Department of Applied Physics

Rota - Topological superfluids

Our research is focused on the properties of superfluid 3He at ultra-low temperatures. The superfluid phases of 3He are the best experimentally accessible examples of topological superfluids, which share many properties with popular topological insulators and superconductors.
A half-quantum vortex combines circular spin flow and circular mass flow, leading to the 
formation of vortex pairs that can be observed experimentally. Image: Ella Maru Studio.

Group leader

Dr. Vladimir Eltsov

We are interested in particular in emergent fermion zero energy modes, like Majorana fermions at the surfaces and in the cores of the topological defects of the order parameter. The dynamic behaviour and interaction between objects of different topologies are also investigated.

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

One of our main research topics 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 studies the dynamics of quantum matter in a rotating refrigerator (see the video on right). We use superfluid 3He as the substrate. 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.

Quantum Matter and Topological Superfluids

Bose-Einstein Condensation 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.


Exotic Fermions

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 so called 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.

Dynamics : Quantum Turbulence and Dissipation in 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 (see the figure on right). 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.


Cryostat ROTA

Main characteristics 

  • Minimum temperature in 3He sample: 140 µK (combination of dilution refrigerator and nuclear cooling stage)

  • Rotation velocity up to 4 rad/s
  • Heat leak to sample in rotation: below 25 pW
  • Cooldown time to the lowest temperatures: 1-2 weeks
  • He boiloff: total 30 liters/day


  • Low temperature NMR for 3He

  • Interface between superfluid 3He-A and 3He-B phases

  • Magnon Bose-Einstein condensates

  • Quartz tuning forks

Rotating refrigerator

LTL - Rotating refrigerator (ROTA)

Rotating cryostat with 140 μK base temperature


Latest publications

Amplitude of Waves in the Kelvin-wave Cascade

V. B. Eltsov, V. S. L’vov 2020 JETP Letters

On Dimension of Tetrads in Effective Gravity

G. E. Volovik 2020 JETP Letters

Kelvin-Helmholtz instability of AB interface in superfluid He 3

V. B. Eltsov, A. Gordeev, M. Krusius 2019 Physical Review B

Tetrads and q-theory

F. R. Klinkhamer, G. E. Volovik 2019 JETP Letters

Half-quantum vortices and walls bounded by strings in the polar-distorted phases of topological superfluid 3He

Jere Mäkinen, Vlaidimir Dmitriev, Jaakko Nissinen, Juho Rysti, Grigory Volovik, Yudin Alexey, Kuang Zhang, Vladimir Eltsov 2019 Nature Communications
More information on our research in the Research database.
Research database
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