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.
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.
We describe a thin-film superconducting Nb microwave resonator, tunable to within 0.3 ppm of the hyperfine splitting of 87Rb at fRb = 6.834683 GHz. We coarsely tuned the resonator using electron-beam lithography, decreasing the resonance frequency from 6.8637 GHz to 6.8278 GHz. For in situ fine tuning at 15 mK, the resonator inductance was varied using a piezoelectric stage to move a superconducting pin above the resonator. We found a maximum frequency shift of about 8.7 kHz per 60-nm piezoelectric step and a tuning range of 18 MHz.
I report measurements of two different types of superconducting devices illuminated by 780 nm light, one of the wavelengths needed in a proposed atom-superconductor hybrid quantum system. I illuminated a thin-film Al lumped-element resonator and observed the resonator quality factor and resonance frequency as a function of illumination intensity, microwave power, and temperature. The resonator was mounted in a 3d aluminum cavity. The variation in optically-induced loss due to microwave power was similar to the behavior expected for loss from a distribution of two-level systems. Although this behavior may suggest the presence of optically activated two-level systems, I found that the loss is better explained by the presence of nonequilibrium quasiparticles generated by the illumination and excited by the microwave drive. I described a model of the system where optical absorption creates an effective source of phonons and solved the coupled quasiparticle-phonon rate equations. I found good agreement between the simulation and the measured resonator quality factor and frequency shift as a function of temperature, microwave power, and optical illumination. I fabricated a transmon qubit and studied the qubit transition frequency and relaxation time as a function of illumination intensity and temperature. The qubit was mounted in a 3d aluminum cavity and coupled to the cavity forming a Jaynes-Cummings system. Qubit relaxation showed non-exponential behavior that I fit to a quasiparticle fluctuation model with two characteristic times. The transition frequency and both characteristic times decreased with increasing illumination intensity. For comparison, I described a nonequilibrium quasiparticle model for the expected frequency shift and relaxation time due to quasiparticle tunneling through the Josephson junction. While the quasiparticle simulation predicted the general qualitative behavior of the frequency shift and relaxation time, there were some significant discrepancies with the data. This suggests the model needs to be extended, for example by including a different gap in the two superconductor layers forming the junction, and by taking into account other possible sources of loss and decoherence.
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.