Four-wave Mixing Mediated Synchronization of Localized Polariton Condensates

Abstract

The Letter is devoted to new frequencies generation and its role in the synchronization of two spatially separated polariton condensates affected by the coherent pump with the frequency detuned from the frequencies of the condensates. We focus on the case where the distance between the condensates is so long that their interaction through the evanescent tails is negligible. By numerical simulation we show that the four-wave mixing of the polaritons with the coherent drive produces the free propagating polaritons that can mediate the inter-condensate interaction resulting in the phase-locking of the condensates.

Figures (3)

• Figure 1: The temporal evolution of the polariton field is shown in panel (a) for the condensates trapped in super-Gaussian potential. The depth of the potential is $V_0=40$ and its half-width is $W=0.15$, the amplitude and the frequency of the coherent pump are $p_0=3$ and $\delta=19.3$. The frequencies are defined as the detunings from the cavity cut-off frequency in the center of the potential well. The polariton condensates are supported by the incoherent pump with the intensity $\mu=3$ and half-width $w_{\mu}=0.25$, see text for the details. The spatio-temporal spectrum of the field is shown in panel (b). The pattern corresponding to the localized potential is marked by yellow $c$, the spectral pattern corresponding to the direct response to the coherent drive is marked by $p_{ch}$. The sidebands appearing due to four wave mixing of the condensate with the coherent drive are marked as $m_1$-$m_3$ (up-converted) and $m_{-1}$ (down-converted). The wite curve shows the dispersion of the polaritons away from the potential well. The spatial distributions of the filtered fields corresponding to the condensate (black curve) and $m_1$ side-band (red curve) are shown in panel (c).
• Figure 2: The spatial evolution of the field and the corresponding spatio-temporal spectrum for two condensates forming the two wells super-Gaussian potential. The parameters are the same as in Fig. \ref{['fig1']}, see text for details. The spectral patterns marking is also the same as in Fig. \ref{['fig1']}.
• Figure 3: The filtered filed distributions are shown in panels (a) for the system parameters as in Fig. \ref{['fig2']}. The black and red curves correspond to the condensate and the first up-converted side band (marked as $c$ and $m_1$ in Fig. \ref{['fig2']}). The filed for $m_1$ in the middle between the condensates is shown in the inset where the vertical dashed line marks $x=0$. Panel (b) shows the same as panel (a) but for the coherent pump frequency $\delta=17.9$. The evolution of the mutual phase $\varphi$ of the condensates are shown in panels (c) ( $\delta=19.3$) and (d) ($\delta=17.9$) by the blue curves for the case where the direct drive contains the coherent pump contains and weak noise. The equilibrium values of the mutual phases are shown by the horizontal black dashed lines. The typical evolution of the mutual phases in the absence of the coherent drive are shown by the green curves.