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arXiv:2208.11750 · Journal of Low Temperature Physics

Magnetic Cooling and Vibration Isolation of a Sub-kHz Mechanical Resonator

Bernard van Heck, Tim M. Fuchs, Jaimy Plugge, W.A. Bosch, Tjerk H. Oosterkamp

Published Feb 4, 2023• 7 citations
arXivHTMLPDF

Abstract

Abstract We report recent progress toward the realization of a sub-mK, low-vibration environment at the bottom stage of a dry dilution refrigerator for use in mechanical tests of quantum mechanics. Using adiabatic nuclear demagnetization, we have cooled a silicon cantilever force sensor to $$T\approx 1$$ T ≈ 1 mK. The temperature of the tip holder of the cantilever chip was determined via a primary magnetic flux noise thermometer. The quality factor of the cantilever continues to increase with decreasing temperature, reaching $$Q\approx 4\cdot 10^4$$ Q ≈ 4 · 10 4 at 2 mK. To demonstrate that the vibration isolation is not compromised, we report the detection of the thermal motion of the cantilever down to $$T \approx 20$$ T ≈ 20 mK, only limited by the coupling to the SQUID readout circuit. We discuss feasible improvements that will allow us to probe unexplored regions of the parameter space of continuous spontaneous localization models.

DOI
10.1007/s10909-022-02933-3

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•Sep 20, 2019•0 citations
Abstract We report recent progress toward the realization of a sub-mK, low-vibration environment at the bottom stage of a dry dilution refrigerator for use in mechanical tests of quantum mechanics. Using adiabatic nuclear demagnetization, we have cooled a silicon cantilever force sensor to T≈1T\approx 1T≈1 T ≈ 1 mK. The temperature of the tip holder of the cantilever chip was determined via a primary magnetic flux noise thermometer. The quality factor of the cantilever continues to increase with decreasing temperature, reaching Q≈4⋅104Q\approx 4\cdot 10^4Q≈4⋅104 Q ≈ 4 · 10 4 at 2 mK. To demonstrate that the vibration isolation is not compromised, we report the detection of the thermal motion of the cantilever down to T≈20T \approx 20T≈20 T ≈ 20 mK, only limited by the coupling to the SQUID readout circuit. We discuss feasible improvements that will allow us to probe unexplored regions of the parameter space of continuous spontaneous localization models.
Due to their exceptional isolation from the environment, magnetically levitated particles are explored as extremely sensitive mechanical sensors. For future gravity experiments on quantum superpositions, such systems need to be cooled close to their ground state. To demonstrate the combination of state of the art vibration isolation, milligram levitated high Q mechanical resonators and position detection with low noise, we present linear feedback cooling of a magnetically levitated gravity sensor to below 2 picometer amplitude and below 10 millikelvin mode temperature for two translational modes (the x- and y-mode) simultaneously. The sensor is a levitating permanent magnet in a type I superconducting trap, where its six resonance frequencies are measured with a superconducting coil coupled to a DC SQUID. This signal is measured with a lock-in amplifier and a feedback signal is sent to a piezoelectric actuator, allowing the cooling of resonant modes at 50.6 and 68.0 Hz simultaneously. These two translational modes have Q factors of 3.8⋅1063.8 \cdot 10^63.8⋅106 and 5.5⋅1065.5 \cdot 10^65.5⋅106 respectively. The experiment is mounted inside a dry dilution refrigerator where it is vibrationally attenuated with 110-130 dB at these frequencies. In this work, we discuss future improvements on the setup which may enable quantum ground state cooling on a magnetically levitated particle, that has previously been shown to be a gravitational sensor.
When operated in a dilution cryostat, a MHz-frequency nanomechanical device relies on active cooling to reach its quantum ground state. However, a proper understanding of its environmental interactions and mechanical quantum decoherence would require in-equilibrium cooling, with the thermal bath reaching sub-mK temperatures. This is very demanding and requires cooling via adiabatic nuclear demagnetization. The authors successfully demonstrate the technique, with a scheme to measure the temperature on-chip to verify equilibrium with the cryostat. An unexpected instability of unknown origin is observed at very low temperatures, presenting a strong limitation to progress in this field.
Access to lower temperatures has consistently enabled scientific breakthroughs. Pushing the limits of \emph{on-chip} temperatures deep into the microkelvin regime would open the door to unprecedented quantum coherence, novel quantum states of matter, and also the discovery of unexpected phenomena. Adiabatic demagnetization is the workhorse of microkelvin cooling, requiring a dilution refrigerator precooling stage. Pulse-tube dilution refrigerators have grown enormously in popularity due to their vast experimental space and independence of helium, but their unavoidable vibrations are making microkelvin cooling very difficult. On-chip thermometry in this unexplored territory is also not a trivial task due to extreme sensitivity to noise. Here, we present a pulse-tube compatible microkelvin sample holder with on-board cooling and microwave filtering and introduce a new type of temperature sensor, the gate Coulomb blockade thermometer (gCBT), working deep into the microkelvin regime. Using on- and off-chip cooling, we demonstrate electronic temperatures as low as 224$\pm777μK,remainingbelow300K, remaining below 300K,remainingbelow300μKfor27hours,thusprovidingsufficienttimeformeasurements.Finally,wegiveanoutlookforcoolingbelow50K for 27 hours, thus providing sufficient time for measurements. Finally, we give an outlook for cooling below 50Kfor27hours,thusprovidingsufficienttimeformeasurements.Finally,wegiveanoutlookforcoolingbelow50μ$K for a new generation of microkelvin transport experiments.
The application of quantum mechanics to macroscopic motion suggests many counterintuitive phenomena. While the quantum nature of the motion of individual atoms and molecules has long been successfully studied, an equivalent demonstration of the motion of a near-macroscopic structure remains a challenge in experimental physics. A nanomechanical resonator is an excellent system for such a study. It typically contains > 10 10 atoms, and it may be modeled in terms of macroscopic parameters such as bulk density and elasticity. Yet it behaves like a simple harmonic oscillator, with mass low enough and resonant frequency high enough for its quantum zero-point motion and single energy quanta to be experimentally accessible. In pursuit of quantum phenomena in a mechanical oscillator, two important goals are to prepare the oscillator in its quantum ground state, and to measure its position with a precision limited by the Heisenberg uncertainty principle. In this work we have demonstrated techniques that advance towards both of these goals. Our system comprises a 30 micron × 170 nm, 2.2 pg, 5.57 MHz nanomechanical resonator capacitively coupled to a 5 GHz superconducting microwave resonator. The microwave resonator and nanomechanical resonator are fabricated together onto a single silicon chip and measured in a dilution refrigerator at temperatures below 150 mK. At these temperatures the coupling of the motion to the thermal environment is very small, resulting in a very high mechanical Q, approaching ∼ 10 6 . By driving with a microwave pump signal, we observed sidebands generated by the mechanical motion and used these to measure the thermal motion of the resonator. Applying a pump tone red-detuned from the microwave resonance, we used the microwave field to damp the mechanical resonator, extracting energy and "cooling" the motion in a manner similar to optical cooling of trapped atoms. Starting from a mode temperature of ∼ 150 mK, we reached ∼ 40 mK by this "backaction cooling" technique, corresponding to an occupation factor only ∼ 150 times above the ground state of motion. We also determined the precision of our device in measurement of position. Quantum mechanics dictates that, in a continuous position measurement, the precision may be no better than the zero-point motion of the resonator. Increasing the coupling of the resonator to detector will eventually result in back-action driving of the motion, adding imprecision and enforcing this limit. We demonstrated that our system is capable of precisions approaching this limit, and identified the primary experimental factors preventing us from reaching it: noise added to the measurement by our amplifier, and excess dissipation appearing in our microwave resonator at high pump powers. Furthermore, by applying both red- and blue-detuned phase-coherent microwave pump signals, we demonstrated back-action evading (BAE) measurement sensitive to only a single quadrature of the motion. By avoiding the back-action driving in the measured quadrature, such a technique has the potential for precisions surpassing the limit of the zero-point motion. With this method, we achieved a measurement precision of ∼ 100 fm, or 4 times the quantum zero-point motion of the mechanical resonator. We found that the measured quadrature is insensitive to back-action driving by at least a factor of 82 relative to the unmeasured quadrature. We also identified a mechanical parametric amplification effect which arises during the BAE measurement. This effect sets limits on the BAE performance but also mechanically preamplifies the motion, resulting in a position resolution 1.3 times the zero-point motion. We discuss how to overcome the experimental limits set by amplifier noise, pump power and parametric amplification. These results serve to define the path forward for demonstrating truly quantum-limited measurement and non-classical states of motion in a nearly-macroscopic object.
Magnetically levitated superconducting microparticles provide a promising platform for fundamental quantum experiments and quantum-limited sensing. In the Meissner state, the levitated particle is trapped without mechanical clamping, allowing its center-of-mass motion to exhibit ultralow dissipation. The particle's displacement can be read out dispersively via magnetic flux coupling to superconducting resonators. A challenge for magnetomechanical coupling is to realize a flux-tunable microwave circuit that provides strong flux-to-frequency transduction, low dissipation, and a sufficiently large linear operating range for readout and cooling. This thesis develops and characterizes a chip-based superconducting platform for realizing this transduction.Chip-based levitation of a superconducting microparticle is demonstrated at 40 mK. Passive cryogenic vibration isolation is developed to increase the mechanical quality factors of the levitated particle. For coupling to a microwave circuit, a superconducting flip-chip process based on indium microspheres was developed. The need for Au passivation of Nb or NbN under-bump metallization is demonstrated, and indium-based superconducting interconnects are shown to carry ampere-scale currents. Flux-tunable resonators with 100-200 µm SQUID loops and integrated input coils are designed, fabricated, and characterized. A peak flux responsivity of 20 GHz/Φ₀ is achieved, with one flux quantum modulation requiring only 10-20 µA of input-coil current. Two integrated flux-biasing architectures are developed with flip-chip and on-chip input coils, achieving a total flux transfer efficiency of 1.6%. Junction asymmetry is shown to suppress branch-switching behavior associated with finite SQUID screening.Together, these results establish the superconducting subsystems required for dispersive microwave readout of the center-of-mass motion of a levitated microparticle. Such a magnetomechanical coupling provides a route toward cooling the center-of-mass motion to the ground state, paving the way for the preparation of nonclassical motional states. More broadly, such systems are well-suited for quantum-limited force and acceleration sensing, as well as for probing quantum physics in a previously unexplored mass regime.
A cryogen-free cryostat was set up in order to perform measurements at ultra low temperatures. The setup involved the removal of an adiabatic demagnetization refrigerator (ADR) and replacing it with a dilution refrigerator system. The modified cryostat is able to provide continuous cooling power, enabling greater flexibility over the ADR in the type of low temperature experiments that can be performed. Condensation stages, main flow impedance and radiation baffles were designed, constructed and installed into the cryostat. Several general cryostat design considerations are also discussed. Condensation of the incoming 3He - 4He mixture utilizes only the cooling power of the two-stage pulse tube refrigerator. For a circulation rate of 120 μmols/sec, the base temperature of the cryostat is 70 mK with a cooling power of 33 μW of heat at 100 mK. \nWith this cryostat, a measurement system is developed for studying superconducting microwave resonators. Residual losses in these devices continue to impede their performance in applications such as ultra sensitive detectors and quantum computing. A microwave circuit consisting of coaxial cables, attenuators and amplifiers was installed on the cryostat to measure losses in these devices. Data analysis and fitting procedures were written in Python programming language to extract key resonator properties. Characterizing and understanding loss mechanisms for these devices will lead to improved materials and fabrication methods. This will ultimately result in losses that approach the fundamental limit set by the Mattis-Bardeen theory.