Research ArticleAPPLIED PHYSICS

Superconducting cavity electro-optics: A platform for coherent photon conversion between superconducting and photonic circuits

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Science Advances  17 Aug 2018:
Vol. 4, no. 8, eaar4994
DOI: 10.1126/sciadv.aar4994
  • Fig. 1 Coherent conversion with cavity electro-optics.

    (A) Schematic of cavity electro-optic systems. The optical cavity is made of materials with Pockels nonlinearity (χ(2)) and placed in the capacitor of the LC circuit. At the same time, optical and microwave cavities are coupled to optical and microwave bus waveguides, respectively. (B) Integrated superconducting cavity electro-optic device. The red part is the optical cavity and coupling waveguide, and the yellow part is the superconducting microwave cavity. A buffer layer (semitransparent) is placed between optical devices and the superconducting cavity to prevent metallic absorption of optical photons. (C) Diagram of frequencies in the conversion process. Strong control light is applied to the TE optical mode (pump mode), and photons can be converted between the microwave mode and the TM optical mode (signal mode). Microwave photons are converted to optical photons through sum frequency generation, and optical photons are converted to microwave photons through difference frequency generation, as shown in insets. The mode distribution in the cross section is shown for (D) the microwave mode, (E) the TE optical mode, and (F) the TM optical mode. Arrow direction and length represent the electric field direction and strength in log scale, respectively. Colors in (D) represent the voltage distribution, and colors in (E) and (F) represent the energy density. In simulation, the optical waveguide is 2 μm wide and 800 nm thick, and the sidewall angle is 8°. The distance between microwave electrodes is 2.8 μm. The material boundary is plotted in gray.

  • Fig. 2 Integrated superconducting cavity electro-optic device.

    (A) Optical image of the superconducting cavity electro-optic device. Scale bar, 100 μm. (B) TE optical spectrum with different dc voltages. The azimuthal number difference between the TE and TM optical modes is 1. The mode anti-crossing gap is 2gx ~ 6.1 GHz, and the original dissipation rates for TM and TE optical modes without optical mode mixing are 190 and 480 MHz, respectively. (C) TE optical spectrum with dc voltages of −400 V (green), 300 V (red), and 900 V (orange), corresponding to the green, red, and orange dashed lines in (B), respectively. (D) Schematic of the microwave resonator and electric field distribution of the microwave mode, as well as the equivalent circuit. (E) Measured reflection spectrum of the microwave cavity. a.u., arbitrary units.

  • Fig. 3 Electromagnetically induced transparency with cavity electro-optics.

    (A) Measured optical reflection spectrum as a function of the modulation frequency. (B) Zoom-in of the optical reflection spectrum centered at the transparency window. Each spectrum in (A) and (B) corresponds to a different dc voltage (thus different frequency detuning between pump and signal modes). Spectrums are offset for clarity. (C) Transparency window with the control light power of 8 dBm (blue), 5 dBm (orange), and 0 dBm (green). Circles are measured data, and solid lines are fitted spectra with eq. S13 in section S1. (D) Cooperativity and internal conversion efficiency versus control light power. The blue, orange, and green points correspond to the blue, orange, and green curves in (C), respectively. Gray lines are the fitted result based on measured data.

  • Fig. 4 Bidirectional frequency conversion.

    (A) Schematic showing the full conversion process. (B) The optical reflection Soo, (C) microwave-to-optical conversion Soe, (D) optical-to-microwave conversion Seo, (E) and microwave reflection See are measured to calibrate the on-chip conversion efficiency. The control light power is 8 dBm, and the dc voltage is 297 V. All conversion matrix coefficients are normalized to the radio frequency (RF) output power of the network analyzer (section S6).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/8/eaar4994/DC1

    Section S1. Theory of cavity electro-optics and its utility for microwave-to-optical conversion

    Section S2. Device fabrication procedure

    Section S3. Identifying phase-matching conditions for optical modes

    Section S4. Influence of optical mode mixing on the vacuum coupling rate geo

    Section S5. Microwave resonator design

    Section S6. Measurement setup

    Section S7. Device temperature calibration

    Section S8. Efficiency calibration

    Section S9. Added noise during conversion

    Fig. S1. Calculated internal conversion efficiency.

    Fig. S2. Scanning electron microscopy picture of the cross section of a superconducting cavity electro-optic device.

    Fig. S3. Anti-crossing between TE and TM optical modes.

    Fig. S4. Measured spectrum signature of mixing between TE and TM modes.

    Fig. S5. Wavelength difference between adjacent resonances.

    Fig. S6. Phase-matching wavelength and anti-crossing strength.

    Fig. S7. Vacuum coupling rate with hybrid optical modes.

    Fig. S8. Microwave resonator simulation.

    Fig. S9. Experiment setup for microwave-to-optical photon conversion.

    Fig. S10. Microwave resonator performance under different temperatures.

    References (33, 34)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Theory of cavity electro-optics and its utility for microwave-to-optical conversion
    • Section S2. Device fabrication procedure
    • Section S3. Identifying phase-matching conditions for optical modes
    • Section S4. Influence of optical mode mixing on the vacuum coupling rate geo
    • Section S5. Microwave resonator design
    • Section S6. Measurement setup
    • Section S7. Device temperature calibration
    • Section S8. Efficiency calibration
    • Section S9. Added noise during conversion
    • Fig. S1. Calculated internal conversion efficiency.
    • Fig. S2. Scanning electron microscopy picture of the cross section of a superconducting cavity electro-optic device.
    • Fig. S3. Anti-crossing between TE and TM optical modes.
    • Fig. S4. Measured spectrum signature of mixing between TE and TM modes.
    • Fig. S5. Wavelength difference between adjacent resonances.
    • Fig. S6. Phase-matching wavelength and anti-crossing strength.
    • Fig. S7. Vacuum coupling rate with hybrid optical modes.
    • Fig. S8. Microwave resonator simulation.
    • Fig. S9. Experiment setup for microwave-to-optical photon conversion.
    • Fig. S10. Microwave resonator performance under different temperatures.
    • References (33, 34)

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