Session L34: Superconducting Qubits: Two-level Systems & Decoherence

Anomalous Behavior of High Quality Factor Planar Superconducting Resonators

Superconducting coplanar waveguide resonators have proven to be invaluable tools in studying some of the decoherence mechanisms found in superconducting qubits. Surface two-level states tend to dominate decoherence at temperatures below ~ Tc/10 and at very low microwave powers, assuming loss through other channels (e.g. quasiparticles, vortices, and radiation loss) has been mitigated through proper shielding and design. I will present recent measurements of resonators whose behavior diverges significantly from the standard two-level state model at low temperatures and low excitation energies, resulting in startling behavior of the internal quality factor.   

Microscopic origin of dissipative two-level systems in Al$_2$O$_3$

Resonant absorption of two-level systems (TLS) poses a serious limitation to the performance of superconducting qubit devices for quantum computing. Experiments indicate that the TLS is associated with defects in the dielectric layers of the device. However, the nature of these defects has yet to be established. Using hybrid functional calculations, we investigate possible defects in Al$_2$O$_3$ that can act as sources of resonant absorption. Hydrogen is a ubiquitous impurity, and easily incorporates in the interstitial sites (H$_i$) in Al$_2$O$_3$. In the positive charge state, H$_i$ is bonded to one oxygen atom, but also interacts with a secondary oxygen atom. At particular O-O distances, close to those found in amorphous Al$_2$O$_3$ or near the Al$_2$O$_3$/Al interface, the H atom is effectively in a double well. We calculate the three-dimensional potential energy surface (PES) for the H atom in a so-called ``coincidence configuration,'' which allows for tunneling between two equivalent positions. Using the calculated PES, we solve the Schr\"odinger equation for the tunneling proton and determine the tunneling frequency. We find that H$_i$ gives rise to resonant absorption in the range of 10-100 GHz, in agreement with experimental observations.   

Individual two level fluctuators in the tunneling conductance of Al/AlO$_{x}$/Al Josephson junctions for superconducting qubits

Two level system (TLS) defects in AlO$_{x}$ tunnel barriers can lead to low-frequency $1/f$ critical current noise and losses in coherent superconducting circuits. Understanding the nature of these defects and how to eliminate them are critical in order to achieve ultra-long coherence times. We present measurements of the tunneling conductance of ultrasmall, $A<(100~\textrm{nm})^{2}$, Al/AlO$_{x}$/Al shadow evaporated junctions. The tunneling conductance of these junctions exhibits several isolated TLSs, which permitted the detailed analysis of the individual switching rates and behavior of the TLSs. We have studied the thermal activation behavior of these TLSs, and in some cases observe a crossover into quantum-limited tunneling at lower temperatures. Tracking the TLS switching rates as a function of the applied voltage bias provides an estimate of the TLS charge dipole moment. In some quantum tunneling limited TLSs we have observed a non-equilibrium enhancement of the switching rates that cannot be explained by simple dissipative heating of the TLSs. Further investigations into these TLS defects may lead to the identification of their physical origins and strategies to eliminate them.   

Cavity QED of individual two-level systems observed in insulating films

Previous work shows that individual two-level systems (TLS) can be observed in alumina tunnel barriers and used as quantum memory. We investigate the TLS within insulating films using superconducting microwave resonators of different electric-field volumes. The insulating film, made of hydrogenated amorphous silicon nitride, is orders of magnitude thicker than tunneling barriers and its volume is many orders of magnitude larger than that of qubit junction barriers where individual TLS are routinely observed. In the largest-volume resonators we observe bulk dielectric behavior of TLS. In the smallest-volume resonators, strong coupling to the TLS is observed and explained by cavity QED. When two resonances are observed, the data are fit to quantum theory, showing that the strongly coupled TLS have coherence times on the order of microseconds. Furthermore, the power dependence of transmission in the TLS-cavity hybrid system is measured, which shows clear saturation of the TLS near a single photon.   

Efficient characterization of spurious two-level systems in superconducting qubits under non-ideal conditions

The presence of spurious two-level systems (TLSs) is a long-standing problem in superconducting qubits. We present a characterization method that is able to determine both the TLS frequency $\omega$ and its coupling strength $g$ with the qubit efficiently. With the method, the mean squared error of the estimates decreases exponentially with the number of measurement shots in contrast to power-law scalings exhibited by the conventional methods. Significantly, our method also works in the presence of decoherence and measurement errors. This is accomplished by applying Bayesian inference in a feedback algorithm that updates the measurement setup based on the previous measurement outcomes while data is being collected. Surprisingly, we find that it is usually possible to characterize $\omega$ and $g$ with high precision with only some hundreds of measurement shots - even if the same set of measurements does not allow establishing highly precise expectation values for a quantum state. In addition to TLSs, our method can also be used to precisely characterize stripline resonators.   

Stimulated microwave photon transfer through dielectric two-level systems

Two level systems (TLS) in dielectrics are a major source of energy loss for superconducting circuits at milli-kelvin temperatures. We will show measurements taken with a bias-bridge resonator circuit, which allows the simultaneous application of an electric dc field, while measuring the loss tangent of applied microwave fields. Previous measurements with this device show that 10$^{\mathrm{9}}$ TLS can be tuned through the microwave resonance and the loss of these can be changed due to rapid passage of the TLS. We extend these studies by concurrently applying multiple microwave frequencies, and explore the possible transfer of photons from one frequency to the other using stimulated processes with the TLS and resonator fields. These experiments show that the background of disordered TLS, usually thought of as deleterious, may be controlled in potentially useful ways.   

Photon Correlations in a Waveguide Coupled to Multiple Two- and Three- Level Systems

We study photon-photon correlations in a waveguide strongly coupled to multiple qubits (up to 10) described by either two-level systems (2LS) or three-level systems (3LS). The calculated second-order correlation function $g_2(t)$ for this ``waveguide QED'' system has rich structure that is sensitive to the frequency of the incident photons and the separation between the qubits, arising from the interference among photons scattered multiple times by the qubits. In the multiple 2LS case [1], transmitted and reflected photons can both be bunched initially and then oscillate between bunched and anti-bunched for a long time interval that increases as the number of impurities, N, increases (up to 10). For 3LS qubits, when operating at the peak of electromagnetically induced transparency (EIT), the N=2 case generates bunched photons persisting for a long time, comparable to that in the N=10 2LS case. To probe the interplay between the time-delay inherent in the 3LS under EIT conditions and the 2LS-produced correlations, we study the hybrid structures 3LS-2LS-3LS and 2LS-3LS-2LS. [1] For first results see Y.-L. L. Fang, H. Zheng, and H. U. Baranger, arXiv/1308.6551   

An efficient method for studying low-frequency two-state fluctuators

We propose a driven-evolution-based pulse sequence as an efficient tool to study low-frequency random telegraph noise. The sequence originates from the two-dimensional chemical exchange experiment in NMR, but dramatically reduces measuring time with a one-dimensional modification. The sequence is also more sensitive to weak fluctuators than the dynamical-decoupling-type sequences. By applying the sequence to a qubit, the existence of a two-state fluctuator is characterized by an oscillating signal, whose frequency and amplitude correspond to the fluctuator's strength and correlation time respectively. The method opens a way to investigate noise in the quasistatic regime, which cannot be resolved by conventional coherence-characterization methods. The pulse sequence can be used to study phenomena in Josephon-junction qubits such as quasiparticle tunneling. The Lincoln Laboratory portion of this work was sponsored by the Assistant Secretary of Defense for Research \& Engineering under Air Force Contract number FA8721-05-C-0002. Opinions, interpretations, conclusions and recommendations are those of the author and are not necessarily endorsed by the United States Government.   

Optically Activated Two-Level Systems in a Thin-Film Superconducting Microwave Resonator

We have fabricated an isolated thin-film superconducting Al lumped-element resonator (resonant frequency 6.72 GHz) on a sapphire substrate and mounted it inside an Al 3d cavity (TE101 mode frequency 7.50 GHz). The thin-film resonator is very weakly coupled to the microwave drive line with $Q_e \approx 5 \times 10^9$. We illuminated the resonator with 780 nm light from an optical fiber and measured the internal loss in the resonator and its dependence on applied optical and rf powers at temperatures as low as 20 mK. With no applied optical power, the resonator reaches an internal quality factor $Q_i \approx 2 \times 10^6$ at high rf photon numbers. Our measurements show that the applied optical power causes an increase in loss due to an apparent increased contribution from two-level systems as well as the expected increase from quasiparticles. We discuss our results and possible mechanisms for the optical activation of two-level systems.   

Discrete Two-Level Systems and Two-Level Fluctuators in a Superconducting Microwave Resonator

We measure the effect of two-level systems on a thin-film superconducting Al microwave resonator at 6.83 GHz that is weakly coupled to an on-chip transmission line [1]. The device is intended for coupling to the hyperfine splitting of trapped $^{\mathrm{87}}$Rb atoms. At 12 mK the internal quality factor at low microwave power is typically 100,000. Applying a dc voltage to the transmission line leads to reproducible shifts of up to 6 kHz in the resonance frequency. These shifts are more pronounced at lower RF power, suggesting that discrete charged two-level systems in the sapphire substrate or surface Al oxide are responsible, and that the dc voltage shifts the transition energy of the two-level systems. We also see evidence for thermally activated two- level fluctuators which can be turned on and off by the applied dc voltage. We discuss our results and the characteristics of the underlying two-level systems and two-level fluctuators.\\[4pt] [1] Z. Kim et al., AIP ADVANCES 1, 042107 (2011).   

Etch Effects on Surface loss in High Quality Aluminum on Silicon Superconducting Coplanar Resonators

Superconducting coplanar resonators are a powerful tool for studying capacitive loss from two level states (TLS's) in superconducting qubits. We have found evidence that standard processing of aluminum on sapphire superconducting devices leaves behind $\approx$2 nm organic residues which can contribute to loss at the Q$> 10^{6}$ level that we are presently working with. Removing these residues is possible on a silicon substrate as it allows various sidewall etchings and profilings via chemical and physical etches. I will present recent Q factor measurements of aluminum on silicon resonators that were defined through a variety of etching conditions.   

Lift-Off Processing and Superconducting Circuit Coherence

As superconducting circuit coherence continues to increase, careful attention must be paid to device fabrication techniques. Substantial evidence points to dielectric loss from two-level state defects in thin amorphous interfacial regions as a limiting relaxation mechanism for superconducting qubits. Transmon qubits have traditionally been fabricated using lift-off aluminum deposited together with their Josephson junctions; however, improved coherence times have recently been found in transmons which use lift-off metal for only a small fraction of the qubit. To better understand this improvement and predict any remaining limits imposed by the incorporation of lift-off, we characterize the increased loss found in coplanar waveguide resonators formed with lift-off metal. We vary surface treatment such as oxygen ashing and ion milling, and study the effects of double-angle evaporation, e-beam resist residue, and surface roughness on resonator quality factors.   

Hydrogen-free amorphous silicon with no tunneling states

The ubiquitous low-energy excitations, known as the two-level tunneling systems (TLS), are one of the universal phenomena of amorphous solids. These excitations dominate the acoustic, dielectric, and thermal properties of structurally disordered solids. One exception has been a type of hydrogenated amorphous silicon (a-Si:H) with 1 at.{\%} hydrogen. Using low temperature elastic measurements of electron-beam evaporated amorphous silicon (a-Si), a model monatomic amorphous system, we show that TLS are also diminished in this system as the films become denser and more structurally ordered. Our results demonstrate that TLS are not intrinsic to the glassy state but instead reside in low density regions of the amorphous network. This work obviates the role hydrogen was previously thought to play in removing TLS in a-Si:H and favors an ideal four-fold covalently bonded amorphous structure as the cause for the disappearance of TLS. Our result supports the notion that a-Si can be made a ``perfect glass'' with ``crystal-like'' properties, thus offering an encouraging opportunity to use it as a simple crystal alternative in applications, such as in modern quantum devices where TLS are the source of dissipation, decoherence and 1/f noise.   

Noise study of insulating films within superconducting LC resonators

Two-level systems (TLS) in amorphous dielectrics, known to be a major source of decoherence in superconducting qubits, are also known to cause low-frequency phase noise in resonating superconducting circuits. Here we will report on an effort to characterize this noise using microwave LC resonators fabricated with a trilayer capacitor containing a deposited silicon nitride dielectric film containing TLS, sandwiched by superconducting electrodes. The resonators are probed at frequencies of approximately 6 GHz and at temperatures of 10-200 mK. The noise dependence on temperature, microwave power, and dielectric volume will be discussed in the context of standard tunneling model of two level systems and newer models.   

Overcoming charge noise decoherence by photon-assisted pair-breaking in a charge qubit

We report on recent measurements [1] of a charge qubit, a Cooper-pair box, coupled to a high-Q microwave cavity in the strong driving regime. This we model using a dressed state formalism, and we find evidence for a process that involves energy transfer corresponding to a large number ($\sim$14) of photons. This energy is sufficient to break a Cooper-pair on the island, and it results in a new relaxation channel for the qubit. Specifically, this relaxation resets the qubit into a charge state determined by the static bias conditions, resulting in a sudden population inversion around each dressed state degeneracy point. At low driving strengths, decoherence is governed by charge noise in the environment, while in the discovered strong driving regime the relaxation rate due to pair-breaking can overcome the environmental charge relaxation rate. This results in a regime that is especially attractive for charge sensing since the qubit response becomes immune to non-equilibrium quasiparticle poisoning and less susceptible to its charge noise environment. \\[4pt] [1] S. E. de Graaf et al. PRL 111, 137002 (2013); J. Lepp\"{a}kangas et al., J. Phys. B, 46, 224019