We measured ion binding to cavities and determined the effect of optical light on the microwave resonator and atomic properties. Finally, the temperature of the components within the transducer, including the erbium ions and the microwave resonator, are characterized during transducer operation.
INTRODUCTION
- Quantum Networks
- Superconducting Qubits
- Quantum Transduction
- Rare-earth Ion Properties
- Rare-earth Ion Transducers
- On-chip Quantum Transduction with Rare-Earth Ions
- Structure of this Thesis
Another factor that can cause inhomogeneity is the doping concentration of the rare earth ion type itself. A crystal doped with rare earth ions is in the optical cavity and in the microwave cavity inductor.
REI TRANSDUCTION THEORY
Adiabatic Model
When 𝑅 is small (i.e. 𝑅 ≪ 1), the bandwidth follows the bandwidth of the narrowest cavity, in this case the microwave cavity. We can see from Equation 2.12 what the important spectroscopic properties of the rare earth ensemble are and also what microwave and optical cavity mode profiles should be used to magnify this.
Numerical Model
To have high transduction efficiency, we want the rare earth ion ensemble to have large optical and microwave dipole moments (i.e. 𝑑31, 𝑑32 & 𝜇21), high density and narrow inhomogeneity in the optical and spin transitions (as light-atom tunings should be large compared to the transition inhomogeneities). That is, in the low efficiency limit, the efficiency scales with the spectroscopic parameters as: 2.16) whereΔ𝑜andΔ𝜇 are the optical and microwave transition linewidths.
Linear Model
We can combine this result with the cavity motion equations (Equation 2.17 & 2.18) after tracking over all atoms. 2.28). We can use those initial guesses to estimate the density matrix of all atoms.
Analytical Efficiency Equation from the Density Matrix Formalism In this section, we will look at deriving an analytical transduction efficiency equationIn this section, we will look at deriving an analytical transduction efficiency equation
Transduction can also be performed by coupling the field of the microwave cavity to the microwave transitions in the excited state of the group of rare earth ions (Figure 2.3). Also, parasitic spins will cause microwave cavity drag that depends on power, temperature, and enunciation, which can make transduction in the ground more complicated to implement experimentally compared to the excited state.
YVO 4 SPECTROSCOPY
- Er 3+ :YVO 4 Properties
- Bulk Spectroscopy Setup
- Bulk Spectroscopy
- Magnetic Field Orientation
- Calculated 𝛼 Parameter
- YVO 4 Crystal Axis Orientation
𝑔𝑑𝑐 for 𝑍1, 𝑌1and𝑌2 as a function of the angle of the magnetic field from the c-axis are shown in Figure 3.5. Finally, the orientation of the magnetic field can be determined for the branching ratio of the optical transition dipoles.
TRANSDUCER DESIGN AND SIMULATION
Transducer Design Figure of Merits
From a geometric perspective of the optical cavity, the optical Rabi frequency will increase as we decrease the mode volume of the optical cavity. If we combine the two geometric factors from the mode overlap and the optical Rabi frequency to get a total optical geometric dependence of the transducer efficiency.
Transducer Design
The first is the orientation of the magnetic field relative to the resonator plane. Another important parameter of the superconducting resonator is the kinetic inductance or fraction of the kinetic inductance.
Optical Cavity Modelling
Another aspect of the optical cavity is the coupling to the optical transitions of rare earth ions. The electric and magnetic fields of the fundamental mode of TM optical waves are shown in Figure 4.3.
Microwave Cavity Modelling
We can also look at the cross section of the mode in Figure 4.15c and see how the magnetic field strength is attenuated by the inductive wire. Next, we can simulate how the magnetic field decays as a function of distance from the induction wire (Figure 4.16).
Transduction Efficiency Modelling
In Figure 4.19e we look at the efficiency as a function of the optical and spin dephasing rates. Finally, we look at the efficiency as a function of the ion-light tuning for both the optical and microwave transitions in Figure 4.19f.
FABRICATION PROCESS
Sample and Surface Preparation
After polishing, the samples are cleaned with solvent in acetone and isopropyl alcohol and then rinsed in deionized (DI) water. The samples are coated with a ~5 nm thick aluminum oxide (Al2O3) film using an Oxford Instruments FlexAL ALD System.
Niobium Fabrication
In order to remove the resist residue remaining on the niobium surface after development, a 1-minute O2 plasma descum was done at 150 W. The niobium films were etched using an inductively coupled plasma reactive ion etch ( ICP-RIE) process in an Oxford Plasmalab System 100 (III-V) etcher to transfer the pattern from the aluminum hard mask to the niobium film.
Amorphous Silicon Fabrication
The SF6/C4F8 ratio was chosen to maintain vertical sidewalls in the amorphous silicon during etching. Importantly, the hard aluminum mask on the niobium surface also protects the niobium film during etching of amorphous silicon.
Transducer Packaging
The amorphous silicon films were etched using a pseudo-Bosch process with parameters detailed in Table 5.4. Figure 5.7 shows an image of the packaging without a lid and with a lid.
Sputtering Tool
After several months of pumping with the cryopump, the pressure would drop below the range of the ion gauge (ie, one way to determine the quality of the niobium films is to measure the film's critical temperature.
Dilution Fridge Set-Up
These focus on the cryogenic components within the dilution refrigerator and also on the associated room temperature components used for device characterization and transduction measurements. The experimental transduction setup includes 4) a superconducting magnet, 5) gas tuning line, 6) microwave coax, 7) sample and package, and 8) optical fiber and piezo stack.
Microwaves
This includes optical and microwave signal generation, dilution refrigerator setup, and optical and microwave signal detection. The output microwave signal from the refrigerator is amplified with an LNA (WanTcom WBA2080-35A) at room temperature to further amplify the signal before detection on a network analyzer (Copper Mountain C1209), spectrum analyzer (Keysight FieldFox N9915A), or digitizer (AlazarTech ATS9130).
Optics
A fiber circulator (OZ Optics) is used to input light onto the optical fiber entering the refrigerator and direct the output photons from the device to the detection path.
Magnetic Fields
Gas Tuning
Due to the multimode nature of our optical cavity, we would need to tune the optical cavity up to -3 nm at most. To condense the gas into the optical cavity, a resistance heater (typically set to ~8 W) is applied to the copper tube of the 4 K stage, which heats the tube and allows some of the frozen gas to deposit on the optical resonator.
Transduction Detection Set-Ups
The Fabry-Perot filters are frequency stabilized to the transduction light frequency by PDH locking using a low-frequency phase EOM on the laser, and feedback from the laser servo is applied to the Fabry-Perot piezo through a high-voltage amplifier (Vescent SLICE-DHV) in a pulsed operation. The SNSPD has a total detection efficiency of 50%, which includes all losses from the fiber outside the refrigerator to the detector itself (ie fiber loss from the coiled fiber in the refrigerator and splice loss).
Filter Characterization
The insertion loss at the filter arrangement is 12 dB, with most of the loss coming from the insertion loss of the two Fabry-Perot filters (∼7.8 dB) and the remaining loss coming from the optical MEMS switches, fiber circulators, the 2 km delay fiber and all fiber optic connections. While the cavity is actively locked, the normalized transmittance remains approximately 98.5% of maximum transmittance for the duration of the measurement.
Microwave Noise Measurements
6.1) where 𝑃𝑜𝑢𝑡 is the detected power on the spectrum analyzer or digitizer, 𝑁𝑜𝑢𝑡 is the output noise photon number (reference before the amplifier chain), BW is the detection bandwidth of the detector, 𝐺 is the gain of the detection the temperature, and𝑁𝑎 𝑑𝑑 is the additional noise of the tracking setup. This is the calibration for𝜔𝜇/2𝜋=4.933 GHz, but we observe similar parameters for nearby frequencies that we also calibrate.
TRANSDUCER MEASUREMENTS
Preliminary Devices
These measurements were performed in a confocal microscope setup at room temperature (more details on the setup can be found in Evan Miyazono's thesis [161]) using an erbium-doped fiber amplifier (EDFA) as a broadband source and a spectrometer (Princeton Instruments SP2750i) for optical detection. The different amplitude of the modes and the envelope of the reflection measurement are given by the EDFA output power spectrum.
Transducer Device Characterization
At high microwave power, the intrinsic quality factor is lower compared to no optical power. We then looked at how the intrinsic quality factor changed as a function of optical power at three different microwave power levels, as shown in Figure 7.10.
CW Microwave to Optical Transduction
At about 60 mT, we observe a split in the signal corresponding to strong coupling of the ground state spins to the microwave cavity. For microwave input, we need to calibrate the microwave losses of the input microwave signal from the microwave source to the superconducting coupling waveguide.
Pulsed Excited Transduction with Single Photon Detection
We also measured the pulse transduction efficiency as a function of the input microwave power (Figure 7.22b). Next, we looked at the transduction efficiency as a function of the magnetic field in Figure 7.23a.
Pulsed Ground State Transduction with Single Photon Detection
First, we are not taking into account hyperfine 167Er transitions in the simulation, which may degrade the efficiency slightly, although we choose the magnetic field to minimize their effect. Also, the optical dephasing and spin rates used in the simulation (i.e.
Transducer Temperature and Noise Measurements
First, we looked at the microwave noise as a function of the waiting time between pulses (Figure 7.30). Finally, we looked at the microwave noise as a function of the optical pulse power (Figure 7.32).
Other Transducer Device Results
We also found that this noise corresponds to photoluminescence from ions in the bulk of the crystal (i.e. not from our cavity), so this is not fundamental to an REI transducer and not a problem if we remove those ions in future devices. Nevertheless, the value is already quite small due to the high extinction of the filtering that removes most of the photoluminescence noise and the time domain filtering associated with short transduction pulses (i.e. the pulse length is much shorter than the optical lifetime).
CONCLUSIONS
Summary of Results
We also characterized the temperature of the erbium spins and microwave resonator during transduction and identified regimes where the spin and microwave resonator temperatures reach 100 mK while the transducer is operating in a pulsed mode.
Future Works
One possible solution is to replace the intermediate finger capacitor with a parallel plate capacitor, which will have negligible parasitic inductance. 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].
BIBLIOGRAPHY
Tkalčec, A.et al. Strong coupling of an Er3-doped YAlO3 crystal to a superconducting resonator. Physical Review B90.https://doi.org/10.1103/. Xie, T.et al.Characterization of Er3+:YVO4 for microwave-to-optical transduction.Physical Review B104.https://doi.org/10.1103/physrevb.
FIB NANOBEAM FABRICATION
Another issue during pinhole milling of photonic crystals was the displacement of the FIB relative to the sample. The 45° couplers would be milled as the final FIB step, which was our method for coupling light into and out of the photonic crystal cavities.
CW TRANSDUCTION AT HIGH MICROWAVE POWER
