Cryogenic geometric anti-spring vibration isolation system

TL;DR

The paper tackles the problem of pervasive low-frequency vibrations in closed-cycle cryostats, which hinder ultrasensitive cryogenic measurements. It introduces a cryogenic geometric anti-spring (GAS) vibration isolation system built from radially arranged titanium blade springs with in-situ magnetic tuning, and demonstrates a vertical resonance frequency of $f_0=185\ \mathrm{mHz}$ at $T=7\ \mathrm{K}$, achieving substantial attenuation of the problematic $1\ \mathrm{Hz}$ cooler noise. The authors develop a GAS theory, present a monolithic blade design, and integrate a compact cryostat with fast turn-over capability and mass-tuning capabilities, validating the near-zero stiffnessWorking Point via S-curve measurements and cryogenic testing. The work establishes GAS-based cryogenic vibration isolation as a viable path toward ultra-stable environments for scanning probe microscopy, large-mass quantum experiments, and cryogenic gravitational-wave sensing, while outlining practical routes to address residual horizontal modes and center-of-percussion effects.

Abstract

The combination of low temperature and low vibration levels is key for ultrasensitive sensing applications such as scanning probe microscopy, large-mass quantum mechanics, and gravitational wave detection. Unfortunately, closed-cycle cryostats using pulse tube or GM coolers introduce strong low-frequency vibrations starting at 1 Hz. Mass-spring systems allow passive isolation, but for low-frequency applications the required spring constants and masses become impractical. Blade-based geometric anti-spring systems are compact isolators that operate from sub-Hz frequencies, but have not been demonstrated at cryogenic temperatures. Here, we characterize a geometric anti-spring system tuned to operate at cryogenic temperatures. Our cryogenic filter uses radially arranged titanium blade springs whose effective spring constant can be tuned in-situ using a magnetic actuator. Our system achieves a vertical resonance frequency of 185 mHz at 7K, which allows reduction of vibrations at the problematic 1 Hz cooler frequency by an order of magnitude.

Figures (6)

• Figure 1: A comparison of vertical vibrations of the 4K-plate of our GM based cryostat (see Fig 2 for a schematic), measured by a geophone. If the GM cooler is on, vibrations are stronger by orders of magnitude. The strongest noise is visible at a frequency of 1Hz and harmonics thereof, the first four of which are indicated with arrows.
• Figure 2: a) To develop the linear model for GAS, the vertical and compressive horizontal force components are separated. The vertical force is represented as a simple coil spring. The horizontal forces are transferred to the key stone via compressed springs. At the working height, the compressed springs are horizontal and the compressive forces cancel each other out. Adapted from Blom blom_seismic_2015. b) S-curves following Eq. \ref{['Eq:k_eff']} for different compressive forces $F_c$. At $\delta y = 0$, all curves obtain minimal effective stiffness $k_\text{eff}$. The critical green curve has exactly $k_\text{eff}(\delta y) = 0$. The red curve represents the bistable state, where the minimal stiffness is negative.
• Figure 3: An overview of the presented cryogenic geometric anti-spring system is shown. a) A model of our monolithic GAS system, showing the six blade springs mounted on the spring plate. Notice the radially configured slits that alow tuning of the spring compression. b) Owing to the symmetry of the system, the system can be characterized by regarding a cross section. In this cross sectional view, the blade springs can be seen to be approximately uniformly bent, approaching the desired constant curvature under load. c) A photo of the experimental apparatus is shown. The bottom copper plate is the 4K-plate. The spring plate, hosting the GAS blades, is located directly above the 4K plate. d) A schematic cross-sectional view demonstrates the main components of the experimental apparatus.
• Figure 4: An iterative tuning process for our GAS filter based on recording S-curves, position-load diagrams. Initially, the compression is too low, so it is increased by shifting the spring bases inward by $\Delta L_x$ until reaching a near-vertical slope. The voice coil current is converted to a mass difference $\Delta M$.
• Figure 5: Characterization of the GAS filter. a) The S-curve of the tuned filter. Note that the zero-point $y=0$ is chosen differently from the data presented in Fig. \ref{['fig:tuning']}. b) For the tuned filter, the resonance frequency is recorded as a function of the applied load. We record a minimal frequency of 185mHz. c) As a function of temperature, the slope at the working point, shown in the top panel, undergoes slight changes due to the different thermal expansion coefficients of the blades and the base. Much more pronounced is the decreasing working point load due to the reducing Young's modulus, shown in the bottom panel.