Temperature Dependence of Coherent Oscillations in Josephson Phase Qubits

We experimentally investigate the temperature dependence of Rabi oscillations and Ramsey fringes in superconducting phase qubits. In a wide range of temperatures, we find that both the decay time and the amplitude of these coherent oscillations remain nearly unaffected by thermal fluctuations. In the two-level limit, coherent qubit response rapidly vanishes as soon as the energy of thermal fluctuations $k_{\mathrm{B}}T$ becomes larger than the energy level spacing $\hslash \omega$ of the qubit. In contrast, a sample of much shorter coherence times displayed semiclassical oscillations very similar to Rabi oscillation, but showing a qualitatively different temperature dependence. Our observations shed new light on the origin of decoherence in superconducting qubits. The experimental data suggest that, without degrading already achieved coherence times, phase qubits can be operated at temperatures much higher than those reported till now.

Figure 1

(a) Schematic of the phase qubit circuit. The qubit junction is embedded in a superconducting loop which is coupled inductively to the flux-biasing coil and readout dc SQUID. (b) Sketch of the qubit potential $U(\phi )$. On the right side, a zoom into the shallow left potential well indicates the wave functions describing the two qubit states $|0⟩$ and $|1⟩$.

Figure 2

(a) Temperature dependence of the $T_1$ time of Nb-based sample no. 1, measured by monitoring the lifetime of the excited state after populating it by a resonant $\pi$-pulse of duration 1.9 ns and frequency 16.5 GHz. The dashed line is a plot of Eq. (2), showing the temperature dependence as expected from the spin-boson model. (b) Rabi-like oscillations in sample no. 1 observed at the indicated temperatures using resonant microwaves of 16.5 GHz frequency. Solid lines are fits to exponentially decaying sine functions.

Figure 3

Rabi oscillations observed in Al-based sample no. 2 featuring ${\mathrm{SiN}}_x$ insulation, at the indicated temperatures. The frequency of the driving microwave signal was 7.4 GHz. Solid lines are fits to exponentially decaying sine functions from which Rabi amplitude and decay time are extracted.

Figure 4

Amplitude (right axis) and decay time (left axis) of Rabi oscillation observed in sample no. 2, plotted versus temperature. Dashed lines are guides to the eye.

Figure 5

Data obtained on sample no. 2. Top panel: Ramsey oscillation amplitude (filled squares, right axis) and decay time (open circles, left axis) vs temperature. Dashed lines are guides to the eye. Bottom panel: Directly measured decay time $T_1$ of the excited qubit state vs temperature. Two data sets correspond to different magnetic field biases, respectively, resulting in resonance at a frequency of 7.4 GHz (circles) and 8.0 GHz (squares). The 8.0 GHz data has been scaled as described in the text. The dashed line is a plot of Eq. (2), showing the theoretically expected temperature dependence for an energy level spacing of 8.0 GHz.