Figure 1

(a) Schematic of the phase qubit circuit. (b) Qubit spectroscopy. Probability to measure the excited qubit state $P_e$ after a long (300 ns) microwave pulse of small amplitude as a function of the qubit flux bias and microwave frequency. Two avoided level crossings, denoted “TLS 1” and “TLS 2”, are observed at 7.735 and 7.947 GHz with magnitudes $S=23$ and 36 MHz, respectively.Reuse & Permissions

Figure 2

Coherent response of TLS 1 to standard microwave pulse sequences as depicted in the insets. (a) Relaxation of the excited TLS state after its preparation using a microwave $\pi$ pulse of duration 62 ns. Here, $\Delta t$ indicates the time delay between state preparation and readout. (b) Rabi oscillation observed by driving the TLS resonantly for a duration $\Delta t$. (c) Ramsey oscillation measured by varying the delay $\Delta t$ between two $\pi /2$ pulses (of duration 31 ns each) which were detuned from the TLS’ resonance frequency by about 10 MHz. The data shown in panels (a)–(c) were obtained at a detuning $\delta =502\mathrm{MHz}$. Panels (d),(e) and (f) show the energy relaxation time $T_1^{\mathrm{TLS}1}$, the Rabi decay time $T_d^{\mathrm{TLS}1}$, and the dephasing time $T_2^{\mathrm{TLS}1}$ as a function of the detuning $\delta$ between TLS and qubit.Reuse & Permissions

Figure 3

(a) Rabi frequency vs detuning between TLS 1 and qubit. The two curves correspond to microwave powers differing by 9 dBm. (b) Ramsey frequency vs detuning between TLS 1 and qubit. Solid lines are calculated from theory.Reuse & Permissions

Figure 4

Signal amplitudes obtained from Ramsey (curve starting at $P_e=0.6$) and Hahn-echo (curve starting at $P_e=0.2$) sequences for TLS 2. Solid lines are exponential fits resulting in a dephasing time of $551\pm 41\mathrm{ns}$ (Ramsey) and $743\pm 62\mathrm{ns}$ (Hahn echo), respectively.Reuse & Permissions

Figure 5

Temperature dependence of coherence times in (a) TLS 1 and (b) TLS 2. The value of $2·T_1$ is indicated by open circles. Solid lines are parabolas as described in the text, dotted lines are functions $T_1(T)\propto \tanh (\Delta E/2k_{B}T)$. Insets: (a) Temperature dependence of the qubit $T_1$ time. (b) Extracted pure dephasing time $T_{\phi }=1/[T_2^{-1}-(2T_1{)}^{-1}]$.Reuse & Permissions