Quantum Noise in the Josephson Charge Qubit

We study decoherence of the Josephson charge qubit by measuring energy relaxation and dephasing with help of the single-shot readout. We found that the dominant energy relaxation process is a spontaneous emission induced by quantum noise coupled to the charge degree of freedom. Spectral density of the noise at high frequencies is roughly proportional to the qubit excitation energy.

Figure 1

(a) Schematic device representation. (b) State manipulation diagram for measurements of the qubit relaxation rate. The inset shows operation pulse sequence.

Figure 2

(a) Energy relaxation rate ${\Gamma }_1$ measured by the SET normally set in the $JQP$ peak (closed circles) and in blockade regime (open squares) and phase decoherence rate ${\Gamma }_2$ (open circles) versus gate induced charge $q$ of sample I ($E_J/h=5.1\mathrm{G}\mathrm{H}\mathrm{z}$). The inset exemplifies a decay of probability $P$ to detect charge in the trap as a function of the adiabatic pulse length $t_a$, measured at $q=-0.36e$. ${\Gamma }_1$ is derived from exponential fit of the decay. (b) ${\Gamma }_1$ measured in sample II for three different Josephson energies.

Figure 3

Relaxation rate ${\Gamma }_1$ as a function of $E_J$ measured at the degeneracy point (open triangles) and off the degeneracy point (open circles) at $\Delta E/h\approx 100\mathrm{G}\mathrm{H}\mathrm{z}$ for sample I.

Figure 4

(a) Noise $S_U/{\hslash }^2$ derived from ${\Gamma }_1-q$ dependences of the sample I (closed circles) and sample II (open circles). Open triangles show ${\Gamma }_1$ dependences of sample II at the degeneracy point. A dash-dotted line represents a linear rise $(4e^2/\pi )R\hslash \omega /{\hslash }^2$ ($f$ noise) with $R=6\Omega$. A dashed line is the $1/f$ noise from Eq. (3) with $\alpha \approx (1.3\times {10}^{-3}e{)}^2$ derived from ${\Gamma }_2$ measurements. (b) A schematic representation of the classical $S_U^C(\omega )$ and quantum $S_U^Q(\omega )$ noise behavior. At frequencies $\omega <kT/\hslash$, $S_U^Q(\omega )\approx S_U^C(\omega )$ and behaves like a $1/f$ noise. At frequencies $|\omega |>kT/\hslash$, $S_U^Q(\omega )>S_U^C(\omega )$ and the quantum noise is proportional to $\omega$.