Nanowire Superinductance Fluxonium Qubit

We characterize a fluxonium qubit consisting of a Josephson junction inductively shunted with a NbTiN nanowire superinductance. We explain the measured energy spectrum by means of a multimode theory accounting for the distributed nature of the superinductance and the effect of the circuit nonlinearity to all orders in the Josephson potential. Using multiphoton Raman spectroscopy, we address multiple fluxonium transitions, observe multilevel Autler-Townes splitting and measure an excited state lifetime of $T_1=20\mu \mathrm{s}$. By measuring $T_1$ at different magnetic flux values, we find a crossover in the lifetime limiting mechanism from capacitive to inductive losses.

Figure 1

(a) The circuit diagram for the qubit, with the first antisymmetric standing wave nanowire mode in blue. $\psi (\mathsf{x},t)$ denotes the flux operator as a function of the dimensionless coordinate $\mathsf{x}=x/l$. An off-chip coil generates the magnetic flux (${\mathrm{\Phi }}_{\mathrm{ext}}$) that is threaded through the loop formed by the nanowire and the junction. $C_g$ and $C_0$ are the coupling capacitances to the readout resonator and to ground, respectively. (b) The first few fluxonium eigenstates plotted for ${\mathrm{\Phi }}_{\mathrm{ext}}/{\phi }_0=-0.38\pi$, and the respective qubit potential with wells around $\varphi /{\phi }_0=-2\pi$ and $\varphi /{\phi }_0=0$, where ${\phi }_0=\hslash /2e$. (c) False colored image of the device with the NbTiN nanowire shown in blue, the single Josephson junction and gate capacitors in red, the readout resonator in purple, and the input transmission line in green.

Figure 2

Two-tone spectroscopy of device 1 (a) and device 2 (b) as a function of ${\mathrm{\Phi }}_{\mathrm{ext}}$. The experimentally measured transition frequencies are indicated with blue markers. The result of a fit to the two-mode Hamiltonian in Eq. (5) and detailed in Ref. [30] is shown with red dashed lines corresponding to the fluxonium spectrum and with purple dashed lines indicating sideband transitions [31]. In (a), the inscription “JJ mode” (Josephson junction mode) identifies the second antisymmetric nanowire mode.

Figure 3

The multitone spectroscopy data, taken at ${\mathrm{\Phi }}_{\mathrm{ext}}/{\phi }_0=-0.46\pi$, demonstrating population transfer between $|g_0⟩$ and $|h_0⟩$ (a) with ${\mathrm{\Omega }}_{\gamma }=0$, and $|h_0⟩$ to $|e_{-1}⟩$ (b) with fixed ${\omega }_{\alpha }/2\pi =7.78\mathrm{GHz}$. The white dashed lines indicate the maximum population from a multilevel master equation simulation [30]. (c) A schematic diagram of the device 2 level structure in the presence of coherent external drives. The drives, with frequencies ${\omega }_i/2\pi$ and amplitudes ${\mathrm{\Omega }}_i$ are detuned from the levels by ${\mathrm{\Delta }}_i/2\pi$. (d) Three sequential $\pi$ pulses ($\sigma =15\mathrm{ns}$) are applied at the transition frequencies to perform $T_1$ measurements of the $|g_{-1}⟩$ state. The demodulated homodyne voltage from the readout resonator is measured as a function of $t_{\mathrm{wait}}$.

Figure 4

(a) Low frequency spectroscopy data from device 3. (b) $T_1$ (red) and $T_{2\mathrm{Ramsey}}$ (blue) data taken at ${\mathrm{\Phi }}_{\mathrm{ext}}/{\phi }_0=-\pi$. (c) $T_1$ as a function of qubit frequency. The lines represent the theory fits for total (red), inductive (blue), and capacitive (green) $T_1$. The $T_1$ values were obtained with both pulsed and mixed state driving. Measurements using both types of excited state preparation at the same flux gave the same value of $T_1$.