Abstract

Linking classical microwave electrical circuits to the optical telecommunication band is at the core of modern communication. Future quantum information networks will require coherent microwave-to-optical conversion to link electronic quantum processors and memories via low-loss optical telecommunication networks. Efficient conversion can be achieved with electro-optical modulators operating at the single microwave photon level. In the standard electro-optic modulation scheme, this is impossible because both up- and down-converted sidebands are necessarily present. Here, we demonstrate true single-sideband up- or down-conversion in a triply resonant whispering gallery mode resonator by explicitly addressing modes with asymmetric free spectral range. Compared to previous experiments, we show a 3 orders of magnitude improvement of the electro-optical conversion efficiency, reaching 0.1% photon number conversion for a 10 GHz microwave tone at 0.42 mW of optical pump power. The presented scheme is fully compatible with existing superconducting 3D circuit quantum electrodynamics technology and can be used for nonclassical state conversion and communication. Our conversion bandwidth is larger than 1 MHz and is not fundamentally limited.

© 2016 Optical Society of America

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References

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2015 (9)

D. Ristè, S. Poletto, M.-Z. Huang, A. Bruno, V. Vesterinen, O.-P. Saira, and L. DiCarlo, “Detecting bit-flip errors in a logical qubit using stabilizer measurements,” Nat. Commun. 6, 6983 (2015).
[Crossref]

X. Fernandez-Gonzalvo, Y.-H. Chen, C. Yin, S. Rogge, and J. J. Longdell, “Coherent frequency up-conversion of microwaves to the optical telecommunications band in an Er:YSO crystal,” Phys. Rev. A 92, 062313 (2015).
[Crossref]

M. Leidinger, S. Fieberg, N. Waasem, F. Kühnemann, K. Buse, and I. Breunig, “Comparative study on three highly sensitive absorption measurement techniques characterizing lithium niobate over its entire transparent spectral range,” Opt. Express 23, 21690–21705 (2015).
[Crossref]

M. Goryachev, N. Kostylev, and M. E. Tobar, “Single-photon level study of microwave properties of lithium niobate at millikelvin temperatures,” Phys. Rev. B 92, 060406 (2015).
[Crossref]

N. G. Pavlov, N. M. Kondratyev, and M. L. Gorodetsky, “Modeling the whispering gallery microresonator-based optical modulator,” Appl. Opt. 54, 10460–10466 (2015).
[Crossref]

S. Huang, “Quantum state transfer in cavity electro-optic modulators,” Phys. Rev. A 92, 043845 (2015).
[Crossref]

W. Weng and A. N. Luiten, “Mode-interactions and polarization conversion in a crystalline microresonator,” Opt. Lett. 40, 5431–5434 (2015).
[Crossref]

R. W. Andrews, A. P. Reed, K. Cicak, J. D. Teufel, and K. W. Lehnert, “Quantum-enabled temporal and spectral mode conversion of microwave signals,” Nat. Commun. 6, 10021 (2015).
[Crossref]

G. Schunk, U. Vogl, D. V. Strekalov, M. Förtsch, F. Sedlmeir, H. G. L. Schwefel, M. Göbelt, S. Christiansen, G. Leuchs, and C. Marquardt, “Interfacing transitions of different alkali atoms and telecom bands using one narrowband photon pair source,” Optica 2, 773–778 (2015).
[Crossref]

2014 (5)

S. Ramelow, A. Farsi, S. Clemmen, J. S. Levy, A. R. Johnson, Y. Okawachi, M. R. E. Lamont, M. Lipson, and A. L. Gaeta, “Strong polarization mode coupling in microresonators,” Opt. Lett. 39, 5134–5137 (2014).
[Crossref]

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

L. Chen, Q. Xu, M. G. Wood, and R. M. Reano, “Hybrid silicon and lithium niobate electro-optical ring modulator,” Optica 1, 112–118 (2014).
[Crossref]

L. A. Williamson, Y.-H. Chen, and J. J. Longdell, “Magneto-optic modulator with unit quantum efficiency,” Phys. Rev. Lett. 113, 203601 (2014).
[Crossref]

2013 (3)

M. H. Devoret and R. J. Schoelkopf, “Superconducting circuits for quantum information: an outlook,” Science 339, 1169–1174 (2013).
[Crossref]

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

I. Breunig, B. Sturman, F. Sedlmeir, H. G. L. Schwefel, and K. Buse, “Whispering gallery modes at the rim of an axisymmetric optical resonator: analytical versus numerical description and comparison with experiment,” Opt. Express 21, 30683–30692 (2013).
[Crossref]

2012 (4)

C. Rigetti, J. M. Gambetta, S. Poletto, B. L. T. Plourde, J. M. Chow, A. D. Córcoles, J. A. Smolin, S. T. Merkel, J. R. Rozen, G. A. Keefe, M. B. Rothwell, M. B. Ketchen, and M. Steffen, “Superconducting qubit in a waveguide cavity with a coherence time approaching 0.1  ms,” Phys. Rev. B 86, 100506 (2012).
[Crossref]

J. Li, H. Lee, K. Y. Yang, and K. J. Vahala, “Sideband spectroscopy and dispersion measurement in microcavities,” Opt. Express 20, 26337–26344 (2012).
[Crossref]

C. Xiong, W. H. P. Pernice, and H. X. Tang, “Low-loss, silicon integrated, aluminum nitride photonic circuits and their use for electro-optic signal processing,” Nano Lett. 12, 3562–3568 (2012).
[Crossref]

M. Hafezi, Z. Kim, S. L. Rolston, L. A. Orozco, B. L. Lev, and J. M. Taylor, “Atomic interface between microwave and optical photons,” Phys. Rev. A 85, 020302 (2012).
[Crossref]

2011 (3)

M. Tsang, “Cavity quantum electro-optics. II. Input-output relations between traveling optical and microwave fields,” Phys. Rev. A 84, 043845 (2011).
[Crossref]

H. Paik, D. I. Schuster, L. S. Bishop, G. Kirchmair, G. Catelani, A. P. Sears, B. R. Johnson, M. J. Reagor, L. Frunzio, L. I. Glazman, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture,” Phys. Rev. Lett. 107, 240501 (2011).
[Crossref]

D. Bozyigit, C. Lang, L. Steffen, J. M. Fink, C. Eichler, M. Baur, R. Bianchetti, P. J. Leek, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Antibunching of microwave-frequency photons observed in correlation measurements using linear detectors,” Nat. Phys. 7, 154–158 (2011).
[Crossref]

2010 (2)

M. Tsang, “Cavity quantum electro-optics,” Phys. Rev. A 81, 063837 (2010).
[Crossref]

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105, 210501 (2010).
[Crossref]

2009 (6)

J. Verdú, H. Zoubi, C. Koller, J. Majer, H. Ritsch, and J. Schmiedmayer, “Strong magnetic coupling of an ultracold gas to a superconducting waveguide cavity,” Phys. Rev. Lett. 103, 043603 (2009).
[Crossref]

A. Imamoğlu, “Cavity QED based on collective magnetic dipole coupling: spin ensembles as hybrid two-level systems,” Phys. Rev. Lett. 102, 083602 (2009).
[Crossref]

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
[Crossref]

D. V. Strekalov, A. A. Savchenkov, A. B. Matsko, and N. Yu, “Efficient upconversion of subterahertz radiation in a high-Q whispering gallery resonator,” Opt. Lett. 34, 713–715 (2009).
[Crossref]

A. A. Savchenkov, W. Liang, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Tunable optical single-sideband modulator with complete sideband suppression,” Opt. Lett. 34, 1300–1302 (2009).
[Crossref]

D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery resonator for efficient optical up-conversion,” Phys. Rev. A. 80, 033810 (2009).
[Crossref]

2008 (2)

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

R. J. Schoelkopf and S. M. Girvin, “Wiring up quantum systems,” Nature 451, 664–669 (2008).
[Crossref]

2007 (1)

2006 (2)

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
[Crossref]

J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006).
[Crossref]

2003 (1)

2001 (1)

D. Cohen, M. Hossein-Zadeh, and A. Levi, “Microphotonic modulator for microwave receiver,” Electron. Lett. 37, 300–301 (2001).
[Crossref]

1994 (1)

U. Schlarb and K. Betzler, “Influence of the defect structure on the refractive indices of undoped and mg-doped lithium niobate,” Phys. Rev. B 50, 751–757 (1994).
[Crossref]

1982 (1)

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817–1839 (1982).
[Crossref]

Aguado, R.

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105, 210501 (2010).
[Crossref]

Andrews, R. W.

R. W. Andrews, A. P. Reed, K. Cicak, J. D. Teufel, and K. W. Lehnert, “Quantum-enabled temporal and spectral mode conversion of microwave signals,” Nat. Commun. 6, 10021 (2015).
[Crossref]

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

Appel, J.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

Awschalom, D. D.

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

Bagci, T.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

Baur, M.

D. Bozyigit, C. Lang, L. Steffen, J. M. Fink, C. Eichler, M. Baur, R. Bianchetti, P. J. Leek, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Antibunching of microwave-frequency photons observed in correlation measurements using linear detectors,” Nat. Phys. 7, 154–158 (2011).
[Crossref]

Bernier, N.

C. Javerzac-Galy, K. Plekhanov, N. Bernier, L. D. Toth, A. K. Feofanov, and T. J. Kippenberg, “On-chip microwave-to-optical quantum coherent converter based on a superconducting resonator coupled to an electro-optic microresonator,” arXiv:1512.06442 (2015).

Betzler, K.

U. Schlarb and K. Betzler, “Influence of the defect structure on the refractive indices of undoped and mg-doped lithium niobate,” Phys. Rev. B 50, 751–757 (1994).
[Crossref]

Bianchetti, R.

D. Bozyigit, C. Lang, L. Steffen, J. M. Fink, C. Eichler, M. Baur, R. Bianchetti, P. J. Leek, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Antibunching of microwave-frequency photons observed in correlation measurements using linear detectors,” Nat. Phys. 7, 154–158 (2011).
[Crossref]

Bishop, L. S.

H. Paik, D. I. Schuster, L. S. Bishop, G. Kirchmair, G. Catelani, A. P. Sears, B. R. Johnson, M. J. Reagor, L. Frunzio, L. I. Glazman, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture,” Phys. Rev. Lett. 107, 240501 (2011).
[Crossref]

Blais, A.

D. Bozyigit, C. Lang, L. Steffen, J. M. Fink, C. Eichler, M. Baur, R. Bianchetti, P. J. Leek, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Antibunching of microwave-frequency photons observed in correlation measurements using linear detectors,” Nat. Phys. 7, 154–158 (2011).
[Crossref]

Bochmann, J.

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

Bozyigit, D.

D. Bozyigit, C. Lang, L. Steffen, J. M. Fink, C. Eichler, M. Baur, R. Bianchetti, P. J. Leek, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Antibunching of microwave-frequency photons observed in correlation measurements using linear detectors,” Nat. Phys. 7, 154–158 (2011).
[Crossref]

Breunig, I.

Bruno, A.

D. Ristè, S. Poletto, M.-Z. Huang, A. Bruno, V. Vesterinen, O.-P. Saira, and L. DiCarlo, “Detecting bit-flip errors in a logical qubit using stabilizer measurements,” Nat. Commun. 6, 6983 (2015).
[Crossref]

Buse, K.

Carmon, T.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

Catelani, G.

H. Paik, D. I. Schuster, L. S. Bishop, G. Kirchmair, G. Catelani, A. P. Sears, B. R. Johnson, M. J. Reagor, L. Frunzio, L. I. Glazman, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture,” Phys. Rev. Lett. 107, 240501 (2011).
[Crossref]

Caves, C. M.

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817–1839 (1982).
[Crossref]

Chen, L.

Chen, Y.-H.

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Schuster, D. I.

H. Paik, D. I. Schuster, L. S. Bishop, G. Kirchmair, G. Catelani, A. P. Sears, B. R. Johnson, M. J. Reagor, L. Frunzio, L. I. Glazman, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture,” Phys. Rev. Lett. 107, 240501 (2011).
[Crossref]

Schwefel, H. G. L.

G. Schunk, U. Vogl, D. V. Strekalov, M. Förtsch, F. Sedlmeir, H. G. L. Schwefel, M. Göbelt, S. Christiansen, G. Leuchs, and C. Marquardt, “Interfacing transitions of different alkali atoms and telecom bands using one narrowband photon pair source,” Optica 2, 773–778 (2015).
[Crossref]

I. Breunig, B. Sturman, F. Sedlmeir, H. G. L. Schwefel, and K. Buse, “Whispering gallery modes at the rim of an axisymmetric optical resonator: analytical versus numerical description and comparison with experiment,” Opt. Express 21, 30683–30692 (2013).
[Crossref]

D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery resonator for efficient optical up-conversion,” Phys. Rev. A. 80, 033810 (2009).
[Crossref]

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

Sears, A. P.

H. Paik, D. I. Schuster, L. S. Bishop, G. Kirchmair, G. Catelani, A. P. Sears, B. R. Johnson, M. J. Reagor, L. Frunzio, L. I. Glazman, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture,” Phys. Rev. Lett. 107, 240501 (2011).
[Crossref]

Sedlmeir, F.

Seidel, D.

Simmonds, R. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

Simonsen, A.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

Smolin, J. A.

C. Rigetti, J. M. Gambetta, S. Poletto, B. L. T. Plourde, J. M. Chow, A. D. Córcoles, J. A. Smolin, S. T. Merkel, J. R. Rozen, G. A. Keefe, M. B. Rothwell, M. B. Ketchen, and M. Steffen, “Superconducting qubit in a waveguide cavity with a coherence time approaching 0.1  ms,” Phys. Rev. B 86, 100506 (2012).
[Crossref]

Sørensen, A.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

Sørensen, A. S.

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105, 210501 (2010).
[Crossref]

Steffen, L.

D. Bozyigit, C. Lang, L. Steffen, J. M. Fink, C. Eichler, M. Baur, R. Bianchetti, P. J. Leek, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Antibunching of microwave-frequency photons observed in correlation measurements using linear detectors,” Nat. Phys. 7, 154–158 (2011).
[Crossref]

Steffen, M.

C. Rigetti, J. M. Gambetta, S. Poletto, B. L. T. Plourde, J. M. Chow, A. D. Córcoles, J. A. Smolin, S. T. Merkel, J. R. Rozen, G. A. Keefe, M. B. Rothwell, M. B. Ketchen, and M. Steffen, “Superconducting qubit in a waveguide cavity with a coherence time approaching 0.1  ms,” Phys. Rev. B 86, 100506 (2012).
[Crossref]

Stone, A. D.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

Strekalov, D.

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
[Crossref]

Strekalov, D. V.

Sturman, B.

Tang, H. X.

C. Xiong, W. H. P. Pernice, and H. X. Tang, “Low-loss, silicon integrated, aluminum nitride photonic circuits and their use for electro-optic signal processing,” Nano Lett. 12, 3562–3568 (2012).
[Crossref]

Taylor, J. M.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

M. Hafezi, Z. Kim, S. L. Rolston, L. A. Orozco, B. L. Lev, and J. M. Taylor, “Atomic interface between microwave and optical photons,” Phys. Rev. A 85, 020302 (2012).
[Crossref]

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105, 210501 (2010).
[Crossref]

Teufel, J. D.

R. W. Andrews, A. P. Reed, K. Cicak, J. D. Teufel, and K. W. Lehnert, “Quantum-enabled temporal and spectral mode conversion of microwave signals,” Nat. Commun. 6, 10021 (2015).
[Crossref]

Tittel, W.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
[Crossref]

Tobar, M. E.

M. Goryachev, N. Kostylev, and M. E. Tobar, “Single-photon level study of microwave properties of lithium niobate at millikelvin temperatures,” Phys. Rev. B 92, 060406 (2015).
[Crossref]

Toth, L. D.

C. Javerzac-Galy, K. Plekhanov, N. Bernier, L. D. Toth, A. K. Feofanov, and T. J. Kippenberg, “On-chip microwave-to-optical quantum coherent converter based on a superconducting resonator coupled to an electro-optic microresonator,” arXiv:1512.06442 (2015).

Tsang, M.

M. Tsang, “Cavity quantum electro-optics. II. Input-output relations between traveling optical and microwave fields,” Phys. Rev. A 84, 043845 (2011).
[Crossref]

M. Tsang, “Cavity quantum electro-optics,” Phys. Rev. A 81, 063837 (2010).
[Crossref]

Usami, K.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

Vahala, K. J.

J. Li, H. Lee, K. Y. Yang, and K. J. Vahala, “Sideband spectroscopy and dispersion measurement in microcavities,” Opt. Express 20, 26337–26344 (2012).
[Crossref]

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

Vainsencher, A.

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

Verdú, J.

J. Verdú, H. Zoubi, C. Koller, J. Majer, H. Ritsch, and J. Schmiedmayer, “Strong magnetic coupling of an ultracold gas to a superconducting waveguide cavity,” Phys. Rev. Lett. 103, 043603 (2009).
[Crossref]

Vesterinen, V.

D. Ristè, S. Poletto, M.-Z. Huang, A. Bruno, V. Vesterinen, O.-P. Saira, and L. DiCarlo, “Detecting bit-flip errors in a logical qubit using stabilizer measurements,” Nat. Commun. 6, 6983 (2015).
[Crossref]

Villanueva, L. G.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

Vogl, U.

Waasem, N.

Wallraff, A.

D. Bozyigit, C. Lang, L. Steffen, J. M. Fink, C. Eichler, M. Baur, R. Bianchetti, P. J. Leek, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Antibunching of microwave-frequency photons observed in correlation measurements using linear detectors,” Nat. Phys. 7, 154–158 (2011).
[Crossref]

Wang, L. J.

D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery resonator for efficient optical up-conversion,” Phys. Rev. A. 80, 033810 (2009).
[Crossref]

Weng, W.

Wiersig, J.

J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006).
[Crossref]

Williamson, L. A.

L. A. Williamson, Y.-H. Chen, and J. J. Longdell, “Magneto-optic modulator with unit quantum efficiency,” Phys. Rev. Lett. 113, 203601 (2014).
[Crossref]

Wong, K.

K. Wong, Properties of Lithium Niobate, EMIS Datareviews Series (INSPEC/Institution of Electrical Engineers, 2002).

Wood, M. G.

Wubs, M.

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105, 210501 (2010).
[Crossref]

Xiong, C.

C. Xiong, W. H. P. Pernice, and H. X. Tang, “Low-loss, silicon integrated, aluminum nitride photonic circuits and their use for electro-optic signal processing,” Nano Lett. 12, 3562–3568 (2012).
[Crossref]

Xu, Q.

Yang, K. Y.

Yang, L.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

Yin, C.

X. Fernandez-Gonzalvo, Y.-H. Chen, C. Yin, S. Rogge, and J. J. Longdell, “Coherent frequency up-conversion of microwaves to the optical telecommunications band in an Er:YSO crystal,” Phys. Rev. A 92, 062313 (2015).
[Crossref]

Yu, N.

D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery resonator for efficient optical up-conversion,” Phys. Rev. A. 80, 033810 (2009).
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D. V. Strekalov, A. A. Savchenkov, A. B. Matsko, and N. Yu, “Efficient upconversion of subterahertz radiation in a high-Q whispering gallery resonator,” Opt. Lett. 34, 713–715 (2009).
[Crossref]

Zeuthen, E.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

Zoubi, H.

J. Verdú, H. Zoubi, C. Koller, J. Majer, H. Ritsch, and J. Schmiedmayer, “Strong magnetic coupling of an ultracold gas to a superconducting waveguide cavity,” Phys. Rev. Lett. 103, 043603 (2009).
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C. Xiong, W. H. P. Pernice, and H. X. Tang, “Low-loss, silicon integrated, aluminum nitride photonic circuits and their use for electro-optic signal processing,” Nano Lett. 12, 3562–3568 (2012).
[Crossref]

Nat. Commun. (2)

D. Ristè, S. Poletto, M.-Z. Huang, A. Bruno, V. Vesterinen, O.-P. Saira, and L. DiCarlo, “Detecting bit-flip errors in a logical qubit using stabilizer measurements,” Nat. Commun. 6, 6983 (2015).
[Crossref]

R. W. Andrews, A. P. Reed, K. Cicak, J. D. Teufel, and K. W. Lehnert, “Quantum-enabled temporal and spectral mode conversion of microwave signals,” Nat. Commun. 6, 10021 (2015).
[Crossref]

Nat. Photonics (1)

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
[Crossref]

Nat. Phys. (3)

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

D. Bozyigit, C. Lang, L. Steffen, J. M. Fink, C. Eichler, M. Baur, R. Bianchetti, P. J. Leek, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, “Antibunching of microwave-frequency photons observed in correlation measurements using linear detectors,” Nat. Phys. 7, 154–158 (2011).
[Crossref]

Nature (2)

R. J. Schoelkopf and S. M. Girvin, “Wiring up quantum systems,” Nature 451, 664–669 (2008).
[Crossref]

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

Opt. Commun. (1)

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
[Crossref]

Opt. Express (3)

Opt. Lett. (5)

Optica (2)

Phys. Rev. A (5)

S. Huang, “Quantum state transfer in cavity electro-optic modulators,” Phys. Rev. A 92, 043845 (2015).
[Crossref]

M. Tsang, “Cavity quantum electro-optics,” Phys. Rev. A 81, 063837 (2010).
[Crossref]

M. Tsang, “Cavity quantum electro-optics. II. Input-output relations between traveling optical and microwave fields,” Phys. Rev. A 84, 043845 (2011).
[Crossref]

X. Fernandez-Gonzalvo, Y.-H. Chen, C. Yin, S. Rogge, and J. J. Longdell, “Coherent frequency up-conversion of microwaves to the optical telecommunications band in an Er:YSO crystal,” Phys. Rev. A 92, 062313 (2015).
[Crossref]

M. Hafezi, Z. Kim, S. L. Rolston, L. A. Orozco, B. L. Lev, and J. M. Taylor, “Atomic interface between microwave and optical photons,” Phys. Rev. A 85, 020302 (2012).
[Crossref]

Phys. Rev. A. (1)

D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery resonator for efficient optical up-conversion,” Phys. Rev. A. 80, 033810 (2009).
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M. Goryachev, N. Kostylev, and M. E. Tobar, “Single-photon level study of microwave properties of lithium niobate at millikelvin temperatures,” Phys. Rev. B 92, 060406 (2015).
[Crossref]

C. Rigetti, J. M. Gambetta, S. Poletto, B. L. T. Plourde, J. M. Chow, A. D. Córcoles, J. A. Smolin, S. T. Merkel, J. R. Rozen, G. A. Keefe, M. B. Rothwell, M. B. Ketchen, and M. Steffen, “Superconducting qubit in a waveguide cavity with a coherence time approaching 0.1  ms,” Phys. Rev. B 86, 100506 (2012).
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Phys. Rev. D (1)

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Phys. Rev. Lett. (7)

H. Paik, D. I. Schuster, L. S. Bishop, G. Kirchmair, G. Catelani, A. P. Sears, B. R. Johnson, M. J. Reagor, L. Frunzio, L. I. Glazman, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture,” Phys. Rev. Lett. 107, 240501 (2011).
[Crossref]

J. Verdú, H. Zoubi, C. Koller, J. Majer, H. Ritsch, and J. Schmiedmayer, “Strong magnetic coupling of an ultracold gas to a superconducting waveguide cavity,” Phys. Rev. Lett. 103, 043603 (2009).
[Crossref]

A. Imamoğlu, “Cavity QED based on collective magnetic dipole coupling: spin ensembles as hybrid two-level systems,” Phys. Rev. Lett. 102, 083602 (2009).
[Crossref]

D. Marcos, M. Wubs, J. M. Taylor, R. Aguado, M. D. Lukin, and A. S. Sørensen, “Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits,” Phys. Rev. Lett. 105, 210501 (2010).
[Crossref]

L. A. Williamson, Y.-H. Chen, and J. J. Longdell, “Magneto-optic modulator with unit quantum efficiency,” Phys. Rev. Lett. 113, 203601 (2014).
[Crossref]

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[Crossref]

J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006).
[Crossref]

Science (1)

M. H. Devoret and R. J. Schoelkopf, “Superconducting circuits for quantum information: an outlook,” Science 339, 1169–1174 (2013).
[Crossref]

Other (2)

K. Wong, Properties of Lithium Niobate, EMIS Datareviews Series (INSPEC/Institution of Electrical Engineers, 2002).

C. Javerzac-Galy, K. Plekhanov, N. Bernier, L. D. Toth, A. K. Feofanov, and T. J. Kippenberg, “On-chip microwave-to-optical quantum coherent converter based on a superconducting resonator coupled to an electro-optic microresonator,” arXiv:1512.06442 (2015).

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Figures (5)

Fig. 1.
Fig. 1.

Two schemes for suppressing the DFG signal in type-0 conversion are shown. (a) In the case of equally spaced modes, the optical pump has to be detuned to cause the red sideband to be off-resonant. (b) If the mode spacing is asymmetric, the pump can be kept fully resonant while maintaining the suppression of the undesired sideband.

Fig. 2.
Fig. 2.

(a) Photograph of the bottom part of the microwave cavity with silicon coupling prism and the WGM resonator. (b) Simulation of the microwave field distribution in the cavity. Only the z component (TE) of the field is shown. (c) Schematic of the cavity. An optical pump beam (red dashed) couples through a prism into the WGM, and part of the light is directly reflected. The sideband is given in blue. In the side view, the metallic tuning screw to perturb the microwave mode and the coaxial pin coupler are shown. The pin coupler is defined as the input port of the converter and the output port is the optical outcoupling spot inside of the prism (solid lines). (d) Reflection spectrum of the optical mode used for sum frequency conversion (compare Fig. 5). Also shown are the linewidth and the corresponding Q factors. (e) Microwave spectrum in reflection from the coaxial pin coupler. The m Ω = ± 1 mode is shown for tuning screw position inside (red) and outside (black) the cavity.

Fig. 3.
Fig. 3.

On the left, the resonance position of a TE mode experiencing an avoided crossing with a TM mode is shown for different temperature settings. On the right, the WGM spectrum around the avoided crossing is plotted for different temperatures.

Fig. 4.
Fig. 4.

(a) Resonance frequencies of three TE modes that are separated by one azimuthal mode number m corresponding to the free spectral range FSR ± 9    GHz . Each mode experiences avoided crossings of different strength for some temperatures. (b) Frequency difference of the m + 1 and m 1 mode from the m mode. One can see that FSR + and FSR are functions of the temperature and differ by up to 50 MHz. This allows selective up- and down-conversion as depicted in (c): The temperature was set to 27.88°C, indicated by the dashed line in (a) and (b), where FSR + FSR = 18.1    MHz . The optical pump is locked to the m mode. A microwave signal sweeping over the microwave resonance is indicated by the gray Lorentzian, while the generated sidebands are measured with an optical spectrum analyzer (see Fig. 5). The shown sidebands are separated by 18.1 MHz and the suppression of the down-conversion at the maximum of the up-conversion is about 23 dB.

Fig. 5.
Fig. 5.

Power of the up-converted sideband as a function of the microwave power sent to the cavity. With increasing microwave power, the optical pump mode depletes and the conversion efficiency decreases. A linear fit in the undepleted regime (gray) yields a slope of P + / P Ω = 23.68 ± 0.46 , corresponding to a photon number conversion efficiency of η + = ( 1.09 ± 0.02 ) × 10 3 . The inset shows an OSA spectrum (resolution 2.5 GHz) of the reflected pump power and the generated up-converted sideband.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

H ^ int = g ( a ^ b ^ c ^ + a ^ b ^ c ^ ) DFG + g + ( a ^ b ^ + c ^ + a ^ b ^ + c ^ ) SFG ,
g ± = n p n ± n Ω r ω p ω ± Ω 0 8 ε 0 V p V ± V Ω × d V Ψ p Ψ Ω Ψ ± ,
P ± = 8 g 2 Ω γ 2 γ Ω | Γ p | 2 | Γ ± | 2 | Γ Ω | 2 ζ ± P p P Ω and η ± = Ω ω ± ζ ± P p ,
Γ p = i ( ω ω p ) + γ + γ ,
Γ Ω = i ( Ω Ω 0 ) + γ Ω + γ Ω ,
Γ ± = i ( ω ± Ω ω ± ) + γ + γ .
G 0 = | α g | 2 Γ ± Γ Ω Γ ± Γ Ω 4 γ ± γ Ω η ± ,
S = P + P = Δ 2 ( γ + γ ) 2 + 1 .
η + = Ω ω + P + P Ω .
η + = 4 γ γ Ω ( γ + γ ) ( γ Ω + γ Ω ) G 0 ( 1 + G 0 ) 2 .

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