Session V29: Focus Session: Superconducting Qubits: Epitaxial Junctions and Two-Level Systems

Coherence in a transmon qubit with epitaxial tunnel junctions

We developed transmon qubits based on epitaxial tunnel junctions and interdigitated capacitors. This multileveled qubit, patterned by use of all-optical lithography, is a step towards scalable qubits with a high integration density. The relaxation time $T_1$ is $.72-.86\;\rm{\mu sec}$ and the ensemble dephasing time $T_2^*$ is slightly larger than $T_1$. The dephasing time $T_2$ ($1.36\;\rm{\mu sec}$) is nearly energy-relaxation-limited. Qubit spectroscopy yields weaker level splitting than observed in qubits with amorphous barriers in equivalent-size junctions. The qubit's inferred microwave loss closely matches the weighted losses of the individual elements (junction, wiring dielectric, and interdigitated capacitor), determined by independent resonator measurements.   

Superconducting qubits consisting of epitaxially-grown NbN/AlN/NbN Josephson junctions

We demonstrate superconducting qubits using epitaxially-grown Josephson junctions. A fully epitaxial NbN/AlN/NbN trilayer on MgO (100) substrate is processed by photolithography and dry-etching into transmon qubits with a large Josephson energy. The tunnel barrier made of cubic-phase AlN, rather than the ordinary hexagonal phase, is the key to avoid piezoelectric coupling to the phonon bath. The energy-relaxation time and the spin-echo decay time of $\sim 500$~ns are observed in the qubits that are coupled to a monolithically-made coplanar waveguide resonator.   

Josephson phase qubits incorporating high-Q crystalline dielectrics

The energy relaxation times of Josephson phase qubits are currently limited by spurious coupling of the qubit to unsaturated two level system (TLS) defects of the amorphous dielectrics. It is expected that incorporation of defect-free crystalline dielectrics into qubit circuits will dramatically improve coherence. Here, we describe the growth and characterization of novel crystalline dielectrics for superconducting qubit applications, including grown Al2O3 on epitaxial Re underlayers. We discuss the incorporation of epitaxial dielectrics into phase qubit circuits, and present data on qubit coherence.   

Growth of epitaxial Al/AlOx/Re using a sputtering PLD hybrid system with \textit{in-situ} RHEED

Our objective is the growth of epitaxial dielectrics on crystalline superconducting underlayers to improve the performance of superconducting Qubits. We have grown epitaxial Re thin films on a c-plane sapphire substrate using RF magnetron sputtering, and then transferred \textit{ex-situ} to a pulsed laser deposition (PLD) system where dielectrics thin film layer is deposited. One drawback of this fabrication approach is the necessity to expose the sample to air when the sample is transferred to different deposition chambers. In order to avoid these drawbacks, we have employed a hybrid PLD-sputtering deposition that will allow us to grow the oxide dielectric/Re heterostructures in an \textit{in-situ} environment without breaking vacuum. The system is also equipped with reflection high energy electron diffraction (RHEED) which will allow us to perform \textit{in-situ} characterization of the structure and growth dynamics. We will discuss our strategy of epitaxial growth of various single crystal dielectrics on superconducting thin films in this system and their structural and electrical properties of the heterostructures.   

Transport Characteristics of Self-Aligned Josephson Junctions Grown using co-Deposited Molecular Beam Epitaxy

Low noise Josephson junctions are extremely desirable in SQUIDs and qubit circuits. Sources of flux noise and critical current noise can be reduced by using both clean, single crystal junctions to lower the density of fluctuators and by decreasing the size of the junctions to lower the absolute number of fluctuators. We report transport characteristics of small, single crystal Josephson junctions grown using a co-deposited aluminum-oxide barrier molecular beam epitaxy process. We also report a novel self-aligned fabrication process that allows us to produce sub-micron junctions from these single crystal films. We show that our co-deposited junctions have more ideal transport characteristics than those junctions grown with only a diffused barrier. -   

Internal loss of superconducting resonators induced by interacting two level systems

In a number of recent experiments with microwave superconducting resonators the anomalously slow dependence of the quality factor on the power was observed. This observation implies that the monochromatic radiation does not saturate two level systems in the surrounding oxides as predicted by the standard model of two-level systems (TLS). We argue that these observations suggest the importance of interactions between TLS in these materials. We show that interactions between TLS lead to a drift of their energies that result in much slower, logarithmic dependence of their absorption on the radiation power in a reasonable agreement with the data.   

Two-level system dynamics in amorphous dielectrics probed with a dc electric field

We report loss in~a thin-film dc electric-field tunable LC resonator built with superconducting aluminum and silicon nitride dielectric. To measure the loss we continually apply microwave power on resonance and monitor the transmitted power. At milli-Kelvin temperatures, loss is limited by two-level systems in the dielectric which are saturated with high microwave excitation power. Measurements show that a sudden change of applied dc field causes the dielectric loss to increase to the intrinsic low power loss tangent of the dielectric. We study the subsequent relaxation of the loss tangent caused by two-level system saturation and interactions. We discuss how this arises from the dynamics of a distribution of two-level system defects and compare it with new theoretical work on interacting two-level systems.   

Studying two-level systems in Josephson junctions with a Josephson junction defect spectrometer

We have fabricated and measured Josephson junction defect spectrometers (JJDSs), which are frequency-tunable, nearly-harmonic oscillators that probe two-level systems (TLSs) in the barrier of a Josephson junction (JJ). A JJDS consists of the JJ under study fabricated with a parallel capacitor and inductor such that it can accommodate a wide range of junction inductances, L$_{J0}$, while maintaining an operating frequency, f$_{01}$, in the range of 4-8 GHz. In this device, the parallel inductance helps the JJ maintain linearity over a wide range of frequencies. This architecture allows for the testing of JJs with a wide range of areas and barrier materials, and in the first devices we have tested Al/AlOx/Al JJs. By applying a magnetic flux bias to tune f$_{01}$, we detect TLSs in the JJ barrier as splittings in the device spectrum. We will present our results toward identifying and quantifying these TLSs, which are known to cause decoherence in quantum devices that rely on JJs.   

Relaxation of a Cooper-Pair Box Coupled to Discrete Charge Fluctuators

Recently, Kim \emph{et al.} have reported that the interaction of a Cooper-pair box (CPB) with discrete charge fluctuators can decrease the relaxation time ($T_{1}$) of the first excited state of a CPB when operating the CPB near the transition frequency of a charged two-level system (TLS).\footnote{Z. Kim \emph{et al.,} Physical Review B, \textbf{78} 144506 (2008).} Using a density matrix approach and a 4-level Hilbert space, we have simulated the $T_{1}$ of a CPB coupled to a TLS and a dissipative bath. We model the TLS with asymmetry and tunneling parameters which we obtain along with the CPB parameters from fits to microwave spectroscopic measurements.\footnote{Ibid.}$^,$\footnote{F. C. Wellstood, Z. Kim, and B. S. Palmer, arXiv:0805.4429.} To model the bath, the CPB is coupled to a source of charge noise which causes relaxation and dephasing while the TLS is coupled to its own dissipative source of energy. Results of the simulation are presented and compared to the experimental measurements.   

Microwave Frequency Loss in Aluminum Nanobridge Josephson Junctions

Dielectric loss is a major source of decoherence in many superconducting qubits. Weak link Josephson junctions have the potential advantage of eliminating any loss associated with the insulating barrier in conventional tunneling type devices. We present quality factor measurements of 6 GHz superconducting resonators realized from three dimensional aluminum nanobridges shunted by single crystal silicon overlap capacitors. We compare the measured Q values with those obtained from similar resonators with aluminum tunnel junctions, with critical currents also in the microamp range. We discuss potential relaxation mechanisms specific to weak link junctions, and describe nanobridge qubit designs.   

$T_1$-echo sequence - Preserving the state of a qubit in the presence of coherent interaction

We propose a sequence of pulses intended to preserve the state of a qubit in the presence of strong, coherent coupling to another quantum system. The sequence can be understood as a generalized SWAP and works in formal analogy to the well-known spin echo. Since the resulting decoherence rate of the qubits state is strongly influenced by the additional system, this sequence might serve to protect its quantum state. A possible area of application would be in superconducting circuits, where often spurious two-level system interact strongly with the qubits and might thus provide the necessary resource.   

Circuit quantum electrodynamics with a scanning qubit

We report measurements of the coupling between a superconducting microwave resonator and a transmon qubit fabricated on a separate chip and mounted to a three-dimensional cryogenic translation stage. The qubit-resonator system reached the strong coupling regime with a coupling strength in excess of 80 MHz. We use the translation stage to explore the position dependence of the coupling strength. With a scanning qubit stage, it is possible to measure many qubits in succession and study the statistics of the fabrication process. The system can also be used as a local probe of a large array of microwave cavities and superconducting qubits.   

Noise and microresonance of critical current in Josephson junction induced by Kondo trap states

We analyze the impact of trap states in the oxide layer of a superconducting tunnel junctions, on the fluctuation of the Josephson critical current, thus on coherence in superconducting qubits. We use second order perturbation theory which allows to obtain analytical formulae for the interacting bound states and spectral weights, limited to small and intermediate repulsions. Remarkably, it still reproduces the main features of the model as identified from the Numerical Renormalization Group. We present analytical formulations for the subgap bound state energies, the singlet-doublet phase boundary, and the spectral weights. We show that interactions can reverse the supercurrent across the trap. We finally work out the spectrum of junction resonators for qubits in the presence of on-site repulsive electrons and analyze its dependence on microscopic parameters that may be controlled by fabrication.   

Probing coupling mechanism between microscopic two-level system and superconducting qubits

We propose a scheme to clarify the microscopic nature of Josephson qubits interacting with the two-level systems, coming from microscopic defects located inside insulation layer. We found that the sensitivity of the generally used spectral method in phase qubit is not sufficient to evaluate the exact form of the coupling. On the contrary, our numerical calculation shows that the coupling strength changes remarkably with flux bias for a flux qubit, providing a useful tool to investigate the coupling mechanism between the two-level systems and qubits.