Exploring Ultrastrong Coupling Effects Using a Josephson Mixer

We use the Josephson Ring Modulator (JRM) to demonstrate new signatures of the ultrastrong coupling between two bosonic modes. The JRM implements a three wave mixer between two microwave modes $a$ and $b$. When pumping the JRM at a red (blue) frequency $f_R^{(0)}=f_a-f_b$ ($f_B^{(0)}=f_a+f_b$), we realize frequency conversion between modes at a rate $G_R$ (two mode squeezing at a rate $G_B$). The effective ultrastrong coupling is obtained when the JRM is pumped by these two tones simultaneously so that $G_B=G_R$ is larger than the relaxation rate of the modes $a$ and $b$. We reach this regime by weakly coupling the modes of a Josephson mixer to measurement transmission lines compared to the rates $G_{B,R}$. By detuning the blue pump at a frequency $f_B=f_B^{(0)}+2\delta$, two peaks appear in the spectral density of each mode output, separated by $2\delta$. A key signature of ultrastrong coupling corresponds to the splitting of each of these peaks in two other peaks whose separation is set by $G_R$. We present preliminary experimental results that demonstrate this behavior and reach the regime where a strong (20~dB) peak appears in the spectral density of each mode output at $G_R=G_B=\delta/2$. We should be able to demonstrate both two-mode and single mode squeezing.