Topological Quantum Fluids (ROTA)

Group leader

Dr. Vladimir Eltsov

Our group studies the dynamics of topological quantum matter in a rotating refrigerator. We use superfluid ³He as the model system. Our cryostat can cool ³He in rotation to lower temperatures than any other refrigerator in the world, below 140µK.

One of our main research subjects is studying topological defects in superfluid ³He. An example of such defects are quantized vortices. The dynamics of these objects are probed using non-invasive NMR (Nuclear Magnetic Resonance) and mechanical oscillators. We study dynamic processes such as vortex motion, onset and transition to turbulence, turbulent front propagation, dissipation of turbulence, and the electromagnetic resonances of the ³He superfluid order parameter.

Our group has also a strong theoretical support for fundamental properties of quantum condensed matter systems using superfluid phases of ³He as the main source of inspiration. The theoretical studies help in planning and conducting experiments and providing the theory for the observed phenomena, which in turn triggers new experiments.

Our theory research makes close connection also with other areas of physics: cosmology, particle physics, black hole physics, classical and quantum turbulence, superconductivity, physics of topological media including topological insulators and systems exhibiting intrinsic quantum Hall effect, cold gases, magnetism, physics of topological defects, etc.

Topological Defects: Quantized vortices

Most collective physical systems freeze and become immobile at zero temperature. Thus, there exist few systems where hydrodynamics can be experimentally studied in the zero-temperature limit. Most notable among these are the helium superfluids which remain in liquid state down to zero temperature and may support dissipationless superflow at sufficiently low flow velocities.

A superfluid is phenomenologically a composition of a normal component and a superfluid component. When a superfluid is brought into rotation, the non-classical behavior of the superfluid component can lead to the creation of rectilinear vortices, where the flow as a whole mimics classical solid body rotation. The main focus of our group in the past few years has been studying the dynamics of these vortices, especially both laminar and turbulent dissipation of superfluid motion.

Time Crystals built with Bose-Einstein Condensates of Magnons

Another line of our research is connected to Bose-Einstein condensation of quasiparticles, which has become a popular topic of studies in the recent years. In ³He suitable quasiparticles are spin waves, or magnons, which are collective bosonic excitations existing in magnetically ordered systems. In superfluid ³He it is possible to use nuclear magnetic resonance techniques to create spin states, where the magnetization in a macroscopic volume precesses around the applied magnetic field with a common phase.

We have studied a Bose-Einstein condensation of magnons, which is created inside a magnetic trap. The height of the trap is controlled by externally applied magnetic field and the radial width of the trap can be modified by the angular velocity of the container. The NMR signal from the condensate can be used, e.g., to investigate the vortex dynamics at ultralow temperatures.

We have already been able to solve some unsettled questions concerning trapped magnon condensates in ³He-B, in particular by controlling the trapping potential provided by the rotation of the sample. We have also studied the relaxation properties of these condensates.

Topological excitations

A Majorana fermion is a more than 70-years old mathematical construction, which describes a spin-1/2 particle for which the creation and annihilation operators coincide. Thus one can say that the particle is its own antiparticle. It has been realised that in the topological matter, such as the superfluid phases of ³He, these fermions can appear as bound states on either the container wall or in vortex cores.

One of the goals of our ongoing research is to use the NMR techniques, in which we are experts on the worldwide level, to search for both the surface-bound and core-bound Majorana states using magnon condensates. The signal of the exotic fermions should be seen among other things as a power-law type of behavior of the specific heat, opposed to the exponential dependence for the excitations in the bulk superfluid.

In future, we plan to extend the use of liquid ³He as a model system of topological matter by probing other massless fermions, the so-called Weyl and flat-band fermions in ³He-A.

Quantum Turbulence and Dissipation in the T→0 limit

At very low temperatures, in the absence of normal fluid, turbulence in a superfluid condensate consists of a tangle of singly quantized stable vortex filaments with the same core size and circulation. The long-term goal of experiments on quantum turbulence is to further our understanding of turbulence in general by studying, at least in microscopic scale, a somewhat simpler case of turbulence in pure quantum fluids.

The equilibrium state of a superfluid condensate in a rotating container is a state in which the container is filled with a uniform array of rectilinear vortices. In superfluid ³He it is possible to create a metastable state in which the normal component is in co-rotation with the container but there are no vortices. In practice, this so-called Landau state requires very smooth container walls (fused quartz glass in our case) and relatively low rotation velocities, typically below 2 rad/s.

It is possible to destroy the metastable state in a controlled way by triggering a sudden localized turbulent burst on one end of the sample. The turbulence in our cylindrical sample cell then spreads as an axially propagating precessing vortex front. The front motion releases the free energy of the system into heat. The dissipation rate depends both on temperature and the rotation velocity of the container. Some time ago, we measured for the first time the thermal signal from dissipation of quantum turbulence in the front.

In the low-temperature limit, the dissipation of kinetic energy was expected to vanish, since the density of thermal excitations decreases exponentially. However, our measurements of the vortex front propagation into the region of vortex-free flow show a saturation of dissipation rate with decreasing temperature. This is in contrast to our measurements of a ³He sample in rapid deceleration, where a vortex cluster expands, and in which no turbulence is observed even at very low temperatures. Our experiments of the front propagation velocity and the vortex density behind the front show that turbulence significantly enhances dissipation but does not improve the momentum transfer. Consequently, the superfluid effectively decouples from the reference frame of the container at low temperatures.

Recently, we have been carrying out experiments, where we drive oscillations on vortices at low temperatures. This develops a cascade of Kelvin waves, which are helical perturbations of vortex lines. The Kelvin-wave cascade is thought to be an essential ingredient of quantum turbulence at ultra-low temperatures. In addition to Kelvin-waves, we have managed to create large-scale collective motion of vortices, the so-called inertial waves. Our future goal is to use micro-electro-mechanical oscillators to directly probe the dissipation provided by the Kelvin waves.

Main facility: the ROTA Cryostat

World-wide unique instrument capable of cooling superfluid ³He down to 140 μK in rotation up to 4 rad/s.

LTL - Rotating refrigerator (ROTA): Go to infrabooking