We have illuminated a thin-film superconducting Al lumped-element microwave resonator with 780 nm light and observed the resonator quality factor and resonance frequency as a function of illumination and microwave power in the 20 to 300 mK temperature range. The optically induced microwave loss increases with increasing illumination but decreases with increasing microwave power. Although this behavior may suggest the presence of optically activated two-level systems, we find that the loss is better explained by the presence of nonequilibrium quasiparticles generated by the illumination and excited by the microwave drive. We model the system by assuming that the illumination creates an effective source of phonons with energy higher than double the superconducting gap and solve the coupled quasiparticle-phonon rate equations. We fit the simulation results to our measurements and find good agreement with the observed dependence of the resonator quality factor and frequency shift on temperature, microwave power, and optical illumination. Examination of the model reveals approaches to reducing optically induced loss and improving the relaxation time of superconducting quantum devices.
I describe my contributions towards a hybrid quantum system that would have coupled 87Rb atoms to a superconducting device. I first discuss my work coupling an optical fiber to a translatable thin-film LC lumped-element superconducting Al microwave resonator operating at 100 mK in a dilution refrigerator. The LC resonators had resonance frequencies f0 of 6.15 GHz, quality factors Q of 1.5 x 105 to 6.5 x 105 at high powers, and were mounted inside a superconducting aluminum 3D cavity with a resonance frequency of 7.5 GHz and Q of 8 x 103. An optical microfiber (60 µm diameter) passed through a hole in the 3D cavity near the LC resonator. The 3D cavity was mounted on an x-z attocube-translation stage that allowed the LC resonator to be moved relative to the fiber. The resonator’s f0 and Q were affected both by the fiber dielectric perturbing the resonator’s electric field and from scattered light from the fiber. I measured both effects as a function of fiber-resonator position. I modeled the resonator’s optical response by accounting for optical production, recombination, and diffusion of quasiparticles and the non-uniform position-dependent illumination of the resonator. Using the model, I extracted key parameters describing quasiparticles in the resonator. The hybrid quantum system requires the 87Rb and LC resonator resonance to be tuned to the same frequency. I describe our LC resonator tuning method which moves a superconducting Al pin into the resonator’s electric field, decreasing the resonator capacitance and increasing its resonance frequency up to 137 MHz. This was done at 15 mK using an attocube translation stage. I also investigated two-level system (TLS) defects in an LC resonator by applying a dc voltage. I describe a model in which the TLS causes a capacitive perturbation to the resonator rather than the ‘standard’ electric-dipole coupling model. I use this model of a capacitive TLS or cTLS, to describe intermittent telegraph noise measured in the transmission S21 through the resonator. I measured shifts in f0 of more than 6 kHz corresponding to a cTLS fluctuating its capacitance contribution by 430 zF.
This dissertation describes energy dissipation and microwave loss due to non-equilibrium quasiparticles in superconducting transmon qubits and titanium nitride coplanar waveguide resonators. During the measurements of transmon T1 relaxation time and resonator quality factor QI, I observed reduced microwave loss as the temperature increased from 20 mK to approximately Tc/10 at which the loss takes on a minimum value. I argue that this effect is due to non-equilibrium quasiparticles. I measured the temperature dependence of the relaxation time T1 of the excited state of an Al/AlOx/Al transmon and found that, in some cases, T1 increased by almost a factor of two as the temperature increased from 30 mK to 100 mK with a best T1 of 0.2 ms. I present an argument showing this unexpected temperature dependence occurs due to the behavior of non-equilibrium quasiparticles in devices in which one electrode in the tunnel junction has a smaller volume, and slightly smaller superconducting energy gap, than the other electrode. At sufficiently low temperatures, non-equilibrium quasiparticles accumulate in the electrode with the smaller gap, leading to a relatively high density of quasiparticles at the junction and a short T1. Increasing the temperature gives the quasiparticles enough thermal energy to occupy the higher gap electrode, reducing the density at the junction and increasing T1. I present a model of this effect, extract the density of quasiparticles and the two superconducting energy gaps, and discuss implications for increasing the relaxation time of transmons. I also observed a similar phenomenon in low temperature microwave studies of titanium nitride coplanar waveguide resonators. I report on loss in a resonator at temperatures from 20 mK up to 1.1 K and with the application of infrared pair breaking radiation (λ=1.55 μm). With no applied IR light, the internal quality factor increased from QI = 800,000 at T < 70 mK up to QI=(2×10^6 ) at 600 mK. The resonant frequency f0 increased by 2 parts per million over the same temperature range. Above 600 mK both QI and f0 decreased rapidly, consistent with the increase in the density of thermally generated quasiparticles. With the application of IR light and for intensities below 1 aW μm^(-2) and T < 400 mK, QI increased in a similar way to increasing the temperature before beginning to decrease with larger intensities. I show that a model involving non-equilibrium quasiparticles and two regions of different superconducting gaps can explain this unexpected behavior.
I discuss the design, fabrication and measurement at millikelvin-temperatures of Al/AlO
x/Al Josephson junction-based transmon qubits coupled to superconducting thin-film lumped element microwave resonators made of aluminum on sapphire. The resonators had a center frequency of around
6GHz, and a total quality factor ranging from 15,000 to 70,000 for the various devices. The area of the transmon junctions was about
150nm×150nm and with Josephson energy
EJ such that
10GHz≤EJ/h≤30GHz. The charging energy of the transmons arising mostly from the large interdigital shunt capacitance, was
Ec/h≈300MHz. I present microwave spectroscopy of the devices in the strongly dispersive regime of circuit quantum electrodynamics. In this limit the ac Stark shift due to a single photon in the resonator is greater than the linewidth of the qubit transition. When the resonator is driven coherently using a coupler tone, the transmon spectrum reveals individual ``photon number'' peaks, each corresponding to a single additional photon in the resonator. Using a weighted average of the peak heights in the qubit spectrum, I calculated the average number of photons
nˉ in the resonator. I also observed a nonlinear variation of
nˉ with the applied power of the coupler tone
Prf. I studied this nonlinearity using numerical simulations and found good qualitative agreement with data. In the absence of a coherent drive on the resonator, a thermal population of
5.474GHz photons in the resonator, at an effective temperature of
120mK resulted in a weak
n=1 thermal photon peak in the qubit spectrum. In the presence of independent coupler and probe tones, the
n=1 thermal photon peak revealed an Autler-Townes splitting. The observed effect was explained accurately using the four lowest levels of the dispersively dressed Jaynes-Cummings transmon-resonator system, and numerical simulations of the steady-state master equation for the coupled system. I also present time-domain measurements on transmons coupled to lumped-element resonators. From
T1 and Rabi oscillation measurements, I found that my early transmon devices (called design LEv5) had lifetimes (
T1∼1μs) limited by strong coupling to the
50Ω transmission line. This coupling was characterized by the the rate of change of the Rabi oscillation frequency with the change in the drive voltage (
dfRabi/dV) -- also termed the Rabi coupling to the drive. I studied the design of the transmon-resonator system using circuit analysis and microwave simulations with the aim being to reduce the Rabi coupling to the drive. By increasing the resonance frequency of the resonator
ωr/2π from 5.4
GHz to 7.2
GHz, lowering the coupling of the resonator to the transmission line and thereby increasing the external quality factor
Qe from 20,000 to 70,000, and reducing the transmon-resonator coupling
g/2π from 70
MHz to 40
MHz, I reduced the Rabi coupling to the drive by an order of magnitude (
∼ factor of 20). The
T1∼4μs of devices in the new design (LEv6) was longer than that of the early devices, but still much shorter than the lifetimes predicted from Rabi coupling, suggesting the presence of alternative sources of noise causing qubit relaxation. Microwave simulations and circuit analysis in the presence of a dielectric loss tangent
tanδ≃5×10−6 agree reasonably well with the measured
T1 values, suggesting that surface dielectric loss may be causing relaxation of transmons in the new designs.
The loss in superconducting microwave resonators at low-photon numbers and low temperatures is not well understood but has implications for achievable coherence times in superconducting qubits. We have fabricated single-layer resonators with a high quality factor by patterning a superconducting aluminum film on a sapphire substrate. Four resonator geometries were studied with resonant frequencies ranging from 5 to 7 GHz: a quasi-lumped element resonator, a coplanar strip waveguide resonator, and two hybrid designs that contain both a coplanar strip and a quasi-lumped element. Transmitted power measurements were taken at 30 mK as a function of frequency and probe power. We find that the resonator loss, expressed as the inverse of the internal quality factor, decreases slowly over four decades of photon number in a manner not merely explained by loss from a conventional uniform spatial distribution of two-level systems in an oxide layer on the superconducting surfaces of the resonator.
Superconducting resonators are widely used in many applications such as qubit readout for quantum computing applications, and kinetic inductance detectors. These resonators are susceptible to numerous loss and noise mechanisms under microwave excitation, especially the dissipation due to non-equilibrium quasi-particles and two-level systems (TLS), which can result in a decrease of the superconducting intrinsic quality factor (
Qi) in high quality superconducting resonators. Particularly in the few-photon and low temperature (T) regime, TLS losses can become a dominant loss mechanism. In this study, novel aluminum half-wavelength resonators are investigated, focusing on the loss properties at extra-low power and low temperature. An unusual increase of
Qi(T) with deceasing temperature is observed. This behavior is attributed to the increase of TLS coherence time (
T2) at ultra-low temperatures and powers. This
T2 increase is consistent with other work on resonant frequency noise in resonators and measurements of individual TLS, and likely arises from interacting TLS in the aluminum half-wavelength resonators.