Temperature dependence of the frequency and noise of superconducting coplanar waveguide resonators

Abstract

We present measurements of the temperature and power dependence of the resonance frequency and frequency noise of superconducting niobium thin-film coplanar waveguide resonators carried out at temperatures well below the superconducting transition ͑T c = 9.2 K͒. The noise decreases by nearly two orders of magnitude as the temperature is increased from 120 to 1200 mK, while the variation of the resonance frequency with temperature over this range agrees well with the standard two-level system ͑TLS͒ model for amorphous dielectrics. These results support the hypothesis that TLSs are responsible for the noise in superconducting microresonators and have important implications for resonator applications such as qubits and photon detectors. 23 have highlighted TLS effects in superconducting microcircuits. While the TLS energy splitting ⌬E has a broad distribution, 22 a resonator with frequency f r is most sensitive to TLS with ⌬E ϳ hf r . The level populations and relaxation rates of such TLS vary strongly at temperatures T ϳ hf r / 2k B , or around 100 mK for the device studied here. Furthermore, such near-resonant TLS may saturate 18 for strong resonator excitation power P w . Hence, measurements of the power and temperature variation of the resonator frequency and noise, as presented in this letter, provide a strong test of the TLS hypothesis.We studied coplanar waveguide ͑CPW͒ quarterwavelength resonators 2,18 fabricated on a high-resistivity ͑ ജ 10 k⍀ cm͒ crystalline silicon substrate by patterning a 200 nm thick niobium film using a photoresist mask and a SF 6 inductively coupled plasma etch. In this device, TLS may be present in the native oxide surface layers on the metal film or substrate. 18 The resonator is capacitively coupled to a CPW feedline ͑Fig. 1͒ that has a 10 m wide center strip and 6 m gaps between the center strip and the ground plane. For the resonator, these dimensions are 5 and 1 m, respectively. The resonator length is 5.8 mm, corresponding to f r = 4.35 GHz. The coupling strength is set lithographically 17,18 ͑see Fig. 1͒ and is characterized by the coupling-limited quality factor Q c =5ϫ 10 5 . The device was cooled using a dilution refrigerator, and its temperature was measured to Ϯ5 mK accuracy using a calibrated RuO 2 thermometer mounted on the copper sample enclosure. The microwave readout ͑Fig. 1͒ uses a standard IQ homodyne mixing technique. 2,17 The IQ mixer's complex output voltage ͑f͒ = I͑f͒ + jQ͑f͒ follows a circular trajectory in the complex plane as the microwave excitation frequency f is varied, 18 and f r and Q r are determined by complex leastsquares fitting of this trajectory to a ten-parameter model:Here ␦x = ͑f − f r ͒ / f r is the fractional frequency offset, S 21 ͑r͒ is the complex forward transmission on resonance, B 0 + B 1 ␦x allows for a linear gain variation, 0 + 1 ␦x allows a similar linear phase variation, and B 2 and 2 specify the output offset voltages of the IQ mixer. The combined noise of the resonator and readout electronics is measured by tuning the synthesi...

A semiempirical model for two-level system noise in superconducting microresonators

“…͑5͒ predicts that the resonator noise is independent of microwave power, contrary to our observations 3,7,8 which are made at the relatively high power levels of interest for detector applications.…”

“…Excess frequency noise is universally observed in these resonators 2,5,6 and is very likely caused by two-level systems ͑TLSs͒ in dielectric materials. 3,7 Indeed, the TLS hypothesis is supported by the observed dependence of the noise on resonator internal power 7,8 and temperature. 3 In a recent paper 4 ͑paper A hereafter͒, we presented measurements of the TLS-induced low-temperature frequency shifts of five niobium ͑T c = 9.2 K͒ coplanar waveguide ͑CPW͒ resonators with varying center strip widths s r .…”

“…All resonators display a power dependence close to S ␦f / f r 2 ϰ P int −1/2 as we have previously observed. 3,7,8 In order to study the geometrical scaling of the noise in more detail, we first fit the noise versus power data for each resonator to a simple power law, and retrieve the values of the noise S ␦f ͑2 kHz͒ / f r 2 at P int = −25 dBm for each geometry. These results ͑Fig.…”

Microwave Resonators for Weak Light Detection at Telecom Wavelength

“…As a consequence, the relevant observations could not be explained by the standard MBT. Recently, an approach beyond the MBT has been proposed by considering the coherent effects of the quantized two-level systems [16,[21][22][23] on top of the resonator film due to the existence of native oxides layer [14,16]. Practically, before the measurement, the device has to be exposed to the air environment for preparation, thus a severalnanometer-thick native oxide layer could be formed on top surface of the resonator.…”

“…At around 20 mK base temperature of the DR, we measured the microwave transport characteristics |S 21 | curves of the CPW using the connected vector network analyzer (VNA) with a −48 dBm driving power. As the λ/4 resonator will reflect the signals at its resonant points, the resonant feature of the S 21 parameter through the VNA should be a series of narrow dips, showing the frequency-dependent feature of the measured superconducting resonator.…”