Decoherence in Josephson Phase Qubits from Junction Resonators

Although Josephson junction qubits show great promise for quantum computing, the origin of dominant decoherence mechanisms remains unknown. Improving the operation of a Josephson junction based phase qubit has revealed microscopic two-level systems or resonators within the tunnel barrier that cause decoherence. We report spectroscopic data that show a level splitting characteristic of coupling between a two-state qubit and a two-level system. Furthermore, we show Rabi oscillations whose “coherence amplitude” is significantly degraded by the presence of these spurious microwave resonators. The discovery of these resonators impacts the future of Josephson qubits as well as existing Josephson technologies.

Figure 1

(a) Circuit diagram for the Josephson junction qubit. Junction current bias $I$ is set by $I_{\varphi }$ and microwave source $I_{\mu \mathrm{w}}$. Parameters are $I_0\simeq 11.659\mu \mathrm{A}$, $C\simeq 1.2\mathrm{p}\mathrm{F}$, $L\simeq 168\mathrm{p}\mathrm{H}$, and $L/M\simeq 81$. (b) Potential energy diagram of qubit, showing qubit states $|0⟩$ and $|1⟩$ in cubic well at left. Measurement of $|1⟩$ state performed by driving the $1\to 3$ transition, tunneling to right well, then relaxation of state to bottom of right well. Postmeasurement classical states “0” and “1” differ in flux by ${\Phi }_0$, which is readily measured by readout SQUID. (c) Schematic description of tunnel-barrier states $A$ and $B$ in a symmetric well. Tunneling between states produces ground $|g⟩$ and excited $|e⟩$ states separated in energy by $\hslash {\omega }_r$. (d) Energy-level diagram for coupled qubit and resonant states for ${\omega }_{10}\simeq {\omega }_r$. Coupling strength between states $|1g⟩$ and $|0e⟩$ is given by ${\tilde{H}}_{\mathrm{i}\mathrm{n}\mathrm{t}}$.

Figure 2

(a) Measured probability of state “1” versus microwave excitation frequency $\omega /2\pi$ and bias current $I$ for a fixed microwave power. Data indicate ${\omega }_{10}$ transition frequency. Dotted vertical lines are centered at spurious resonators. (b) Measured occupation probability of $|1⟩$ versus Rabi-pulse time $t_r$ and bias current $I$. In (b), a color change from dark blue to red corresponds to a probability change of 0.4. Color modulation in time $t_r$ (vertical direction) indicates Rabi oscillations.

Figure 3

(a)–(c) Measured occupation probability of $|1⟩$ versus time duration of Rabi pulse $t_r$ for three values of microwave power, taken at bias $I=11.609\mu \mathrm{A}$ in Fig. 2. The applied microwave powers for (a), (b), and (c) correspond to $0.1$, $0.33$, and $1.1\mathrm{m}\mathrm{W}$, respectively. (d) Plot of Rabi oscillation frequency versus microwave amplitude. A linear dependence is observed, as expected from theory.

Figure 4

Measured occupation probability of $|1⟩$ versus time duration of Rabi pulse $t_r$ for current biases (a)–(f) as noted by arrows in Fig. 2. Data (a)–(e) are offset for clarity. Note that when the bias is changed, the coherence is degraded mainly as a loss in amplitude, not by a decrease in coherence time.