Dilution Refrigerator Research Articles

Numerical analysis of a novel coaxial annular tube convective heat switch

Heat switches are commonly used in cryogenic instruments to provide thermal contact or isolation between the hot and cold masses over a temperature range from millikelvin to room temperature. This study presents a new type of convective thermal switch that implements an annular tube design replacing the twin-tube structure. To study the effects of geometry and operating parameters on thermal performance, a computational fluid dynamics (CFD) model is developed. The results show that the designed heat switch provides a thermal conductance of 33.79 mW/K when the end temperatures are 4.2 K and 40 K. In addition, it can automatically change to thermal isolation mode with a residual thermal conductance of 0.19 mW/K. The thermal conductance is increased from 33.79 mW/K to 38.90 mW/K by extending the length of the inner tube. This novel heat switch holds promise for precooling the modern cryogen-free dilution refrigerator (DR) and adiabatic demagnetization refrigerator (ADR).

Conceptual study of a two-layer silicon pixel detector to tag the passage of muons from cosmic sources through quantum processors

Recent studies in quantum computing have shown that quantum error correction with large numbers of physical qubits are limited by ionizing radiation from high-energy particles. Depending on the physical setup of the quantum processor, the contribution of muons from cosmic sources can constitute a significant fraction of these interactions. As most of these muons are difficult to stop, we perform a conceptual study of a two-layer silicon pixel detector to tag their hits on a solid-state quantum processor instead. With a typical dilution refrigerator geometry model, we find that efficiencies greater than 50% are most likely to be achieved if at least one of the layers is operated at the deep-cryogenic (<1 K) flanges of the refrigerator. Following this finding, we further propose a novel research program that could allow the development of silicon pixel detectors that are fast enough to provide input to quantum error correction algorithms, can operate at deep-cryogenic temperatures, and have very low power consumption.

Membrane-in-the-middle optomechanics with a soft-clamped membrane at milliKelvin temperatures

Soft-clamped silicon nitride membrane resonators are capable of coherence times τ exceeding 100 ms at millikelvin bath temperatures. However, harnessing strong optomechanical coupling in dry dilution refrigerators remains a challenge due to vibration issues and heating by optical absorption. Here, we address these issues with an actuator-free optical cavity and mechanical resonator design, with the cavity mounted on a simple vibration-isolation platform. We observe dynamical backaction when the cavity is driven with a free-space optical beam stabilized close to the red sideband using a two-beam locking scheme. Finally, we characterize the effect of absorption heating on coherence time, finding it scales with the intracavity power P as τ ∝ P−(0.34±0.04).

Enhanced Delivery and Detection of Terahertz Frequency Radiation from a Quantum Cascade Laser Within Dilution Refrigerator

We report on significant enhancements to the integration of terahertz (THz) quantum cascade lasers (QCL) and THz detection with a two-dimensional electron gas (2DEG) within a dilution refrigerator obtained by the inclusion of a multi-mesh 6 THz low-pass filter to block IR radiation, a Winston cone to focus light output, and gating the 2DEG for optimised sensitivity. We show that these improvements allow us to obtain a > 2.5 times reduced sample electron temperature (160 mK compared with 430 mK previously), during cyclotron resonance (CR) measurements of a 2DEG under QCL illumination. This opens up a route to performing sub-100 mK experiments using excitation by THz QCLs.

A platform for far-infrared spectroscopy of quantum materials at millikelvin temperatures.

Optical spectroscopy of quantum materials at ultralow temperatures is rarely explored, yet it may provide critical characterizations of quantum phases not possible using other approaches. We describe the development of a novel experimental platform that enables optical spectroscopic studies, together with standard electronic transport, of materials at millikelvin temperatures inside a dilution refrigerator. The instrument is capable of measuring both bulk crystals and micrometer-sized two-dimensional van der Waals materials and devices. We demonstrate its performance by implementing photocurrent-based Fourier transform infrared spectroscopy on a monolayer WTe2 device and a multilayer 1T-TaS2 crystal, with a spectral range available from the near-infrared to the terahertz regime and in magnetic fields up to 5T. In the far-infrared regime, we achieve spectroscopic measurements at a base temperature as low as ∼43 mK and a sample electron temperature of ∼450 mK. Possible experiments and potential future upgrades of this versatile instrumental platform are envisioned.

Experimental and numerical study of a condensation-driven dilution refrigerator

Dilution refrigerators are widely used in the fields of condensed-matter physics and quantum technology. For small cooling power applications, condensation-driven dilution refrigerator utilizes a condensation pump to achieve 3He cryogenic circulation and has advantages of compact structure, small 3He usage, and convenient operation. Related published research mainly focused on the overall system performances, and in-depth thermodynamics and fluid dynamics analyses are lacking. In this paper, a condensation-driven dilution refrigerator was experimentally studied and corresponding numerical simulations were performed. The results of experiments and simulations were compared and analyzed. In the experiments, lowest no-load temperature was 84.4 mK. The experimental cooling power was 1.91 μW @100 mK with a still heating power of 280 μW and the corresponding COP and second-law efficiency of the dilution cold cycle at 100 mK reached 0.0068 and 2.4% with the high temperature of 452 mK, respectively. The experiments also revealed that the charged mixture amount had a certain influence on the performance. With the help of simulations, the heat leak to the mixing chamber was estimated and certain intrinsic features of the cycle were enlightened. The heat leak and Kapitza resistance in the mixing chamber are possibly the main reasons for the differences between experimental and simulation results. Extended study based on the simulation also showed how flowrate variation changed the liquid column height difference and how the requirement of gas circulation and liquefaction set the limit on the minimum still temperature.

MilliKelvin microwave impedance microscopy in a dry dilution refrigerator.

Microwave impedance microscopy (MIM) is a near-field imaging technique that has been used to visualize the local conductivity of materials with nanoscale resolution across the GHz regime. In recent years, MIM has shown great promise for the investigation of topological states of matter, correlated electronic states, and emergent phenomena in quantum materials. To explore these low-energy phenomena, many of which are only detectable in the milliKelvin regime, we have developed a novel low-temperature MIM incorporated into a dilution refrigerator. This setup, which consists of a tuning-fork-based atomic force microscope with microwave reflectometry capabilities, is capable of reaching temperatures down to 70 mK during imaging and magnetic fields up to 9T. To test the performance of this microscope, we demonstrate microwave imaging of the conductivity contrast between graphite and silicon dioxide at cryogenic temperatures and discuss the resolution and noise observed in these results. We extend this methodology to visualize edge conduction in Dirac semi-metal cadmium arsenide in the quantum Hall regime.

Performance optimization of a mK dilution refrigerator based on the first law of thermodynamics

This paper analyzes and optimizes performance characteristics of the dilution refrigerator (DR) based on the first law of thermodynamics. The properties of the 3He-4He mixture below 0.7 K are analyzed and a simplified method to obtain the enthalpy of the working fluid in the whole dilution cycle is proposed. Then an enthalpy flow model is built, based on which the variations of the specific cooling capacity, specific still heating power and gross cooling capacity with the precooling temperature and upstream pressure are studied at the cooling temperature of 10 mK, and the effect of the first-stage heat exchanger efficiency on the gross cooling capacity is further analyzed. The results indicate that there exists an optimal upstream pressure which maximizes the gross cooling capacity for a given precooling temperature. The optimal upstream pressure and the maximum gross cooling capacity are investigated based on the fitting functions of precooling temperatures. Given a heat exchanger efficiency of 97 %, it is found that the optimal upstream pressure and precooling temperature should be 1.41 × 105 Pa and around 4 K, respectively, to achieve the maximum cooling capacity of 38.5 μW at 10 mK. This study provides a helpful theoretical guidance for the performance optimization of the DR.

Performance benchmarking of an ultra-low vibration laboratory to host a commercial millikelvin scanning tunnelling microscope

Ultra-low temperature scanning tunnelling microscopy and spectroscopy (STM/STS) achieved by dilution refrigeration can provide unrivalled insight into the local electronic structure of quantum materials and atomic-scale quantum systems. Effective isolation from mechanical vibration and acoustic noise is critical in order to achieve ultimate spatial and energy resolution. Here, we report on the design and performance of an ultra-low vibration (ULV) laboratory hosting a customized but otherwise commercially available 40 mK STM. The design of the vibration isolation consists of a T-shaped concrete mass block (∼55t), suspended by actively controlled pneumatic springs, and placed on a foundation separated from the surrounding building in a ‘room-within-a-room’ design. Vibration levels achieved are meeting the VC-M vibration standard at >3 Hz, reached only in a limited number of laboratories worldwide. Measurement of the STM’s junction noise confirms effective vibration isolation on par with custom built STMs in ULV laboratories. In this tailored low-vibration environment, the STM achieves an energy resolution of 43 μeV (144 mK), promising for the investigation and control of quantum matter at atomic length scales.

Numerical study on the influence of the mixing chamber structure in a dilution refrigerator on the heat and mass transfer characteristics of 3He-4He at ultralow temperatures

The acquisition and utilization of ultralow temperatures has become a popular research topic with great value. Dilution refrigerators (DRs) with 3He-4He mixtures as refrigerants are the main tool to obtain millikelvin temperatures and have been applied in space exploration, low-temperature physics experiments and other fields. As the mixing chamber at the cold end of DR, direct study on the influence of its structural parameters on heat and mass transfer at ultralow temperatures is still lacking. In this study, a coupled numerical model of the heat and mass transfer of 3He-4He mixture in the mixing chamber at ultralow temperature is established. The effects of various structural parameters are simulated using a finite element model, and the refrigeration performance of different mixing chambers is evaluated by refrigeration temperature and refrigeration power. First, the molar amount of the mixture in the mixing chamber affects the refrigeration temperature and refrigeration power. When the effective volume of the cylindrical mixing chamber increases twofold, the refrigeration power increases by 11.88%. When the volume of the cylindrical mixing chamber is expanded twofold, the cooling time required to reach 15 mK is increased by 57.29% compared to the standard cylindrical mixing chamber. We further found that appropriately reducing the proportion of the concentrated phase coolant is beneficial for refrigeration performance. In addition, cuboid mixing chambers achieve lower refrigeration temperatures than mixing chambers with other shapes. This study is of great significance to guide the design and optimization of mixing chambers.

Flux-Driven Josephson Parametric Amplifier Fabricated Using the Nb/AlO x /Nb Trilayer Process

In this paper, we report a flux-driven Josephson par-ametric amplifier (JPA) fabricated using the Nb/AlOx/Nb Josephson junction process. The JPA consists of a parallel-plate type coupling capacitor and quarter-wavelength resonator terminated with a DC-SQUID. We adopt a simple 4-layer process using well-estab-lished Nb trilayer technology. The overall configuration time of the Nb-based JPA can be shortened by measuring resonant frequency and its bias dependence in liquid helium. Amplification of the pre-tested device was demonstrated, showing a gain of 20 dB in a -3 dB bandwidth of 17 MHz in a 10 mK dilution fridge.

Versatile Millikelvin Hybrid Cooling Platform for Superconductivity Research

Closed cycle He <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> -He <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> dilution cryostats became the platform of choice in quantum sciences in the era of helium shortage. However, in many experiments, the mechanical vibrations induced by the pulsed cryocoolers present a significant drawback reflected both in electronic and mechanical noises. Here, we present a hybrid dilution cryostat platform; we have automated a commercial closed-cycle system to operate on a cryocooler or on a liquid helium ‘battery’. We implemented a scanning SQUID microscope in the hybrid dilution refrigerator. In this work we show the design of the hybrid setup and how its operation eliminates vibration artefacts in magnetic imaging.

Nb/a-Si/Nb-junction Josephson arbitrary waveform synthesizers for quantum information.

We demonstrate Josephson arbitrary waveform synthesizers (JAWS) with increased operating temperature range for temperatures below 4 K. These JAWS synthesizers were fabricated with externally-shunted Nb/a-Si/Nb junctions whose critical current exhibits improved temperature stability compared to the self-shunted Nb/Nb0.15Si0.85/Nb junctions typically used. Vertical stud resistors made of 230 nm of PdAu were developed to provide the milliohm shunt resistance required for junction overdamping while maintaining a small footprint suitable for high-density series arrays embedded in a coplanar waveguide. We evaluated the performance of these resistors from 3.8 K down to 20 mK. We designed, fabricated and tested a JAWS circuit with 4650 externally shunted Nb/a-Si/Nb JJs with a critical current density () of 0.12 and critical current () of 3 mA. This circuit was designed to be mounted to the 3 K stage of a dilution refrigerator and used to control and calibrate a qubit mounted at the 10 mK stage. To increase the circuit density of the JAWS circuits we made arrays of two-junction vertical stacks. Current-voltage () curves of this JAWS circuit with stacked junctions under microwave excitation show Shapiro steps with quantum-locking ranges similar to those of JAWS circuits used for qubit control.

Amplitude-controllable microwave pulse generator using single-flux-quantum pulse pairs for qubit control

To achieve large-scale quantum processors, cryogenic quantum-bit (qubit) interface circuits that can control qubits inside a dilution refrigerator are indispensable. Superconducting single-flux quantum (SFQ) circuits are a promising building block for qubit interface circuits because SFQ circuits can operate with high clock frequencies and low power dissipation. In the present study, we developed an SFQ-based qubit interface circuit that we refer to as a pulse-pair microwave pulse generator (PP-MPG). The PP-MPG can generate microwave pulses for qubit control, with the microwave amplitude controlled based on the delay between paired SFQ pulses. By finely adjusting the delay with delay controlling circuits, the microwave amplitude can be controlled over a wide range. We fabricated a PP-MPG chip and tested it at 4.2 K, showing that the microwave amplitude can be controlled over a range of approximately 30 dB. Our results show that the PP-MPG has the potential for use in future large-scale quantum processors.

High-Q Magnetic Levitation and Control of Superconducting Microspheres at Millikelvin Temperatures.

We report the levitation of a superconducting lead-tin sphere with 100 μm diameter (corresponding to a mass of 5.6 μg) in a static magnetic trap formed by two coils in an anti-Helmholtz configuration, with adjustable resonance frequencies up to 240Hz. The center-of-mass motion of the sphere is monitored magnetically using a dc superconducting quantum interference device as well as optically and exhibits quality factors of up to 2.6×10^{7}. We also demonstrate 3D magnetic feedback control of the motion of the sphere. The setup is housed in a dilution refrigerator operating at 15mK. By implementing a cryogenic vibration isolation system, we can attenuate environmental vibrations at 200Hz by approximately 7 orders of magnitude. The combination of low temperature, large mass, and high quality factor provides a promising platform for testing quantum physics in previously unexplored regimes with high mass and long coherence times.

Low Noise Opto-Electro-Mechanical Modulator for RF-to-Optical Transduction in Quantum Communications.

In this work, we present an Opto-Electro-Mechanical Modulator (OEMM) for RF-to-optical transduction realized via an ultra-coherent nanomembrane resonator capacitively coupled to an rf injection circuit made of a microfabricated read-out able to improve the electro-optomechanical interaction. This device configuration can be embedded in a Fabry-Perot cavity for electromagnetic cooling of the LC circuit in a dilution refrigerator exploiting the opto-electro-mechanical interaction. To this aim, an optically measured steady-state frequency shift of 380 Hz was seen with a polarization voltage of 30 V and a Q-factor of the assembled device above 106 at room temperature. The rf-sputtered titanium nitride layer can be made superconductive to develop efficient quantum transducers.

A first test of CUPID prototypal light detectors with NTD-Ge sensors in a pulse-tube cryostat

CUPID is a next-generation bolometric experiment aiming at searching for neutrinoless double-beta decay with ∼250 kg of isotopic mass of 100Mo. It will operate at ∼10 mK in a cryostat currently hosting a similar-scale bolometric array for the CUORE experiment at the Gran Sasso National Laboratory (Italy). CUPID will be based on large-volume scintillating bolometers consisting of 100Mo-enriched Li2MoO4 crystals, facing thin Ge-wafer-based bolometric light detectors. In the CUPID design, the detector structure is novel and needs to be validated. In particular, the CUORE cryostat presents a high level of mechanical vibrations due to the use of pulse tubes and the effect of vibrations on the detector performance must be investigated. In this paper we report the first test of the CUPID-design bolometric light detectors with NTD-Ge sensors in a dilution refrigerator equipped with a pulse tube in an above-ground lab. Light detectors are characterized in terms of sensitivity, energy resolution, pulse time constants, and noise power spectrum. Despite the challenging noisy environment due to pulse-tube-induced vibrations, we demonstrate that all the four tested light detectors comply with the CUPID goal in terms of intrinsic energy resolution of 100 eV RMS baseline noise. Indeed, we have measured 70–90 eV RMS for the four devices, which show an excellent reproducibility. We have also obtained high energy resolutions at the 356 keV line from a 133Ba source, as good as Ge semiconductor γ detectors in this energy range.

Design and Analysis of a 4.2 mW 4 K 6–8 GHz CMOS LNA for Superconducting Qubit Readout

This article proposes a cryogenic inverter-based low noise amplifier (LNA) for qubit readout. Its input impedance matching is realized by a high- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> on-chip gate inductor and capacitive load through the gate-to-drain feedback capacitance of the input transistors. Cascode transistors are used to optimize the impedance matching, which results in a larger gate inductor and smaller load capacitor and hence a higher passive and inverter gain. Owing to the high passive gain and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -factor of the gate inductor at 4 K, the noise of the active stages is substantially suppressed with a negligible noise contribution of the gate inductor. Moreover, with the current re-use in the inverter topology, less power consumption is achieved for the given transconductance of transistors. The input impedance, gain, and noise analyses of the proposed LNA are performed for room temperature (RT) operation, and its noise optimization is done by taking the cryogenic operation of the devices into account. We demonstrate with the circuit analysis and measurement results that the input impedance of the LNA has a low sensitivity to variations on device parameters at cryogenic temperatures. The LNA is implemented in a 28 nm CMOS technology. It achieves 0.4–0.7 dB noise figure (NF) with 4.2 mW power consumption at 4 K, and its operating frequency is between 6–8 GHz. The LNA consumes very low power compared to the state-of-the-art cryogenic CMOS LNAs while providing similar NF performance at 4 K, which makes it suitable for dilution refrigerators.

Superconducting Microsphere Magnetically Levitated in an Anharmonic Potential with Integrated Magnetic Readout

Magnetically levitated superconducting microparticles offer a promising path to quantum experiments with picogram to microgram objects. In this work, we levitate a 700ng $\sim 10^{17}$amu superconducting microsphere in a magnetic chip trap in which detection is integrated. We measure the particle's center-of-mass motion using a DC-SQUID magnetometer. The trap frequencies are continuously tunable between 30 and 160 Hz and the particle remains stably trapped over days in a dilution refrigerator environment. We characterize motional-amplitude-dependent frequency shifts, which arise from trap anharmonicities, namely Duffing nonlinearities and mode couplings. We explain this nonlinear behavior using finite element modelling of the chip-based trap potential. This work constitutes a first step towards quantum experiments and ultrasensitive inertial sensors with magnetically levitated superconducting microparticles.

Coherence-limited digital control of a superconducting qubit using a Josephson pulse generator at 3 K

Compared to traditional semiconductor control electronics (TSCE) located at room temperature, cryogenic single flux quantum (SFQ) electronics can provide qubit measurement and control alternatives that address critical issues related to scalability of cryogenic quantum processors. Single-qubit control and readout have been demonstrated recently using SFQ circuits coupled to superconducting qubits. Experiments where the SFQ electronics are co-located with the qubit have suffered from excess decoherence and loss due to quasiparticle poisoning of the qubit. A previous experiment by our group showed that moving the control electronics to the 3 K stage of the dilution refrigerator avoided this source of decoherence in a high-coherence three-dimensional transmon geometry. In this paper, we also generate the pulses at the 3 K stage but have optimized the qubit design and control lines for scalable two-dimensional transmon devices. We directly compare the qubit lifetime T1, coherence time T2*, and gate fidelity when the qubit is controlled by the Josephson pulse generator (JPG) circuit vs the TSCE setup. We find agreement within the daily fluctuations for T1 and T2*, and agreement within 10% for randomized benchmarking. We also performed interleaved randomized benchmarking on individual JPG gates demonstrating an average error per gate of 0.46% showing good agreement with what is expected based on the qubit coherence and higher-state leakage. These results are an order of magnitude improvement in gate fidelity over our previous work and demonstrate that a Josephson microwave source operated at 3 K is a promising component for scalable qubit control.