Superfluid optomechanics

Vibrational modes of two-dimensional superfluid helium are the mechanical oscillators in this cavity-optomechanical system.

Cavity optomechanics focuses on the interaction between confined light and a mechanical degree of freedom. Vibrational modes of superfluid helium-4 have recently been identified as an attractive mechanical element for cavity optomechanics, thanks to their ultra-low dissipation arising from superfluid’s viscosity-free flow. Our approach to superfluid optomechanics is based on nanometer-thick films of superfluid helium which self-assemble on the surface of a microscale optical whispering gallery mode resonator inside our cryostat. Excitations within the film, known as third sound, manifest as surface thickness waves with a restoring force provided by the van der Waals interaction. These excitations, by changing the amount of superfluid in the optical mode’s evanescent field, modulate the effective path length of the optical cavity. This provides a dispersive coupling between the superfluid and the light confined inside the optical resonator. Using this optomechanical coupling mechanism, we experimentally probed the thermodynamics of these superfluid excitations in real-time, and demonstrated, for the first time, both laser cooling and amplification of the superfluid thermal motion [Nature Physics, 12, 8, 788, 2016]. While lasers are widely used to cool gases and solid objects, they had never before been applied to cool a quantum liquid. Recent work includes exploring the rich interaction between quantized vortices and third sound phonons, enabling the first observation of vortex dynamics in a superfluid helium film [Science, 366, 1480, 2019]—read more below, as well as the demonstration of ultra efficient Brillouin lasers based on superfluid helium films—read more below.

Close-up picture of the dilution refrigerator used to reach the millikelvin temperatures required for the superfluid experiments.

Recent work:

Additional information on some of these publications can be found below:

Coherent Vortex Dynamics in a Strongly-Interacting Superfluid on a Silicon Chip

quantized_vortices_helium
Artistic representation of a cluster of vortices orbiting a macroscopic circulation of opposite sign, Science, 366, p. 1480, Dec 2019
3D rendering file can be downloaded here.

Quantized vortices are central to the behavior of two-dimensional superfluids, as recognized by the 2016 Nobel Prize in Physics. They had however not been directly observed in superfluid helium films, due to the following experimental challenges:

  • the normal-fluid core of a vortex in superfluid helium-4 is roughly one Angström in size,
  • the thickness of a superfluid helium film is typically less than 20 nm, and
  • the refractive index of liquid helium is extremely close to that of vacuum (nHe=1.029).

Combined, these characteristics prevent direct optical imaging. In this work, we were able to generate and detect quantized vortices and observe their dynamics through an alternate mechanism, namely through their interaction with sound waves confined on the surface of an optical microresonator. The mechanism can be understood as follows. Waves (i.e. phonons) confined to the surface of the resonator (a silica microtoroid) can exist as either clockwise or counter-clockwise excitations.

  • Clockwise third sound mode
    Clockwise third sound mode
  • Counter-clockwise third sound mode
    Counter-clockwise third sound mode

These normally have the same energy/frequency and therefore appear as a single peak in our experimental spectra. In the presence of the background flow generated by a quantized vortex, however, these frequencies become different, which we can pick up experimentally, see e.g. [Physical review letters, 71, 1577, 1993]. (This is in essence, an acoustic analog of the Sagnac effect in optics, whereby the frequencies of third sound waves shift depending on the net circulation in the film). A third-sound wave traveling along the direction of circulation will be frequency upshifted, while a wave traveling against the vortex’s flow field will be frequency downshifted. Thus initially frequency-degenerate clockwise (cw) and counterclockwise (ccw) rotating third-sound modes will experience a frequency splitting due to the presence of a vortex. The precise strength of the interaction depends both on the sound mode and the spatial location of the vortex, and is discussed in detail in the following reference: [New Journal of Physics, 21, 053029, 2019].
With this understanding and using the techniques outlined in [Nature Physics, 12, 8, 788, 2016], we measure the vortex-induced splitting on several third-sound modes simultaneously. This is the key feature that enables us to discriminate between different vortex numbers and spatial distributions, as the vortices do not affect all third-sound modes identically.
This concept is analogous to sensing with a cantilever (see right image below), where the added mass due to the presence of a particle decreases the cantilever’s resonance frequency. Looking at a single vibrational mode, it is not possible to know whether the frequency change is due to a lighter particle located near the extremity of the cantilever, where its influence is maximal, or a heavier particle located near the cantilever’s anchoring point, where its influence is reduced. Tracking the effect on multiple modes simultaneously allows both particle mass and position to be independently determined, see e.g. [Nature Nano, 10, 339, 2015] — and in our case vortex number and position, enabling effective imaging of the vortex distribution. Using this technique, we first employ a pulse of laser light to initiate two clusters of vortices of opposite sign and then nondestructively observe their decay in a single shot (see GP simulation by Dr Matt Reeves below). Thanks to the resonator’s near atomically flat surface, coherent dynamics dominate, with thermal vortex diffusion suppressed by five orders of magnitude.

vortex_cantilever
G.P. simulation showing the annihilation of two clusters of vortices of opposite sign, with one cluster freely orbiting and the other pinned to the defect at the center of the resonator. Credit: Dr Matt Reeves, UQ.

Read more here:


Strong optical coupling through superfluid Brillouin lasing

Artistic representation of a large amplitude superfluid Brillouin acoustic wave. Nat. Phys., Feb. 2020, doi: 10.1038/s41567-020-0785-0.
3D rendering file can be downloaded here.
Illustration of the mechanism behind low-threshold Brillouin lasing in superfluid films. In the backward Brillouin scattering process described here, pump laser light (red arrow) scatters off a travelling surface wave in the superfluid, which forms a travelling refractive index grating. The acoustic wavelength of the superfluid wave is approximately one-half that of the light, such that it forms an effective Bragg-type reflector. Since the superfluid wave is moving away from the pump, the reflected light (green arrow) is doppler-shifted down in frequency (Stokes process), and the energy difference is provided to the superfluid wave, which grows in amplitude, thus scattering even more pump light. This positive feedback loop leads to a runaway effect (lasing), whereby both the superfluid wave, as well as the scattered Stokes field, display large amplitude, coherent oscillations.
An alternate way of viewing this feedback process, which is visible in this animation, is that the beat between pump and Stokes fields leads to localized optical intensity pattern, which slowly rotates at the speed of the acoustic wave which generated it in the first place. Through a combination of radiation pressure forces and superfluid fountain effect forcing, this optical intensity pattern then pulls in even more superfluid into the regions of high light intensity, thereby reinforcing the superfluid acoustic wave in a positive feedback fashion. 3D rendering file for the animation can be downloaded here.

Brillouin scattering has applications ranging from signal processing, sensing and microscopy, to quantum information and fundamental science. Most of these applications rely on the electrostrictive interaction between light and phonons. Here we show that in liquids optically-induced surface deformations can provide an alternative and far stronger interaction. This allows the demonstration of ultralow threshold Brillouin lasing and strong phonon-mediated optical coupling for the first time. This form of strong coupling is a key capability for Brillouin-reconfigurable optical switches and circuits, for photonic quantum interfaces, and to generate synthetic electromagnetic fields. While applicable to liquids quite generally, our demonstration uses superfluid helium. Configured as a Brillouin gyroscope this provides the prospect of measuring superfluid circulation with unprecedented precision, and to explore the rich physics of quantum fluid dynamics, from quantized vorticity to quantum turbulence.

Read more here:


Theoretical framework for thin film superfluid optomechanics

Illustration of the dispersive optomechanical coupling between an optical whispering gallery mode resonance and a superfluid third sound wave. New J. Phys. 18, 123025 (2016)
Animation displaying the the difference in ‘particle’ trajectory (red dot) between a fluid and solid resonator, accounting for the difference in effective mass.

Acoustic waves in superfluid helium represent attractive mechanical degrees of freedom for cavity optomechanics schemes, thanks to their potential for ultra-low mechanical dissipation. In this work, we investigate the properties of optomechanical resonators formed by thin films of superfluid 4He covering micrometer-scale whispering gallery mode cavities. We predict that through proper optimization of the interaction between film and optical field, large optomechanical coupling rates g0 > 2π × 100 kHz and single photon cooperativities C0 > 10 are achievable. Our analytical model reveals the unconventional behaviour of these thin films, such as thicker and heavier films exhibiting smaller effective mass and larger zero-point motion. Indeed, while the superfluid surface deformation is described by ‘drumhead’-like modes, as would be the case for solid membranes, the difference in ‘particle’ trajectory (as illustrated in the animation above), leads to a radically different R4 scaling of the effective mass with device radius R. This underscores the dramatic gains achieved by going towards smaller microfabricated third sound resonators. The optomechanical system outlined here provides access to unusual regimes such as g0 > ΩM and opens the prospect of laser cooling a liquid into its quantum ground state.

Read more here:

Associated Mathematica workbook for calculation of third sound parameters Download


Microphotonic Forces from Superfluid Flow

Scanning electron microscope image of a silica microtoroid used in the experiments (diameter ~70 microns).

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.

Read more here:


Proposal for a quantum traveling Brillouin resonator

Simulation showing the optical field confined within a nanometer-sized silicon on insulator (SOI) slot waveguide. Optics Express, 28, 22450 (2020).
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.

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.

Thanks to the lower speed of sound in superfluid helium, both the pump and Stokes beam can naturally fall within a single optical resonance, as shown below: This enables counter-modal Brillouin scattering between degenerate, counter-propagating (clockwise and counter-clockwise) whispering gallery modes, automatically enabling triply resonant enhancement (pump, Stokes and acoustic wave) independently of device size.

Illustration of the counter-modal scattering process between degenerate counter-propagating (clockwise and counter-clockwise) whispering gallery modes.

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.

Read more here:

  • “Proposal for a quantum traveling Brillouin resonator”,
    Optics Express, 28, 22450 (2020).
  • See also our experimental work on Brillouin scattering with third sound in superfluid helium films here.


Modelling of vorticity, sound and their interaction in two-dimensional superfluids

Vorticity in two-dimensional superfluids is subject to intense research efforts due to its role in quantum turbulence, dissipation and the BKT phase transition. Interaction of sound and vortices is of broad importance in Bose–Einstein condensates and superfluid helium. However, both the modelling of the vortex flow field and of its interaction with sound are complicated hydrodynamic problems, with analytic solutions only available in special cases.

The interaction between acoustic waves and vortices can be understood by considering the example-case of a simple circular resonator. Waves confined to the surface of the resonator can exist as either clockwise or counter-clockwise excitations, which initially possess the same frequency. In the presence of the background flow generated by a quantized vortex, however, these frequencies become different: a third-sound wave traveling along the direction of circulation will be frequency upshifted, while a wave traveling against the vortex’s flow field will be frequency downshifted. Thus initially frequency-degenerate clockwise (cw) and counterclockwise (ccw) rotating third-sound modes will experience a frequency splitting Δf due to the presence of a vortex. The precise strength of the interaction depends both on the sound mode and the spatial location of the vortex, as illustrated in the figure below. It shows the splitting per vortex as a function of vortex radial position for four different acoustic modes. Critically, the presence of a vortex affects each acoustic mode in a unique fashion. Leveraging this unique fingerprint, the work presented here enabled both the number and the spatial distribution of vortices in a cluster to be extracted independently, by tracking several sound modes simultaneously [read more here].

Frequency splitting dependence of four different third-sound modes on the radial offset of the vortex from the disk origin. Spatial profiles of the modes are shown as insets.

In this work, we also develop methods to compute both the vortex and sound flow fields in any arbitrary two-dimensional domain, possibly non-simply connected, and obtain their interaction strength by exploiting analogies with fluid dynamics of an ideal gas and electrostatics (see animation below, and COMSOL model files). As an example application we use this technique to propose an experiment that should be able to unambiguously detect single circulation quanta in a helium thin film.

Left: Background flow field caused by quantized circulation around the defect at the center of an annular resonator. Right figure shows how the superfluid normal mode basis gradually shifts from orthogonal standing waves to counter-rotating waves in the presence of an increased circulation around the resonator’s central defect, and the associated increased frequency splitting between the acoustic waves. Acoustic modes are not frequency-degenerate even in the abscence of background flow due to the symmetry breaking introduced by the resonator’s inner spoke. The interaction of vortices with sound modes can be quantified for any vortex distribution on any two-dimensional bounded domain, even non-simply connected. COMSOL files used to calculate the modified acoustic eigenmodes and generate the plots in the paper are provided below.

Read more here:

COMSOL model third sound disk resonator with point vortexDownload
COMSOL model annular third sound resonator with quantized circulationDownload


Laser cooling and control of excitations in superfluid helium

False-color scanning electron microscope image, showing a silica microtoroid resonator (blue) positioned atop a silicon pedestal on a silicon substrate (gray).
“Laser cooling and control of excitations in superfluid helium,” [Nature Phys, 12, 788, 2016]

Superfluidity is a quantum state of matter that exists macroscopically in helium at low temperatures. The elementary excitations in superfluid helium have been probed with great success using techniques such as neutron and light scattering. However, measurements of phonon excitations have so far been limited to average thermodynamic properties or the driven response far out of thermal equilibrium. Here, we use cavity optomechanics to probe the thermodynamics of phonon excitations in real time.

In order to do so, we use ultra-high optical Q silica whispering gallery mode (WGM) microcavities fabricated on a silicon chip (see scanning electron microscope above, and read more here). These store light for extended periods of time at their periphery, as illustrated below. They reside within a cryogenic vacuum chamber filled with low pressure helium-4 gas, and are optically excited with 1550 nm light using a tapered nanofibre. Below the superfluid transition temperature, van der Waals forces attract superfluid up the sides of the chamber, coating the microcavity with a nanometer-thick self-assembled film. Superfluid sound waves present in the film (called third-sound) are confined on the microcavity by the change in speed of sound caused by the additional surface tension at sharp boundaries. This simple approach means the same geometry which confines the light field also provides confinement for a microscale two-dimensional “quantum droplet” of superfluid helium.

Displacement profile of a superfluid acoustic mode confined to a circular resonator.

The dispersive optomechanical coupling between light and superfluid is enabled by the evanescent portion of the optical field of the cavity which senses the presence and motion of the superfluid on its surface. In essence, when a superfluid wave sloshes back and forth between the center and the periphery of the resonator (where the light is located), this periodically changes the effective size of the optical cavity felt by the photons.

Optical intensity modulation (black), resulting from the periodic modulation of the resonance wavelength of an optical mode (blue trace). (Positioning the laser on resonance rather than detuned off resonance would switch from intensity modulation to phase modulation).

This leads the optical resonance wavelength to be modulated in time (see blue trace in the animation on the left). Because of this, the level of light transmission through the resonator (red dot) fluctuates in time, even for a laser beam of fixed wavelength and intensity (materialized by the dashed black line). This ultra-precise interferometric detection technique can resolve fluctuations in film thickness much below an atomic monolayer, and is used to detect sound waves in superfluid films in real-time for the first time. (The precise strength of the optomechanical coupling between cavity photons and superfluid phonons is discussed in more detail here). Furthermore, strong light-matter interactions allow both laser cooling and amplification of these excitations. This represents a new tool to observe and control superfluid excitations that may provide insight into phonon-phonon interactions, quantized vortices and two-dimensional phenomena such as the Berezinskii-Kosterlitz-Thouless transition. The third sound modes studied here also offer a pathway towards quantum optomechanics with thin superfluid films, including the prospect of femtogram masses, high mechanical quality factors, strong phonon-phonon and phonon-vortex interactions, and self-assembly into complex geometries with sub-nanometre feature size.

Read more here:

  • “Laser cooling and control of excitations in superfluid helium”,
    Nature Physics, 12, 788 (2016). (pdf) (Supplementary Information)
  • Featured in Phys.org: “Using laser light to cool a quantum liquid” (link).

Keywords: Superfluid optomechanics, superfluid helium, Helium-4, quantized vortices, superfluid Brillouin laser, third sound, whispering gallery mode, microtoroid, laser cooling, vortex-sound interactions, superfluid thin films, superfluid film effective mass.

Miscellaneous links:

We gratefully acknowledge funding from:

Australian Research Council
US Army Research Office
ARC Centre of Excellence for Engineered Quantum Systems