A domestic refrigerator relies on this cycle of evaporation and condensation using a low boiling point refrigerant to produce a cooling effect. Inside the compartment, the liquid refrigerant is made to expand rapidly before evaporating, undergoing the liquid-gas phase transition. As it does this, the refrigerant absorbs energy from its surroundings, cooling the inside of the compartment. The efficiency of the refrigerator cycle is improved by coiling several meters of tubing inside the compartment, ensuring the refrigerant has ample time to evaporate and remove as much heat as possible. This coil of tubing, known as a heat exchanger, is hidden inside one or more walls of the compartment and is usually surrounded by metal fins to improve heat transfer.
The gaseous refrigerant is returned to the outside of the refrigerator compartment and is forced to condense, releasing the energy it has absorbed as heat. Physically this is achieved by the use of a mechanical compressor, driven by an electrical motor, and by passing the refrigerant through another heat exchanger, mounted on the rear or underside of the refrigerator.
Cooling far below 1 K is not possible using conventional refrigeration techniques; however, a 'dilution refrigerator' can cool below 2 mK in continuous operation. This section describes the basic operation of a dilution refrigerator.
Of the numerous unique features exhibited by helium, one of the most convenient for a low temperature physicist is that at sufficiently low temperatures (about 0.8 K), a mixture of helium-3 and helium-4 will spontaneously separate, with the lighter helium-3 rich fraction floating on top of the heavier helium-4 rich fraction.
All helium atoms (whether the lighter helium-3 atoms or the more abundant helium-4 atoms) are attracted to one another by van der Waals forces; however, as a helium-3 atom is much lighter than its helium-4 counterpart, it has a much more violent zero-point motion. As a consequence, the helium-3 atoms are further apart from each other than the helium-4 atoms; as a comparison helium-3 is 26% less dense than helium-4. As the atoms in the helium-4 rich fraction can pack together more closely, the forces between the atoms are greater. As a result, all helium atoms prefer to be surrounded by helium-4 atoms.
Conveniently for low-temperature researchers, this means that the heavier fraction also attracts helium-3 atoms and the fraction is not entirely pure, typically containing 94% helium-4 and 6% helium-3; while the lighter fraction contains only helium-3 atoms. These two fractions are referred to by their relative proportions of helium-3 atoms; the lighter, pure helium-3 fraction is known as the Concentrated phase, while the heavier helium-4 rich mixture is known as the Dilute phase.
Consider a mug of hot tea (or your favourite warm beverage!). Some of the hot water molecules at the surface of the tea cross the liquid-gas phase boundary, that is, the surface of the liquid. However, as energy is needed to convert water into water vapour, the water molecules must absorb heat from their surroundings before leaving the liquid as steam. This removes energy from the liquid, cooling the tea.
Similarly, if a helium-3 atom can be persuaded to move from a highly ordered state in the Concentrated phase (surrounded by other helium-3 atoms) across the phase boundary to a disordered state in the Dilute phase (with few other helium-3 atoms), it must absorb heat from its surroundings in the process. This transport of helium-3 atoms across the phase boundary cools the dilution refrigerator and provides (relatively) easy accessibility to the millikelvin temperature range.
Once the dilution refrigerator has cooled the experiment down to a sufficiently low temperature (around 5 mK), the final push to ultra low temperatures is achieved by using 'adiabatic demagnetisation'.
A standard Lancaster experimental cell is a small closed volume (about the size of a small coffee cup) packed with copper plates, with space between the plates for the helium-3 we are investigating.
It is these copper plates packed into the experimental cell that cool the helium-3 sample to the ultra-low temperatures we perform our experiments at.
In order to understand how this process works, let us consider the copper plates to be a simple ideal solid. In this ideal solid, quantum mechanics tells us the atoms have 'spin' which can be in one of two states.
Under normal conditions, half of the atoms in this ideal solid will occupy 'spin up' states and half will occupy 'spin down' states. However, if a sufficiently strong magnetic field is applied, half of the spin states will become more energetically favourable, while the other half become less energetically favourable.
The dilution refrigerator will cool the copper plates and remove energy from the experimental cell, depopulating the upper energy level of spins in favour of the lower energy level. This process is known as 'Precooling'.
Using a clever trick of physics, we are able to thermally disconnect the experimental cell packed with copper plates from the dilution refrigerator. The cell is then 'demagnetised' by slowly reducing the applied magnetic field.
While the magnetic field is reduced, the highly populated, lowest energy level is forced to increase in energy. As the experimental cell is now isolated, energy must be absorbed from the surroundings, cooling the copper metal refrigerant and the helium-3 in the experimental cell.
The process is said to be 'adiabatic', as there can be no change in the disorder of the system, hence 'adiabatic demagnetisation'
In the ULT Group, most of our experimental measurements are made using Vibrating Wire Resonators (VWRs). These VWRs are tiny loops of superconducting wire, barely visible with the naked eye.
By placing the VWR in a low magnetic field and applying a small AC drive signal through it, the VWR can be made to oscillate perpendicular to the applied field, due to the Lorentz force.
The voltage generated as the VWR moves in the magnetic field is measured using a lock-in amplifier. If we monitor the voltage response and the frequency at which mechanical resonance occurs, we can calculate the damping that the VWR experiences.
When the temperature of the fluid that the VWR is immersed in changes, so will the damping on the VWR. As the wires are very thin it allows us to accurately measure tiny changes in temperature in our experiments.
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