Abstract

A design for an ultrahigh Q/V nanobeam cavity engineered to interact with Germanium-vacancy (GeV) centers is presented. The nanobeam cavity supports a mode with Q/V>108 with transmission over 70%. The proposed design is based on a new scalable approach developed to reduce the footprint of nanobeam cavities by more than 50% without losing the cavity Q/V value and transmission. Cavity quantum electrodynamics analysis reveals that strong coupling between the zero-phonon line transition of GeV centers and the cavity mode can be achieved for a range of nanobeam dimensions.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (1)

M. K. Bhaskar, D. D. Sukachev, A. Sipahigil, R. E. Evans, M. J. Burek, C. T. Nguyen, L. J. Rogers, P. Siyushev, M. H. Metsch, H. Park, F. Jelezko, M. Lončar, and M. D. Lukin, “Quantum Nonlinear Optics with a Germanium-Vacancy Color Center in a Nanoscale Diamond Waveguide,” Phys. Rev. Lett. 118(22), 223603 (2017).
[Crossref] [PubMed]

2016 (3)

U. Jantzen, A. B. Kurz, D. S. Rudnicki, C. Schäfermeier, K. D. Jahnke, U. L. Andersen, V. A. Davydov, V. N. Agafonov, A. Kubanek, L. J. Rogers, and F. Jelezko, “Nanodiamonds carrying silicon-vacancy quantum emitters with almost lifetime-limited linewidths,” New J. Phys. 18(7), 073036 (2016).
[Crossref]

K. Li, Y. Zhou, A. Rasmita, I. Aharonovich, and W. B. Gao, “Nonblinking Emitters with Nearly Lifetime-Limited Linewidths in CVD Nanodiamonds,” Phys. Rev. Appl. 6(2), 024010 (2016).
[Crossref]

A. Sipahigil, R. E. Evans, D. D. Sukachev, M. J. Burek, J. Borregaard, M. K. Bhaskar, C. T. Nguyen, J. L. Pacheco, H. A. Atikian, C. Meuwly, R. M. Camacho, F. Jelezko, E. Bielejec, H. Park, M. Lončar, and M. D. Lukin, “An integrated diamond nanophotonics platform for quantum-optical networks,” Science 354(6314), 847–850 (2016).
[Crossref] [PubMed]

2015 (3)

Y. N. Palyanov, I. N. Kupriyanov, Y. M. Borzdov, and N. V. Surovtsev, “Germanium: a new catalyst for diamond synthesis and a new optically active impurity in diamond,” Sci. Rep. 5(1), 14789 (2015).
[Crossref] [PubMed]

E. A. Ekimov, S. G. Lyapin, K. N. Boldyrev, M. V. Kondrin, R. Khmelnitskiy, V. A. Gavva, T. V. Kotereva, and M. N. Popova, “Germanium–vacancy color center in isotopically enriched diamonds synthesized at high pressures,” JETP Lett. 102(11), 701–706 (2015).
[Crossref]

T. Iwasaki, F. Ishibashi, Y. Miyamoto, Y. Doi, S. Kobayashi, T. Miyazaki, K. Tahara, K. D. Jahnke, L. J. Rogers, B. Naydenov, F. Jelezko, S. Yamasaki, S. Nagamachi, T. Inubushi, N. Mizuochi, and M. Hatano, “Germanium-Vacancy Single Color Centers in Diamond,” Sci. Rep. 5(1), 12882 (2015).
[Crossref] [PubMed]

2014 (5)

I. I. Vlasov, A. A. Shiryaev, T. Rendler, S. Steinert, S.-Y. Lee, D. Antonov, M. Vörös, F. Jelezko, A. V. Fisenko, L. F. Semjonova, J. Biskupek, U. Kaiser, O. I. Lebedev, I. Sildos, P. R. Hemmer, V. I. Konov, A. Gali, and J. Wrachtrup, “Molecular-sized fluorescent nanodiamonds,” Nat. Nanotechnol. 9(1), 54–58 (2014).
[Crossref] [PubMed]

R. Schirhagl, K. Chang, M. Loretz, and C. L. Degen, “Nitrogen-vacancy centers in diamond: nanoscale sensors for physics and biology,” Annu. Rev. Phys. Chem. 65(1), 83–105 (2014).
[Crossref] [PubMed]

A. Reiserer, N. Kalb, G. Rempe, and S. Ritter, “A quantum gate between a flying optical photon and a single trapped atom,” Nature 508(7495), 237–240 (2014).
[Crossref] [PubMed]

A. Goban, C. L. Hung, S. P. Yu, J. D. Hood, J. A. Muniz, J. H. Lee, M. J. Martin, A. C. McClung, K. S. Choi, D. E. Chang, O. Painter, and H. J. Kimble, “Atom-light interactions in photonic crystals,” Nat. Commun. 5(1), 3808 (2014).
[Crossref] [PubMed]

N. Thomas, R. J. Barbour, Y. Song, M. L. Lee, and K.-M. C. Fu, “Waveguide-integrated single-crystalline GaP resonators on diamond,” Opt. Express 22(11), 13555–13564 (2014).
[Crossref] [PubMed]

2013 (3)

H. Kim, R. Bose, T. C. Shen, G. S. Solomon, and E. Waks, “A quantum logic gate between a solid-state quantum bit and a photon,” Nat. Photonics 7(5), 373–377 (2013).
[Crossref]

J. H. Li, R. Yu, and X. X. Yang, “Achieving slow and fast light with high transmission by nanodiamond nitrogen-vacancy center coupling to photonic crystal cavity,” J. Appl. Phys. 114(12), 124312 (2013).
[Crossref]

H. J. Mamin, M. Kim, M. H. Sherwood, C. T. Rettner, K. Ohno, D. D. Awschalom, and D. Rugar, “Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor,” Science 339(6119), 557–560 (2013).
[Crossref] [PubMed]

2012 (2)

P. C. Maurer, G. Kucsko, C. Latta, L. Jiang, N. Y. Yao, S. D. Bennett, F. Pastawski, D. Hunger, N. Chisholm, M. Markham, D. J. Twitchen, J. I. Cirac, and M. D. Lukin, “Room-temperature quantum bit memory exceeding one second,” Science 336(6086), 1283–1286 (2012).
[Crossref] [PubMed]

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109(3), 033604 (2012).
[Crossref] [PubMed]

2011 (4)

G. D. Fuchs, G. Burkard, P. V. Klimov, and D. D. Awschalom, “A quantum memory intrinsic to single nitrogen-vacancy centres in diamond,” Nat. Phys. 7(10), 789–793 (2011).
[Crossref]

Q. Quan and M. Loncar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express 19(19), 18529–18542 (2011).
[Crossref] [PubMed]

L. Robledo, H. Bernien, T. Van Der Sar, and R. Hanson, “Spin dynamics in the optical cycle of single nitrogen-vacancy centres in diamond,” New J. Phys. 13(2), 025013 (2011).
[Crossref]

P. E. Barclay, K.-M. C. Fu, C. Santori, A. Faraon, and R. G. Beausoleil, “Hybrid Nanocavity Resonant Enhancement of Color Center Emission in Diamond,” Phys. Rev. X 1(1), 011007 (2011).
[Crossref]

2010 (5)

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10(10), 3922–3926 (2010).
[Crossref] [PubMed]

B.-H. Ahn, J.-H. Kang, M.-K. Kim, J.-H. Song, B. Min, K.-S. Kim, and Y.-H. Lee, “One-dimensional parabolic-beam photonic crystal laser,” Opt. Express 18(6), 5654–5660 (2010).
[Crossref] [PubMed]

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96(20), 203102 (2010).
[Crossref]

P. Neumann, R. Kolesov, B. Naydenov, J. Beck, F. Rempp, M. Steiner, V. Jacques, G. Balasubramanian, M. L. Markham, D. J. Twitchen, S. Pezzagna, J. Meijer, J. Twamley, F. Jelezko, and J. Wrachtrup, “Quantum register based on coupled electron spins in a room-temperature solid,” Nat. Phys. 6(4), 249–253 (2010).
[Crossref]

Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J. F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, “Strong coupling of a spin ensemble to a superconducting resonator,” Phys. Rev. Lett. 105(14), 140502 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

2007 (2)

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[Crossref] [PubMed]

M. V. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum register based on individual electronic and nuclear spin qubits in diamond,” Science 316(5829), 1312–1316 (2007).
[Crossref] [PubMed]

2006 (1)

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443(7112), 671–674 (2006).
[Crossref] [PubMed]

2005 (2)

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95(6), 067401 (2005).
[Crossref] [PubMed]

D. Englund, I. Fushman, and J. Vucković, “General recipe for designing photonic crystal cavities,” Opt. Express 13(16), 5961–5975 (2005).
[Crossref] [PubMed]

2004 (2)

J. A. Sauer, K. M. Fortier, M. S. Chang, C. D. Hamley, and M. S. Chapman, “Cavity QED with optically transported atoms,” Phys. Rev. A 69(5), 51804 (2004).
[Crossref]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431(7005), 162–167 (2004).
[Crossref] [PubMed]

2003 (1)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

2002 (1)

2000 (1)

C. J. Hood, T. W. Lynn, A. C. Doherty, A. S. Parkins, and H. J. Kimble, “The atom-cavity microscope: single atoms bound in orbit by single photons,” Science 287(5457), 1447–1453 (2000).
[Crossref] [PubMed]

Acosta, V. M.

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109(3), 033604 (2012).
[Crossref] [PubMed]

Agafonov, V. N.

U. Jantzen, A. B. Kurz, D. S. Rudnicki, C. Schäfermeier, K. D. Jahnke, U. L. Andersen, V. A. Davydov, V. N. Agafonov, A. Kubanek, L. J. Rogers, and F. Jelezko, “Nanodiamonds carrying silicon-vacancy quantum emitters with almost lifetime-limited linewidths,” New J. Phys. 18(7), 073036 (2016).
[Crossref]

Aharonovich, I.

K. Li, Y. Zhou, A. Rasmita, I. Aharonovich, and W. B. Gao, “Nonblinking Emitters with Nearly Lifetime-Limited Linewidths in CVD Nanodiamonds,” Phys. Rev. Appl. 6(2), 024010 (2016).
[Crossref]

Ahn, B.-H.

Akahane, Y.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

Andersen, U. L.

U. Jantzen, A. B. Kurz, D. S. Rudnicki, C. Schäfermeier, K. D. Jahnke, U. L. Andersen, V. A. Davydov, V. N. Agafonov, A. Kubanek, L. J. Rogers, and F. Jelezko, “Nanodiamonds carrying silicon-vacancy quantum emitters with almost lifetime-limited linewidths,” New J. Phys. 18(7), 073036 (2016).
[Crossref]

Antonov, D.

I. I. Vlasov, A. A. Shiryaev, T. Rendler, S. Steinert, S.-Y. Lee, D. Antonov, M. Vörös, F. Jelezko, A. V. Fisenko, L. F. Semjonova, J. Biskupek, U. Kaiser, O. I. Lebedev, I. Sildos, P. R. Hemmer, V. I. Konov, A. Gali, and J. Wrachtrup, “Molecular-sized fluorescent nanodiamonds,” Nat. Nanotechnol. 9(1), 54–58 (2014).
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Aoki, T.

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Nat. Photonics (1)

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Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
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New J. Phys. (2)

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Other (2)

S. V. Bolshedvorskii, A. I. Zeleneev, V. V. Vorobyov, V. V. Soshenko, O. R. Rubinas, L. A. Zhulikov, P. A. Pivovarov, V. N. Sorokin, A. N. Smolyaninov, L. F. Kulikova, A. S. Garanina, V. N. Agafonov, R. E. Uzbekov, V. A. Davydov, and A. V. Akimov, “Single SiV centers in ultranano-sized diamonds,” http://arxiv.org/abs/1812.06534 (2018).

A. Yariv, Quantum Electronics (John Wiley & Sons, Incorporated, 1975).

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Figures (8)

Fig. 1
Fig. 1 (a) A sketch of tapered nanobeam cavity with semicircular holes and E y field distribution of the TE fundamental mode. (b) Mirror strength as a function of nanobeam final width W f for three configurations: only central holes (green), central holes with in-phase semicircular holes (orange), central holes with out-of-phase semicircular holes (blue). (c) Mirror strength as a function of the hole segment number after parabolic tapering using this formula: W f = W 0 +2 R w 2 R w 1 ( N/ R w ) 2 , where W 0 /a=1.5 (1st hole) and W f /a=1.8 (15th hole). The dashed line is a linear fit with R 2 =0.98. (d) TE band structure for the proposed design. The dashed line marks the cavity resonant frequency.
Fig. 2
Fig. 2 (a) & (b) The cavity transmission and number of holes as a function of Q/V value for different nanobeam final widths, respectively. The nanobeam initial width in (a) & (b) is fixed, W 0 /a=1.5. (c) The dependence of Q/V value taken at 90% cavity transmission on the nanobeam initial width. The difference between the final and initial width is fixed, ΔW/a = 0.3. (d) Number of holes as a function of Q/V value for different nanobeam initial widths.
Fig. 3
Fig. 3 (a) A sketch of DNC placed on top of a nanobeam cavity. (b) Relevant cavity QED rates as a function of number of holes. κ/2π is the cavity decay rate, γ/2π is the atomic decay rate of the GeV center, and g/2π is the single photon coupling rate. (c) Cooperativity (dots) and weak/strong coupling index (open circles) as a function of number of holes. (d) cooperativity as a function of number of holes for different DNC sizes.
Fig. 4
Fig. 4 Mirror strength as a function of hole radius for two nanobeam designs with (blue) and without (orange) semicircular holes. The design in (a) is obtained from Notomi et al. [40], and the design in (b) is obtained from Qimin et al. [35]. The enhancement of the mirror strength (a) and (b) is 70% and 40%, respectively.
Fig. 5
Fig. 5 (a) TE band structure for a tapered nanobeam cavity with only central holes. (b) Mirror strength as a function of hole position after parabolic tapering. (c) The dependence of Q/V value with 90% transmission on the nanobeam initial width W 0 . (d) Number of holes as a function of Q/V value. We considered the same initial and final width in both designs.
Fig. 6
Fig. 6 Reduction in the number of holes gained by the design demonstrated in the main text as a function of Q/V value for different initial widths (a) and final widths (b).
Fig. 7
Fig. 7 (a) E y field distribution for the TE fundamental mode obtained from FDTD simulations (blue dots) and from an analytical formula (red line). (b) E y cross sections of the TE fundamental mode. α 2 is the ratio of the energy density in the GaP nanobeam cavity to the maximum energy density at the DNC calculated for different nanobeam thicknesses. (c) The cavity transmission as a function of Q/V value for dielectric-centered cavity (blue) and air-centered cavity (orange).
Fig. 8
Fig. 8 (a) The cavity transmission as a function of Q/V value for different nanobeam thicknesses. (b) Cooperativity (dots) and weak/strong coupling index (open circles) as a function of nanobeam thickness. We considered cavities with Q/V = 10 6 for all thicknesses in (b) to maintain the cavity transmission.

Equations (3)

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d= 1 2  3 γ sp ε 0 λ 3   2 π 2 n dnc ,
E= πc ε 0  λ n GaP 2 V ,
g= η 2α  3c λ 2   τ n dnc n 0 2 V  ,

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