Flux Qubits with Long Coherence Times for Hybrid Quantum Circuits

We present measurements of superconducting flux qubits embedded in a three dimensional copper cavity. The qubits are fabricated on a sapphire substrate and are measured by coupling them inductively to an on-chip superconducting resonator located in the middle of the cavity. At their flux-insensitive point, all measured qubits reach an intrinsic energy relaxation time in the $6–20\mu \mathrm{s}$ range and a pure dephasing time comprised between 3 and $10\mu \mathrm{s}$. This significant improvement over previous works opens the way to the coherent coupling of a flux qubit to individual spins.

Figure 1

(a) Cutaway representation of the 3D cavity, with the $LC$ circuit (in blue) on its sapphire chip. The green arrow represents the applied magnetic field $B$. The red arrow represents the ac electric field $E(t)$ of the first mode of the cavity. (b) Transmission spectrum of the cavity coupled to the $LC$ resonator. The first peak at frequency ${\omega }_{LC}/2\pi =4.643\mathrm{GHz}$ corresponds to the resonance of the $LC$ resonator while the two other peaks correspond to the first modes of the cavity. (c)–(d) Circuit diagram and colorized SEM micrograph showing the FQ (in red) inductively coupled to the $LC$ resonator (in blue). (e) Amplitude of the transmitted signal at frequency ${\omega }_{LC}$ as a function of $B$, showing the signal from the six qubits.

Figure 2

Characterization of $Q3$ (top panels) and $Q4$ (bottom panels): (a)–(b) (left panels) Measured qubit frequency ${\omega }_{01}({\mathrm{\Phi }}_b)$ (blue dots) and fit (red curve) yielding the qubit parameters $\mathrm{\Delta }$ and $I_P$. (Right panels) Spectroscopy data at ${\mathrm{\Phi }}_b=0$ (blue dots). $Q3$ spectrum is fitted with a single Lorentzian peak; $Q4$ spectrum is fitted with a sum of two Lorentzian peaks separated by 150 kHz. (c)–(d) (left panels) Qubit energy relaxation and spin-echo measurements. The excited state probability is plotted as a function of the delay between the $\pi$ pulse and readout pulse (blue dots) or between the two $\pi /2$ pulses of the echo sequence (purple dots). Red (orange) solid line is an exponential fit to the energy relaxation (spin-echo) data. (Right panels) Measured Ramsey fringes (blue solid line), with fit (red solid line) to exponentially damped single (top) and double (bottom) sine curves.

Figure 3

Pure dephasing rates of $Q4$ as a function of ${\mathrm{\Phi }}_b$: Experimental (dots) and fitted (line, see text) echo (a) and Ramsey (b) dephasing rates.

Figure 4

Frequency dependence of the relaxation rate ${\mathrm{\Gamma }}_1$ of $Q4$ in the vicinity of its optimal point at $T=33\mathrm{mK}$ (blue squares) and $T=150\mathrm{mK}$ (red circles), showing an increased relaxation rate caused by quasiparticles.