Suppressing charge noise decoherence in superconducting charge qubits

We present an experimental realization of the transmon qubit, which is an improved superconducting charge qubit derived from the Cooper pair box. We experimentally verify the predicted exponential suppression of sensitivity to $1∕f$ charge noise. This removes the leading source of dephasing in charge qubits which results in homogeneously broadened transitions with relaxation and dephasing times in the microsecond range. Our systematic characterization of the qubit spectrum, anharmonicity, and charge dispersion shows excellent agreement with theory.

Figure 1

(Color online) Spectrum of two transmon qubits coupled to a cavity. (a) Observed spectrum as a function of magnetic field. Data was obtained in several runs with both transmission and spectroscopy measurements and manually stitched together [stitch points are given by vertical lines in (b)–(d)]. The dashed line is the theoretical fit to the data (only shown on the right for clarity). The charging energies $E_{C1}∕h=386\mathrm{MHz}$ and $E_{C2}∕h=332\mathrm{MHz}$ are obtained from the charge dispersion and held fixed. Fit parameters and their obtained optimal values are the maximum Josephson energies $E_{J1}^{\max }∕h=17.45\mathrm{GHz}$ and $E_{J2}^{\max }∕h=18.06\mathrm{GHz}$, coupling strengths $g_1∕2\pi =47\mathrm{MHz}$ and $g_2∕2\pi =169\mathrm{MHz}$, cavity frequency ${\omega }_c∕2\pi =6.84\mathrm{GHz}$, and the flux periodicity for each qubit with ${\Phi }_1=0.67{\Phi }_2$. (b), (c), and (d) show the absolute errors of the model fit for the cavity, qubit 1, and qubit 2, respectively. (f) shows the only spurious avoided crossing, while (e) and (g) show typical line cuts from spectroscopy and transmission.

Figure 2

(Color online) Anharmonicity of a transmon qubit. Data presented for qubit 1 at $E_J∕E_C=40$. Three qubit transitions are measured: the 01 transition in a single tone spectroscopic measurement (bottom), the two-photon 02 process with a $35\mathrm{dB}$ stronger drive (middle, offset), and the 12 transition (top, offset) while populating the transmon excited state with a second drive on the 01 transition. The second excited state of the transmon is not populated with either the two-photon 02 process or a tone on the 12 transition at normal spectroscopy powers (bottom). The 01 and 12 transitions are separated by $455\mathrm{MHz}$; the transmon can therefore be treated as a two-level system even during fast control operations.

Figure 3

Exponential suppression of charge dispersion. Data are presented for qubit 2 at four different values of $E_J$, where (a) $E_J∕E_C=28.6$, (b) 16.3, (c) 13.3, and (d) 10.4. Spectroscopic measurements of qubit frequency while changing the gate voltage reveal the expected sinusoidal frequency bands. The width of the band (charge dispersion) is decreased from $74\text{to}0.8\mathrm{MHz}$. Two sinusoids are evident as random quasiparticle tunneling events cause the frequency curve to shift by one electron. The measured charge dispersion agrees well with the theoretical prediction (right).

Figure 4

(Color online) High fidelity qubit control and long coherence times in a transmon. Data from a third qubit, measured at the flux sweet spot with $E_C\sim 380\mathrm{MHz}$ and $E_J∕E_C\sim 50$. (a) Rabi oscillations with $100.5\pm 2\%$ visibility. (b) Relaxation from excited state. Measurements of qubit state while varying delay after a $\pi$ pulse yield $T_1=1.87\mu \mathrm{s}$. (c) Ramsey fringes, measured by varying a delay between two $\pi ∕2$ pulses, show a long dephasing time $T_2^{*}=2.22\mu \mathrm{s}$ (no echo).