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The Enigmatic Universality of Glass

Periodic Reporting for period 3 - UNIGLASS (The Enigmatic Universality of Glass)

Reporting period: 2020-09-01 to 2022-02-28

An improved understanding of amorphous solids (glasses) is important in areas ranging from cryopreservation of biological samples to the solubility and stability of amorphous pharmaceuticals, but glasses are not as well understood as crystals. The way in which the bulk properties of glasses arise from their microscopic structure remains one of the deepest mysteries of condensed matter physics. The low temperature properties of glass are particularly intriguing. Below 1 kelvin, the thermal and mechanical behaviour of glass is very different from that of crystals. For example, the temperature dependence of the heat capacity is approximately linear in glasses and much greater than in crystals. This implies the existence of some type of low energy excitations (LEEs) not present in crystals. It is known that the LEEs are generally not impurities and are intrinsic to the glass since the same characteristic low temperature behaviour is observed even in very pure glass specimens. The phenomenological “tunnelling model” proposes that these excitations are atoms in the glass that can tunnel between two nearly degenerate states. These atoms or groups of atoms are called two level systems (TLSs). But the true identity of the LEEs is a long standing open question that continues to generate intense interest. Furthermore, the tunnelling model does not explain the remarkable quantitative universality of quantities such as the mechanical dissipation 1/Q~3×10^-4 of glasses near 1 kelvin, which is observed despite wide variations in glass composition, impurity concentration and structure.

The goal of the project is to achieve the following objectives by carrying out experiments on small glass samples with few TLSs and even individual resonant TLSs:

Objective 1: Demonstrating the existence of TLSs (with the expected number density).
Objective 2: Making a microscopic test of the phenomenological tunnelling model.
Objective 3: Determining the origin of universality.
A goal of the project is to control and measure the quantum state of individual TLSs in a glass nanomechanical resonator, using the strain field within the mechanical resonator to tune and probe the TLSs. This is an analog of cavity quantum electrodynamics in a new hybrid quantum system where the TLS plays the role of the atom and the mechanical mode plays the role of the optical cavity. I order to achieve this goal, the entire mechanical resonator, including all its degrees of freedom, must be cooled to such a low temperature that its fundamental mechanical mode is in the quantum ground state. Otherwise, higher states of the Jaynes-Cummings ladder formed by the TLS and mechanical mode become occupied, thus smearing the spectroscopic signature of the TLS. For the ~100 MHz modes of interest, this means cooling the resonator to about 1 mK for negligible occupation of the mechanical mode. Thus the mechanical resonator must be in thermal equilibrium with the cold finger of an adiabatic nuclear demagnetization refrigerator; optomechanical techniques that directly cool the mechanical mode are not sufficient.

We have constructed a system that integrates microwave optomechanical measurement capabilities with an adiabatic nuclear demagnetization refrigerator. The system reaches temperatures well below 1 mK, which is sufficient for passive cooling. We have also demonstrated thermal equilibrium of a nanomechanical mode and the cold finger of the cryostat down to 10 mK. Below this temperature, we did not observe signs of thermal decoupling of the sample, but measuring the occupation of the mechanical mode became impossible due to the increasing influence of a new force noise acting on the mechanics. We are studying this force noise in detail for two reasons: (1) to determine its origin and eliminate it and (2) because it is of basic scientific interest.

Interactions between two level systems are thought to be responsible for the quasi-universal properties of amorphous solids. It is thus natural to investigate glass samples that are smaller than the expected interaction length scale (~300 nm) to check whether the effects of interactions become less significant. We are studying both nanomechanical strings, in which two dimensions are sub-micron, and thin films, in which one dimension is sub-micron. In the case of the thin films, we have eliminated an unexpected parasitic heat source in our new cryogen-free dilution refrigerator in order to eliminate thermal decoupling of the sample down to 10 mK. These measurements reveal that, below 30 mK, the internal friction of a 300 nm thick glass film exceeds the internal friction expected in the absence of TLS/TLS interactions. Since 300 nm is the expected interaction length scale, this suggests that the interaction length scale is much less than 300 nm or that the internal friction has a different origin.
Microkelvin refrigeration technology has enabled ultra-low temperature measurements of condensed matter for decades. Traditional quantum optomechanics, and now microwave quantum optomechanics, are also becoming mature technologies. We have developed the first measurement platform combining high sensitivity optomechanical measurements with a refrigerator reaching sub-mK temperatures. This capability will be instrumental for the success of the second half of UNIGLASS, in which we will pursue passive cooling of a nanomechanical mode to 1 mK. This has not yet been achieved in the case of a ~100 MHz, high quality mechanical mode. Ground state cooling of the mechanical mode and resonant two level systems will allow measurements that reveal a great deal about the nature of amorphous solids.

Our existing nuclear demagnetization refrigerator reaches 300 microkelvin, making it one of only a few cryostats in the world that can cool condensed matter samples well below 10 mK. However, the pre-cooling stage is a conventional “wet” dilution refrigerator. The system therefore has some disadvantages. In particular there is limited space for the bulky microwave components our experiments require, it uses a great deal of liquid helium, and it must be thermally cycled after approximately two weeks. Consequently, we are developing the first continuous nuclear demagnetization refrigerator (CNDR), which will be integrated with our modern cryogen-free “dry” dilution refrigerator. The system will provide much more experimental space, will maintain sub-mK temperature continuously and will be fully automated. One challenging aspect of this work is that the pulse tube in cryogen-free systems that replaces the liquid helium bath in conventional systems produces vibrations that will lead to a larger heat load on the integrated CNDR. Consequently, we need to achieve an extremely low thermal resistance between the two stages of the CNDR, in particular at the joint between the copper and aluminum parts of the superconducting heat switch. We recently discovered a relatively simple method for joining aluminum and copper such that the thermal resistance requirements are satisfied. Furthermore, we found that using a CNDR configuration with two nuclear stages in parallel will be much more efficient than one with two stages in series for the same thermal resistance of the heat link. These promising results make the construction of a prototype CNDR appear feasible. Such a system would open the microkelvin temperature range to a much broader segment of the physical sciences community.
Glass nanomechanical resonator with atomic tunneling two level systems
Amorphous silicon nitride nanoelectromechanical system