Session Y29: Focus Session: Superconducting Qubits - Coherence and Materials II

Investigating decoherence in the transmon qubit using a 3D resonator

We studied the coherence times of transmon qubits using three-dimensional resonators. The three-dimensional (3D) superconducting resonant cavity is machined with aluminum alloy, whose quality factor is higher than 5 million at 10 mK inside a magnetic shield. The transmons are fabricated on sapphire substrates whose internal Q was not lower than 2 million when evaluated in the 3D resonator. We measured the relaxation and dephasing times of the qubits and were able to draw a lower bound on these numbers.   

Decoherence in Improved Transmon Qubits

The transmon is a simple superconducting qubit which has less dependence on the usual sources of 1/f noise, and has coherence which is mostly limited by a source of anomalous dissipation. The quality factors of transmon qubits on sapphire are observed to be $\sim$ 50,000, similar to that of transmission line resonators made with the same geometry. It is likely that both these devices may be limited by surface dielectric losses. We will report on the design and characterization of transmon qubits which are fabricated with reduced dielectric losses to possibly increase coherence times.   

Measurements of quasiparticle tunneling rate in a superconducting transmon qubit

A practical quantum computer requires qubits with long coherence times in order to perform many quantum gates. For a superconducting qubit, non-equilibrium quasiparticle tunneling is one possible source of decoherence. Spectroscopy measurements of a superconducting transmon qubit can be used to set a bound on the quasiparticle tunneling rate. When operated in the low $E_J$/$E_C$ regime, the transmon qubit transition frequency switches between two well-resolved branches due to quasiparticle tunneling. A selective $\pi$ pulse applied to one of these two branches can excite the qubit only if the qubit is at that frequency. Thus by repeatedly applying $\pi$ pulses to interrogate the qubit state, the quasiparticle dynamics can be studied. We will present our results on the quasiparticle tunneling rate in a transmon qubit.   

Dynamical decoupling and noise spectroscopy with a superconducting flux qubit

We demonstrate dynamical decoupling in a superconducting flux qubit with a long energy-relaxation time, $T_1 = 12\,\mu$s. Low-frequency noise acts to dephase the qubit, reducing its transverse coherence time $T_2$. At the noise-optimal bias point we observe a free-induction decay time $T_2^* = 2.5\,\mu$s and $T_1$-limited spin-echo decay, $T_{2E} = 2\,T_1$. Biased away from this point, the increased sensitivity to flux noise leads to increased echo and free-induction decay rates. We moderate the dephasing effects of this noise by applying dynamical-decoupling sequences with up to 200 $\pi$-pulses. Using the CPMG sequence, we achieve a more than 50-fold enhanced decay time over $T_2^*$, and Gaussian pure-dephasing times $T_\varphi > 100\,\mu$s. We use the filtering property of this pulse sequence to facilitate spectroscopy of the environmental noise and reconstruct its $1/f$ power spectral density, which we independently confirm by a Rabi-spectroscopy approach. We characterize the noise sources coupling to the energy-bias and tunnel-coupling terms of the Hamiltonian.   

Multi-mode circuit quantum electrodynamics

In circuit QED experiments with low anharmonicity superconducting qubits, like the transmon, it has been shown how the many-level structure of the qubits can give rise to non-trivial effects. Examples are the straddling regime [1] and high-power qubit readout induced by qubit nonlinearities [2]. In the same spirit, there are also clear experimental evidences to the effect that higher resonator modes play an important role in setting the size of the qubit-qubit flip-flop interaction mediated by virtual resonator photons [3] and the qubit decay rate due to the Purcell effect [4]. In this talk we explore how these higher modes can be taken into account in a theoretical description of the system, and how they affect the flip-flop and Purcell decay rates. \\[4pt] [1] Houck et al., Phys Rev. A 76, 042319 (2007); Srinivasan et al, V26.00006, 2010 March Meeting. \\[0pt] [2] Reed et al, Phys. Rev. Lett. 105, 173601 (2010), Bishop et al, Phys. Rev. Lett. 105, 100505 (2010), Boissonneault et al, Phys. Rev. Lett. 105, 100504 (2010). \\[0pt] [3] Filipp et al, arXiv:1011.3732v1 \\[0pt] [4] Houck et al, PRL 101, 080502 (2008)   

Dissipation in the ultra-strong coupling regime

It has recently been shown that the ultra-strong coupling regime, in which the rotating-wave approximation breaks down, can be obtained using a flux qubit coupled to a transmission line [1]. This regime has been observed experimentally in [2, 3]. We will show the usual quantum optics master equation fails in this context and give a more accurate one. We will also explain how non-trivial properties of the ground state could be experimentally studied.\\[3pt] [1] J. Bourassa et al, Phys. Rev. A 80, 32109 (2009)\\[0pt] [2] T. Niemczyk et al, Nature Physics 6, 772-776 (2010)\\[0pt] [3] P. Forn-D\'iaz et al., arXiv:1005.1559v1 (2010)\\[0pt]   

Strong frequency dependence of coupling of a Cooper- pair box qubit to Quantum Noise

Our system consists of an Al/AlO$_{\mbox{x}}$/Al Cooper-pair box (CPB) charge qubit coupled to a lumped element resonator, which in turn is coupled to a transmission line. From the measured Rabi frequency, for a given microwave frequency $f$ and amplitude in the transmission line, we can extract the coupling of qubit to the transmission line. We observe an order of magnitude variation in this coupling over the range of $f$ = 4 to 8GHz which is in agreement with the variation of our measured lifetimes. Assuming that our qubit is coupled directly to a $50 \Omega $ impedance with the measured coupling, we find that for $f = $ 6 to 7 GHz the lifetime of $30 \mu$s measured at the charge sweet spot can be well explained by quantum noise. At $f = 4$GHz, we observe an order of magnitude weaker coupling and a $T_1$ of $ 200\mu$s .   

Dephasing Measurements of a Cooper-pair box

We present data on the dephasing properties of our Al/AlO$_{\mbox{x}}$/Al Cooper-pair box (CPB) qubit. The CPB had a charging energy $E_{C}/h$ = 6.25 GHz and a maximum $E_{J}/h$ = 19 GHz which was decreased by an external magnetic field to an effective $E_{J}/h$ of 6.1 GHz. The qubit was capacitively coupled to a lumped element microwave resonator ($f_{0} = 5.446$ GHz, $Q_{L} = 1.8\times10^{4}$) which was in turn coupled to a transmission line. To manipulate the qubit, a microwave pulse at 6.1 GHz was sent to the transmission line. The state of the qubit was then measured by sending a second microwave pulse at $f_{0}$ and measuring the amplitude and phase of the transmitted power. We observed Rabi oscillations with Rabi frequencies from 1.94 to 5.32 MHz decay with time constants in the range T' = 0.6 to 1.6 $\mu$s. We measured an inhomogeneous dephasing time ($T_{2}${*}) of 322 ns by performing a Ramsey fringe experiment. Assuming $1/f$ charge noise is the dominant dephasing mechanism we extracted a $1/f$ charge noise amplitude of 1.6$\times$10$^{-3} e/\sqrt{Hz}$ at 1 Hz.   

Improved T2 in Josephson Phase Qubits

Phase qubit gate fidelities are limited by individual device dephasing times (T2). Reduction of dephasing is therefore an important immediate goal for phase qubit experiments. A simple way to reduce dephasing is to increase the device loop inductance in order to lower the noise currents driven by magnetic flux noise; T2 should scale linearly with loop inductance. Surface spin models for flux noise also predict that wider loop traces should reduce the noise. We present data on T2 for phase qubits with varied loop inductance and trace width. We present data from experiments in which we find that doubling the loop inductance increases T2 by 25\%.   

Evidence for coherent quantum phase slips from dephasing of fluxonium qubit

Phase slips are events in which the phase across a superconducting wire changes by 2$\pi$. The thermally activated phase slips at high temperatures are well understood but the coherent phase slips caused by quantum fluctuations well below the critical temperature have, so far, eluded observation. We report new decoherence data for the fluxonium qubit [1] that provide evidence for coherent quantum phase slips across the qubit inductance, implemented with a long array of Josephson tunnel junctions. Coherent quantum phase slips result in broadening of the qubit transition frequency due to Aharonov-Casher interference of multiple phase slip paths (or flux tunneling through different junctions) encircling random offset charges on array islands [2]. \\[4pt] [1] V.E. Manucharyan et al., Science 326, 113 (2009).\\[0pt] [2] D. Ivanov et al., Phys. Rev. B 65, 024509 (2002).   

Relaxation mechanisms of the fluxonium qubit

Fluxonium is a highly anharmonic artificial atom, which utilizes an inductance formed by an array of large Josephson junctions to shunt the junction of a Cooper-pair box. The first excited state transition frequency is widely tunable with flux, yet can be read out over the entire five octave range due to interactions of the 2nd excited state with the readout cavity, enabling a dispersive readout. We present T1 times of several fluxonium samples over the full range of flux dependent transition energies. By mapping out the qubit lifetimes we are able to distinguish between the contributions due to the Purcell effect and quantify dissipation internal to the qubit. With this understanding, we can design a qubit with minimized contribution from internal losses, which should push lifetimes further into the tens of microseconds. [1] V. E. Manucharyan et al., Science 326, 113 (2009).   

1/f noise and susceptibility-magnetization correlation in disordered ferromagnets

We consider a strongly disordered ferromagnet modeled by Ising spins placed at random in 2D with ferromagnetic interactions decaying exponentially with inter-site distance. Ferromagnetic phase in this model arises due to formation of infinite percolation cluster of strongly interacting spins. Fractal nature of the percolation cluster manifests itself in the dynamics of the system in the vicinity of the percolation transition. Simulating the dynamics with single spin flip Monte Carlo algorithm we observe 1/f power spectra of magnetization noise in a wide temperature range near the transition. Subjected to external AC magnetic field the system shows significant cross-correlation between susceptibility and magnetization in the ferromagnetic phase. This results suggest a possible explanation of the inductance-flux cross-correlation recently observed in SQUIDs [1]. \\[4pt] [1] S. Sendelbach, D. Hover, M. Muck, and R. McDermott, Phys. Rev. Lett. 103, 117001 (2009)   

Are ``pinholes'' the cause of excess current in superconducting tunnel junctions? A study of Andreev current in highly resistive junctions

In highly resistive superconductor---insulator---superconductor (SIS) and superconductor---insulator---normal-metal (SIN) junctions, ``excess'' subgap current is usually observed. We have studied subgap conductance in Al/AlO$_x$/Al and Al/AlO$_x$/Cu tunnel junctions. In the former, we observed a huge (two orders of magnitude) decrease in subgap conductance upon the transition from the SIS to the SIN regime. In the latter, we observed several signatures of coherent diffusive two-particle transport. We use the quasiclassical Keldysh-Green function theory to quantify the contributions of the single- and two-particle processes on subgap conductance. Our observations indicate insignificance of highly transparent microscopic defects (``pinholes'') in the tunneling barrier, and we therefore argue that the common ``pinhole'' scenario is not the explanation for the observed excess subgap current in SIS tunnel junctions.   

Critical current noise and junction resonators in Josephson junction from interacting trap states

We analyze the impact of trap states in the oxide layer of superconducting tunnel junctions on the fluctuation of the Josephson current. These are known to inhibit the coherent operation of superconducting qubits. These have a twofold effect: Occupying trap states blocks out parts of the critical current of the Josephson junction. Electrons can also cross the junction via hopping across a trap. We are extending previous studies of noninteracting traps to the case where the traps have on-site electron repulsion. We use second order perturbation theory which allows to obtain analytical results but limited to small and intermediate repulsion. 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, which are in agreement with recent Numerical Renormalization Group analysis. We show that interactions can reverse the supercurrent across the trap. We finally work out the resonance noise spectrum in the presence of on-site repulsive electrons and suggest a criteria for the fabrication of parameters that may help to suppress low frequency noise from superconducting quantum computation devices.   

Energy relaxation mechanisms in capacitively shunted flux qubits

Energy losses in superconducting qubits remain a major object of study in the road towards scalable, highly coherent qubit devices. The current understanding of the loss mechanisms in these devices is far from being complete and it is sometimes difficult to experimentally separate the different contributions to decoherence. Here we compare a traditional three Josephson-junction flux qubit to the recently implemented capacitively shunted flux qubit [1], whose energy decay is thought to be limited by dielectric losses arising from native oxides in the shunting capacitor. Keeping all parameters identical except for the shunting capacitance, we obtain energy relaxation times that are comparable for both types of qubit. This suggests that the energy relaxation time is not limited by junction losses in capacitively shunted flux qubits. We discuss some other possible loss mechanisms present in these devices. \\[4pt] [1] M. Steffen \textit{et al}. Phys. Rev. Lett. \textbf{105}, 100502 (2010)