Session T17: Focus Session: Materials in Superconducting Qubits

Noise and Dephasing from Surface Magnetic States in Superconducting Circuits

Superconducting qubits are a leading candidate for scalable quantum information processing. In order to realize the full potential of these qubits, it is necessary to develop a more complete understanding of the microscopic physics that governs dissipation and dephasing of the quantum state. In the case of the Josephson phase and flux qubits, the dominant dephasing mechanism is an apparent low-frequency magnetic flux noise with a $1/f$ spectrum and a magnitude of several $\mu \Phi_0$/Hz$^ {1/2}$ at 1 Hz, where $\Phi_0 = h/2e$ is the magnetic flux quantum. Recent qubit results are compatible with the excess low-frequency noise measured by researchers at Berkeley more that 20 years ago in a series of experiments on SQUIDs cooled to millikelvin temperatures. The origin of this excess noise was never understood. Here we describe studies of flux noise and temperature- dependent magnetization in SQUIDs cooled to millikelvin temperatures. We observe that the flux threading the SQUIDs increases as $1/T$ as temperature is lowered; moreover, the flux change is proportional to the density of trapped vortices. The data is compatible with the thermal polarization of unpaired surface spins in the trapped fields of the vortices. In the absence of trapped flux, we observe evidence of spin- glass freezing at low temperature. These results suggest a microscopic explanation for the universal $1/f$ flux noise in SQUIDs and superconducting qubits, and suggest that suitable surface treatments of the superconducting films will lower the density of magnetic states, leading to superconducting devices with lower noise and solid-state qubits with improved coherence times.   

Susceptibility of Magnetic Surface States in Superconducting Circuits.

Recent experiments indicate that there is a high density of unpaired spins residing on the surfaces of superconducting thin films used to implement SQUIDs and superconducting qubits. Fluctuations of these spins give rise to low frequency flux noise and dephasing of the qubit state. Realization of phase and flux qubits with improved dephasing times will require a deeper understanding of the microscopic physics that governs fluctuations of the surface spins. Here we describe experiments that probe the ac spin susceptibility of the surface magnetic states. The detector is a dc SQUID-based susceptometer optimized for the study of surface spins. We discuss the temperature and frequency dependence of the spin susceptibility, and relate these to interactions between spins, the distribution of spin relaxation times, and possible spin-glass freezing.   

Reflectometry measurements of 1/f noise in SQUID phase qubits at mK temperatures

We measure 1/f noise spectra in dc SQUID phase qubits using a microwave reflectometry technique. One of the SQUID junctions is shunted by a large capacitor, forming a microwave frequency resonator biased and driven to show nonlinear response, typically at 1.5 GHz. This nonlinearity means small current or flux fluctuations produce large changes in reflected phase which we can measure using homodyne detection. Measurements from aluminum qubits on sapphire are compared to previous measurements of 1/f flux noise in SQUIDs and a similarly designed Nb/AlOx/Nb on silicon dc SQUID qubit fabricated by Hypres; data was taken at temperatures ranging from 50 mK to 500 mK.   

Crystalline Silicon Dielectrics for Superconducting Qubit Circuits

Superconducting qubit energy relaxation times are limited by microwave loss induced by a continuum of two-level state (TLS) defects in the dielectric materials of the circuit. State-of-the-art phase qubit circuits employ a micron-scale Josephson junction shunted by an external capacitor. In this case, the qubit T$_1$ time is directly proportional to the quality factor (Q) of the capacitor dielectric. The amorphous capacitor dielectrics that have been used to date display intrinsic Q of order 10$^3$ to 10$^4$. Shunt capacitors with a Q of 10$^6$ are required to extend qubit T1 times well into the microsecond range. Crystalline dielectric materials are an attractive candidate for qubit capacitor dielectrics, due to the extremely low density of TLS defects. However, the robust integration of crystalline dielectrics with superconducting qubit circuits remains a challenge. Here we describe a novel approach to the realization of high-Q crystalline capacitor dielectrics for superconducting qubit circuits. The capacitor dielectric is a crystalline silicon nanomembrane. We discuss characterization of crystalline silicon capacitors with low-power microwave transport measurements at millikelvin temperatures. In addition, we report progress on integrating the crystalline capacitor process with Josephson qubit fabrication.   

Testing of qubit materials and fabrication using superconducting resonators

We will present the results of measurements made on superconducting resonators fabricated using different substrates and superconducting metals. Specifically, the quality factor of these resonators will be shown to be closely related to not only the purity of the substrates and metals used in the process but also to the details of the fabrication. We will demonstrate the change in quality factor of a bare resonator when subjected to the qubit process. Based on our measurements we propose that superconducting resonators may form a test bed for troubleshooting the fabrication process for minimizing the materials related dissipation in the qubits.   

Optimizing silicon nitride for superconducting quantum circuits

Amorphous dielectrics are prevalent in lithographic circuits, but their presence can decohere superconducting qubits. We investigate the relationship between stoichiometry and low- temperature loss in silicon nitride dielectric films, where two- level system defects are unsaturated. The silicon nitride films are deposited by plasma-enhanced chemical vapor deposition at 300 degrees celsius, with silane and nitrogen as precursor gases. The precursor gas ratio is changed and film density, crystalline order, stress, and hydrogen incorporation are measured. Hydrogen, silicon and nitrogen content are monitored with FTIR spectroscopy. The loss is measured at low-field strengths at temperature of 30 mK with lumped-element superconducting resonators, where silicon nitride is used as the dielectric within a parallel-plate capacitor. Our data show that N-rich silicon nitride with a high concentration of nitrogen-hydrogen bonds exhibit a factor of 10 higher loss tangent than Si-rich films. The loss of the better film rivals other on-chip insulating techniques, and allows us to fabricate Josephson junctions next to silicon nitride with a negligible loss contribution from this dielectric.   

Low-photon number studies of inductively-coupled superconducting resonators

Quality factors near one million have been observed in on-chip superconducting resonators for many years, but new studies on resonators reveal much lower quality factors at low-photon numbers, perhaps due to the presence of anomalous two-level system defects. We have designed and fabricated four new aluminum thin-film resonator types near 6 GHz. They include a lumped-element resonator, a slot-line resonator, and two hybrids, both of which contain a slot line and either an inductor or a capacitor. The resonator types have a consistent line width and are fabricated on a sapphire substrate to facilitate the study of surface defects, such as two-level systems. We plan to compare their quality factors in an effort to better understand the loss mechanism associated with the surface. All the resonator types have inductive coupling to a coplanar waveguide with geometrical symmetry that can be used to construct useful Josephson junction resonators.   

LC Filtered dc SQUID Phase Qubit with Low Dielectric Loss

We have investigated a dc SQUID phase qubit with LC filter, which has a relatively small ($\sim $4 $\mu $m$^{2})$ Al/AlO$_{x}$/Al Josephson junction shunted by an additional capacitor built using low-stress thin film SiN$_{x}$. The LC isolation provides an additional isolation factor at the junction plasma frequency and allows flexibility in the choice of SQUID parameters. We report Rabi oscillations with a 42 ns envelope decay time (T'), and a 32 ns energy relaxation time (T$_{1})$, consistent with a loss tangent of about 7 x 10$^{-4}$ in the loss-stress SiN$_{x}$. We also report on progress towards getting longer coherence times using a high-stress SiN$_{x}$ with a lower loss tangent.   

Microwave response of vortices in Al and Re superconducting thin films

Vortices trapped in superconducting microwave resonant circuits contribute excess loss and can result in substantial reductions in the quality factor. Thus, characterizing the microwave vortex response in superconducting thin films is important for the design of superconducting qubits, which are typically operated in small, but non-zero, magnetic fields. By cooling in fields of the order of 1 Gauss and below, we have characterized the magnetic field and frequency dependence of the microwave response of a small density of vortices in resonators fabricated from thin films of Re and Al. Above a certain threshold cooling field, vortices become trapped in the resonators and vortices in the Al resonators contribute greater loss and are influenced more strongly by flux creep effects than in the Re resonators. This different behavior can be described in the framework of a general vortex dynamics model related to the interplay between the vortex pinning in the films and the flux-flow viscosity.   

One- and two-photon spectroscopy of a flux qubit coupled to a microscopic defect

We observed the dynamics of a superconducting flux qubit coupled to a microscopic defect. The presence of the defect is visible as an anticrossing in the spectroscopy of the flux qubit, as measured using one-photon excitation. We analyze the energy- level structure of the combined qubit-defect system using both one- and two- photon spectroscopy. The use of two-photon spectroscopy allows us to extract important additional information about the anharmonicity and coupling of the defect. We find that the system coupled to the qubit can be a two-level system, but not a harmonic oscillator. We consider two basic models, for a microscopic defect which is coupled to the qubit either magnetically or electrically respectively. We conclude that the large coupling constant, of approximately 200 MHz, can only be accounted for by electric coupling, and not by magnetic coupling. This shows that electrically coupled microscopic two- level systems are relevant to decoherence of superconducting flux qubits.   

Probing anomalous two-level systems with a Cooper-pair box

We have used an Al/AlO$_{x}$/Al Cooper-pair box (CPB) qubit to detect coupling to anomalous ``two-level'' quantum systems. By measuring the excitation spectrum and lifetime of the first excited state from 15 GHz to 50 GHz of the CPB at a temperature of 40 mK, one can identify anomalous levels and ascertain the magnitude of the quantum noise that is coupled to the qubit. It was found that the frequency of a distinct avoided level crossing depends on gate voltage and the size of the splitting depends on the effective Josephson energy. Both the gate voltage and Josephson energy dependence are consistent with coupling to extraneous charged two-level systems formed by point charges that can tunnel between two positions in the oxide of the Josephson junction. By fitting a model Hamiltonian to our data, we are able to extract microscopic information about the charge fluctuator such as the well asymmetry ($\sim$ 130 micro-eV), tunneling rate ($\sim$ 8 GHz) and a minimum hopping distance for the charge fluctuators ($\sim$ 0.8 Angstroms).