Thanks also to Peter Day, Byeong Ho Eom, and Rick LeDuc at JPL for the construction and initial testing of the array of resonator bolometers. This resonator bolometer takes advantage of the scalability offered by the use of superconducting microresonator technology, together with the versatility offered by the use of a thermally isolated island. The quantities C,G and noise equivalent in the bolometer can be calculated based on the fundamental dimensions and properties of the device.
The presence of quasiparticles and the finite inertia of the Cooper pairs result in a complex conductivity σ(ω) =σ1(ω)−iσ2(ω) as described by the Mattis-Bardeen theory [10]. By varying the capacitor area, the capacitance and thus the characteristic resonant frequency of the pixel can be varied in a controlled manner according to ω= (LC)−1/2. By varying the frequency of the current on the feed line and thus sampling many points near and within the resonance, the dissipation and phase changes can be quantified and the original absorbed energy determined.
The interlocking capacitor, at the top, can be varied in size to control the pixel's resonant frequency. In the center, the meandering inductor, which acts as a photon absorber, takes up most of the pixel area.
Frequency multiplexing
Photon absorption
Two level systems
The resonator bolometer
Fabrication
To begin exploring the feasibility of the resonator bolometer concept, a series of prototypes were built at NASA's Jet Propulsion Laboratory (Figure 1.6). NbTiN was deposited and patterned on a silicon nitride layer on a silicon substrate. Finally, silicon was etched from under the grid to suspend the inductors and thus thermally isolate them.
Overview
Measurement setup
Fitting for the resonant frequency and quality factor
The uncalibrated data trace a circle centered at the origin of the off-resonance frequencies. Points at frequencies away from the resonance cluster around (1,0). d) Amplitude and (e) phase of the calibrated transmitted signal, with the plotted points equal in frequency. The measurements obtained can be neatly divided into dark measurements, where the array and cryostat windows were covered to prevent optical radiation from reaching the array, and measurements under illumination, where a controlled radiation source was placed in front of the cryostat window to illuminate the detector. .
Both types of measurements are of interest for the characterization of this group; Dark measurements provide a glimpse into operating capabilities in very low light conditions and allow the most fundamental and characteristic sources of noise to dominate and be studied. In contrast, illuminated measurements are more similar to how this array might be used for science, so they provide a more concrete picture of the array's potential performance. I will start by presenting the results of the dark measurement and later I will compare them with the results of the illuminated measurements.
Temperature dependence
The data points are plotted in red, with the fit from Mattis-Bardeen theory (Appendix A) in blue. The fit is a best fit line; the superconducting transition temperature Tc was allowed to vary to find the curve that best fit the data. The curve shown corresponds to Tc = 13.7K, which is the value for which the material is designed.
The gap in the data near 2.2 K is the lambda point of liquid helium, where it transitions from superfluid to normal liquid and the associated large change in heat capacity causes a jump in temperature. For the region where Mattis-Bardeen theory is valid, the points map to a line whose slope is β, the ratio of the change in frequency to the change in dissipation from the same signal. The resonance frequency fr before the change is at a different position after the change; the fractional frequency shiftxis therefore (frold−frnew)/frnew.
Response
Thermal conductance calculation
Measurements of the phonon noise (see section 3.3.3 below) fit the yield of the T3power law, in nW/K.
Results
Noise
Data collection and processing
From the initial resonance scan, a mapping is made between the generator frequencies and the points on the resonant loop, and the fractional frequency shiftx for each point is calculated (Eq. The power spectral density quantifies the power carried by each frequency component of a stochastic process (in this case, a noise data stream) and is usually given in watts/Hz This is normalized by dividing by the total power in the signal to give the fractional frequency noise Sxxin (Hz)−1.
Noise sources
Each data point in the green spread is assigned to a frequency using the fit to a frequency scan across the resonance (black points). The green box indicates the frequencies that are important for the NEP calculation; higher frequencies will not be used for scientific applications and non-detector based noise takes over at lower frequencies.
Dark noise results
While most of the procedure remains the same for the corresponding measurements under illumination, especially the data processing, the experimental setup changes significantly with the addition of an external light source. In this chapter I will explain some of these extra procedural challenges and present the results compared to the corresponding dark measurement.
Optical response measurement
Time Constant
Light from a black body held at a fixed temperature is modulated by rotation of the chopper wheel. An aluminum plate covered with an absorbent material placed in front of the chopper with a small hole for the opening ensures that off-axis radiation entering the cryostat comes from a homogeneous source. temperature under optical strain, with a polynomial fit to the data. A terahertz radiation source was used to ensure that the transitions between low and high intensity were fast compared to the time constant of the bolometer. a) Response to a pulse of THz radiation (b) Fit to the response decay.
Noise under illumination
Although the overall structure is similar, the noise under illumination is higher than the roll-off of phonon noise, reflecting the presence of photon noise. The red data points are the noise under illumination, while the blue data points are under dark conditions. Adding a constant photon NEP, modulated by the detector response and added to the phonon and TLS noise determined from the dark data, yields good agreement with the data for T>2.5K.
Photon noise is added to phonon and TLS noise as appropriate from the dark data.
Noise equivalent power
The discrepancy between photon NEP and NEP measured under illumination is being investigated. P is the power absorbed by the detector, and as such depends on (1) the optical charge entering the cryostat, (2) the characteristics of the filters in the light path, and finally (3) the spectral dependence of the detector absorption. 2) and (3) are currently uncertain and under investigation: (2) because out-of-band transmission can contribute significantly to detector loading and (3) because, as this is a new prototype device, the absorption properties of resonator bolometers have been neither experimentally measured nor modeled. Starting with this simpler case, I used finite element structure simulator software to approximate the design of the device.
The measurements presented here form a comprehensive characterization of the array of resonator bolometers and point towards several avenues of further research. For example, depositing the capacitor directly on the silicon substrate instead of a silicon nitride layer should significantly reduce TLS noise. Removing this analog component not only reduces complexity, but significantly lowers cost and removes a potential source of electronic noise from the system.
One of the first applications envisioned for this technology is monitoring Earth's climate from a satellite in low Earth orbit. For this application, the loading conditions measured in the laboratory and shown here are comparable. Under these conditions the device has been shown to be photon noise limited with sufficient dynamic range and therefore almost an ideal device.
To increase the mapping speed, the optical efficiency of the detector must be improved and we are actively working on this aspect of the device. The Mattis-Bardeen theory of the anomalous skin effect in superconductors [10] can be used to infer the behavior of the resonance when the temperature of the superconductor varies.
Temperature dependence of f r
2−(E−~ω)2[1−2f(E)], (A.1) where σn is the normal state conductivity, ∆≈3.5kBTc is half of the Cooper pair binding energy, ω is the angular resonant frequency, and (E) is the distribution function for quasi-particles, given by f(E) = 1/(eE/kT + 1) in thermal equilibrium.
Temperature dependence of Q i
The resonator ring-down time τres is defined as the inverse of damping, so in terms of quantities that can be easily found from fitting resonances. Physically, the resonator ring-down time is the time scale on which the resonator loses energy during oscillation. The bolometer time constant (sec 4.2) is by design much larger than the decay time of the resonator, so the quantity dominates in our measurements.
An accurate NEP under load can only be determined if the optical power reaching the detector is known. This requires knowledge of both the absorption of the filters in front of the detector and the spectral dependence of the absorption of the detector itself. To reliably report the amount of radiation absorbed by the detector, we modeled the absorption of a single pixel.
Description of circuit
Analytic solution to simplest case
The former is provided by the specification sheets for the filters, but the latter must be measured or modeled. Minimum transmission occurs when the substrate thickness is an even integer multiple of a quarter wavelength. In the case where n is even, we are dealing with multiples of half-wavelengths, so the magnitude of the voltage is the same at both ends of the silicon section.
A simplified circuit is a free space in series with the free space and a 50 Ω sheet resistor to ground in parallel. In case n is odd, the equivalent impedance of the Si section plus the load (free space in parallel with the 50 Ω sheet resistance) is ZSi2/Load, so the reflection coefficient is the same.
