Quantum Zeno Effects from Measurement Controlled Qubit-Bath Interactions

The Zeno and anti-Zeno effects are features of measurement-driven quantum evolution where frequent measurement inhibits or accelerates the decay of a quantum state. Either type of evolution can emerge depending on the system-environment interaction and measurement method. In this experiment, we use a superconducting qubit to map out both types of Zeno effect in the presence of structured noise baths and variable measurement rates. We observe both the suppression and acceleration of qubit decay as repeated measurements are used to modulate the qubit spectrum causing the qubit to sample different portions of the bath. We compare the Zeno effects arising from dispersive energy measurements and purely dephasing “quasimeasurements,” showing energy measurements are not necessary to accelerate or suppress the decay process.

Figure 1

Experimental setup. (a) The system consists of a transmon circuit dispersively coupled to a waveguide cavity, where the $|g⟩$ and $|e⟩$ states define the qubit and $|f⟩$ is an auxiliary state. (b) The qubit-cavity interaction results in a state-dependent phase shift on a probe near the cavity frequency, ${\omega }_c$, allowing the single-shot measurement of the qubit state. (c) A standard inversion recovery ($T_1$) measurement (inset) is used to characterize the effect of repeated projective measurements. A slight increase in the decay rate as the intermeasurement time interval $T_m$ is decreased is expected from the non-QND character of the measurement.

Figure 2

Synthesized noise bath and Zeno effects. (a) A structured thermal noise bath is created from a filtered white-noise source mixed up to the qubit transition frequency. The bath is characterized by a Lorentzian squared power spectrum (shown here at the input plane of the dilution refrigerator), with a center frequency that is tunable from the low-frequency modulation ${\omega }_{ge}-{\omega }_{\mathrm{LO}}+\delta$. (b) Inversion recovery measurements in the presence of the noise bath show how the thermal photons decrease the effective decay time when the bath is centered near the qubit transition. (c) The fractional change in the qubit $T_1$ decay time, $\mathrm{\Delta }{T}_1=(T_1-T_1^0)/T_1^0$, versus qubit-bath detuning, where $T_1^0$ is the $T_1$ time in the absence of additional measurement, as shown in (b). Repeated projective measurements, applied at a rate $1/T_m=2\mathrm{MHz}$ (green) and $1/T_m=1\mathrm{MHz}$ (blue), alter the coupling of the qubit to the bath. This either enhances (anti-Zeno effect, below the horizontal line) or suppresses (Zeno effect, above the horizontal line) the decay relative to the case without measurements.

Figure 3

Dephasing measurements. (a) The proposed quasimeasurement from [33] involves excitation to an auxiliary state and spontaneous decay. An alternative, dephasing, measurement uses a second $\pi$ rotation to return the system to the $|e⟩$ state. (b) A Ramsey measurement on the qubit state to characterize the effect of the dephasing measurement. The phase difference of the two rotations in the dephasing measurement imprints a Berry phase on the state $|e⟩$. Thus by randomizing the Berry phase, the interaction dephases the qubit. (c) Measured $T_1$ times for different measurement rates in the absence of the synthesized noise bath. The black line indicates the expected systematic shift in the measured $T_1$ time due to the time the circuit spends outside of the qubit manifold [34]. (d) Fractional change in the qubit $T_1$ decay times in the presence of the synthesized noise bath for different qubit-bath detunings and different measurement rates.

Figure 4

Spectroscopy. A continuous weak probe at frequency ${\omega }_{\mathrm{p}}$ is applied for a duration of $80\mu \mathrm{s}$ followed by a projective measurement. The power-broadened qubit transition frequency is revealed as an increase in the final excited state population (black traces). To probe the effects of dispersive (a) and quasimeasurements (b), we apply these measurements at different rates: 0.5, 1, and 2 MHz (red, blue, and green, respectivley).