Resonance Fluorescence from an Artificial Atom in Squeezed Vacuum

We present an experimental realization of resonance fluorescence in squeezed vacuum. We strongly couple microwave-frequency squeezed light to a superconducting artificial atom and detect the resulting fluorescence with high resolution enabled by a broadband traveling-wave parametric amplifier. We investigate the fluorescence spectra in the weak and strong driving regimes, observing up to 3.1 dB of reduction of the fluorescence linewidth below the ordinary vacuum level and a dramatic dependence of the Mollow triplet spectrum on the relative phase of the driving and squeezed vacuum fields. Our results are in excellent agreement with predictions for spectra produced by a two-level atom in squeezed vacuum [Phys. Rev. Lett. 58, 2539 (1987)], demonstrating that resonance fluorescence offers a resource-efficient means to characterize squeezing in cryogenic environments.

Popular Summary

Atomic fluorescence, which results from the interaction of light and matter, depends sensitively on the vacuum fluctuations of the electromagnetic field. While these fluctuations result from Heisenberg’s uncertainty principle and fundamentally cannot be eliminated, researchers discovered in the 1980s that the fluctuations could be “squeezed.” This process involves, for example, reducing the in-phase part of the field while, at the same time, amplifying the out-of-phase part. Scientists predicted that an atom interacting with squeezed light would fluoresce with a dramatically modified spectrum. It has remained a challenge to demonstrate this effect experimentally, in part because of the stringent requirement that the atom must interact nearly exclusively with squeezed light. Here, our work circumvents this challenge by embedding a superconducting artificial atom in a microwave-frequency electrical circuit, a low-dimensional setting that enables strong coupling between squeezed light and the artificial atom.

We cool the artificial atom, consisting of a superconducting qubit coupled to an aluminum waveguide cavity, to below 30 mK such that at equilibrium its electromagnetic environment is very nearly in its quantum-mechanical ground state. We actively manipulate this environment by squeezing the fluctuations with a superconducting parametric amplifier and efficiently detect the low-energy microwave photons emitted by this system using a second superconducting amplifier. We demonstrate a dramatic sensitivity of the artificial atom’s fluorescence to the properties of squeezed vacuum, and we observe fluorescence linewidths that are reduced by more than 3.1 dB (i.e., a factor of 2) below their ordinary vacuum level. As such, the artificial atom provides a metrological measurement of the nonclassical fluctuations in its cryogenic environment, mapping the properties of the fragile squeezed state onto fluorescence linewidths that, once amplified, can readily be measured with room-temperature electronics.

We expect that our results and methodology will stimulate novel studies of squeezed light-matter interactions and will aid efforts to enhance superconducting qubit measurements with squeezed light.

Figure 1

(a) Simplified experimental setup. A qubit-cavity system is driven by a coherent drive combined with squeezed vacuum from a JPA. The resulting fluorescence is amplified by a JTWPA. (b,c) False-colored photomicrograph and schematic of the JPA. The port (red) at left flux-couples a pump tone to the JPA, producing quadrature squeezing. (d) Coupling to the qubit splits the cavity states into polariton states. Driving Rabi oscillations between $|0⟩$ and $|1,+⟩$ splits each state into a doublet. The three distinct transition frequencies produce the Mollow triplet spectrum. (e) Mollow triplet spectra in ordinary vacuum, normalized by the power spectrum with no coherent drive to account for the JTWPA’s gain ripple.

Figure 2

(a) Reflected power as a function of frequency for excitation with only squeezed vacuum ($G_{\mathrm{JPA}}=1.4\mathrm{dB}$). The spectrum is normalized by a measurement in ordinary vacuum to account for the JTWPA’s gain ripple. Zero relative power corresponds to the background level of the broadband squeezed power. The red ellipses are phase-space representations of the squeezed states inside and outside the cavity as inferred from the fit to Eq. (2). (b) Reflected power measured over a constant frequency span as the frequency of the JPA pump is varied. The peak in the spectrum diminishes and broadens as the JPA pump is detuned from the polariton resonance.

Figure 3

Reflection spectra for excitation with a coherent drive (a) in ordinary vacuum, (b) with $\mathrm{\Phi }=\pi /2$ ($G_{\mathrm{JPA}}=1.5\mathrm{dB}$), and (c) with $\mathrm{\Phi }=0$ ($G_{\mathrm{JPA}}=1.5\mathrm{dB}$), where $\mathrm{\Phi }+\pi /2$ is the phase angle between the coherent drive and the squeezing axis (see Appendix pp2 for definitions). The spectra are normalized to account for the JTWPA’s gain ripple such that the background level in ordinary vacuum is 1; the parabolic backgrounds (orange dashed line) in (b) and (c) result from the reflected JPA noise power. (d) The black dashed curves are fit using an approximate three-Lorentzian model; linewidths of this fit are plotted in (d) as a function of $\mathrm{\Phi }$. Error bars reflect fit uncertainties. The two dashed curves are out-of-phase sine functions fit to the central-peak and sideband linewidths inferred from measurements in squeezed vacuum, while the dashed horizontal lines indicate the corresponding linewidths inferred from measurements in ordinary vacuum.

Figure 4

The squeezing level in the artificial atom’s environment as a function of gain $G_{\mathrm{JPA}}$. The quantity $M\text{−}N$ determines the minimal quadrature variance of a squeezed state as indicated in the inset. The values of $M\text{−}N$ are inferred from measurements of the fluorescence spectrum in squeezed vacuum with (red) and without (blue) a coherent Rabi drive. The error bars reflect fit uncertainties. The measurements with no Rabi drive give a more reliable indication of the squeezing level as they are less sensitive to background effects and experimental drift. The dashed orange curve is a one-parameter fit to the blue data points yielding $\eta =0.55$.

Figure 5

Experimental setup diagram. The JPA pump tone, which enters the cryostat at (1), is generated through a frequency doubler followed by a voltage variable attenuator that allows programmatic control of the JPA gain. The gain can be measured by the VNA at (2). Power from the same generator is split off before doubling to create the phase-locked coherent drive at (3). The relative phase of this drive is controlled through dc voltages on the IQ mixer. Each time the phase is stepped, the two switches just before the spectrum analyzer are thrown such that the analyzer samples the drive power, which is fed back on to ensure power flatness versus phase. These switches are toggled back before measurement of fluorescence spectra on the spectrum analyzer.

Figure 6

States of light can be fully described by quasiprobability distributions (here, Wigner functions) in phase space, where $X_1$ and $X_2$ are the two quadratures of the light field. (a) The vacuum state is described by a circular Gaussian distribution of width $1/2$ centered at the origin. The red disk indicates the area in which the distribution is greater than its half-maximum value. (b) The distribution for a squeezed vacuum state has an increased width along the amplification axis at angle $\phi$ and a decreased width along the squeezing axis at angle $\phi +\pi /2$. A slice of this distribution taken through the origin at angle $\theta$ has a variance given by Eq. (1) of the main text, with the amplified variance given by $1/2(N+M+1/2)$ and the squeezed variance given by $1/2(N-M+1/2)$. Note an angular factor of 2 has been introduced in Eq. (1) in the main text compared to Refs. [7, 8] to simplify the phase-space picture. (c) Similarly, $\mathrm{\Phi }$, as used in Fig. 3 of the main text, indicates the angle of the amplification axis of a displaced squeezed state relative to the displacement angle, ${\phi }_c$. Experimentally, ${\phi }_c$ is set by the phase of the coherent Rabi drive.

Figure 7

Mollow triplet spectra measured at $G_{\mathrm{JPA}}=6.6\mathrm{dB}$. The spectra are measured near $\mathrm{\Phi }=\pi /2$, the relative phase between the squeezed-vacuum and coherent-drive fields that minimizes the center-peak linewidth. Even though the Rabi frequency (1.2 MHz as in Fig. 3) is small compared to the measured frequency range, the sidebands are broadened such that they are no longer apparent. The dashed black line represents the best fit to the power spectra, taking into account both the fluorescence spectrum and the frequency-dependent squeezer background. The spectra are simultaneously fit with $\gamma$ fixed by measurements of the Mollow triplet in ordinary vacuum and also constrained by the relative phase difference between each measurement. From these measurements, we infer $M-N=0.24$ for these conditions.