Microphotonic Forces from Superfluid Flow

In cavity optomechanics, radiation pressure and photothermal forces are widely utilized to cool and control micromechanical motion, with applications ranging from precision sensing and quantum information to fundamental science. Here, we realize an alternative approach to optical forcing based on superfluid flow and evaporation in response to optical heating. We demonstrate optical forcing of the motion of a cryogenic microtoroidal resonator at a level of 1.46 nN, roughly 1 order of magnitude larger than the radiation pressure force. We use this force to feedback cool the motion of a microtoroid mechanical mode to 137 mK. The photoconvective forces we demonstrate here provide a new tool for high bandwidth control of mechanical motion in cryogenic conditions, while the ability to apply forces remotely, combined with the persistence of flow in superfluids, offers the prospect for new applications.

Popular Summary

When helium is cooled to very low temperatures, it becomes a superfluid and one of few naturally occurring forms of quantum matter. Much like the flow of an electrical current in a superconductor, the flow of atoms in a superfluid occurs without dissipation and can therefore, in principle, continue indefinitely. One dramatic consequence of this phenomenon is the well-known superfluid fountain effect in which superfluids flow toward localized heat sources and, since they experience no viscous drag, overshoot to form a fountain. Here, we apply the superfluid fountain effect, for the first time, to actuate a microphotonic system, providing a new tool for the control of photonic circuitry.

We use the momentum from a convective superfluid flow to actuate the motion of an on-chip optical microresonator. We condense a nanometer-thick film of superfluid upon the resonator by placing it inside a helium gas environment, which is cooled to temperatures below 1 K. Heating due to localized optical absorption from a laser within the microresonator then generates superfluid flow and allows forces to be exerted on the resonator that are 1 order of magnitude larger than those achievable with radiation pressure. We employ these forces to cool a vibrational mode of the resonator to a final temperature of 137 mK.

In future experiments, our technique may enable both ground-state cooling and the preparation of nonclassical states of mechanical motion. In addition, while the radiation pressure force exerted by a photon lasts for only the duration that the photon stays within the microphotonic element—typically less than a microsecond—the superflow forces this photon can generate can persist billions of times longer. This phenomenon opens up unique, new capabilities that may be used, for instance, to enable nonvolatile microphotonic memories and routers.

Figure 1

(a) In bulk, a local heat source generates flow of superfluid helium (blue arrows) and counterflow of normal fluid (red arrow), imparting momentum onto the oscillator. (b) Representation of a microtoroid covered in a thin film of superfluid helium. Heat around the periphery caused by optical absorption generates fluid flow (blue arrows). At low pressures the superfluid then transitions directly into the gas phase and imparts momentum on evaporation (red arrows). (c) Superfluid-mediated photoconvective forcing may be readily extended to other optomechanical systems such as photonic-phononic crystal cavities, membranes, and nanostrings. Evaporation of a thin film from a photonic-phononic crystal cavity (left) due to localized optical heating would actuate the mechanical breathing modes commonly used in quantum optomechanics experiments. A mechanical membrane (middle) could be driven by bulk flow if one half was immersed in bulk superfluid helium via the mechanism of (a). The string modes of a nanostring (right) could be actuated by coating its top surface with an absorbing material upon which light is focused. This would cause preferential vertical evaporation of a thin superfluid film self-assembled on the device.

Figure 2

(a) Experimental schematic. A microtoroid is nested inside an all-fiber interferometer and cooled by a He-3 refrigerator (BS, beam splitter; AM, amplitude modulator; SA, spectrum analyzer; NA, network analyzer). (b) Optical microscope image of the microtoroid used in these experiments, showing the support beams, one on either side, that are used to stabilize the tapered optical fiber. (c) Zoomed-in microscope image of the microtoroid. Scale bar is $20\mu \mathrm{m}$ long. (d) Zoomed-in microscope image of a stabilization beam. The circular pads support a suspended beam that has been thinned to 200 nm thickness in order to minimize optical scattering loss. Scale bar is $100\mu \mathrm{m}$ long. (e) Thermal motion of the flexural mode of a microtoroid at 3 K. Inset: FEM simulation of the mechanical displacement profile.

Figure 3

(a) Mode temperature of the microtoroid flexural mode as the cryostat is cooled from 10 to 0.32 K. The microtoroid reaches a base temperature of 0.56 K with 100 nW of injected optical power. (b) Mode temperature of the flexural mode as the probe laser is increased from 10 nW to $3.3\mu \mathrm{W}$. Below $2.2\mu \mathrm{W}$ the temperature increases slightly as the laser power is increased. Above $2.2\mu \mathrm{W}$ the superfluid boils off, causing a sharp rise in mode temperature.

Figure 4

Driven response of the flexural mode as the cryostat is cooled (red points), showing a step increase in response at the superfluid transition temperature. Black line represents a theoretical fit to the data. The gray shaded area indicates that a superfluid layer has formed on the microtoroid surface. The pink shaded area represents the theoretical force if $T_{\mathrm{evap}}$ is up to 1 K higher than the mode temperature. Inset: Displacement spectrum of the flexural mode at 0.7 and 2 K with a coherent drive applied via optical amplitude modulation. The response to coherent drive is shown to increase with the presence of superfluid helium.

Figure 5

Feedback cooling of the flexural mode from 715 to 137 mK using superfluid-mediated photoconvective forcing. With a fixed probe power of $1.9\mu \mathrm{W}$, the feedback gain is varied over 3 orders of magnitude, showing good agreement with the estimated mode temperature from in-loop measurements (solid line). The out-of-loop mode temperature is then inferred by a transformation (dashed line) that is derived in the Supplemental Material [36]. Inset: Displacement spectrum of the flexural mode with varying feedback gain.

Figure 6

By varying the geometry, superfluid flow could be used to apply a large range of different forces including (a), (b) linear force, (c) torque, (d)–(f) examples of geometries designed to efficiently leverage forces from superfluid flow. (d) Expansive force that is efficiently coupled to a microdisk or microtoroid, (e) compressive force, and (f) long-lived centrifugal forces resulting from persistent current flow.