Kibble-Zurek Mechanism in Topologically Nontrivial Zigzag Chains of Polariton Micropillars

We consider a zigzag chain of coupled micropillar cavities, taking into account the polarization of polariton states. We show that the TE-TM splitting of photonic cavity modes yields topologically protected polariton edge states. During the strongly nonadiabatic process of polariton condensation, the Kibble-Zurek mechanism leads to a random choice of polarization, equivalent to the dimerization of polymer chains. We show that dark-bright solitons appear as domain walls between polarization domains, analogous to the Su-Schrieffer-Heeger solitons in polymers. The soliton density scales as a power law with respect to the quenching parameter.

Figure 1

A scheme of a zigzag chain with even and odd numbers of polariton pillars: $a$ and $b$ form a unit cell marked in dark grey. (a),(d) Diagonal polarization, $t^{\prime }>t$. (b),(e) Antidiagonal polarization, $t^{\prime }<t$. (c),(f) Energy band of 30 (c) and 31 (f) pillar chains obtained from the tight-binding Hamiltonian. The color shows the diagonal polarization degree of the states.

Figure 2

Calculated spatial images of the difference in diagonal polarization emission $I_D-I_A$. (a) Edge states in a chain with an even number of pillars. (b) Edge states in a chain with an odd number of pillars. (c) Emission of the condensed states under localized pumping (marked $P$). Opposite diagonal polarization is observed on opposite sides.

Figure 3

(a),(b) Difference in diagonal polarization intensities for two examples of polarization textures in a zigzag chain. Colors are as in Fig. 2. (c) Average number of solitons as a function of effective pumping fitted by a power law.