Abstract

Brillouin systems operating in the quantum regime have recently been identified as a valuable tool for quantum information technologies and fundamental science. However, reaching the quantum regime is extraordinarily challenging, owing to the stringent requirements of combining low thermal occupation with low optical and mechanical dissipation, and large coherent phonon-photon interactions. Here, we propose an on-chip liquid based Brillouin system that is predicted to exhibit large phonon-photon coupling with exceptionally low acoustic dissipation. The system is comprised of a silicon-based “slot” waveguide filled with superfluid helium. This type of waveguide supports optical and acoustical traveling waves, strongly confining both fields into a subwavelength-scale mode volume. It serves as the foundation of an on-chip traveling wave Brillouin resonator with an electrostrictive single photon optomechanical coupling rate exceeding 240 kHz. Such devices may enable applications ranging from ultra-sensitive superfluid-based gyroscopes, to non-reciprocal optical circuits. Furthermore, this platform opens up new possibilities to explore quantum fluid dynamics in a strongly interacting condensate.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (3)

F. Gyger, J. Liu, F. Yang, J. He, A. S. Raja, R. N. Wang, S. A. Bhave, T. J. Kippenberg, and L. Thévenaz, “Observation of stimulated brillouin scattering in silicon nitride integrated waveguides,” Phys. Rev. Lett. 124(1), 013902 (2020).
[Crossref]

Y.-H. Lai, M.-G. Suh, Y.-K. Lu, B. Shen, Q.-F. Yang, H. Wang, J. Li, S. H. Lee, K. Y. Yang, and K. Vahala, “Earth rotation measured by a chip-scale ring laser gyroscope,” Nat. Photonics 14(6), 345–349 (2020).
[Crossref]

X. He, G. I. Harris, C. G. Baker, A. Sawadsky, Y. L. Sfendla, Y. P. Sachkou, S. Forstner, and W. P. Bowen, “Strong optical coupling through superfluid brillouin lasing,” Nat. Phys. 16(4), 417–421 (2020).
[Crossref]

2019 (12)

Y. P. Sachkou, C. G. Baker, G. I. Harris, O. R. Stockdale, S. Forstner, M. T. Reeves, X. He, D. L. McAuslan, A. S. Bradley, M. J. Davis, and W. P. Bowen, “Coherent vortex dynamics in a strongly interacting superfluid on a silicon chip,” Science 366(6472), 1480–1485 (2019).
[Crossref]

G. S. Wiederhecker, P. Dainese, and T. P. Mayer Alegre, “Brillouin optomechanics in nanophotonic structures,” APL Photonics 4(7), 071101 (2019).
[Crossref]

G. Enzian, M. Szczykulska, J. Silver, L. D. Bino, S. Zhang, I. A. Walmsley, P. Del’Haye, and M. R. Vanner, “Observation of brillouin optomechanical strong coupling with an 11ghz mechanical mode,” Optica 6(1), 7–14 (2019).
[Crossref]

A. B. Shkarin, A. D. Kashkanova, C. D. Brown, S. Garcia, K. Ott, J. Reichel, and J. G. E. Harris, “Quantum optomechanics in a liquid,” Phys. Rev. Lett. 122(15), 153601 (2019).
[Crossref]

S. Gundavarapu, G. M. Brodnik, M. Puckett, T. Huffman, D. Bose, R. Behunin, J. Wu, T. Qiu, C. Pinho, N. Chauhan, J. Nohava, P. T. Rakich, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Sub-hertz fundamental linewidth photonic integrated brillouin laser,” Nat. Photonics 13(1), 60–67 (2019).
[Crossref]

A. H. Safavi-Naeini, D. V. Thourhout, R. Baets, and R. V. Laer, “Controlling phonons and photons at the wavelength scale: integrated photonics meets integrated phononics,” Optica 6(2), 213–232 (2019).
[Crossref]

B. J. Eggleton, C. G. Poulton, P. T. Rakich, M. J. Steel, and G. Bahl, “Brillouin integrated photonics,” Nat. Photonics 13(10), 664–677 (2019).
[Crossref]

L. Zhou, Y. Lu, Y. Fu, H. Ma, and C. Du, “Design of a hybrid on-chip waveguide with giant backward stimulated brillouin scattering,” Opt. Express 27(18), 24953–24971 (2019).
[Crossref]

S. Forstner, Y. Sachkou, M. Woolley, G. I. Harris, X. He, W. P. Bowen, and C. G. Baker, “Modelling of vorticity, sound and their interaction in two-dimensional superfluids,” New J. Phys. 21(5), 053029 (2019).
[Crossref]

A. Shkarin, A. Kashkanova, C. Brown, S. Garcia, K. Ott, J. Reichel, and J. Harris, “Quantum Optomechanics in a Liquid,” Phys. Rev. Lett. 122(15), 153601 (2019).
[Crossref]

T. P. McKenna, T. P. McKenna, R. N. Patel, R. N. Patel, J. D. Witmer, J. D. Witmer, R. V. Laer, R. V. Laer, J. A. Valery, and A. H. Safavi-Naeini, “Cryogenic packaging of an optomechanical crystal,” Opt. Express 27(20), 28782–28791 (2019).
[Crossref]

G. Koolstra, G. Yang, and D. I. Schuster, “Coupling a single electron on superfluid helium to a superconducting resonator,” Nat. Commun. 10(1), 5323 (2019).
[Crossref]

2018 (5)

C. F. Ockeloen-Korppi, E. Damskägg, J. M. Pirkkalainen, M. Asjad, A. A. Clerk, F. Massel, M. J. Woolley, and M. A. Sillanpää, “Stabilized entanglement of massive mechanical oscillators,” Nature 556(7702), 478–482 (2018).
[Crossref]

P. Rakich and F. Marquardt, “Quantum theory of continuum optomechanics,” New J. Phys. 20(4), 045005 (2018).
[Crossref]

N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, and P. T. Rakich, “A silicon Brillouin laser,” Science 360(6393), 1113–1116 (2018).
[Crossref]

E. A. Kittlaus, N. T. Otterstrom, P. Kharel, S. Gertler, and P. T. Rakich, “Non-reciprocal interband brillouin modulation,” Nat. Photonics 12(10), 613–619 (2018).
[Crossref]

D. B. Sohn, S. Kim, and G. Bahl, “Time-reversal symmetry breaking with acoustic pumping of nanophotonic circuits,” Nat. Photonics 12(2), 91–97 (2018).
[Crossref]

2017 (7)

F. Souris, X. Rojas, P. H. Kim, and J. P. Davis, “Ultralow-dissipation superfluid micromechanical resonator,” Phys. Rev. Appl. 7(4), 044008 (2017).
[Crossref]

A. Kashkanova, A. Shkarin, C. Brown, N. Flowers-Jacobs, L. Childress, S. Hoch, L. Hohmann, K. Ott, J. Reichel, and J. Harris, “Superfluid brillouin optomechanics,” Nat. Phys. 13(1), 74–79 (2017).
[Crossref]

M. Merklein, B. Stiller, K. Vu, S. J. Madden, and B. J. Eggleton, “A chip-integrated coherent photonic-phononic memory,” Nat. Commun. 8(1), 574 (2017).
[Crossref]

L. A. De Lorenzo and K. C. Schwab, “Ultra-High Q Acoustic Resonance in Superfluid 4He,” J. Low Temp. Phys. 186(3-4), 233–240 (2017).
[Crossref]

A. D. Kashkanova, A. B. Shkarin, C. D. Brown, N. E. Flowers-Jacobs, L. Childress, S. W. Hoch, L. Hohmann, K. Ott, J. Reichel, and J. G. E. Harris, “Superfluid brillouin optomechanics,” Nat. Phys. 13(1), 74–79 (2017).
[Crossref]

J. Li, M.-G. Suh, and K. Vahala, “Microresonator Brillouin gyroscope,” Optica 4(3), 346–348 (2017).
[Crossref]

A. D. Kashkanova, A. B. Shkarin, C. D. Brown, N. E. Flowers-Jacobs, L. Childress, S. W. Hoch, L. Hohmann, K. Ott, J Reichel, and J. G. E. Harris, “Optomechanics in superfluid helium coupled to a fiber-based cavity,” J. Opt. 19(3), 034001 (2017).
[Crossref]

2016 (7)

G. Yang, A. Fragner, G. Koolstra, L. Ocola, D. Czaplewski, R. Schoelkopf, and D. Schuster, “Coupling an Ensemble of Electrons on Superfluid Helium to a Superconducting Circuit,” Phys. Rev. X 6(1), 011031 (2016).
[Crossref]

C. J. Sarabalis, J. T. Hill, and A. H. Safavi-Naeini, “Guided acoustic and optical waves in silicon-on-insulator for Brillouin scattering and optomechanics,” APL Photonics 1(7), 071301 (2016).
[Crossref]

E. A. Kittlaus, H. Shin, and P. T. Rakich, “Large brillouin amplification in silicon,” Nat. Photonics 10(7), 463–467 (2016).
[Crossref]

C. G. Baker, G. I. Harris, D. L. McAuslan, Y. Sachkou, X. He, and W. P. Bowen, “Theoretical framework for thin film superfluid optomechanics: towards the quantum regime,” New J. Phys. 18(12), 123025 (2016).
[Crossref]

R. Van Laer, R. Baets, and D. Van Thourhout, “Unifying brillouin scattering and cavity optomechanics,” Phys. Rev. A 93(5), 053828 (2016).
[Crossref]

G. I. Harris, D. L. McAuslan, E. Sheridan, Y. Sachkou, C. Baker, and W. P. Bowen, “Laser cooling and control of excitations in superfluid helium,” Nat. Phys. 12(8), 788–793 (2016).
[Crossref]

D. McAuslan, G. Harris, C. Baker, Y. Sachkou, X. He, E. Sheridan, and W. Bowen, “Microphotonic Forces from Superfluid Flow,” Phys. Rev. X 6(2), 021012 (2016).
[Crossref]

2015 (1)

2014 (3)

L. A. D. Lorenzo and K. C. Schwab, “Superfluid optomechanics: coupling of a superfluid to a superconducting condensate,” New J. Phys. 16(11), 113020 (2014).
[Crossref]

C. Baker, W. Hease, D.-T. Nguyen, A. Andronico, S. Ducci, G. Leo, and I. Favero, “Photoelastic coupling in gallium arsenide optomechanical disk resonators,” Opt. Express 22(12), 14072–14086 (2014).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

2013 (3)

T. A. Palomaki, J. W. Harlow, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Coherent state transfer between itinerant microwave fields and a mechanical oscillator,” Nature 495(7440), 210–214 (2013).
[Crossref]

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3(3), 031012 (2013).
[Crossref]

C. G. Poulton, R. Pant, and B. J. Eggleton, “Acoustic confinement and stimulated Brillouin scattering in integrated optical waveguides,” J. Opt. Soc. Am. B 30(10), 2657–2664 (2013).
[Crossref]

2012 (1)

P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated brillouin scattering in the subwavelength limit,” Phys. Rev. X 2(1), 011008 (2012).
[Crossref]

2011 (3)

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2010 (2)

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2008 (2)

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2006 (1)

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Figures (4)

Fig. 1.
Fig. 1. (a) Schematic description of the backward Brillouin scattering process: a pump photon $\omega _p$ scatters off a moving refractive index grating creating a red-shifted Stokes photon $\omega _S$ and forward propagating acoustic phonon $\Omega _B$ . (b) Optical field distribution inside a dielectric ridge waveguide. $K$ refers to the bulk modulus, on the order of hundreds of gigapascals for many solids. (c) Field distribution in a slot waveguide, where the peak field intensity is located within the mechanically compliant ( $K=0.08$ GPa) superfluid filling the void.
Fig. 2.
Fig. 2. (a) Illustration of the proposed device. The silicon is shown in purple and the underlying silica in white. Superfluid helium fills the narrow slot between the silicon waveguides, where the optical field intensity is largest. (b) Cross-section of the electric field intensity distribution $\left |E\right |^2$ for the transverse electric (TE) whispering gallery mode (WGM) guided within the slot waveguide resonator. White arrows represent the electric field orientation predominantly along $\textbf {e}_r$ . Scale bar corresponds to 200 nm. (c) Illustration of the slot filling with superfluid by capillarity for sufficiently thick (exceeding $\sim 2$ nm) films. (d) Finite element simulation of the zero-point pressure excursion due to the Brillouin density wave inside the superfluid, in the case of fixed (left) and free (right) boundary conditions for superfluid flow at the top of the slot. Zero-point pressure excursions are typically on the order of a few Pascal, with values provided here for a 50 nm wide slot. Only one acoustic wavelength is shown here; this pressure pattern is repeated along the entire slot circumference.
Fig. 3.
Fig. 3. Backward Brillouin scattering schemes in microresonators. (a) Optical dispersion diagram. Light blue and green lines represent the dispersion branches for different optical modes, and ellipses the discrete optical resonances of differing azimuthal order. Solid, dashed and dashed-dotted arrows respectively represent the counter-modal, intra-modal and inter-modal backward Brillouin scattering cases. (b) Frequency space illustration of the intra-modal, inter-modal and counter-modal (inset) scattering cases, where $\kappa$ is the optical linewidth. WGMs of a same family, separated by a free spectral range (FSR)—i.e. differing by one azimuthal node—are shown with the same color shading. Inset: illustration of counter-modal Brillouin scattering [31], where pump and Stokes beams are hosted by degenerate clockwise and counter-clockwise whispering gallery modes of identical azimuthal order.
Fig. 4.
Fig. 4. (a) Single photon optomechanical coupling rate $g_0$ as a function of slot width $w$ , for fixed (blue) and free (orange) boundary conditions for the acoustic wave (see Fig. 2(c)). (b) Fraction of the WGM electromagnetic energy contained within the slot, as a function of slot width. Insets show the electric field intensity distribution $\left |E\right |^2$ in the resonator for slots widths of 15 nm; 50 nm and 130 nm. Resonator diameter and slot height are kept fixed at 20 $\mu$ m and 220 nm respectively, see Table 1.

Tables (1)

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Table 1. Values of the parameters used in the numerical simulation.

Equations (3)

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g 0 , e s = ω 2 γ e ϵ ~ v ( r ) E p ( r ) E s ( r ) d 3 r ε r E p ( r ) d 3 r ε r E s ( r ) d 3 r ,
γ e = ( ρ ε r ρ ) ρ = ρ 0 = ( ε r 1 ) ( ε r + 2 ) / 3
g 0 , e s = ω 2 ( ε s f 1 ) s l o t ϵ ~ v ( r ) E 2 ( r ) d 3 r a l l ε r ( r ) E 2 ( r ) d 3 r ,

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