### 4 results for qubit oscillator frequency

Contributors: Ballard, Cody James

Date: 2018-01-01

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. ... 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.

Data types:

Contributors: Güngördü, Utkan, Kestner, J. P.

Date: 2018-01-01

Characterizing charge noise is of prime importance to the semiconductor spin **qubit** community. We analyze the echo amplitude data from a recent experiment [Yoneda et al., Nat. Nanotechnol. 13, 102 (2018)] and note that the data shows small but consistent deviations from a 1/fˣ noise power spectrum at the higher **frequencies** in the measured range. We report the results of using a physical noise model based on two-level fluctuators to fit the data and find that it can mostly explain the deviations. While our results are suggestive rather than conclusive, they provide what may be an early indication of a high-**frequency** cutoff in the charge noise. The location of this cutoff, where the power spectral density of the noise gradually rolls off from 1/f to 1/f² , crucial knowledge for designing precise **qubit** control pulses, is given by our fit of the data to be around 200 kHz....cutoff **frequency**...spin **qubit** ... Characterizing charge noise is of prime importance to the semiconductor spin **qubit** community. We analyze the echo amplitude data from a recent experiment [Yoneda et al., Nat. Nanotechnol. 13, 102 (2018)] and note that the data shows small but consistent deviations from a 1/fˣ noise power spectrum at the higher **frequencies** in the measured range. We report the results of using a physical noise model based on two-level fluctuators to fit the data and find that it can mostly explain the deviations. While our results are suggestive rather than conclusive, they provide what may be an early indication of a high-**frequency** cutoff in the charge noise. The location of this cutoff, where the power spectral density of the noise gradually rolls off from 1/f to 1/f² , crucial knowledge for designing precise **qubit** control pulses, is given by our fit of the data to be around 200 kHz.

Data types:

Top results from Data Repository sources. Show only results like these.

Contributors: Zhao, Beihan

Date: 2018-01-01

In this thesis, the effects of a flow-induced **oscillating** flexible structure on the convective heat transfer of a plate heat exchanger in a vertical rectangular wind tunnel were experimentally investigated. A variable speed fan was used to create an air flow with speed ranging from 9 m/s to 20 m/s. A flexible structure was placed in the front of the plate heat exchanger, which would **oscillate** in the air flow. Different shapes and dimensions of flexible structures were tested. The temperature of the plate was monitored, and the steady-state temperature was recorded for each experimental condition. The **oscillating** motions of the flexible structures were captured with a high-speed camera. Compared to the steady flow convection, the use of the **oscillation** flexible structure can enhance the mixing of the high-temperature boundary flow with the lower temperature flow and disrupt the boundary layer. The length and width of the rectangular structures were found to have large influence on the **oscillating** characteristics and the convective heat transfer enhancement. Dimensionless parameters including flow-induced **oscillation** **frequency**, f^*, and coverage ratio, A^*, were also studied in order to discover the relationship between them. Experimental results showed that the structures with a rectangular shape can most significantly improve the convective heat transfer among those various shapes used in the present study. The average heat transfer coefficient was improved from 113 [W/(m^2*K)] to 161 [W/(m^2*K)] when the inlet wind velocity was 17.2 m/s, and that specific rectangular structure had a length of 0.075 [m] and a width of 0.102 [m].In addition, highest heat transfer performance was found when 0.22≤f^*≤0.32, which could be used for possible further design optimizations. ... In this thesis, the effects of a flow-induced **oscillating** flexible structure on the convective heat transfer of a plate heat exchanger in a vertical rectangular wind tunnel were experimentally investigated. A variable speed fan was used to create an air flow with speed ranging from 9 m/s to 20 m/s. A flexible structure was placed in the front of the plate heat exchanger, which would **oscillate** in the air flow. Different shapes and dimensions of flexible structures were tested. The temperature of the plate was monitored, and the steady-state temperature was recorded for each experimental condition. The **oscillating** motions of the flexible structures were captured with a high-speed camera. Compared to the steady flow convection, the use of the **oscillation** flexible structure can enhance the mixing of the high-temperature boundary flow with the lower temperature flow and disrupt the boundary layer. The length and width of the rectangular structures were found to have large influence on the **oscillating** characteristics and the convective heat transfer enhancement. Dimensionless parameters including flow-induced **oscillation** **frequency**, f^*, and coverage ratio, A^*, were also studied in order to discover the relationship between them. Experimental results showed that the structures with a rectangular shape can most significantly improve the convective heat transfer among those various shapes used in the present study. The average heat transfer coefficient was improved from 113 [W/(m^2*K)] to 161 [W/(m^2*K)] when the inlet wind velocity was 17.2 m/s, and that specific rectangular structure had a length of 0.075 [m] and a width of 0.102 [m].In addition, highest heat transfer performance was found when 0.22≤f^*≤0.32, which could be used for possible further design optimizations.

Data types:

Contributors: Boyer, Lance L.

Date: 2019-01-01

Since 2006 it has been discovered experimentally that the superconducting state spontaneously breaks time-reversal symmetry (TRS) in several materials, such as Sr2RuO4, UPt3, URu2Si2, PrOs4Sb12, and Bi/Ni bilayers. This dissertation studies three physical phenomena related to time-reversal symmetry breaking (TRSB) in these superconductors. The experimental evidence for TRSB comes from the magneto-optical polar Kerr effect, which is determined by the high **frequency** ac Hall conductivity. However, these superconductors are also expected to exhibit a spontaneous dc Hall effect in the absence of an applied magnetic field. In the first part of this dissertation we propose a method for measuring the low **frequency** Hall conductivity in superconductors with TRSB. The method is based on a Corbino disk geometry where an **oscillating** co-axial magnetic field induces circular electric field, which, in turn, induces radial charge **oscillations** due to the Hall conductivity. In the second part, we propose an explanation for the polar Kerr effect observed in the Hidden-Order phase of the heavy-fermion superconductor URu2Si2. Using a Ginzburg-Landau model for a complex order parameter, we show that the system can have a metastable ferromagnetic state, which produces the Kerr signal, even if the Hidden-Order state respects TRS. We predict that applying a reversed magnetic field should reset the system to the non-magnetic ground state, resulting in zero Kerr signal. In the third part of the dissertation, we investigate the conditions for the existence of a Majorana bound state on a vortex in a 2D d+id superconductor with strong spin-orbit coupling. This TRSB pairing was proposed earlier for the Ni/Bi bilayer. We find that the Majorana bound state can exist for a d+id pairing under conditions similar to those for s-wave pairing. ... Since 2006 it has been discovered experimentally that the superconducting state spontaneously breaks time-reversal symmetry (TRS) in several materials, such as Sr2RuO4, UPt3, URu2Si2, PrOs4Sb12, and Bi/Ni bilayers. This dissertation studies three physical phenomena related to time-reversal symmetry breaking (TRSB) in these superconductors. The experimental evidence for TRSB comes from the magneto-optical polar Kerr effect, which is determined by the high **frequency** ac Hall conductivity. However, these superconductors are also expected to exhibit a spontaneous dc Hall effect in the absence of an applied magnetic field. In the first part of this dissertation we propose a method for measuring the low **frequency** Hall conductivity in superconductors with TRSB. The method is based on a Corbino disk geometry where an **oscillating** co-axial magnetic field induces circular electric field, which, in turn, induces radial charge **oscillations** due to the Hall conductivity. In the second part, we propose an explanation for the polar Kerr effect observed in the Hidden-Order phase of the heavy-fermion superconductor URu2Si2. Using a Ginzburg-Landau model for a complex order parameter, we show that the system can have a metastable ferromagnetic state, which produces the Kerr signal, even if the Hidden-Order state respects TRS. We predict that applying a reversed magnetic field should reset the system to the non-magnetic ground state, resulting in zero Kerr signal. In the third part of the dissertation, we investigate the conditions for the existence of a Majorana bound state on a vortex in a 2D d+id superconductor with strong spin-orbit coupling. This TRSB pairing was proposed earlier for the Ni/Bi bilayer. We find that the Majorana bound state can exist for a d+id pairing under conditions similar to those for s-wave pairing.

Data types: