Probing Two-Dimensional Quantum Fluids with Cavity Optomechanics

Abstract

Superfluidity is an emergent quantum phenomenon intrinsic to a wide range of condensed mattersystems, such as ultracold quantum gases, polaritons, and superfluid helium. It had been longbelieved that condensation into the superfluid phase in two-dimensional matter is precluded due tothermal fluctuations, which destroy the long-range phase coherence. However, superfluidity wasexperimentally observed in a variety of two-dimensional physical systems. The key to superfluidtopological phase transitions is quantized vortices. These elementary excitations and their interactionswith phonons and rotons – other types of elementary excitations – determine the dynamics of two-dimensional quantum fluids. Dynamics of superfluids with weak atom-atom interactions, such asBose-Einstein condensates in dilute gases, are typically well described within the framework of theGross-Pitaevskii equation. Moreover, behaviour of weakly interacting quantum fluids is subject toan exquisite experimental control enabled by advanced methods of quantum optics. In contrast, acomplete microscopic model for superfluids with strong atom-atom interactions, such as superfluidhelium, is still an active area of research. This is accompanied by the absence of experimental methodscapable of probing thermodynamics and microscopic behaviour of strongly interacting quantum fluidsboth in real time, and nondestructively in a single shot. The major goal of the research presented in this thesis is to bring a comprehensive level of controlto strongly interacting two-dimensional quantum fluids, such as superfluid helium. We achieve thisby leveraging methods of cavity optomechanics, which provides a toolkit for ultraprecise opticalreadout of superfluid dynamics. The optomechanical system reported in this thesis is comprised of awhispering-gallery-mode optical microcavity coated with a few-nanometer thick film of superfluidhelium. The combination of the small electromagnetic mode volume and the high optical qualityfactor of these microcavities enables enhanced light-matter interactions at the interface of such adevice, allowing the microscopic dynamics of two-dimensional superfluid helium to be probed withunprecedented resolution and precision. Throughout this thesis we first describe the theoretical aspects of coupling between light, confinedwithin a high-quality whispering-gallery-mode microcavity, and the mechanical motion of a superfluidhelium film. Experimental realization of such an optomechanical system allowed us, for the first time,to track thermomechanical motion of superfluid helium in real time, i.e. faster than the oscillator’sdecay timescale. Furthermore, by damping and amplifying sound waves on superfluid thin films, weshow the ability to control thermal motion of a quantum fluid. Exploiting our superfluid optomechanical system, we also demonstrate a new approach to generat-ing strong microphotonic forces on a chip in cryogenic conditions. Utilising the superfluid fountaineffect, we are able to control superfluid flow, which is directed towards the localised heat sourceprovided by absorption of light in the material of the optical microcavity. Upon evaporation in thevicinity of the heat source, helium atoms recoil and exert force on the resonator. We experimentallyachieve microphotonic forces one order of magnitude larger than is possible with radiation pressurein cryogenic conditions. We utilise these forces to feedback cool a vibrational mode of the opticalmicrocavity down to 137 mK. Having demonstrated the ability to track and manipulate thermal excitations in superfluid heliumand to control superfluid flow with laser light – prerequisites for generating and tracking quantizedvortices in our system – we then move on to study vortex-phonon interactions in two-dimensionalsuperfluid helium. We first develop a theoretical framework for these interactions and rigorouslyquantify them. This framework allows us to analytically calculate the rate of the vortex-phononcoupling for any arbitrary distribution of vortices within a cylindrical geometry. Moreover, we developa finite-element method to model the interaction of an arbitrarily distributed vortex ensemble withsound in any arbitrary, perhaps multiply-connected geometry. We furthermore analyse the prospect ofdetecting a single quantum of circulation in a two-dimensional strongly interacting quantum fluid. One of the core results of this thesis is the first hitherto experimental observation of the coherentdynamics of nonequilibrium vortex clusters in a strongly interacting two-dimensional superfluid. Weachieve this by confining superfluid helium on the atomically-smooth surface of a silicon chip, ordersof magnitude more strongly than has previously been possible, resulting in greatly enhanced coherentinteractions between vortices. The atomically-smooth surface of the chip combined with a superfluidtemperature much lower than the Berezinskii-Kosterlitz-Thouless phase transition temperature enablethe vortex diffusivity six orders of magnitude lower than in previous measurements with unpinnedvortices in superfluid helium films. The observed microscopic dynamics are supported by point-vortexsimulations. Our results open up new prospects for studying two-dimensional quantum turbulence,phase transitions, and dissipation mechanisms in two-dimensional strongly interacting quantum fluids.