Dry demagnetization cryostat for sub-millikelvin helium experiments: Refrigeration and thermometry

Abstract

We demonstrate successful "dry" refrigeration of quantum fluids down to T = 0.16 mK by using copper nuclear demagnetization stage that is pre-cooled by a pulse-tube-based dilution refrigerator. This type of refrigeration delivers a flexible and simple sub-mK solution to a variety of needs including experiments with superfluid 3 He. Our central design principle was to eliminate relative vibrations between the high-field magnet and the nuclear refrigeration stage, which resulted in the minimum heat leak of Q = 4.4 nW obtained in field of 35 mT. For thermometry, we employed a quartz tuning fork immersed into liquid 3 He. We show that the fork oscillator can be considered as self-calibrating in superfluid 3 He at the crossover point from hydrodynamic into ballistic quasiparticle regime.

Probing Liquid $$^4$$ 4 He with Quartz Tuning Forks Using a Novel Multifrequency Lock-in Technique

“…The difference between the measurements is negligible and the red solid line shows the expected Lorentzian lineshape for a driven damped harmonic oscillator in a fluid [10] Here f 0 is the vacuum frequency of the oscillator, and γ = γ 2 + iγ 1 describes the complex drag force, where the real component γ 2 corresponds to the dissipative drag forces, and the non-dissipative imaginary component γ 1 arises from the backflow of fluid around the oscillator and the mass enhancement due to the normal component clamped around the oscillator. The least-squares fit yields a resonance width of f 2 = γ 2 /2π = 8.3 Hz, and resonance frequency of 11597.6 Hz in superfluid 4 He at 1.45 K. The fork constants deduced from the resonance curves are (9.12 ± 0.02) × 10 −8 N V −1 and (9.04 ± 0.03) × 10 −8 N V −1 correspondingly for SR830 and MLA measurements. The non-zero quadrature component at resonance frequency is due to the intrinsic capacitance of the fork and can be used to verify that the current amplifier and our electronic circuit are working as expected even in the absence of the resonance.…”

“…After the cryostat was filled with 4 He and left to settle for a period of about 20 minutes, the temperature of the cryostat was reduced from 4.2 K down to the base temperature of about 1.5 K by pumping the helium bath over a period of approximately 3-4 h. The frequency response of the 12 kHz tuning fork near resonance was measured continually during cooling by alternating between the conventional lock-in technique using the SR830 and the multifrequency mode using the MLA. Figure 2 shows the frequency dependence of the 12 kHz fork response normalised by the excitation voltage at the base temperature of the cryostat, 1.45 K at saturated vapour pressure.…”

“…All measurements on the tuning forks were conducted in a simple 4 He immersion cryostat that operates in the temperature range from 4.2 K down to a base temperature of ∼1.5 K using the evaporative cooling technique. The temperature of the liquid helium was deduced from the vapour pressure [20].…”

“…Quartz tuning forks were relatively recently introduced for probing quantum liquids [1] and were quickly adopted for low temperature thermometry [2][3][4], the generation and detection of quantum turbulence [5][6][7][8] and studies of acoustic emission [9][10][11] and cavitation [12]. The popularity of quartz tuning forks is driven by their availability, high quality factor and ease of use.…”

“…The majority of tuning forks studied so far in quantum fluids research have been common off-the-shelf electronic components and depending on the manufacturer had different physical dimensions, length, width and thickness, even though the resonance frequencies are the same. Previously, to investigate the frequency dependence of acoustic emission and the critical velocity for the generation of turbulence in superfluid 4 He [7,10], we had manufactured custom-designed tuning forks on a 75-micron quartz wafer 1 and used the length of the forks to control resonance frequencies. Here we present the temperature dependence of damping experienced by two forks manufactured on a 25 µm thick wafer.…”