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.
