Giant Cross–Kerr Effect for Propagating Microwaves Induced by an Artificial Atom

We investigate the effective interaction between two microwave fields, mediated by a transmon-type superconducting artificial atom which is strongly coupled to a coplanar transmission line. The interaction between the fields and atom produces an effective cross–Kerr coupling. We demonstrate average cross–Kerr phase shifts of up to 20 degrees per photon with both coherent microwave fields at the single-photon level. Our results provide an important step toward quantum applications with propagating microwave photons.

Figure 1

A micrograph of device 1 in (a) and device 2 in (b) with measurement setup using heterodyne detection (HD). Devices 1 and 2 have an artificial atom, a transmon qubit, embedded in a one-dimensional open transmission line and at the end of a transmission line, respectively. In (b), we measure the reflection coefficient of the probe and control fields simultaneously. (c) The three-level artificial atom driven by a probe tone at ${\omega }_p$ (red) and a control tone at ${\omega }_c$ (blue). The artificial atom acts as a Kerr medium, which enables photon-photon interaction.

Figure 2

Transmission coefficient for the probe, as a function of ${\omega }_p$ and control power, $P_c$, for low probe powers, ${\Omega }_p\ll {\gamma }_{10}$ in device 1 (see the Supplemental Material [27] for device 2). (a) Top: measured transmission coefficient with $P_c=-116$ dBm, $|t_p^{(on)}|$ (black), and $P_c$ turned off, $|t_p^{(\mathrm{off})}|$ (gray). Bottom: corresponding phase response. (b) Measured amplitude response, $\Delta t_p$. (c) Measured phase response, $\Delta {\phi }_p$. Top panels: as a function of probe frequency and control power. Bottom panels: horizontal line cuts (dots) and theory curves (solid lines). The (brown) arrows along the bottom axes show the frequency that maximizes the phase response. The theory curves [28, 30] are fit simultaneously to extract ${\gamma }_{20}/2\pi =150\mathrm{MHz}$ along with the control field coupling. The following other parameters, also used in the calculations, are independently measured with single-tone and two-tone spectroscopy: ${\omega }_{10}/2\pi =7.10\mathrm{GHz}$, ${\omega }_{21}/2\pi =6.38\mathrm{GHz}$, ${\Gamma }_{10}/2\pi =74\mathrm{MHz}$, ${\gamma }_{10}/2\pi =60\mathrm{MHz}$ and the probe field coupling.

Figure 3

Probe phase shift, $\Delta {\phi }_p$, induced by a weak control pulse. Solid curves are theoretical fits to the data, including additional data in the Supplemental Material[27]. The fitting parameters for each device are ${\gamma }_{20}$ and the control field coupling. Other parameters are measured independently through spectroscopy. All parameters are listed in Table . (a) The control pulse induces a phase shift, $\Delta {\phi }_p$, of the continuous probe in the time domain. The length of the pulse is 1 $\mu$s for device 1 and $7\mu \mathrm{s}$ for device 2. (b) $\Delta {\phi }_p$ as a function of ${\omega }_p$ for three different probe powers and $⟨N_c⟩\simeq 0.3$, for device 1. Note that here the $|0⟩\leftrightarrow |1⟩$ transition is 7.26 GHz (due to a different external magnetic flux, $\Phi$). (c) $\Delta {\phi }_p$ as a function of $⟨N_c⟩$ for a weak probe at a probe frequency that maximizes the probe phase shift. Each data point is an average over 2 million control pulses. An average phase shift of 10 degrees per control photon is observed in device 1, and 20 degrees per control photon in device 2. (d) $|r_{p,2}|$ and $|r_{c,2}|$ as a function of $⟨N_c⟩$. The dashed (blue) line indicates $|r_{c,2}|=0.9$. Extensive measurements of $r_{p,2}$ are presented in Fig. S4A of the Supplemental Material [27].