Stroboscopic Qubit Measurement with Squeezed Illumination

Microwave squeezing represents the ultimate sensitivity frontier for superconducting qubit measurement. However, measurement enhancement has remained elusive, in part because integration with standard dispersive readout pollutes the signal channel with antisqueezed noise. Here we induce a stroboscopic light-matter coupling with superior squeezing compatibility, and observe an increase in the final signal-to-noise ratio of 24%. Squeezing the orthogonal phase slows measurement-induced dephasing by a factor of 1.8. This scheme provides a means to the practical application of squeezing for qubit measurement.

Figure 1

(a) Simplified experimental setup. A first Josephson parametric amplifier (SQZ) injects squeezed vacuum into a super-conducting cavity containing a qubit. The qubit is Rabi-driven at ${\mathrm{\Omega }}_R$ about ${\widehat{\sigma }}_x$ and measured by two tones at frequencies ${\omega }_c\pm {\mathrm{\Omega }}_R$, resulting in a qubit-state-dependent displacement of the squeezed field in phase space. A second Josephson parametric amplifier (AMP) followed by a Josephson traveling wave parametric amplifier (JTWPA) perform phase-sensitive and phase-preserving amplification, respectively, of the output signal. Insets show phase-space representations of an ideal lossless measurement with (solid) and without (shaded) squeezing. (b) We choose the two tones’ relative phase ${\varphi }_s$ such that the envelope of the resulting measurement field is in phase with ${\widehat{\sigma }}_z$. (c) Whereas dispersive readout rotates the output field in phase space, stroboscopic readout displaces the output field, providing greater potential for enhancement by squeezing.

Figure 2

(a) Ensemble-averaged Ramsey decay traces during a stroboscopic ${\widehat{\sigma }}_z$ measurement with no squeezing (brown) or with squeezing in phase (purple) or out of phase (cyan) with the measurement signal. Each trace is normalized by its initial $t=0$ value, ${\sigma }_{x,0}$. Here the squeezer is pumped for 3.8 dB of phase-preserving gain as determined by Lorentzian fits of $S_{21}$ vs probe frequency. (b) Steady-state dephasing rates ${\mathrm{\Gamma }}_{\phi }=1/T_{\phi }$ were acquired via Ramsey measurements as in (a), repeated for a range of phases and squeezer gains. The orange horizontal band is the dephasing rate with the squeezer off. Error bars, including the width of the horizontal band, represent statistical fit uncertainties. The dashed curves are the results of a joint fit of all data in Figs. 2 and 3.

Figure 3

(a) Data points are normalized histograms of the mean homodyne voltage integrated for $1.8\mu \mathrm{s}$ conditioned on preparing the qubit in the ground (blue colors) or excited (red colors) states. Curves are Gaussian fits. Measurements were repeated with squeezed (stars, solid), unsqueezed (circles, dashed) and antisqueezed (squares, dot-dashed) noise. Fits of data conditioned on excited-state preparation include a small second Gaussian to capture ground-state population ($\lesssim 2\%$) attributable to qubit relaxation before and during the Rabi ramp-up. The overlap area is smaller with squeezing ($A_1$) than without squeezing ($A_1+A_2$). (b) The measurement rate ${\mathrm{\Gamma }}_{\text{meas}}$ is determined for multiple phases and amounts of squeezing. The orange horizontal band is ${\mathrm{\Gamma }}_{\text{meas}}$ with SQZ off. Error bars, including the width of the horizontal band, are standard errors of fits of SNR(t). The dashed curves are results of a joint fit of all the data in Figs. 2 and 3 with free parameters ${\epsilon }_{\text{in}}$, $\delta$, and a global phase.

Figure 4

The overall measurement efficiency $\eta (\mathrm{\Phi })$ is shown for several values of $G_{\mathrm{SQZ}}$. The data and fits are computed from the corresponding elements in Figs. 2 and 3. We attribute the asymmetry about phases where $\mathrm{\Phi }$ is a multiple of $\pi /2$ to misalignment of the signal quadrature with the amplification quadrature of the second JPA. A small increase in $\eta$ above ${\epsilon }_{\text{out}}$ can be resolved at low squeezer gain near $\mathrm{\Phi }=\pi /2$.