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OPTICAL AND ELECTRICAL RESPONSE OF SUPERCONDUCTING RESONATORS FOR A HYBRID QUANTUM SYSTEM

Kristen Voigt

Published Jan 1, 2021• 0 citations
Publisher

Abstract

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.

DOI
10.13016/byfg-cemz

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•Apr 9, 2015•1 citation
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.
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.
We have coupled a tapered optical microfiber to a translatable thin-film lumped-element superconducting Al microwave resonator that is cooled to 15 mK. The thin-film resonator has a resonance frequency of 6.14 GHz, a quality factor of Q = 2.59 × 105, and is mounted inside a 3-D Al microwave cavity that provides a well-isolated electromagnetic environment. The microfiber is held fixed while the cavity is mounted on an x-z translation stage that allows the lumped-element resonator and the optical fiber to be brought close to each other (less than 1 mm). When 780-nm light is sent through the fiber, Rayleigh scattering in the fiber causes a weak position-dependent nonuniform illumination of the thin-film resonator, exciting quasiparticles in the superconducting film and thereby affecting its resonance frequency foand Q. We report on the response of the resonator to both the scattered optical power and the presence of the fiber's dielectric, as the thin-film resonator is moved in situ with respect to the fiber.
This dissertation examines the design, fabrication, and characterization of a superconducting lumped-element tunable LC resonator that is used to vary the coupling between two superconducting qubits. Some level of qubit-qubit coupling is needed to perform gating operations. However, with fixed coupling, single qubit operations become considerably more difficult due to dispersive shifts in their energy levels transitions that depend on the state of the other qubit. Ideally, one wants a system in which the qubit-qubit coupling can be turned off to allow for single qubit operations, and then turned back on to allow for multi-qubit gate operations. I present results on a device that has two fixed-frequency transmon qubits capacitively coupled to a tunable thin-film LC resonator. The resonator can be tuned in situ over a range of 4.14 GHz to 4.94 GHz by applying an external magnetic flux to two single-Josephson junction loops, which are incorporated into the resonator’s inductance. The qubits have 0-to-1 transition frequencies of 5.10 GHz and 4.74 GHz. To isolate the system and provide a means for reading out the state of the qubit readout, the device was mounted in a 3D Al microwave cavity with a TE101 mode resonance frequency of about 6.1 GHz. The flux-dependent transition frequencies of the system were measured and fit to results from a coupled Hamiltonian model. With the LC resonator tuned to its minimum resonance frequency, I observed a qubit-qubit dispersive shift of 2χ_qq≈ 0.1 MHz, which was less than the linewidth of the qubit transitions. This dispersive shift was sufficiently small to consider the coupling “off”, allowing single qubit operations. The qubit-qubit dispersive shift varied with the applied flux up to a maximum dispersive shift of 2χ_qq≈ 6 MHz. As a proof-of-principle, I present preliminary results on performing a CNOT gate operation on the qubits when the coupling was “on” with 2χ_qq≈ 4 MHz. This dissertation also includes observations of the temperature dependence of the relaxation time T1 of three Al/AlOx/Al transmons. We found that, in some cases, T1 increased by almost a factor of two as the temperature increased from 30 mK to 100 mK. We found that this anomalous behavior was consistent with loss due to non-equilibrium quasiparticles in a transmon where one electrode in the tunnel junction had 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 a smaller gap, leading to an increased density of quasiparticles at the junction and a corresponding decrease in the relaxation time. I present a model of this effect, use the model to extract the density of non-equilibrium quasiparticles in the device, and find the values of the two superconducting energy gaps.
We report our development on design, fabrication and characterization of various superconducting resonators for quantum device applications. The resonators are developed mainly for superconducting qubit implementation in circuit QED structure, but future application will include photon detectors such as microwave kinetic inductance detectors. First we designed and fabricated half-wavelength coplanar waveguide resonators with niobium thin film on a high resistive silicon wafer, with the fundamental frequencies in the range of 1 to 8 GHz. The loaded quality factors are controlled by the coupling capacitors, and the lower bound of the intrinsic quality factor was measured down to 7 mK in the dilution refrigerator. We have also designed quarter-wavelength resonators and lumped LC resonators coupled to a transmission line, and characterized multiple resonators in a single transmission line. For the 3D transmon qubit application, we designed and fabricated a rectangular box resonator with superconducting aluminum. The intrinsic quality factor of the box resonator exceeds three million at 7 mK. We will also present basic results on the integration of a transmon qubit in the superconducting resonator.
I discuss the design, fabrication and measurement at millikelvin-temperatures of Al/AlOx_xx​/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 6 6\,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 150 nm×150 nm150\, \mathrm{nm} \times 150\, \mathrm{nm}150nm×150nm and with Josephson energy EJE_JEJ​ such that 10 GHz≤EJ/h≤30 10\,\text{GHz} \leq E_J / h \leq 30\,10GHz≤EJ​/h≤30GHz. The charging energy of the transmons arising mostly from the large interdigital shunt capacitance, was Ec/h≈300 E_c / h \approx 300\,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\bar{n}nˉ in the resonator. I also observed a nonlinear variation of nˉ\bar{n}nˉ with the applied power of the coupler tone PrfP_{rf}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 5.474 5.474\,5.474GHz photons in the resonator, at an effective temperature of 120 120\,120mK resulted in a weak n=1n=1n=1 thermal photon peak in the qubit spectrum. In the presence of independent coupler and probe tones, the n=1n=1n=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 T1T_1T1​ and Rabi oscillation measurements, I found that my early transmon devices (called design LEv5) had lifetimes (T1∼1 μT_1 \sim 1\,\muT1​∼1μs) limited by strong coupling to the 50 Ω50\,\Omega50Ω 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\mathrm{d}f_{Rabi}\, / \mathrm{d}VdfRabi​/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\omega_r/2\piωr​/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 QeQ_eQe​ from 20,000 to 70,000, and reducing the transmon-resonator coupling g/2πg/2\pig/2π from 70 \,MHz to 40 \,MHz, I reduced the Rabi coupling to the drive by an order of magnitude (∼\sim∼ factor of 20). The T1∼4 μT_1 \sim 4\,\muT1​∼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 tan⁡δ≃5×10−6\tan \delta \simeq 5\times10^{-6}tanδ≃5×10−6 agree reasonably well with the measured T1T_1T1​ values, suggesting that surface dielectric loss may be causing relaxation of transmons in the new designs.
Superconducting quantum devices have gained increasing interest over the past 15 years because of their role as promising candidates for implementing a large-scale quantum computer and as ultra-sensitive detectors. Superconducting resonators are one type of superconducting device which are used in a variety of applications including quantum computing and radioastronomy. They can achieve large quality factors which are important for these applications and a variety of others. Specific examples of these applications include the readout and coupling of superconducting qubits and also microwave kinetic inductance detector arrays for sub-mm wavelength astronomical measurements. High quality factors also enable the study of very subtle features in the electromagnetic response of the resonator. This feature in turn offers provides a method to characterize loss mechanisms which affect the performance of superconducting qubits, by measuring the quality factor of a resonator. Dielectric loss is an example of such a loss mechanism, and is considered to be one of, if not \\it the \\rm major obstacle to overcome in order to construct scalable quantum technologies based on superconducting devices. This type of loss arises from the coupling of the electric field in the device to spurious degrees of freedom which arise naturally the dielectric environment of the device. The fast-growing interest in the physics and applications of superconducting resonators has renewed interest in an improving our fundamental understanding of dielectric loss. This interest involves the study of a much bigger and older question in condensed matter physics; namely, what is the microscopic physics which governs the behaviour and of an amorphous material at low-temperatures? \n \nIn this thesis, we present a systematic study of dielectric loss in amorphous aluminum oxide using superconducting microwave resonators. Measurements of the intrinsic loss tangent over a large temperature range of 40~mK to 1~K are presented and analyzed in detail. Some aspects of the data are well understood in terms of the standard tunnelling two-level system model, while others require a deeper analysis of the electrodynamics of the resonator and insights from more advanced theories. We employ a consistent approach using numerical simulations of the resonator to understand loss mechanisms arising from both an inhomogeneous electric field and multiple dielectric layers. We measure saturation effects which provide insight into coherent properties of two-level system ensembles and the mutual interaction between them. Excellent agreement with the two-level system model is found for intrinsic losses, however the strong dependence on temperature which we observe for saturation effects is not predicted in the standard form of the model. We find that this dependence can be understood in terms of the theory of spectral diffusion which is consistent with a strong mutual interaction between two-level systems contributes to broadening of their spectral linewidths.