503 (2009).
[Crossref]

2008 (4)

S. C. Buswell, V. A. Wright, J. M. Buriak, V. Van, and S. Evoy, “Specific detection of proteins using photonic crystal waveguides,” Opt. Express 16(20), 15949–15957 (2008).
[Crossref] [PubMed]

K. A. Atlasov, K. F. Karlsson, A. Rudra, B. Dwir, and E. Kapon, “Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities,” Opt. Express 16(20), 16255–16264 (2008).
[Crossref] [PubMed]

O. Frazão, J. L. Santos, F. M. Arajo, and L. A. Ferreira, “Optical sensing with photonic crystal fibers,” Laser Photonics Rev. 2(6), 449–459 (2008).
[Crossref]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

2007 (1)

2005 (1)

W. C. L. Hopman, P. Pottier, D. Yudistira, J. van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. J. W. M. Hoekstra, and R. M. de Ridder, “Quasi-one-dimensional photonic crystal as a compact building-block for refractometric optical sensors,” IEEE J. Sel. Top. Quantum Electron. 11(1), 11–16 (2005).
[Crossref]

2004 (1)

E. Chow, A. Grot, L. W. Mirkarimi, M. Sigalas, and G. Girolami, “Ultracompact biochemical sensor built with two-dimensional photonic crystal microcavity,” Opt. Express 29(10), 1093–1095 (2004).

2001 (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[Crossref] [PubMed]

1999 (1)

L. A. A. Pettersson, L. S. Roman, and O. Inganas, “Modeling photocurrent action spectra of photovoltaic devices based on organic thin films,” J. Appl. Phys. 86(1), 487–496 (1999).
[Crossref]

1997 (1)

M. M. A. Marte and S. Stenholm, “Paraxial light and atom optics: the optical Schrödinger equation and beyond,” Phys. Rev. A 56(4), 2940 (1997).
[Crossref]

1996 (1)

S. L. Braunstein, C. M. Caves, and G. J. Milburn, “Generalized uncertainty relations: Theory, examples, and Lorentz invariance,” Ann. Phys. 247, 135–173 (1996).
[Crossref]

1993 (1)

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71(9), 1355 (1993).
[Crossref] [PubMed]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044 (1987).
[Crossref] [PubMed]

Arajo, F. M.

O. Frazão, J. L. Santos, F. M. Arajo, and L. A. Ferreira, “Optical sensing with photonic crystal fibers,” Laser Photonics Rev. 2(6), 449–459 (2008).
[Crossref]

Asher, S. A.

J. T. Zhang, L. Wang, J. Luo, A. Tikhonov, N. Kornienko, and S. A. Asher, “2-D array photonic crystal sensing motif,” J. Am. Chem. Soc. 133(24), 9152–9155 (2011).
[Crossref] [PubMed]

Atlasov, K. A.

Bachor, H. A.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H. A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Bajcsy, M.

A. Faraon, A. Majumdar, D. Englund, E. Kim, M. Bajcsy, and J. Vuckovi, “Integrated quantum optical networks based on quantum dots and photonic crystals,” New J. Phys. 13(5), 055025 (2011).
[Crossref]

Bakarov, A. K.

E. Stock, W. Unrau, A. Lochmann, J. A. Töfflinger, M. Öztürk, A. I. Toropov, A. K. Bakarov, V. A. Haisler, and D. Bimberg, “High-speed single-photon source based on self-organized quantum dots,” Semicond. Sci. Technol. 26(1), 014003 (2011).
[Crossref]

Baptista, J. M.

A. M. R. Pinto, J. M. Baptista, J. L. Santos, M. Lopez-Amo, and O. Frazão, “Micro-displacement sensor based on a hollow-core photonic crystal fiber,” Sensors 12(12), 17497–17503 (2012).
[Crossref]

Beaudoin, G.

S. Haddadi, A. M. Yacomotti, I. Sagnes, F. Raineri, G. Beaudoin, L. Le Gratiet, and J. A. Levenson, “Photonic crystal coupled cavities with increased beaming and free space coupling efficiency,” Appl. Phys. Lett. 102(1), 011107 (2013).
[Crossref]

Bennett, S. D.

S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335(6076), 1603–1606 (2012).
[Crossref] [PubMed]

Bergquist, J. C.

R. Maiwald, D. Leibfried, J. Britton, J. C. Bergquist, G. Leuchs, and D. J. Wineland, “Stylus ion trap for enhanced access and sensing,” Nat. Phys. 5(8), 551–554 (2009).
[Crossref]

Bimberg, D.

E. Stock, W. Unrau, A. Lochmann, J. A. Töfflinger, M. Öztürk, A. I. Toropov, A. K. Bakarov, V. A. Haisler, and D. Bimberg, “High-speed single-photon source based on self-organized quantum dots,” Semicond. Sci. Technol. 26(1), 014003 (2011).
[Crossref]

Blais, A.

C. Lang, C. Eichler, L. Steffen, J. M. Fink, M. J. Woolley, A. Blais, and A. Wallraff, “Correlations, indistinguishability and entanglement in Hong-Ou-Mandel experiments at microwave frequencies,” Nature Phys. 9(6), 345–348 (2013).
[Crossref]

Blasius, T. D.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6(11), 768–772 (2012).
[Crossref]

Booth, M. J.

Bowen, W. P.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H. A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nat. Photonics 7(3), 229–233 (2013).
[Crossref]

Braunstein, S. L.

S. L. Braunstein, C. M. Caves, and G. J. Milburn, “Generalized uncertainty relations: Theory, examples, and Lorentz invariance,” Ann. Phys. 247, 135–173 (1996).
[Crossref]

Britton, J.

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Rep. Prog. Phys. (1)

S. Buckley, K. Rivoire, and J. Vuckovic, “Engineered quantum dot single-photon sources,” Rep. Prog. Phys. 75(12), 126503 (2012).
[Crossref] [PubMed]

Science (2)

S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335(6076), 1603–1606 (2012).
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Semicond. Sci. Technol. (1)

E. Stock, W. Unrau, A. Lochmann, J. A. Töfflinger, M. Öztürk, A. I. Toropov, A. K. Bakarov, V. A. Haisler, and D. Bimberg, “High-speed single-photon source based on self-organized quantum dots,” Semicond. Sci. Technol. 26(1), 014003 (2011).
[Crossref]

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Y. Yang, D. Yang, H. Tian, and Y. Ji, “Photonic crystal stress sensor with high sensitivity in double directions based on shoulder-coupled aslant nanocavity,” Sens. Actuators A 193, 149–154 (2013).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Schematic of quantum PhC sensor. Coupled PhC resonators implement an effective beam splitter interaction between the input single photon fields resulting in HOM interference effect observed in detected output fields. G(2)(τ) is a measure of the number of coincidences which is a function of the time shift between the photons entering the beam splitter. By compressing or stretching the distance between optical resonators or through changes in refractive index of the medium between the resonators, the coupling between the cavities changes. This results in a change in transmission and reflection of the beam splitter and therefore results in a change in the measured HOM visibility.

Fig. 2
Fig. 2

Sensor response to variations in g. (a) Shows the behavior of the estimator, coincidence detection probability G(2)(0), for indistinguishable input photons versus g/γ and κ/γ. (b) Shows how responsivity of the sensor varies by operating the sensor at different regimes of g/γ and κ/γ. The white dashed lines show the operating points for which sensor response is maximum and linear over the range of small changes in signal.

Fig. 3
Fig. 3

Linear dynamic range. (a) Shows how sensor response changes at different operating points. If we operate the sensor on a bias g0 where sensor response is maximum, we can take advantage of the sensor linear response, up to small variations in g. (b) Shows LDR for bias g 0 γ = 1.8 shown in (a) for different detection frequency bandwidths over γ, f γ. The red star shows the upper LDR limit that is the point up to which sensor responds linearly within 1% variation.

Fig. 4
Fig. 4

Performance of HOM sensor as a force sensor. This figure is a fabrication guide to building a HOM force sensor with maximum performance. (a) Shows how the estimator evolves by changing the operating point xbias for an input photon bandwidth of γ = 1GHz. (b) For the given γ and κ, the responsivity is of the order of 10−3(nm)−1. The white dashed lines show the operating points where system response to displacement shift is linear. (c) Shows that the minimum detectable change in distance is of the order of 10 3 nm / Hz). (d) For PhC made of GaAs/AlGaAs, the given value for minimum detectable x corresponds to minimum detectable forces of the order of 10−7N. Our calculations show that as we reduce kappa, gradually we loose the linear behaviour of the sensor (white dashed lines) for smaller xbias as the best bias points shifts towards larger x or smaller g without improving or decreasing the sensor resolution.

Fig. 5
Fig. 5

Performance of HOM sensor as a refractive index sensor. This figure is a fabrication guide to building a HOM refractive index sensor with maximum performance. (a) Shows responsivity of the refractive index sensor for different operating points xbias for an input photon bandwidth of γ = 1GHz. The white dashed lines show the bias points where sensor response changes linearly for very small changes in refractive index. Our theory predicts that responsivity does not depend on single photon band width γ. (b) Predicts that for γ = 1GHz the minimum detectable refractive index shift is of the order of 10 6 RIU / Hz.

Fig. 6
Fig. 6

Approximating the optical coupling between two GaAs cavities (L = 450 nm) placed in the middle of a distributed Bragg reflector (DBR) stack comprising GaAs (d=225 nm) and air (d=112 nm) pairs versus cavities separation (a,c) and air holes refractive index (b,d). (a) Normalised transmission of the stack showing the normal modes of the two cavities for different x. The dashed line corresponds to the unperturbed single cavity mode confined by the DBR stack. (b) Normal modes shown for x=449 nm (two air and one GaAs layers) and varying the refractive index of the air layers between the cavities. By increasing the air hole refractive index the mode separation increases which corresponds to stronger coupling between the cavities due to the decrease in the refractive index offset of the DBR layers. (c) coupling frequency calculated from (a) versus cavity separation. The dashed line corresponds to an exponential decay fitting. (d) coupling frequency as a function of air hole refractive index calculated from figure (b). The dashed curve corresponds to an exponential fitting of aebn2.

Fig. 7
Fig. 7

Functionality estimation of g versus x and n. Fit on experimental data (red points) given in figure 2 of citation [12] to find the coefficient a, b and d in functionality of g versus x and n that we found of the form g ( x , n ) = π c Δ λ / λ 2 = π c λ 2 a e b x + d n 2 where λ = 1000nm.

Equations (19)

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H I = g ( a 1 a 2 + a 1 a 2 ) ,
a j , out ( t ) = κ j a j ( t ) a j , in ( t ) ,
d a 1 ( t ) d t = i g a 2 ( t ) κ 2 a 1 ( t ) + κ a 1 , in ( t ) , d a 2 ( t ) d t = i g a 1 ( t ) κ 2 a 2 ( t ) + κ a 2 , in ( t ) ,
G ( 2 ) ( τ ) = 0 0 a 1 , out ( t ) a 2 , out ( t ) a 2 , out ( t ) a 1 , out ( t ) d t d t 0 a 1 , out ( t ) a 1 , out ( t ) d t 0 a 2 , out ( t ) a 2 , out ( t ) d t .
ρ in = T 1 T 2 | 1 1 1 | | 1 2 1 | + T 1 R 2 | 1 1 1 | | 0 2 0 | + R 1 T 2 | 0 1 0 | | 1 2 1 | + R 1 R 2 | 0 1 0 | | 0 2 0 | .
R g ( g 0 , κ ) = | d G ( 2 ) ( 0 ) d g | .
δ g noise = | d G ( 2 ) ( 0 ) d g | 1 δ G ( 2 ) ( 0 ) noise ,
δ G ( 2 ) ( 0 ) noise = G 2 ( 0 ) ( 1 G ( 2 ) ( 0 ) ) N ( 1 ε ) ,
δ g min > 2 f G ( 2 ) ( 0 ) ( 1 G ( 2 ) ( 0 ) ) R g min { γ , κ } ( 1 ε ) .
LDR = 20 log δ g max δ g min ,
a 1 ( t ) = κ [ A ( t ) 0 t d t ( C ( t ) a 1 , in ( t ) + D ( t ) a 2 , in ( t ) ) + B ( t ) 0 t d t ( D ( t ) a 1 , in ( t ) + C ( t ) a 2 , in ( t ) ) ] , a 2 ( t ) = κ [ B ( t ) 0 t d t ( C ( t ) a 1 , in ( t ) + D ( t ) a 2 , in ( t ) ) + A ( t ) 0 t d t ( D ( t ) a 1 , in ( t ) + C ( t ) a 2 , in ( t ) ) ] ,
G ( 2 ) ( τ ) = e 3 2 τ ( κ + γ ) A ( B e 3 2 τ ( κ + γ ) + C e 1 2 τ ( 3 κ + γ ) + D e 1 2 τ ( κ + 3 γ ) + E e τ ( κ + γ ) ) ,
A = ( 4 g 2 + κ 2 ) 2 ( 16 g 4 + ( γ 2 κ 2 ) 2 + 8 g 2 ( γ 2 + κ 2 ) ) 2 ,
B = ( 4 g 2 + ( γ κ ) 2 ) 2 ( 256 g 8 + κ 4 ( γ + κ ) 4 + 8 g 2 ( γ 2 2 κ 2 ) ( 16 g 4 + κ 2 ( γ + κ ) 2 ) + 16 g 4 ( γ 4 + 2 γ 2 κ 2 + 20 γ κ 3 + 22 κ 4 ) ) ,
C = 32 g 2 κ 2 ( 4 g 2 + γ 2 κ 2 ) 2 ( 4 g 2 + κ 2 ) 2 ,
D = 32 g 2 γ 2 κ 2 F 2 ,
E = 64 g 2 γ κ 2 ( 4 g 2 + γ 2 κ 2 ) ( 4 g 2 + κ 2 ) F ,
F = κ ( 12 g 2 γ 2 + κ 2 ) cos ( g τ ) + 2 g ( 4 g 2 + γ 2 3 κ 2 ) sin ( g τ ) .
ρ in = T 1 T 2 | 1 1 1 | | 1 2 1 | + T 1 R 2 | 1 1 1 | | 0 2 0 | + R 1 T 2 | 0 1 0 | | 1 2 1 | + R 1 R 2 | 0 1 0 | | 0 2 0 | .

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