CONCLUSIONS

8.1 Summary of Results

In this thesis, we presented our progress towards a microwave-to-optical transducer using rare-earth ions simultaneously coupled to a microwave and optical cavity.

We identified a promising material in Er³⁺:YVO₄and performed spectroscopy and simulations to characterize its performance.

We then designed the transducer using a Er³⁺:YVO₄substrate with a superconduct- ing microwave resonator and photonic crystal optical resonator patterned on the substrate. The design was optimized to maximize the efficiency and relative ease of fabrication.

A new nanofabrication process was developed to deposit and pattern both the optical and microwave resonators on the Er³⁺:YVO₄ substrate. A microwave, optical, and cryogenic measurement set-up was assembled for characterizing the transducers.

These included optical, microwave, and magnetic field control within a dilution fridge, a heterodyne detection setup for transduction readout, narrowband optical filtering for single photon detection of transduced photons, and microwave device readout with a network analyzer, spectrum analyzer, and digitizer.

The rare-earth ion microwave-to-optical transducer was then characterized in the dilution fridge. This included characterization of the optical and microwave cavity independently and also the effects of co-localizing the two resonators. Next, the transducer efficiency was characterized. We measured continuous-wave transduc- tion efficiency up to𝜂_𝑑 =3·10⁻⁹. In pulsed operation, the efficiency increased up to 𝜂_𝑑 = 2· 10⁻⁷ when 𝑃_𝑜 = 5 mW and 𝜂_𝑑 = 8· 10⁻⁸ when 𝑃_𝑜 = 550 𝜇W for 1 𝜇s pulses and 10 ms wait time between pulses. Based on the cavity coupling rates and grating coupler efficiency, an internal efficiency of 𝜂_{𝑑 ,𝑖𝑛𝑡} ∼ 1· 10⁻⁵ could be achieved at the highest optical power.

We also characterized the temperature of the erbium spins and the microwave resonator during transduction and identified regimes where the spin and microwave resonator temperatures reach 100 mK while the transducer operates in a pulsed mode. This involved either long wait times (i.e. 𝑡_{𝑤 𝑎𝑖𝑡}> 100 ms) or low optical power power (i.e. 𝑃_𝑜< 10𝜇W).

8.2 Future Works

The main improvements needed for a future device include increasing the transduc- tion efficiency and achieving low noise operation with higher duty-cycle transduction pulses at the same time. Part of this can be solved at the same time by more efficient use of the optical photons with a significantly over-coupled optical cavity and on/off chip coupling with near unity efficiency. This would allow for lower optical power to be used for similar optical Rabi frequencies to reduce the noise and higher efficiency due to better collection of the transduced photons.

Another issue with the current device is the parasitic spins. This included the even isotope erbium spins that were within the microwave cavity, but not the optical cavity that impacted the ground state transduction efficiency and the ¹⁶⁷Er spins that impacted the excited state transduction. The¹⁶⁷Er spins are easier to avoid by moving to an isotopically purified sample.

Removing the parasitic even isotope spins likely involves moving to a different fabrication platform, where the erbium spins are only within the optical cavity. This could be achieved with ion implantation (although some initial attempts at this with Er³⁺:YVO₄were unsuccessful) or by changing the platform more substantially and patterning the optical resonator directly out of the Er³⁺:YVO₄ material instead of relying on patterning amorphous silicon. This would also increase the number of spins by∼10x and the optical pump Rabi frequency by∼3x (i.e. we are no longer just relying on evanescent optical coupling). Using the adiabatic model formalism, we would expect the device mode overlap to increase by a factor of∼10x. We would expect a factor of∼100x improvement in the device efficiency for the excited state and a factor of∼10⁴x for the ground state from simulation with the linear numerical model to reach an efficiency of 𝜂_{𝑑 ,𝑖𝑛𝑡} ∼ 10⁻². Its worth noting that currently there is not a straight forward way to do this in a way that is readily available and easy to integrate with superconducting microwave resonators, so that is still an area of active research.

Another way to improve the efficiency by improving the mode overlap is to decrease the parasitic inductance of the capacitor that shunts the inductive wire. One possible solution is to change from an interdigitated capacitor to a parallel plate capacitor, which will have negligible parasitic inductance. A concern of this type of capacitor is a significant reduction in the microwave quality factor due to dielectric losses, but for our transducer, we do not require very high quality factors, and others have shown reasonable quality factors with an amorphous silicon dielectric between the parallel plate capacitor [170]. We should also note that this would require more lithography steps and would complicate the fabrication process, but we could expect a∼ 5x improvement in the mode overlap with this implementation.

It is also worth noting that potentially another rare-earth ion/host system can offer better performance compared to Er³⁺:YVO₄. However, at this point it is unclear to us exactly what that would be and it does require a significant amount of spectroscopy to find a better material.

Once a high efficiency and low noise transducer can be achieved, the next step is to integrate it with superconducting qubits. This may be a bit tricky since in the current implementation a high magnetic field of 76 mT was used and traditional superconducting qubits are not known to function within magnetic fields of that magnitude.

One possible solution is to switch to another rare-earth ion/isotope that exhibits GHz microwave transitions at zero or near zero magnetic field [57, 171].

Another possible solution is to use a noveltype of superconducting qubit that can operate in relatively large magnetic fields [172–174]. Admittedly, these are not state- of-the-art qubits as of now, but they could be used for some initial proof-of-principle demonstrations as sources of non-classical light. Potentially, the performance of certain sueprconducting qubits in magnetic fields improves as more work is devel- oped.

Assuming those two solutions are not feasible, another approach would be to have the superconducting qubit spatially decoupled from the transducer and have sufficient magnetic shielding in between the two components, while coupling them with superconducting coaxial cable for a low loss interconnect. This approach is maybe not scalable for larger integration, but could be configured for single device proof- of-principle quantum transduction with rare-earth ions.