Abstract

We propose a potentially practical scheme for realization of electromagnetically induced acoustic wave transparency (EIAT) in a high-Q single-crystal diamond mechanical resonator. Based on the dynamical strain-mediated coupling mechanism, we establish Λ-type and Δ-type transition structures in the subspace spanned by the ground states of the nitrogen-vacancy center, which drives the system into a coherent dark state, the system typically becoming transparent to the acoustic field, giving rise to the EIAT phenomenon. The physical picture behind EIAT is interpreted by using the framework of dressed states. Our work opens up possibilities to utilize this hybrid system as a building block to construct a spin-based physical material for quantum information processing and quantum optics applications, such as “slow sound” and enhanced nonlinear effects.

© 2016 Optical Society of America

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2016 (2)

Z.-T. Liang, X. Yue, Q. Lv, Y.-X. Du, W. Huang, H. Yan, and S.-L. Zhu, “Proposal for implementing universal superadiabatic geometric quantum gates in nitrogen-vacancy centers,” Phys. Rev. A 93, 040305(R) (2016).

S. Meesala, Y.-I. Sohn, H. A. Atikian, S. Kim, M. J. Burek, J. T. Choy, and M. Lončar, “Enhanced strain coupling of nitrogen-vacancy spins to nanoscale diamond cantilevers,” Phys. Rev. Appl. 5, 034010 (2016).
[Crossref]

2015 (13)

A. Barfuss, J. Teissier, E. Neu, A. Nunnenkamp, and P. Maletinsky, “Strong mechanical driving of a single electron spin,” Nat. Phys. 11, 820–824 (2015).
[Crossref]

B. Khanaliloo, M. Mitchell, A. C. Hryciw, and P. E. Barclay, “High-Q/V monolithic diamond microdisks fabricated with quasi-isotropic etching,” Nano Lett. 15, 5131–5136 (2015).
[Crossref]

E. R. MacQuarrie, T. A. Gosavi, A. M. Moehle, N. R. Jungwirth, S. A. Bhave, and G. D. Fuchs, “Coherent control of a nitrogen-vacancy center spin ensemble with a diamond mechanical resonator,” Optica 2, 233–238 (2015).

W. L. Yang, J. H. An, C. J. Zhang, C. Y. Chen, and C. H. Oh, “Dynamics of quantum correlation between separated nitrogen-vacancy centers embedded in plasmonic waveguide,” Sci. Rep. 5, 15513 (2015).
[Crossref]

E. R. MacQuarrie, T. A. Gosavi, S. A. Bhave, and G. D. Fuchs, “Continuous dynamical decoupling of a single diamond nitrogen-vacancy center spin with a mechanical resonator,” Phys. Rev. B 92, 224419 (2015).

Z. Q. Yin, N. Zhao, and T. C. Li, “Hybrid opto-mechanical systems with nitrogen-vacancy centers,” Sci. China Phys. Mech. Astron. 58, 1–12 (2015).

M. J. A. Kessler, E. M. Schuetz, G. Giedke, L. M. K. Vandersypen, M. D. Lukin, and J. I. Cirac, “Universal quantum transducers based on surface acoustic waves,” Phys. Rev. X 5, 031031 (2015).
[Crossref]

L. Jin, M. Pfender, N. Aslam, P. Neumann, S. Yang, J. Wrachtrup, and R.-B. Liu, “Proposal for a room-temperature diamond maser,” Nat. Commun. 6, 8251 (2015).
[Crossref]

A. Feizpour, M. Hallaji, G. Dmochowski, and A. M. Steinberg, “Observation of the nonlinear phase shift due to single post-selected photons,” Nat. Phys. 11, 905–909 (2015).
[Crossref]

S. Novikov, T. Sweeney, J. E. Robinson, S. P. Premaratne, B. Suri, F. C. Wellstood, and B. S. Palmer, “Raman coherence in a circuit quantum electrodynamics lambda system,” Nat. Phys. 12, 75–79 (2015).
[Crossref]

W. Z. Jia, L. F. Wei, Y. Li, and Y.-x. Liu, “Phase-dependent optical response properties in an optomechanical system by coherently driving the mechanical resonator,” Phys. Rev. A 91, 043843 (2015).

J. Kim, M. C. Kuzyk, K. Han, H. Wang, and G. Bahl, “Non-reciprocal Brillouin scattering induced transparency,” Nat. Phys. 11, 275–280 (2015).
[Crossref]

C.-H. Dong, Z. Shen, C.-L. Zou, Y.-L. Zhang, W. Fu, and G.-C. Guo, “Brillouin-scattering-induced transparency and non-reciprocal light storage,” Nat. Commun. 6, 6193 (2015).
[Crossref]

2014 (7)

A. Santillán and S. I. Bozhevolnyi, “Demonstration of slow sound propagation and acoustic transparency with a series of detuned resonators,” Phys. Rev. B 89, 184301 (2014).

J. Cai, F. Jelezko, and M. B. Plenio, “Hybrid sensors based on colour centres in diamond and piezoactive layers,” Nat. Commun. 5, 4065 (2014).

J.-B. You, W. L. Yang, Z.-Y. Xu, A. H. Chan, and C. H. Oh, “Phase transition of light in circuit-QED lattices coupled to nitrogen-vacancy centers in diamond,” Phys. Rev. B 90, 195112 (2014).

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref]

P. Ovartchaiyapong, K. W. Lee, B. A. Myers, and A. C. B. Jayich, “Dynamic strain-mediated coupling of a single diamond spin to a mechanical resonator,” Nat. Commun. 5, 4429 (2014).
[Crossref]

J. Teissier, A. Barfuss, P. Appel, E. Neu, and P. Maletinsky, “Strain coupling of a nitrogen-vacancy center spin to a diamond mechanical oscillator,” Phys. Rev. Lett. 113, 020503 (2014).
[Crossref]

Y. Tao, J. M. Boss, B. A. Moores, and C. L. Degen, “Single-crystal diamond nanomechanical resonators with quality factors exceeding one million,” Nat. Commun. 5, 3638 (2014).
[Crossref]

2013 (8)

E. R. MacQuarrie, T. A. Gosavi, N. R. Jungwirth, S. A. Bhave, and G. D. Fuchs, “Mechanical spin control of nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 111, 227602 (2013).
[Crossref]

V. M. Acosta, K. Jensen, C. Santori, D. Budker, and R. G. Beausoleil, “Electromagnetically induced transparency in a diamond spin ensemble enables all-optical electromagnetic field sensing,” Phys. Rev. Lett. 110, 213605 (2013).
[Crossref]

H. Bernien, B. Hensen, W. Praff, G. Koolstra, M. S. Blok, L. Robledo, T. H. Taminiau, M. Markham, D. J. Twitchen, L. Childress, and R. Hanson, “Heralded entanglement between solid-state qubits separated by three metres,” Nature 497, 86–90 (2013).

C. G. Yale, B. B. Buckley, D. J. Christle, G. Burkard, F. J. Heremans, L. C. Bassett, and D. D. Awschalom, “All-optical control of a solid-state spin using coherent dark states,” Proc. Natl. Acad. Sci. USA 110, 7595–7600 (2013).
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Z. Q. Yin, T. Li, X. Zhang, and L. M. Duan, “Large quantum superpositions of a levitated nanodiamond through spin-optomechanical coupling,” Phys. Rev. A 88, 033614 (2013).

S. D. Bennett, N. Y. Yao, J. Otterbach, P. Zoller, P. Rabl, and M. D. Lukin, “Phonon-induced spin-spin interactions in diamond nanostructures: application to spin squeezing,” Phys. Rev. Lett. 110, 156402 (2013).
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K. V. Kepesidis, S. D. Bennett, S. Portolan, M. D. Lukin, and P. Rabl, “Phonon cooling and lasing with nitrogen-vacancy centers in diamond,” Phys. Rev. B 88, 064105 (2013).

H. Yan, K.-Y. Liao, J.-F. Li, Y.-X. Du, Z.-M. Zhang, and S.-L. Zhu, “Bichromatic electromagnetically induced transparency in hot atomic vapors,” Phys. Rev. A 87, 055401 (2013).

2012 (3)

H. Xiong, L.-G. Si, A.-S. Zheng, X. Yang, and Y. Wu, “Higher-order sidebands in optomechanically induced transparency,” Phys. Rev. A 86, 013815 (2012).

M. W. Doherty, F. Dolde, H. Fedder, F. Jelezko, J. Wrachtrup, N. B. Manson, and L. C. L. Hollenberg, “Theory of the ground-state spin of the NV− center in diamond,” Phys. Rev. B 85, 205203 (2012).

A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, and D. Budker, “Temperature- and magnetic-field-dependent longitudinal spin relaxation in nitrogen-vacancy ensembles in diamond,” Phys. Rev. Lett. 108, 197601 (2012).
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2011 (6)

J. R. Maze, “Properties of nitrogen-vacancy centers in diamond: the group theoretic approach,” New J. Phys. 13, 025025 (2011).
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F. Dolde, H. Fedder, M. W. Doherty, T. Nöbauer, F. Rempp, G. Balasubramanian, T. Wolf, F. Reinhard, L. C. L. Hollenberg, F. Jelezko, and J. Wrachtrup, “Electric-field sensing using single diamond spins,” Nat. Phys. 7, 459–463 (2011).
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Y. Chang, T. Shi, Y.-x. Liu, C. P. Sun, and F. Nori, “Multistability of electromagnetically induced transparency in atom-assisted optomechanical cavities,” Phys. Rev. A 83, 063826 (2011).

S. Huang and G. S. Agarwal, “Electromagnetically induced transparency with quantized fields in optocavity mechanics,” Phys. Rev. A 83, 043826 (2011).

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).

A. Santillán and S. I. Bozhevolnyi, “Acoustic transparency and slow sound using detuned acoustic resonators,” Phys. Rev. B 84, 064304 (2011).

2010 (3)

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature 465, 755–758 (2010).

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
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P. Rabl, S. J. Kolkowitz, F. H. L. Koppens, J. G. E. Harris, P. Zoller, and M. D. Lukin, “A quantum spin transducer based on nanoelectromechanical resonator arrays,” Nat. Phys. 6, 602–608 (2010).
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2009 (4)

P. Rabl, P. Cappellaro, M. V. G. Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79, 041302 (2009).

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009).
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G. D. Fuchs, V. V. Dobrovitski, D. M. Toyli, F. J. Heremans, and D. D. Awschalom, “Gigahertz dynamics of a strongly driven single quantum spin,” Science 326, 1520–1522 (2009).
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X. Yang, M.-B. Yu, D.-L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102, 173902 (2009).
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2008 (4)

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
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N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101, 253903 (2008).
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J.-H. Wu, G. C. L. Rocca, and M. Artoni, “Controlled light-pulse propagation in driven color centers in diamond,” Phys. Rev. B 77, 113106 (2008).

L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, “Manipulation of the Raman process via incoherent pump, tunable intensity, and phase control,” Phys. Rev. A 77, 033833 (2008).

2007 (2)

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98, 213904 (2007).
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X.-T. Xie, W. Li, J. Li, W.-X. Yang, A. Yuan, and X. Yang, “Transverse acoustic wave in molecular magnets via electromagnetically induced transparency,” Phys. Rev. B 75, 184423 (2007).

2006 (3)

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S.-H. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
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N. B. Manson, J. P. Harrison, and M. J. Sellars, “Nitrogen-vacancy center in diamond: model of the electronic structure and associated dynamics,” Phys. Rev. B 74, 104303 (2006).

L. Childress, M. V. G. Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science 314, 281–285 (2006).
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2005 (4)

E. A. Wilson, N. B. Manson, C. Wei, and L. Yang, “Perturbing an electromagnetically induced transparency in a Λ system using a low-frequency driving field. I. Three-level system,” Phys. Rev. A 72, 063813 (2005).

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, “Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid,” Phys. Rev. Lett. 95, 063601 (2005).
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Y. Wu and X. Yang, “Electromagnetically induced transparency in V-, Λ-, and cascade-type schemes beyond steady-state analysis,” Phys. Rev. A 71, 053806 (2005).

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
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2004 (2)

F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
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X.-M. Hu and J. Xu, “Enhanced index and negative dispersion without absorption in driven cascade media,” Phys. Rev. A 69, 043812 (2004).

2003 (2)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
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Y. Wu, J. Saldana, and Y. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electromagnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).

2002 (1)

C. L. G. Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys. 70, 37–41 (2002).
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2001 (3)

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
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C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).

P. R. Hemmer, A. V. Turukhin, M. S. Shahriar, and J. A. Musser, “Raman-excited spin coherences in nitrogen-vacancy color centers in diamond,” Opt. Lett. 26, 361–363 (2001).
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2000 (2)

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).

P. W. May, “Diamond thin films: a 21st-century material,” Philos. Trans. R. Soc. A 358, 473–495 (2000).

1999 (3)

C. Wei and N. B. Manson, “Observation of the dynamic Stark effect on electromagnetically induced transparency,” Phys. Rev. A 60, 2540–2546 (1999).

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).

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1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
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1996 (1)

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, “Experimental demonstration of enhanced index of refraction via quantum coherence in Rb,” Phys. Rev. Lett. 76, 3935–3938 (1996).
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1995 (2)

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
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M. Xiao, Y.-Q. Li, S.-Z. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
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1994 (1)

A. M. Steinberg and R. Y. Chiao, “Dispersionless, highly superluminal propagation in a medium with a gain doublet,” Phys. Rev. A 49, 2071–2075 (1994).

1991 (1)

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
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1977 (1)

C. Cohen-Tannoudji and S. Reynaud, “Dressed-atom description of resonance fluorescence and absorption spectra of a multi-level atom in an intense laser beam,” J. Phys. B 10, 345–363 (1977).

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
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1883 (1)

G. Floquet, “Sur les équations différentielles linéaires à coefficients périodiques,” Ann. Sci. Ec. Normale Super. 12, 47–88 (1883).

Achard, J.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009).
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Acosta, V. M.

V. M. Acosta, K. Jensen, C. Santori, D. Budker, and R. G. Beausoleil, “Electromagnetically induced transparency in a diamond spin ensemble enables all-optical electromagnetic field sensing,” Phys. Rev. Lett. 110, 213605 (2013).
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A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, and D. Budker, “Temperature- and magnetic-field-dependent longitudinal spin relaxation in nitrogen-vacancy ensembles in diamond,” Phys. Rev. Lett. 108, 197601 (2012).
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Agarwal, G. S.

S. Huang and G. S. Agarwal, “Electromagnetically induced transparency with quantized fields in optocavity mechanics,” Phys. Rev. A 83, 043826 (2011).

Alegre, T. P. M.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).

Alzar, C. L. G.

C. L. G. Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys. 70, 37–41 (2002).
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An, J. H.

W. L. Yang, J. H. An, C. J. Zhang, C. Y. Chen, and C. H. Oh, “Dynamics of quantum correlation between separated nitrogen-vacancy centers embedded in plasmonic waveguide,” Sci. Rep. 5, 15513 (2015).
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Appel, P.

J. Teissier, A. Barfuss, P. Appel, E. Neu, and P. Maletinsky, “Strain coupling of a nitrogen-vacancy center spin to a diamond mechanical oscillator,” Phys. Rev. Lett. 113, 020503 (2014).
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Arcizet, O.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
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Artoni, M.

J.-H. Wu, G. C. L. Rocca, and M. Artoni, “Controlled light-pulse propagation in driven color centers in diamond,” Phys. Rev. B 77, 113106 (2008).

Aslam, N.

L. Jin, M. Pfender, N. Aslam, P. Neumann, S. Yang, J. Wrachtrup, and R.-B. Liu, “Proposal for a room-temperature diamond maser,” Nat. Commun. 6, 8251 (2015).
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Atikian, H. A.

S. Meesala, Y.-I. Sohn, H. A. Atikian, S. Kim, M. J. Burek, J. T. Choy, and M. Lončar, “Enhanced strain coupling of nitrogen-vacancy spins to nanoscale diamond cantilevers,” Phys. Rev. Appl. 5, 034010 (2016).
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Awschalom, D. D.

C. G. Yale, B. B. Buckley, D. J. Christle, G. Burkard, F. J. Heremans, L. C. Bassett, and D. D. Awschalom, “All-optical control of a solid-state spin using coherent dark states,” Proc. Natl. Acad. Sci. USA 110, 7595–7600 (2013).
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G. D. Fuchs, V. V. Dobrovitski, D. M. Toyli, F. J. Heremans, and D. D. Awschalom, “Gigahertz dynamics of a strongly driven single quantum spin,” Science 326, 1520–1522 (2009).
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Bahl, G.

J. Kim, M. C. Kuzyk, K. Han, H. Wang, and G. Bahl, “Non-reciprocal Brillouin scattering induced transparency,” Nat. Phys. 11, 275–280 (2015).
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Balasubramanian, G.

F. Dolde, H. Fedder, M. W. Doherty, T. Nöbauer, F. Rempp, G. Balasubramanian, T. Wolf, F. Reinhard, L. C. L. Hollenberg, F. Jelezko, and J. Wrachtrup, “Electric-field sensing using single diamond spins,” Nat. Phys. 7, 459–463 (2011).
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G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009).
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Barclay, P. E.

B. Khanaliloo, M. Mitchell, A. C. Hryciw, and P. E. Barclay, “High-Q/V monolithic diamond microdisks fabricated with quasi-isotropic etching,” Nano Lett. 15, 5131–5136 (2015).
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A. Barfuss, J. Teissier, E. Neu, A. Nunnenkamp, and P. Maletinsky, “Strong mechanical driving of a single electron spin,” Nat. Phys. 11, 820–824 (2015).
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J. Teissier, A. Barfuss, P. Appel, E. Neu, and P. Maletinsky, “Strain coupling of a nitrogen-vacancy center spin to a diamond mechanical oscillator,” Phys. Rev. Lett. 113, 020503 (2014).
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Bassett, L. C.

C. G. Yale, B. B. Buckley, D. J. Christle, G. Burkard, F. J. Heremans, L. C. Bassett, and D. D. Awschalom, “All-optical control of a solid-state spin using coherent dark states,” Proc. Natl. Acad. Sci. USA 110, 7595–7600 (2013).
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Beausoleil, R. G.

V. M. Acosta, K. Jensen, C. Santori, D. Budker, and R. G. Beausoleil, “Electromagnetically induced transparency in a diamond spin ensemble enables all-optical electromagnetic field sensing,” Phys. Rev. Lett. 110, 213605 (2013).
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Beck, J.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387 (2009).
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Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).

Bennett, S. D.

S. D. Bennett, N. Y. Yao, J. Otterbach, P. Zoller, P. Rabl, and M. D. Lukin, “Phonon-induced spin-spin interactions in diamond nanostructures: application to spin squeezing,” Phys. Rev. Lett. 110, 156402 (2013).
[Crossref]

K. V. Kepesidis, S. D. Bennett, S. Portolan, M. D. Lukin, and P. Rabl, “Phonon cooling and lasing with nitrogen-vacancy centers in diamond,” Phys. Rev. B 88, 064105 (2013).

Bernien, H.

H. Bernien, B. Hensen, W. Praff, G. Koolstra, M. S. Blok, L. Robledo, T. H. Taminiau, M. Markham, D. J. Twitchen, L. Childress, and R. Hanson, “Heralded entanglement between solid-state qubits separated by three metres,” Nature 497, 86–90 (2013).

Bhave, S. A.

E. R. MacQuarrie, T. A. Gosavi, S. A. Bhave, and G. D. Fuchs, “Continuous dynamical decoupling of a single diamond nitrogen-vacancy center spin with a mechanical resonator,” Phys. Rev. B 92, 224419 (2015).

E. R. MacQuarrie, T. A. Gosavi, A. M. Moehle, N. R. Jungwirth, S. A. Bhave, and G. D. Fuchs, “Coherent control of a nitrogen-vacancy center spin ensemble with a diamond mechanical resonator,” Optica 2, 233–238 (2015).

E. R. MacQuarrie, T. A. Gosavi, N. R. Jungwirth, S. A. Bhave, and G. D. Fuchs, “Mechanical spin control of nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 111, 227602 (2013).
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M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
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Blok, M. S.

H. Bernien, B. Hensen, W. Praff, G. Koolstra, M. S. Blok, L. Robledo, T. H. Taminiau, M. Markham, D. J. Twitchen, L. Childress, and R. Hanson, “Heralded entanglement between solid-state qubits separated by three metres,” Nature 497, 86–90 (2013).

Bochmann, J.

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature 465, 755–758 (2010).

Boller, K. J.

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
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Y. Tao, J. M. Boss, B. A. Moores, and C. L. Degen, “Single-crystal diamond nanomechanical resonators with quality factors exceeding one million,” Nat. Commun. 5, 3638 (2014).
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M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
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A. Santillán and S. I. Bozhevolnyi, “Demonstration of slow sound propagation and acoustic transparency with a series of detuned resonators,” Phys. Rev. B 89, 184301 (2014).

A. Santillán and S. I. Bozhevolnyi, “Acoustic transparency and slow sound using detuned acoustic resonators,” Phys. Rev. B 84, 064304 (2011).

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C. G. Yale, B. B. Buckley, D. J. Christle, G. Burkard, F. J. Heremans, L. C. Bassett, and D. D. Awschalom, “All-optical control of a solid-state spin using coherent dark states,” Proc. Natl. Acad. Sci. USA 110, 7595–7600 (2013).
[Crossref]

Budker, D.

V. M. Acosta, K. Jensen, C. Santori, D. Budker, and R. G. Beausoleil, “Electromagnetically induced transparency in a diamond spin ensemble enables all-optical electromagnetic field sensing,” Phys. Rev. Lett. 110, 213605 (2013).
[Crossref]

A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, and D. Budker, “Temperature- and magnetic-field-dependent longitudinal spin relaxation in nitrogen-vacancy ensembles in diamond,” Phys. Rev. Lett. 108, 197601 (2012).
[Crossref]

Burek, M. J.

S. Meesala, Y.-I. Sohn, H. A. Atikian, S. Kim, M. J. Burek, J. T. Choy, and M. Lončar, “Enhanced strain coupling of nitrogen-vacancy spins to nanoscale diamond cantilevers,” Phys. Rev. Appl. 5, 034010 (2016).
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C. G. Yale, B. B. Buckley, D. J. Christle, G. Burkard, F. J. Heremans, L. C. Bassett, and D. D. Awschalom, “All-optical control of a solid-state spin using coherent dark states,” Proc. Natl. Acad. Sci. USA 110, 7595–7600 (2013).
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P. Rabl, P. Cappellaro, M. V. G. Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79, 041302 (2009).

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J.-B. You, W. L. Yang, Z.-Y. Xu, A. H. Chan, and C. H. Oh, “Phase transition of light in circuit-QED lattices coupled to nitrogen-vacancy centers in diamond,” Phys. Rev. B 90, 195112 (2014).

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A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).

Chang, D. E.

A. H. Safavi-Naeini, T. P. M. Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).

Chang, Y.

Y. Chang, T. Shi, Y.-x. Liu, C. P. Sun, and F. Nori, “Multistability of electromagnetically induced transparency in atom-assisted optomechanical cavities,” Phys. Rev. A 83, 063826 (2011).

Chemerisov, S.

A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, and D. Budker, “Temperature- and magnetic-field-dependent longitudinal spin relaxation in nitrogen-vacancy ensembles in diamond,” Phys. Rev. Lett. 108, 197601 (2012).
[Crossref]

Chen, C. Y.

W. L. Yang, J. H. An, C. J. Zhang, C. Y. Chen, and C. H. Oh, “Dynamics of quantum correlation between separated nitrogen-vacancy centers embedded in plasmonic waveguide,” Sci. Rep. 5, 15513 (2015).
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Figures (8)

Fig. 1.
Fig. 1.

(a) The system under consideration is a DMR containing many embedded NV centers, where the NV center spins are coupled to a cantilever that is resonantly driven by a piezoelement. (b) Energy levels of the ground-state of the NV center, where the transition | + 1 | 0 is driven by a strong microwave field with Rabi frequency Ω , and the phonon strain field with Rabi frequency G has been employed to drive the transition | + 1 | 1 . Here, Δ 1 ( 2 ) are the detunings.

Fig. 2.
Fig. 2.

(a) Imaginary part of the susceptibility Im ( χ ) and (b) the quantity ξ as functions of detuning Δ 2 . The red solid and green solid lines represent the approximate analytical results of the different driving cases with Ω = 0 and Ω = 1.5 , respectively. The corresponding numerical simulations without any approximations are represented by the black dashed and gray dashed lines, respectively. The other parameters are set as G = 0.01 , γ 1 = 1 , γ 3 = 0.01 , and Δ = Δ 2 .

Fig. 3.
Fig. 3.

Imaginary part of the susceptibility Im ( χ ) : left, as a function of detunings Δ 2 and Δ 1 ; and right, as a function of detunings Δ 2 and Δ . The other parameters are set as Ω = 1.5 , G = 0.01 , γ 1 = 1 , and γ 3 = 0.01 .

Fig. 4.
Fig. 4.

Levels of Δ -type transition of the NV center system, where the transition | + 1 | 0 ( | 0 | 1 ) is coupling with strong microwave fields with Rabi frequencies Ω 1 ( 2 ) . The phonon strain field with Rabi frequency λ has been employed to drive the transition | + 1 | 1 .

Fig. 5.
Fig. 5.

Imaginary part of the susceptibility Im ( χ ) (left panel) and the quantity ξ (right panel) as functions of detuning δ 3 in different driving cases: (a, d) ( Ω 1 = 0 , Ω 2 = 0 ), (b, e) ( Ω 1 = 1.5 , Ω 2 = 0 ), and (c, f) ( Ω 1 = 1.5 , Ω 2 = 1.5 ). The other parameters are set as λ = 0.01 , Γ 32 = Γ 31 = 1 , Γ 21 = 0.01 , γ 2 d = 0.01 , γ 3 d = 1 , and δ 1 = δ 2 = 0 .

Fig. 6.
Fig. 6.

(a) Value of Im ( χ ) as a function of detuning δ 3 and Rabi frequency Ω 2 . (b) Frequency interval between the central EIAT window and the lateral EIAT window as a function of Rabi frequency Ω 2 . The other parameters are set as λ = 0.01 , Γ 32 = Γ 31 = 1 , Γ 21 = 0.01 , γ 2 d = 0.01 , γ 3 d = 1 , Ω 2 = 1.5 , and δ 1 = δ 2 = 0 .

Fig. 7.
Fig. 7.

(a) Value of Im ( χ ) as a function of detuning δ 3 and Rabi frequency Ω 2 . (b) Frequency shift of the central EIAT window as a function of detuning δ 2 in the detuning case with δ 2 0 . (c) Frequency interval between the central EIAT window and the lateral EIAT window as a function of detuning δ 2 . The other parameters are set as λ = 0.01 , Γ 32 = Γ 31 = 1 , Γ 21 = 0.01 , γ 2 d = 0.01 , γ 3 d = 1 , Ω 1 = Ω 2 = 1.5 , and δ 1 = 0 .

Fig. 8.
Fig. 8.

(a) Bare-state and (b) dressed-state energy levels of the Fig. 4. Here, p 1 ( 2 , 3 , 4 ) represent four transition paths in the case of δ 1 = δ 3 , and Ω p is the splitting width on energy levels | m s = 1 and | m s = 0 under the driving of microwave field Ω 2 .

Equations (18)

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H NV = ( D 0 + ε E z ) S z 2 + g s μ B B z S z ε [ E x ( S x S y + S y S x ) + E y ( S x 2 S y 2 ) ] ,
H = Δ 2 σ + 1 , + 1 + Δ σ 0 , 0 ( G σ + 1 , 1 + Ω σ + 1,0 + H.c. ) / 2 ,
ρ ˙ + 1 , 1 = ( γ 1 + i Δ 2 ) ρ + 1 , 1 + i Ω ρ 0 , 1 2 + i G ( ρ 1 , 1 ρ + 1 , + 1 ) 2 ,
ρ ˙ + 1 , 0 = ( γ 2 + i Δ 1 ) ρ + 1 , 0 + i G ρ 0 , 1 * 2 + i Ω ( ρ 0,0 ρ + 1 , + 1 ) 2 ,
ρ ˙ 0 , 1 = ( γ 3 + i Δ ) ρ 0 , 1 i G ρ + 1 , 0 * 2 + i Ω * ρ + 1 , 1 2 ,
ρ + 1 , 1 = 2 i G ( γ 3 + i Δ ) / [ 4 ( γ 1 + i Δ 2 ) ( γ 3 + i Δ ) + | Ω | 2 ] .
H 1 = δ 2 σ 1 , 1 + ( δ 1 + δ 2 ) σ + 1 , + 1 ( Ω 1 σ + 1,0 + Ω 2 σ 0 , 1 + λ e i δ t σ + 1 , 1 + H.c. ) / 2 ,
ρ ˙ = i [ H 1 , ρ ] + L ρ ,
L ρ = Γ 31 ( 2 σ 1 , + 1 ρ σ + 1 , 1 σ + 1 , + 1 ρ ρ σ + 1 , + 1 ) / 2 + Γ 32 ( 2 σ 0 , + 1 ρ σ + 1 , 0 σ + 1 , + 1 ρ ρ σ + 1 , + 1 ) / 2 + Γ 21 ( 2 σ 1 , 0 ρ σ 0 , 1 σ 0 , 0 ρ ρ σ 0 , 0 ) / 2 + γ 2 d ( 2 σ 0 , 0 ρ σ 0 , 0 σ 0 , 0 ρ ρ σ 0 , 0 ) / 2 + γ 3 d ( 2 σ + 1 , + 1 ρ σ + 1 , + 1 σ + 1 , + 1 ρ ρ σ + 1 , + 1 ) / 2 ,
ρ ˙ 1 , 1 = Γ 2 ρ 0 , 0 + Γ 3 ρ + 1 , + 1 / 2 i [ λ e i δ t ρ 1 , + 1 λ e i δ t ρ + 1 , 1 + Ω 2 ( ρ 1 , 0 ρ 0 , 1 ) ] / 2 , ρ ˙ 1 , 0 = γ 2 ρ 1 , 0 / 2 i [ λ e i δ t ρ + 1 , 0 2 δ 2 ρ 1 , 0 + Ω 1 ρ 1 , + 1 + Ω 2 ( ρ 1 , 1 ρ 0 , 0 ) ] / 2 , ρ ˙ 1 , + 1 = γ 3 ρ 1 , + 1 / 2 i [ λ e i δ t ( ρ 1 , 1 ρ + 1 , + 1 ) 2 ( δ 1 + δ 2 ) ρ 1 , + 1 + Ω 1 ρ 1 , 0 Ω 2 ρ 0 , + 1 ] / 2 , ρ ˙ 0 , 1 = γ 2 ρ 0 , 1 / 2 i [ λ e i δ t ρ 0 , + 1 + 2 δ 2 ρ 0 , 1 Ω 1 ρ + 1 , 1 Ω 2 ( ρ 1 , 1 ρ 0 , 0 ) ] / 2 , ρ ˙ 0 , 0 = Γ 2 ρ 0 , 0 + Γ 3 ρ + 1 , + 1 / 2 i [ Ω 1 ( ρ 0 , + 1 ρ + 1 , 0 ) + Ω 2 ( ρ 0 , 1 ρ 1 , 0 ) ] / 2 , ρ ˙ 0 , + 1 = ( γ 2 + γ 3 ) ρ 0 , + 1 / 2 i [ λ e i δ t ρ 0 , 1 2 δ 1 ρ 0 , + 1 + Ω 1 ( ρ 0 , 0 ρ + 1 , + 1 ) Ω 2 ρ 1 , + 1 ] / 2 , ρ ˙ + 1 , 1 = γ 3 ρ + 1 , 1 / 2 + i [ λ e i δ t ( ρ 1 , 1 ρ + 1 , + 1 ) 2 ( δ 1 + δ 2 ) ρ + 1 , 1 + Ω 1 ρ 0 , 1 Ω 2 ρ + 1 , 0 ] / 2 , ρ ˙ + 1 , 0 = ( γ 2 + γ 3 ) ρ + 1 , 0 / 2 + i [ G e i δ t ρ 1 , 0 2 δ 1 ρ + 1 , 0 + Ω 1 ( ρ 0 , 0 ρ + 1 , + 1 ) Ω 2 ρ + 1 , 1 ] / 2 , ρ ˙ + 1 , + 1 = Γ 3 ρ + 1 , + 1 + i [ λ e i δ t ρ 1 , + 1 λ e i δ t ρ + 1 , 1 Ω 1 ( ρ + 1 , 0 ρ 0 , + 1 ) ] / 2 .
R ˙ = M R A ,
R = ( ρ 0 , 0 , ρ + 1 , + 1 , ρ + 1 , 1 , ρ 1 , 0 , ρ 0 , + 1 , ρ + 1 , 0 , ρ 1 , + 1 , ρ 0 , 1 ) T
A = ( 0 , 0 , i λ exp ( i δ t ) / 2 , i Ω 2 / 2 , 0 , 0 , i λ exp ( i δ t ) / 2 , i Ω 2 / 2 ) T ,
A = A 0 + λ exp ( i δ t ) A 1 + λ exp ( i δ t ) A 1 ,
M = M 0 + λ exp ( i δ t ) M 1 + λ exp ( i δ t ) M 1 ,
R ˙ + A 0 + λ exp ( i δ t ) A 1 + λ exp ( i δ t ) A 1 = ( M 0 + λ exp ( i δ t ) M 1 + λ exp ( i δ t ) M 1 ) R .
R = R 0 + λ exp ( i δ t ) R 1 + λ exp ( i δ t ) R 1 .
R 0 = M 0 1 A 0 , R 1 = ( M 0 + i δ ) 1 ( A 1 M 1 R 0 ) .

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