Periodic Reporting for period 4 - UNIGLASS (The Enigmatic Universality of Glass)
Reporting period: 2022-03-01 to 2024-02-29
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 low temperature properties of glass are particularly intriguing. Below 1 kelvin, the thermal and mechanical behavior 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. 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. The goal of the project is to test the tunnelling model by carrying out experiments on small glass mechanical resonators with few TLSs and even individual resonant TLSs
We demonstrated, for the first time, passive cooling of mechanical resonators to their ground state at sub-mK temperatures. We also elucidated a barrier that must be surmounted to cool some glass mechanical resonators all the way to their quantum ground state, particularly those with a string geometry. Surprisingly, the barrier is not thermal decoupling of the vibrating string from the substrate. It is instead a kind of random force noise that we reported for the first time in the scientific literature. This noise is not an artifact of some particularity of our fabrication or measurement process as it was subsequently reproduced on different samples and cryostats and in different laboratories.
While this random force noise is a nuisance in that it prevents us from demonstrating ground state cooling of some devices (especially strings), it is also interesting from a scientific perspective. The fact that it occurs only at specific frequencies, i.e. at the microwave drive frequency +/- the mechanical resonance frequency, implies that it originates from an on-chip optomechanical process. It is not due to, for instance, spurious peaks in the output spectrum of the microwave generator. It is conceivable that the force noise is a signature of the TLS. Theoretical work is required to explore this possibility.
Additional conclusions of the action not foreseen in the project proposal are as follows: understanding the interplay of electron-driven relaxation of TLS and dimensionality in nanomechanical resonators; the contribution of “undercut” in the fabrication of mechanical beams to their soft clamping; the possibility to probe phonon transport by monitoring the vibrations of mechanical resonators; the factors dominating the temperature dependence of optomechanically induced transparency and absorption; the suitability of fully suspending beams for probing quantum fluids; development of components with extremely low thermal resistance and extremely low susceptibility to eddy current heating for powerful continuous nuclear demagnetization refrigerators; models of the cooling power of continuous nuclear demagnetization refrigerators; strong electrostatic coupling to high quality, insulating mechanical resonators; non-linear coupling in microwave optomechanics; and mitigation of sample heating and vibrations in cryogen-free cryostats.
We demonstrated, for the first time, passive cooling of mechanical resonators to their ground state at sub-mK temperatures. We also elucidated a barrier that must be surmounted to cool some glass mechanical resonators all the way to their quantum ground state, particularly those with a string geometry. Surprisingly, the barrier is not thermal decoupling of the vibrating string from the substrate. It is instead a kind of random force noise that we reported for the first time in the scientific literature. This noise is not an artifact of some particularity of our fabrication or measurement process as it was subsequently reproduced on different samples and cryostats and in different laboratories.
While this random force noise is a nuisance in that it prevents us from demonstrating ground state cooling of some devices (especially strings), it is also interesting from a scientific perspective. The fact that it occurs only at specific frequencies, i.e. at the microwave drive frequency +/- the mechanical resonance frequency, implies that it originates from an on-chip optomechanical process. It is not due to, for instance, spurious peaks in the output spectrum of the microwave generator. It is conceivable that the force noise is a signature of the TLS. Theoretical work is required to explore this possibility.
Additional conclusions of the action not foreseen in the project proposal are as follows: understanding the interplay of electron-driven relaxation of TLS and dimensionality in nanomechanical resonators; the contribution of “undercut” in the fabrication of mechanical beams to their soft clamping; the possibility to probe phonon transport by monitoring the vibrations of mechanical resonators; the factors dominating the temperature dependence of optomechanically induced transparency and absorption; the suitability of fully suspending beams for probing quantum fluids; development of components with extremely low thermal resistance and extremely low susceptibility to eddy current heating for powerful continuous nuclear demagnetization refrigerators; models of the cooling power of continuous nuclear demagnetization refrigerators; strong electrostatic coupling to high quality, insulating mechanical resonators; non-linear coupling in microwave optomechanics; and mitigation of sample heating and vibrations in cryogen-free cryostats.
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. In 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. 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.
As explained in the first paragraph of this section, the temperature of the mechanical resonator must be inferred from its thermomechanical noise, measured by coupling the mechanical resonator to a microwave resonator-based interferometer. This is what we achieved in 10.1103/PhysRevApplied.12.044066.
We found that, unlike strings, mechanical resonators with a drum geometry have a much lower susceptibility to the force noise reported in 10.1103/PhysRevApplied.12.044066. As described in 10.1038/s41467-021-26457-8 we achieved ground state cooling of a sample containing TLS. This was the first time that a MHz frequency mechanical mode was cooled to its ground state purely by good coupling to the cryostat, i.e. without using optomechanical damping. This is an essential step toward finding individual TLSs. In 10.1007/s10909-024-03072-7 we argue that no one has achieved this goal so far and that the system we developed in the framework of the UNIGLASS grant is well suited to achieving it.
Achieving quantum control of a mechanical mode requires a long enough mechanical coherence time so that the quantum state of the mode can be manipulated. Furthermore, initialization of the state must be carried out near 1 mK so that the TLS population in the mechanical mode is significantly polarized. Progress toward this goal was presented at the 2024 Gordon Conference on Mechanical Systems in the Quantum Regime. In particular, we succeeded in cooling a highly coherent nanomechanical drum to 1.5 mK. Under the assumption that the mechanical mode remains in thermal equilibrium, this implies a 150 msec mechanical coherence time that matches the state of the art, along with a 10 times higher optomechanical coupling strength.
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.
As explained in the first paragraph of this section, the temperature of the mechanical resonator must be inferred from its thermomechanical noise, measured by coupling the mechanical resonator to a microwave resonator-based interferometer. This is what we achieved in 10.1103/PhysRevApplied.12.044066.
We found that, unlike strings, mechanical resonators with a drum geometry have a much lower susceptibility to the force noise reported in 10.1103/PhysRevApplied.12.044066. As described in 10.1038/s41467-021-26457-8 we achieved ground state cooling of a sample containing TLS. This was the first time that a MHz frequency mechanical mode was cooled to its ground state purely by good coupling to the cryostat, i.e. without using optomechanical damping. This is an essential step toward finding individual TLSs. In 10.1007/s10909-024-03072-7 we argue that no one has achieved this goal so far and that the system we developed in the framework of the UNIGLASS grant is well suited to achieving it.
Achieving quantum control of a mechanical mode requires a long enough mechanical coherence time so that the quantum state of the mode can be manipulated. Furthermore, initialization of the state must be carried out near 1 mK so that the TLS population in the mechanical mode is significantly polarized. Progress toward this goal was presented at the 2024 Gordon Conference on Mechanical Systems in the Quantum Regime. In particular, we succeeded in cooling a highly coherent nanomechanical drum to 1.5 mK. Under the assumption that the mechanical mode remains in thermal equilibrium, this implies a 150 msec mechanical coherence time that matches the state of the art, along with a 10 times higher optomechanical coupling strength.
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 is instrumental for passive cooling of nanomechanical resonators below 1 mK.
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. 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. We recently discovered a relatively simple method for joining aluminum and copper such that the thermal resistance requirements are satisfied, going well beyond the state of the art.
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. 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. We recently discovered a relatively simple method for joining aluminum and copper such that the thermal resistance requirements are satisfied, going well beyond the state of the art.