Superfluid Helium-3 Bolometers
- Superfluid Helium-3 bolometers are cryogenic calorimetric detectors that infer energy deposition from tiny temperature rises in the B phase, where heat capacity is extremely low.
- Their extraordinary sensitivity enables direct calorimetric measurements of Majorana quasiparticle surface states and supports sub-GeV dark matter searches through precise resonator thermometry.
- The detectors integrate advanced techniques such as non-linear vibrating wire dynamics and SQUID-based multiplexed readout, allowing scalable designs and effective background rejection.
Superfluid helium-3 bolometers are calorimetric detectors in which an energy deposition is inferred from the heating of a small volume of superfluid He, usually in the B phase at ultra-low temperatures. The operating principle is that the heat capacity of He-B becomes extremely small because most quasiparticles are bound into Cooper pairs, so even a tiny deposited energy produces a measurable change in the quasiparticle population and therefore in the response of embedded mechanical resonators. In this form, the bolometer is both a low-temperature thermodynamic probe and a rare-event detector platform, with demonstrated use for direct heat-capacity measurements of Majorana quasiparticle surface states and active development for sub-GeV dark matter searches (Bunkov et al., 2016, Collaboration et al., 14 Aug 2025).
1. Definition, operating regime, and detector concept
A superfluid He bolometer is a particle detector that measures energy deposition by observing how an interaction heats a tiny volume of superfluid He. In the implementations described in the literature, the detector volume is thermally linked to an external He bath through a small orifice, while the temperature of the confined fluid is monitored with mechanical resonators whose damping depends on the quasiparticle density (Collaboration et al., 14 Aug 2025).
The B phase is the central operating regime. Below about $0.4$ mK, the heat capacity is especially low, giving the potential for world-leading sensitivity to spin-dependent dark matter interactions in the sub-GeV/ mass range. In the calorimetric Majorana experiment, each bolometer is a copper box filled with superfluid He, with one measuring vibrating wire resonator acting as a thermometer, one heating vibrating wire resonator acting as a controllable energy source, and a small orifice that provides thermal coupling to the surrounding He bath (Bunkov et al., 2016).
Thermal isolation is not achieved by vacuum, but by low-temperature interfacial transport. The He inside the cell is thermally isolated from the walls because of Kapitza resistance, so the temperature rise after a pulse reflects the heat capacity of the fluid in the cell. A plausible implication is that the bolometer should be understood as a quasiparticle calorimeter whose sensitivity is set jointly by the superfluid thermodynamics, the cell geometry, and the readout resonator response (Bunkov et al., 2016).
2. Thermodynamic basis and geometric scaling
The physical distinction that makes 0He-B bolometry unusually powerful is the contrast between bulk and surface excitations. In 1He-B, the bulk Bogolyubov quasiparticles are gapped, so at low temperature their heat capacity is exponentially suppressed,
2
where 3 is the sample volume, 4 is the Fermi momentum, and 5 is the superfluid gap (Bunkov et al., 2016).
Near a boundary, however, the gap is suppressed to zero over a distance of order the coherence length 6. In this surface layer, zero-energy Bogolyubov states become Majorana quasiparticles because of particle-hole symmetry, with 7 and, at 8, 9. These surface states contribute a power-law heat capacity rather than an exponential one,
0
with 1 the surface area. The Majorana contribution therefore scales as surface area times coherence length, reflecting that the relevant states live in a layer of thickness 2 near the wall (Bunkov et al., 2016).
This geometric dependence is experimentally decisive. Because the ratio 3 grows rapidly when 4 decreases and is proportional to 5, cells with larger surface-to-volume ratio should show a larger relative Majorana contribution. The coherence length is crucial because the Majorana surface states live within a layer of thickness 6, the Majorana heat capacity therefore scales as 7, and the coherence length is part of the prefactor in the ratio 8. Physically, 9 controls how much “surface volume” is available to host these zero-energy states (Bunkov et al., 2016).
The thermodynamic logic is not limited to Majorana measurements. The same small-0 regime underlies rare-event detection: when the thermal quasiparticle population is very small, a recoil or other particle interaction can stand out against the thermal background. This suggests a unifying view in which superfluid 1He bolometers exploit the same exponentially depleted bulk response both for spectroscopy of exotic boundary excitations and for low-threshold particle detection (Bunkov et al., 2016, Autti et al., 2024).
3. Resonator thermometry, heating, and readout architectures
The canonical thermometer is a vibrating wire resonator. In the Majorana heat-capacity experiment, the measuring resonator monitors quasiparticle density through its resonance width 2, with
3
where 4 Hz depends on wire geometry and pressure. A heating resonator is driven briefly at resonance, injecting a known amount of energy. The calibration factor is
5
where 6 is the deposited energy and 7 is the 8He heat capacity. If 9 increases, the same injected energy produces a smaller temperature rise and a different calibration slope (Bunkov et al., 2016).
Recent development for QUEST-DMC extends this scheme to micron-scale and sub-micron diameter vibrating wire resonators with a SQUID amplifier-based readout scheme. The bolometer contains two vibrating wire resonators, enabling heat injection calibration and simultaneous bolometer tracking measurements, and a 2-stage SQUID current sensor with flux-locked-loop electronics is used for readout. A key practical result is a simpler, scalable readout chain with only the resonators and an integrated SQUID current sensor as cryogenic electronics (Collaboration et al., 14 Aug 2025).
In that implementation, the resonator response is fitted to a Lorentzian,
0
where 1 is the resonance amplitude, 2 is the resonance frequency, and 3 is the resonance width. The width contains both intrinsic damping and quasiparticle damping from the helium-3 environment. The effective wire length is extracted from the resonance amplitude, with 4 mm for the 5 nm wire and 6 mm for the 7 nm wire, and the wire velocity is obtained from
8
The force is estimated as 9 (Collaboration et al., 14 Aug 2025).
A distinctive methodological point is non-linear operation. The $0.4$0 nm wire is operated in the non-linear regime, but still below the onset of pair breaking. At low velocities, damping is linear, $0.4$1. As velocity increases beyond a few mm/s, the damping becomes nonlinear, around the scale $0.4$2. At still higher velocities, dissipation increases sharply due to emission of bound quasiparticles into the bulk superfluid, occurring near $0.4$3, compared with the Landau critical velocity estimate $0.4$4. Because the thinner $0.4$5 nm wire is mesoscopic, with $0.4$6 and $0.4$7 at $0.4$8 bar, deviations from the ideal macroscopic-wire picture are expected. The required non-linearity correction is therefore essential to recover thermometer width from finite-drive operation (Collaboration et al., 14 Aug 2025).
The same paper also demonstrates simultaneous tracking on both wires, coincidence measurements of the same heating event, and proof-of-concept frequency multiplexed readout with one SQUID. Multiple vibrating wires can be connected to a single SQUID if their resonances are well separated in frequency, and the authors show simultaneous readout of two vibrational modes of the same $0.4$9 nm nanowire with one SQUID. This is significant because it supports scaling to arrays of bolometers or multiple sensors per detector channel (Collaboration et al., 14 Aug 2025).
4. Experimental realizations and direct calorimetric signatures
The most explicit calorimetric demonstration is the measurement of Majorana quasiparticle surface states in 0He-B. Two bolometers with very different surface-to-volume ratios were used, allowing different calibrated contributions from Majorana quasiparticles to the 1He heat capacity. The experiment therefore tested the predicted 2 scaling directly rather than inferring it from a single geometry (Bunkov et al., 2016).
| Cell | Geometry | Observed low-3 deviation |
|---|---|---|
| A | 4, 5, 6, measuring VWR diameter 7 | about 8K |
| B | 9, 0, 1, measuring VWR diameter 2 | about 3K |
The surface in cell B was increased by adding copper slabs thermally connected to the walls. Since the measuring wire diameter determines the temperature range of optimal sensitivity, the 4 wire was used in cell B because the larger 5 was expected to shift the Majorana deviation upward in temperature. In both cells, the experimental calibration factor deviates from the bulk-only 6 behavior as temperature is lowered. The observed data are well fit by including the Majorana heat capacity term, with a common wall roughness factor of about 7 for both cells (Bunkov et al., 2016).
The calibration data were recast as heat capacity and normalized to the bulk heat capacity. The resulting behavior is consistent with
8
In cell B, at about 9K, the Majorana contribution is reported to be about four times larger than the bulk contribution, matching the estimate from the 0-based ratio formula. The paper concludes that Majorana quasiparticles are experimentally confirmed in superfluid 1He-B through direct heat-capacity measurements (Bunkov et al., 2016).
An important controversy concerns whether the extra heat capacity could instead arise from adsorbed 2He layers on the walls. The alternative contribution is magnetic and behaves roughly like
3
which, when combined with the bulk heat capacity, produces a temperature dependence that does not match the observed data. The walls were covered by 4He during condensation of the 5He, which should strongly suppress adsorbed 6He layers. Another discriminator is the thermal relaxation shape after heating: the experiment shows a single exponential decay, whereas adsorbed 7He would typically produce a two-exponential relaxation because of imperfect coupling between the solid and liquid layers. On this basis, adsorbed 8He is not a good explanation for the observed extra heat capacity (Bunkov et al., 2016).
Modern bolometer development emphasizes a different, though related, form of validation. In the QUEST-DMC readout study, the use of the 9 nm wire as a heater and the 0 nm wire as a thermometer produces a linear relation between the calibrated width parameter 1 and injected power, confirming the model and thermal equilibrium assumption. Coincident events measured on both vibrating wire resonators verify their response. This provides an instrumental complement to the thermodynamic validation of the earlier Majorana experiment (Collaboration et al., 14 Aug 2025).
5. Cryogenics, thermalization, and in situ thermometry
Superfluid 2He bolometers operate in a regime where the cryogenic platform is part of the detector physics. A dry nuclear-demagnetization cryostat has been demonstrated for quantum-fluid experiments with explicit application to superfluid 3He, reaching 4 using a copper nuclear demagnetization stage precooled by a pulse-tube dilution refrigerator. The minimum heat leak obtained was 5 at 6, and the hold time in the superfluid state was about 7 hours at 8, extendable to 9 hours by further demagnetization (Todoshchenko et al., 2014).
The architecture of that cryostat is relevant to bolometers because detector operation often requires temperatures well below 00, low vibrational heat input, direct liquid-01He thermometry, and long hold times in the superfluid phase. The design principle was to eliminate relative vibrations between the high-field magnet and the nuclear refrigeration stage, reducing eddy-current heating. Without spacers, the long tail of the stage vibrated in the magnet and caused a few 02W of eddy-current heating in an 03 T field; with spacers this was reduced by about an order of magnitude (Todoshchenko et al., 2014).
The 04He experimental cell inside the nuclear stage had walls coated with silver sinter with an effective area of about 05. This is directly relevant to bolometers because it shows that actual liquid-06He instrumentation can be hosted in the superfluid state with thermalization through a large-area sintered heat exchanger. In the modern QUEST-DMC bolometer, the reservoir volume is about 07 and is likewise cooled by a silver sinter heat exchanger with estimated area 08, indicating continuity between cryogenic platform design and detector-cell engineering (Todoshchenko et al., 2014, Collaboration et al., 14 Aug 2025).
Thermometry must probe the helium, not only the metal stage. At sub-mK temperatures the Kapitza resistance between helium and copper scales as 09, causing helium to become thermally decoupled from the cryostat. A quartz tuning fork immersed in liquid 10He can therefore serve as a direct thermometer. Below about 11, the mean free path of quasiparticles exceeds the oscillator size and the resonance width follows
12
The exact calibration law is
13
where 14 is the width at the ballistic onset temperature 15. The crossover is identified by saturation of the central resonance frequency 16, making the oscillator effectively self-calibrating in the crossover region (Todoshchenko et al., 2014).
This matters operationally because superfluid 17He bolometers depend strongly on quasiparticle density and heat transport. A plausible implication is that reliable detector calibration requires both cell-internal quasiparticle transducers such as vibrating wires and independent in situ thermometry of the surrounding 18He environment, especially when helium and copper are thermally decoupled (Todoshchenko et al., 2014).
6. Rare-event detection, backgrounds, and detector scaling
The dark-matter application is represented by QUEST-DMC, where a superfluid 19He target instrumented with nanomechanical resonators is intended as a sub-GeV dark matter detector. The detector is described as a roughly 20 transparent cell containing superfluid 21He, surrounded by a secondary superfluid volume and connected through a small hole of about 22 in the bolometer wall. The target is cooled to around 23K so that the thermal quasiparticle population is very small. A recoil or other particle interaction can deposit energy through quasiparticle production and scintillation photons, and the quasiparticles are detected via damping of nanomechanical resonators driven on resonance (Autti et al., 2024).
The projected performance is explicitly tied to low-threshold rare-event sensitivity. The paper notes a projected threshold of 24 eV for nuclear recoil interactions, which would allow sensitivity to dark matter masses down to about 25. A complementary instrumentation paper states that the extremely low heat capacity of the B phase of the superfluid helium-3 at ultra-low temperatures offers the potential to reach world leading sensitivity to spin dependent interactions of dark matter in the sub-GeV/26 mass range, and demonstrates development of bolometry using both micron scale and sub-micron diameter vibrating wire resonators with SQUID readout (Autti et al., 2024, Collaboration et al., 14 Aug 2025).
Background control is correspondingly stringent. The QUEST-DMC background study emphasizes that heat leaks in cryogenic and sub-mK experiments must often be kept below the pW level. The work screened 27 common cryogenic materials using Boulby Underground Screening facility HPGe gamma spectroscopy and comparison data from the SNOLAB radiopurity database, then converted measured activities into expected emitted power using
28
The results show large variation across materials. For example, OFHC Cu is reported at 29 pW/kg, 30 pW/kg, and 31 pW/kg, whereas fiberglass is reported at 32 pW/kg, 33 pW/kg, and 34 pW/kg (Autti et al., 2024).
The same study gives representative simulated rates and average heat deposits for a 35 cell operated at saturated vapor pressure and 36: 37
38
39
On the surface, cosmic rays dominate the event rate and contribute more power than radiogenic backgrounds; underground, cosmic-ray backgrounds are suppressed by about six orders of magnitude and radiogenic background becomes the limiting factor. For superfluid 40He bolometers, this establishes that threshold performance is inseparable from radiopurity, geometry, and siting (Autti et al., 2024).
7. Phase stability, textures, and interpretation of bolometric response
Superfluid 41He bolometers are not only thermal systems; they are embedded in a multicomponent order-parameter landscape. A relevant theoretical result is that the long-standing fast A42B transition can be understood as a classical transition induced by collisions of pre-existing domain walls in the A-phase texture, rather than by homogeneous nucleation alone. Superfluid 43He is described by a complex 44 order parameter 45 with spin/orbital symmetry
46
and naturally supports sub-phases, domain walls, and texture dynamics (Yang et al., 2011).
The practical implication for bolometers is that detector response in superfluid 47He can be controlled not just by local heating or energy deposition, but by the dynamics and topology of the order-parameter network. In standard nucleation theory the A phase below 48 would have an astronomically long lifetime, with a tunneling rate estimated as
49
yet experiments observe A-B transitions in minutes or hours. The classical-transition picture resolves this by arguing that disturbances such as radiation, cooling, boundary roughness, or mechanical effects can induce domain walls to move and collide, generating a field excursion into the B-phase basin of attraction (Yang et al., 2011).
This perspective modifies how threshold and metastability are interpreted. The paper’s key falsifiable prediction is that, at fixed disturbance strength, whether the transition occurs should depend primarily on the curve 50 in the 51 plane. It also argues that sensitivity can be texture-dependent, thermal response may be nonlocal and nonthermal, metastability can be fragile, phase stability depends on history, and thresholds are not purely energetic. For superfluid 52He bolometers, this suggests that detector stability and apparent sensitivity may depend on cooling history, roughness, and the pre-existing domain-wall network as well as on deposited energy (Yang et al., 2011).
In that sense, superfluid 53He bolometers occupy a distinctive position among cryogenic detectors. They combine exponentially suppressed bulk heat capacity, geometry-sensitive boundary physics, mechanical quasiparticle thermometry, sub-mK cryogenic engineering, and a nontrivial order-parameter landscape. The resulting devices can function as direct calorimetric probes of Majorana surface states, as ultra-low-threshold detectors for spin-dependent dark matter interactions, and as experimental systems in which thermal response, topology, and phase conversion must all be treated as part of the detector physics (Bunkov et al., 2016, Collaboration et al., 14 Aug 2025).