Kinetic induction detectors (KIDs) are showing promise in a variety of low-light photometry applications, particularly in observing the B-mode polarization of the cosmic microwave background. Under certain noise source assumptions, we propose a new dual-resonator design that would allow TLS noise to be observed independent of the signal and thus canceled. I would like to thank Professor Jonas Zmuidzinas, my advisor, for his guidance on this thesis.
And, of course, I would like to thank my mother and father: my father, who inspired me from an early age for physics and research, and my mother, who ensured that I could write this thesis.
Cosmic Microwave Background
Other disturbances in the cosmic medium, such as local density fluctuations, also create E-mode polarizations, with B-mode polarizations being quadratically suppressed. A number of attempts are underway to make precise measurements of the B-mode polarization of the cosmic microwave background. By placing constraints on the development of the early universe, parameters of cosmological models and standard models can be derived to new levels of accuracy, including inflation rates and neutrino masses.
BICEP and the Keck Array
The circuit material is necessarily superconducting, so losses due to resistance are low (but not zero): on the contrary, imperfect coupling through the coupling capacitor (top of figure 2.1) limits the quality of the resonator. The factor of two arises because Cooper pairs have twice the mass of charge carriers, being formed from two carriers. Since all other parameters in this connection will remain essentially fixed in a given circuit, any change in ns will account for a change in inductance.
By playing tones on the transmission line near the resonant frequency of the resonator and observing what results.
KID Noise
The magnet falls into the new potential of its dipoles, gains thermal excitation, but gives up entropy in the dipoles. In addition to assessing their sensitivity, there is a question of considering what types of noise are observed in the detectors. We chose niobium for our test, which has a relatively large band gap, specifically to suppress this type of noise: its critical temperature is 9.26K, one of the highest of all elemental superconductors.
In order not to "drown" the detector in energy when the test tone is sent to the transmission line, the tone must be very small in power. However, if such a tone is transmitted externally, it will be completely drowned out by thermal noise in the transmission line itself. Radio waves or a pulse tube, for example, can produce oscillating fields that can induce small currents in the resonator.
So there is a small increase in inductance when the average current in the resonator is higher. This effect is actually exploited in so-called non-linear KIDs where deliberate excitations are now used to "tune" the kinetic inductance, and thus the resonator frequency, to a different value at the time of the experiment (Kher, 2017). The last type of noise is the one with the least complete model of its operation, and the one we focus on tackling.
The surface of the superconducting metal is typically coated with a thin oxide layer, which will be amorphous and not participate in the superconductivity. These dominate at relatively low frequencies, below 1Hz, meaning that there is no strict order between TLS and other noise sources in terms of amplitude.
Dynamics: TLS Noise and Resonators
If such a TLS is then coupled to a nearby superconductor, it is possible for the TLS to modulate effective parameters of the superconducting material (such as carrier density or critical temperature) during switching. The blue line is the true resonator response as would be observed at infinitesimal beam power. The energy absorbed is proportional to the excitation of the resonator, so only the near resonance is important.
During a sweep in the tone frequency of the beam, the frequency of the resonator will change. Falling Frequency Chirp: This produces the orange line and pushes the low end of the beak out. This is robust and requires only demodulation (as opposed to a full FFT), but provides less redundancy in fitting the resonance curve.
As to the precise origin of the TLS noise on the circuit, there are mixed results. The evidence is unclear, because a series of unrelated experiments seemed to show that the magnitude of TLS depends only on the width of the wire in the inductor (but not on its length). If we assume that all the radiation ends up on one of the inductors – say L2 – then there are three unknowns: the inductance (which tells us the incoming radiation speed) and the capacitance of each of the two capacitors.
It is worth noting that if it turns out that TLS noise is a function modulating inductance, rather than capacitance, then the above circuit topology will still work due to the reciprocity of capacitors and inductors. However, this would not provide any advantages for light detection, as movement of the inductance would be both our signal and noise and therefore indistinguishable.
Symmetric resonators
Capacitor simulations
All our capacitors had a finger width of 2µm, interfinger spacing of 2µm, a terminal width of 3µm and an end gap of 2µm. The gaps were more conservative (larger) than the gaps in the inductor, because any short circuit in the capacitor would lead to total failure of that entire double resonator. Where the test dimensions were chosen to give a fixed FO/FP ratio of 2.1µm, so we only had to fit along one dimension.
Inductor simulations
Layout
To improve this situation, we etch away the back of the chip, leaving 2 mm of air between the capacitor and the ground plane. This was also what led to our decision on how large our coupling capacitor should actually be. To estimate whether or not the geometric inductance of the layout will play a role, we want to calculate whether or not two resonator loops will couple together.
It is possible that the geometric inductance of the loops could affect the resonant frequencies slightly, but it will do so geometrically: the symmetry of the design means that any geometric inductance will shift the overall system down, but it will still perform well in terms of TLS cancellation if the same each half of the dual resonator affected.
GPU readout
These three were put under a microscope to look for defects - shorts in the capacitors, mainly - and exactly one was defect-free. We believe this can be attributed to geometric inductance in the circuit design, which increases the effective resonant mass. At the bottom is the line connecting the two resonators, pulling down to the right.
Vertically in the middle is the inductor, and to the left is the capacitor. The small box in the middle is the coupling capacitor, which attaches the lumpy element to the transmission line. As a specific example, one spectrum can be seen at Figure 5.4; the others are collected in Figure 5.5.
Here we dominate the uncertainty that comes from the reading itself, the noise in the transmission line. As can be seen in plots 2 and 5 of Figure 5.5, at high enough powers the noise barely starts to creep back up, as we are injecting enough power to excite the device. Ideally we would have seen an upward slope to the left, as TLS noise goes as 1/f1/2 in power (1/f1/4 in amplitude), and so should gradually start to dominate at low frequencies.
The real test for this chip is looking at the cross-correlation in the noise between two resonators in a pair. The intention was that this additional oxide would connect more two-level systems to the wire to create more TLS noise.
Oxidized chips
When it became clear that these devices did not show enough TLS noise that we could find, our group decided to make another batch of chips with a layer of silicon oxide placed over them. To characterize whether this was TLS or not, we did a network analysis of the resonance at a variety of temperatures and tone strengths. The dependence on the resonance frequency and Q (quality factor) would then be a good indicator of the dynamics.
Comparison with expected TLS
We don't really understand why our chips didn't show TLS, or at least failed to show correlated TLS that we could detect. It is also surprising that the addition of the extra SiO coating did not seem to create much more TLS and that the quality of the resonators actually increased noticeably when the oxide layer was applied. Although we initially hoped to see a strong correlation in the TLS noise as soon as we inserted the chip, this did not happen and it is not clear why.
Our group will continue to investigate this issue by more carefully characterizing the sound of each chip. It is possible that TLS is somehow dependent on alumina and other oxides, in a way that is not nearly as evident with niobium and silica. To respond to our specific question of whether this detector design allows us to neutralize TLS, we can only say that this is inconclusive, as we have not yet been able to convincingly identify TLS noise to neutralize.
That the resonators must be coupled in terms of any noise on their capacitors is almost certainly still going to apply, but it is possible that the design will ultimately fail, if the TLS noise manifests mainly on the sense inductor. To outline specifically what we want to do in the future, we need to more carefully characterize the chips we have, both oxidized and not. To be satisfied with our understanding of these chips, we will need to look at a noise spectrum at each of a variety.
