Proposed cavity Josephson plasmonics with complex-oxide heterostructures

We discuss how complex-oxide heterostructures that include high-$T_c$ superconducting cuprates can be used to realize an array of submillimeter cavities that support Josephson plasmon polaritons. These cavities have several attractive features for new types of light-matter interaction studies and we show that they promote “ultrastrong” coupling between THz frequency radiation and Josephson plasmons. Cavity electrodynamics of Josephson plasmons allows us to manipulate the superconducting order-parameter phase coherence. As an example, we discuss how it could be used to cool superconducting phase fluctuations with light.

Figure 1

(a) The layered high-$T_c$ superconductor $\mathrm{L}{\mathrm{a}}_{2-x}\mathrm{S}{\mathrm{r}}_x\mathrm{Cu}{\mathrm{O}}_4$: ${\chi }_n$ is the phase of the superconducting order parameter of the $n\mathrm{th}$ supeconducting plane. Red arrows indicate the Josephson plasma oscillations between the planes at the characteristic frequency ${\nu }_p.$ (b) A single cavity/high-$T_c$ mesa: $\mathrm{Au}$(yellow)/$\mathrm{L}{\mathrm{a}}_2\mathrm{Cu}{\mathrm{O}}_4$ (“LCO,” green)/$\mathrm{L}{\mathrm{a}}_{2-x}\mathrm{S}{\mathrm{r}}_x\mathrm{Cu}{\mathrm{O}}_4$ (“LSCO,” dark blue)/$\mathrm{L}{\mathrm{a}}_2\mathrm{Cu}{\mathrm{O}}_4$ (“LCO,” green)$/\mathrm{SrRu}{\mathrm{O}}_3$ (“SRO,” red). (c) The proposed heterostructure: array of cavity/high-$T_c$ mesas. The electric field distribution of the $\left(n,m\right)=\left(0,1\right)$ fundamental mode of the “bare” cavities is shown (that is without the superconductor, see text for details). The corresponding notations are used thorough the text.

Figure 2

(a) Right: Reflectivity as a function of frequency and inverse patch width for the bare cavity $\left(D=1.2\mu \mathrm{m},p=33\mu \mathrm{m}\right)$. The white solid line shows the JPR frequency ${\nu }_p$. Left: Reflectivity cut of the bare cavity tuned at ${\nu }_p$ $(w=11\mu \mathrm{m}$: corresponding to the white dashed line on the right panel). (b) Right: Reflectivity as a function of frequency and inverse patch width for the cavity/high-$T_c$ heterostructure $(d=200\mathrm{nm},D=1.2\mu \mathrm{m},p=33\mu \mathrm{m}$, corresponding to a filling fraction $f=\frac{d}{D}\approx 17\%)$. The white solid line shows the JPR frequency ${\nu }_p$. The black solid lines are the hybridized resonances $\{{\nu }_{+}\left(w\right),{\nu }_{-}\left(w\right)\}$ (see text for details). Left: Reflectivity cut of the cavity/high-$T_c$ heterostructure when the bare cavity is tuned at ${\nu }_p$ $(w=11\mu \mathrm{m}$: corresponding to the white dashed line on the right panel).

Figure 3

(a) Reflectivity as a function of frequency and filling fraction $f$ for a cavity tuned at ${\nu }_c={\nu }_p$ (computed at fixed $D=1.2\mu \mathrm{m},p=33\mu \mathrm{m},w=11\mu \mathrm{m})$. (b) Normalized Rabi splitting $2\mathrm{\Omega }/{\nu }_c$ as a function of the filling fraction $f$ computed from (a).