Optomechanical Cooling in a Continuous System

Radiation-pressure-induced optomechanical coupling permits exquisite control of micro- and mesoscopic mechanical oscillators. This ability to manipulate and even damp mechanical motion with light—a process known as dynamical backaction cooling—has become the basis for a range of novel phenomena within the burgeoning field of cavity optomechanics, spanning from dissipation engineering to quantum-state preparation. As this field moves toward more complex systems and dynamics, there has been growing interest in the prospect of cooling traveling-wave phonons in continuous optomechanical waveguides. Here, we demonstrate optomechanical cooling in a continuous system for the first time. By leveraging the dispersive symmetry breaking produced by intermodal Brillouin scattering, we achieve continuous-mode optomechanical cooling in an extended 2.3-cm silicon waveguide, reducing the temperature of a band of traveling-wave phonons by more than 30 K from room temperature. This work reveals that optomechanical cooling is possible in macroscopic linear waveguide systems without an optical cavity or discrete acoustic modes. Moreover, through an intriguing type of wave-vector-resolved phonon spectroscopy, we show that this system permits optomechanical control over continuously accessible groups of phonons and produces a new form of nonreciprocal reservoir engineering. Beyond this study, this work represents a first step toward a range of classical and quantum traveling-wave operations in continuous optomechanical systems.

Popular Summary

Optomechanical cooling—in which mechanical motion is slowed down with light—is used in applications ranging from precision metrology to fundamental tests of quantum-mechanical decoherence. Until now, the prototypical approach for optomechanical cooling has centered on a relatively narrow class of devices, in which an optical cavity mode is used to control a single mechanical oscillator. Here, through a new paradigm, we present the first demonstration of optomechanical cooling in a continuous system without the use of an optical cavity or discrete mechanical modes.

We achieve continuum optomechanical cooling by harnessing a form of coupling between traveling light and sound waves—termed intermodal Brillouin scattering—using a chip-integrated silicon waveguide. This process eliminates the requirement for an optical cavity to mediate cooling because it intrinsically decouples heating and cooling processes. Moreover, we demonstrate control of continuously accessible groups of hypersonic waves simply by tuning the wavelength of the incident light. Finally, through a new type of acoustic spectroscopy and complementary theoretical analysis, we show that cooling in our system yields nonreciprocal sound transport, reducing the temperature of thermal sound waves in only one propagation direction.

Our results reveal powerful new dynamics and optomechanical control that are not possible in conventional cavity-optomechanical systems and represent an important first step toward shaping noise and dissipation in a range of traveling-wave photonic and phononic systems.

Figure 1

Panel (a) illustrates the waveguide system and basic operation scheme. Probe light (green) of frequency ${\omega }_p$ is coupled into the symmetric spatial mode of a Brillouin-active silicon waveguide through an integrated mode multiplexer (M1). This light interacts with forward- and backward-propagating thermal phonon fields, which produce respective Stokes (red) and anti-Stokes (blue) sidebands that propagate in the antisymmetric spatial mode. An integrated mode multiplexer (M2) then demultiplexes the scattered light for spectral analysis. (b) illustrates the optical Stokes and anti-Stokes spectra produced by spontaneous intermodal Brillouin scattering due to (bi) forward- and (bii) backward-propagating phonons, respectively. The spectral width of each sideband reveals the temporal dissipation rates and lifetimes of the phonons participating in the Stokes and anti-Stokes processes. Panel (c) depicts the suspended silicon ridge waveguide that guides both optical and acoustic waves. Panels (d)–(f) illustrate the energy-conservation and phase-matching requirements for these spontaneous Brillouin processes. (d) and (e) plot the optical dispersion relations for the symmetric and antisymmetric optical modes as well as the phonons that mediate Stokes and anti-Stokes scattering. In the Stokes process, the phonon that mediates scattering from the initial state (open circle) to the final state (closed circle) is a forward-propagating field. By contrast, as diagrammed in (e), phase matching dictates that the phonon responsible for anti-Stokes scattering must be a backward-propagating wave. These two phonons must satisfy the acoustic dispersion relation for the Lamb-like acoustic mode that mediates intermodal scattering, as shown in (f). In this system, the Stokes and anti-Stokes phonons are essentially degenerate in both Brillouin frequency and wave-vector magnitude but propagate in opposite directions. (g) This spontaneous process simultaneously reduces the thermal occupation $⟨n(q)⟩$ of phase-matched backward-propagating phonons and increases that of the phase-matched forward-propagating phonons. As a result, an incident laser field drives the average momentum of the thermal bath of phonons out of equilibrium, producing a net phonon flux. (hi) diagrams the cross-sectional geometry of the hybrid photonic-phononic waveguide. Panels (hii) and (hiii) plot the $x$-polarized component of the TE-like symmetric [$E_1^x(x,y)$] and antisymmetric [$E_2^x(x,y)$] simulated mode profiles, respectively. (hiv) shows the simulated strain profile of the 6-GHz elastic mode that mediates spontaneous intermodal scattering. Here, we plot ${ϵ}^{xx}$, which is the dominant component in the intermodal acousto-optic coupling.

Figure 2

Experimental heterodyne setup and measurements of spontaneous intermodal Brillouin scattering. Panel (a) diagrams the heterodyne scheme used to modify and probe the phonon dynamics. Experiments are performed at room temperature and atmospheric pressure. A cw laser source (vacuum wavelength of 1535.5 nm) is used to synthesize a strong probe wave (upper arm) and a 44-MHz blueshifted optical local oscillator for heterodyne detection (lower arm). The probe wave intensity is controlled using an EDFA and a VOA before being coupled on chip, where it interacts with a thermal phonon field via intermodal Brillouin scattering. The scattered light propagates in the antisymmetric spatial mode, and then it is combined with the optical LO. The interference of the Stokes and anti-Stokes waves with the optical LO on a photoreceiver produces unique microwave spectra centered at ${\mathrm{\Omega }}_B+2\pi \times 44\mathrm{MHz}$ and ${\mathrm{\Omega }}_B-2\pi \times 44\mathrm{MHz}$, respectively. Panel (b) plots a series of Stokes and anti-Stokes heterodyne spectra at four distinct probe powers. Note the power-dependent asymmetry between the Stokes and anti-Stokes spectra in both the peak spectral density and spectral width. (c) shows the relative scattering efficiencies of the Stokes and anti-Stokes processes (and respective phonon occupations) as the probe power is increased. Panel (d) plots the fitted linewidths of the Stokes and anti-Stokes spectra. The temperature is estimated using the model derived in Appendix pp1. These measurements reveal that the collective lifetime of the anti-Stokes phonons is reduced, while that of the Stokes phonons is enhanced. At a maximum probe power of 42 mW, this asymmetry in spectral width corresponds to more than 30 K of cooling or heating from room temperature. (e) plots the peak spectral density of these spectra as a function of probe power. The overall decrease in scattering efficiencies can be attributed to the power-dependent transmission of the integrated mode multiplexer (M2). As a first-order benchmark, the observed scattering efficiencies for the Stokes and anti-Stokes process are approximately $3.3\times {10}^{-8}$, in agreement with the predicted value ($3.15\times {10}^{-8}$) for spontaneous forward Brillouin scattering [39].

Figure 3

Pump-probe spontaneous Brillouin scattering experimental setup and measurements. Panel (a) diagrams the experimental scheme used for the pump-probe experiments. These measurements involve two tunable cw lasers. The first, labeled the probe laser (indexed by superscript ${}^{(1)}$), which has a fixed power of 8 mW, is used to probe the phonon dynamics. The second source, labeled the pump laser (indexed by superscript ${}^{(2)}$), is used to modify the phonon dynamics. The optical local oscillator used for heterodyne detection is synthesized from the probe wave using an AOM. (ai) Optical spectrum incident on the fast photoreceiver and (aii) the resulting microwave spectrum. Since the optical LO (blueshifted 44 MHz by the AOM) is synthesized from the probe source, the heterodyne Stokes and anti-Stokes signals centered at (${\mathrm{\Omega }}_B+\mathrm{\Delta }$ and ${\mathrm{\Omega }}_B-\mathrm{\Delta }$, respectively) originate entirely from the spontaneously scattered probe light. Panel (b) shows the difference in Stokes and anti-Stokes phonon dissipation rates (spectral widths of the Stokes and anti-Stokes sidebands produced by the probe laser) as a function of probe wavelength, while the pump wavelength remains fixed at ${\lambda }_p^{(2)}=1535.6\mathrm{nm}$. Each data point represents the difference between Stokes and anti-Stokes dissipation rates at a pump power ($P_p^{(2)}$) of 30 mW obtained by fitting the measured spectral widths over a series of ten different pump powers. The average standard deviation is 0.375 MHz. The theoretical trend [see Eq. (3)] is superimposed. The phonon wave vector is calculated from the effective phase and group indices of the two optical spatial modes supported by the silicon waveguide (see Appendices pp3 and pp6), and the anti-Stokes phonon occupation is estimated by a comparison with the spatiotemporal theory. This comparison is verified by additional high-resolution pump-probe experiments (see Appendix pp4). (bi) Example spectra (of the probe sidebands) when the probe wave is not phase matched to the same group of phonons as the pump wave. In this case, the dissipation rates for the Stokes and anti-Stokes phonons remain constant as the pump power increases. (bii) Example spectra (of the probe sidebands) when the probe wave is phase matched to the same group of phonons as the pump wave. Here, increasing the pump power enhances the dissipation rate asymmetry (see also Appendix pp4). These data reveal that the pump wave reduces the phonon occupation over a narrow band of phonon wave vectors, with a bandwidth given by $\mathrm{\Delta }q=2.78/L$ (see Appendix pp3).

Figure 4

Theoretical fractional phonon occupation [numerical integration of Eq. (a18)] as a function of the device length. For the calculated curve $G_B=470{\mathrm{W}}^{-1}{\mathrm{m}}^{-1}$, $P_p=1\mathrm{W}$, and ${\mathrm{\Omega }}_B=2\pi \times 6.02\mathrm{GHz}$—parameters that may be accessible in silicon optomechanical waveguides at mid-IR wavelengths. We note that at large gain-power-length products (i.e., $G_B{P}_{p}L\gg 1$), the Stokes light must be suppressed or removed from the system to avoid pump depletion.

Figure 5

Pump-probe spontaneous Brillouin scattering measurements. Panel (ai)-(aii) plots the salient effects of a strong pump wave on the probe spectra when the pump is within the phase-matching bandwidth (${\lambda }_{\mathrm{p}}^{(2)}=1535.6\mathrm{nm}$, ${\lambda }_{\mathrm{p}}^{(1)}=1535.53\mathrm{nm}$). When this phase-matching condition is satisfied (i.e., the pump wave is interacting with the same band of phonon wave vectors), we observe that the anti-Stokes (Stokes) probe spectra experiences linewidth broadening (narrowing) as the pump power is increased (see panel (ai)), revealing that the pump wave coherently modifies the lifetimes of the Stokes and anti-Stokes phonons. Panel (aii) plots the ratio of Stokes to anti-Stokes power (proportional to the ratio of phonon occupations) as a function of total on-chip power and the theoretical trend from the expected change in Stokes and anti-Stokes phonon occupations. Panel (bi)-(bii) plots the spectral widths and relative powers of the Stokes and anti-Stokes light (along with associated theoretical trends) when the pump wave is not phase-matched to the phonons interacting with the probe wave (${\lambda }_{\mathrm{p}}^{(2)}=1537.3\mathrm{nm}$, ${\lambda }_{\mathrm{p}}^{(1)}=1535.53\mathrm{nm}$). We observe that the spectral widths and ratio of Stokes to anti-Stokes powers remains constant as a function of pump power, which is consistent with the theoretical trend (black). Note that the constant dissipation rate asymmetry is due to the presence of the probe wave.