Session L39: Focus Session: Superconducting Qubits: 3D Cavities

How coherent are Josephson junctions?

Superconducting quantum circuits based on Josephson junctions are a promising technology to realize a electronically controlled, solid-state based large-scale quantum information processor but their future prospects rely on the intrinsic coherence of Josephson junctions and the engineering of the isolated environment for the quantum circuits. We introduce a new architecture for superconducting quantum circuits employing a single-Josephson junction in a three dimensional waveguide cavity where we carefully engineer the environment of the qubit to effectively reduce the coupling of the qubit to the environment while maintaining sufficient coupling to the control signal. With this architecture we demonstrate that Josephson junction qubits are at least an order of magnitude more coherent with $T^{Ramsey}_{2}$ $\sim$ 10 to 20 $\mu$s without the use of spin echo than previously reported and highly stable, enabling us to observe the physics in a Josephson junction with a unprecedented level of precision. These results suggest that the overall quality of Josephson junctions will allow error rates of a few 10$^{-4}$, approaching the error correction threshold. We will also discuss how to scale this architecture and perform two-qubit gates.   

Bottom-up construction of artificial molecules for superconducting quantum processors

Recent experiments on transmon qubits capacitively coupled to superconducting 3-dimensional cavities have shown coherence times much longer than transmons coupled to more traditional planar resonators. For the implementation of a quantum processor this approach has clear advantages over traditional techniques but it poses the challenge of scalability. We are currently implementing multi-qubits experiments based on a bottom-up scaling approach. First, transmon qubits are fabricated on individual chips and are independently characterized. Second, an artificial molecule is assembled by selecting a particular set of previously characterized single-transmon chips. We present recent data on a two-qubit artificial molecule constructed in this way. The two qubits are chosen to generate a strong Z-Z interaction by matching the 0-1 transition energy of one qubit with the 1-2 transition of the other. Single qubit manipulations and state tomography cannot be done with ``traditional'' single tone microwave pulses but instead specifically shaped pulses have to be simultaneously applied on both qubits. Coherence times, coupling strength, and optimal pulses for decoupling the two qubits and perform state tomography are presented   

Quasiparticle tunneling in a single-junction transmon qubit

The recent increase in transmon qubit quality factor into the million range [1] makes non-equilibrium quasiparticle tunneling a potentially limiting mechanism for qubit coherence. We investigate the dynamics of quasiparticle tunneling in a single-junction transmon qubit with relaxation time $T_1=85~\mathrm{\mu s}$ ($Q=2.6$ million). The qubit operates at moderate ratio of Josephson to charging energy, $E_J/E_C\sim30$, where charge parity in the qubit islands is encoded in the qubit transition frequency. Using Ramsey-type and stimulated echo experiments, we investigate quasiparticle tunneling across the qubit junction on time scales short and long compared to $T_1$. We observe that the quasiparticle tunneling time for the single-junction qubit is at least as long as $T_1$, but shorter than the $1~\mathrm{ms}$ repetition rate. This result is consistent with recent theory and qualitatively different from the two-junction transmon. The dephasing time $T_2^{\ast}=10~\mathrm{\mu s}$ is limited by slow background charge fluctuations and extended to $T_2=95~\mathrm{\mu s}$ using dynamical decoupling. \\[4pt] [1] Paik et al. arXiv:1105.4652v4   

Varying Cavity Quality Factor in situ for a Transmon in Circuit QED

Superconducting transmon qubits have recently been studied within 3D cavities. In addition to increasing the coherence times of the qubits this has enabled a simple scheme for varying the quality factor Q (or decay rate $\kappa$) of a cavity in situ. This decay rate plays an important role in our understanding of a number of effects in circuit quantum electrodynamics, many of which have direct bearing on qubit decoherence processes. Here we study how adjusting the cavity Q affects the coherence times of a single qubit within the 3D architecture. We demonstrate that varying the coupling enables us to not only examine the limitations of qubit $T_1$ due to the Purcell Effect, but also probe new decoherence mechanisms such as the dephasing due to photon shot noise. By understanding and minimizing these effects, we obtain record coherences times $T_2$ and $T_2^{Echo}$ of $\sim 27 \mu s$ and $\sim 47 \mu s$ respectively.   

Dephasing Due to Shot Noise in the Strong Dispersive Limit of Circuit QED

The design parameters of superconducting qubits inside resonant cavities have evolved over time to minimize decoherence, allow fast pulses and enable high fidelity readout. The two are often coupled so strongly that the dispersive shift of the qubit due to a single photon in the cavity (or AC Stark shift) is much larger than a linewidth. In this strong dispersive regime, the passage of any photons can lead to an unintended and complete measurement of the qubit state. We study photon shot noise dephasing in this limit for a transmon and derive a simple relation between the dephasing rate and the product $\bar{n}\kappa$, where $\bar{n}$ is the average cavity occupancy and $\kappa$ is the cavity decay rate. We find good experimental agreement for a large range of $\kappa$, varied \textit{in situ} using a simple mechanism, and note several ways this can influence qubit experiments.   

Effective model of nonlinear circuit quantum electrodynamics

Superconducting electronic circuits containing nonlinear elements such as Josephson junctions are of interest for quantum information processing. The low-energy spectrum of such circuits can now be measured to a precision of better than one part per million. A precise knowledge of their Hamiltonian that goes beyond current models is thus desirable. In this talk I will show how to quantize a superconducting, weakly nonlinear circuit from the knowledge of its classical linear admittance matrix. This approach represents a change of paradigm in circuit quantum electrodynamics and may potentially become a useful alternative to the standard models based on the language of atomic physics and quantum optics.   

Designing a three mode circuit QED experiment

Circuit QED employs the coupling of nonlinear elements to resonant modes of an electronic circuit. We demonstrate that all resonant modes will attain some degree of nonlinearity from even a single nonlinear element. This can result in individually addressable transitions for each mode and allow direct control of each quantum state. Furthermore, we show that the transition frequency of any one mode will depend on the state of all other modes. These state dependent shifts can be used to directly readout the quantum state of one mode probing another. We illustrate this behavior by coupling two three-dimensional resonators to a superconducting transmon qubit and present a method to determine the Hamiltonian for this system using a nonlinear circuit QED model.   

Experiments on a three mode circuit QED system

Current research in superconducting circuit QED is working towards combining an increasing number of cavities and qubits to investigate larger scale quantum systems. Here we will discuss measurements on a system consisting of two three-dimensional microwave resonators coupled to a single transmon qubit. We demonstrate that each mode of the system has sufficient anharmonicity to coherently manipulate the state of the lowest two energy levels. This allows us to measure the coherence of a single excitation in a mode and detect the frequency shift due to excitations of the other modes. These effects are important to consider when using a resonator as a quantum memory to decouple the quantum state from the rest of the system. Furthermore we show that we can use the state dependent shifts to detect the quantum state of one mode with another. The full characterization of the system allows us to determine the Hamiltonian and compare it to the theoretical predictions obtained with a nonlinear circuit QED model.   

Material and Geometric Effects in 3D Transmon Qubits

Optimization of coherent behavior is a key ingredient for any scalable architecture using qubits. Recent breakthroughs in novel qubit designs have resulted in significant improvements in coherence by coupling superconducting qubits to 3-dimensional microwave cavities. We are investigating material and geometric factors affecting the coherence of these 3D transmon qubits. Various loss mechanisms limiting the qubit coherence will be discussed. The role played by device geometry and size in determining the effective qubit-cavity coupling will also be explored.   

3D Microwave Cavity for Qubit Measurement

We have investigated the loss mechanisms of the $\textrm{TE}_{101}$ mode (resonant frequency $\textrm{f}_0 = 8\textrm{ GHz}$) of a superconducting Al microwave cavity. The internal quality factor $Q_{int}$ of the cavity has been measured for a range of temperatures from 23 mK to 360 mK in a low photon number regime and from 360 mK to $\textrm{T}_c \sim$ 1.1 K in a high photon number regime, both with and without a sapphire chip in the cavity. With sapphire present, $Q_{int} \sim 10^6$ was strongly reduced by an applied magnetic field. Without sapphire, $Q_{int} \sim 4\times10^6$ was only weakly dependent on the applied field. The frequency stability of the cavity and the use of the cavity for qubit readout (following recent experiments by H. Paik \textit{et. al.}\footnote{arXiv:1105.4652v4}) will be discussed.   

Characterization of superconducting accelerator cavity at millikelvin temperature for use in quantum computation

Quantum computation using 2D superconducting circuits has been advancing rapidly but has been limited to coherence times of a few microseconds.~ On the other hand, 3d superconducting cavities for accelerators routinely achieve quality factors exceeding ten billion, corresponding to coherence times exceeding one second. ~~With the recent demonstration of coupling a superconducting qubit to a 3d resonator [1], it should be possible to take advantage of this advanced accelerator technology. ~However, accelerator cavities are typically used above 2 K and at 1 W input powers. ~The ultimate residual resistance of accelerator cavities is not yet well understood and it is unclear if they will maintain their exceptional properties at millikelvin temperatures and ultra-low powers.~ We present measurements of a 3.9 GHz accelerator cavity from 2K-20mK and at powers less than one attowatt.~~ [1] Paik, et. al. arXiv:1105.4652   

Improving the Coherence Time of Microwave Cavities

A superconducting cavity resonator is able to store quantum states of light, protect qubits from decoherence and place bounds on material losses. The resonator's utility in all three goals is inherently tied to its quality factor. We report recent progress in improving the quality factors of aluminum waveguide cavities in the quantum regime. We will also report on the use of these cavities to measure the dielectric properties of low-loss substrates and the surface impedance of bulk superconductors and thin films.