Nonreciprocal Transport of Exciton Polaritons in a Non-Hermitian Chain

S. Mandal, R. Banerjee, Elena A. Ostrovskaya, and T. C. H. Liew

Phys. Rev. Lett. 125, 123902 – Published 17 September 2020

Abstract

We consider exciton polaritons in a zigzag chain of coupled elliptical micropillars subjected to incoherent excitation. The driven-dissipative nature of the system along with the naturally present polarization splitting inside the pillars gives rise to nonreciprocal dynamics, which eventually leads to the non-Hermitian skin effect, where all the modes of the system collapse to one edge. As a result, the polaritons propagate only in one direction along the chain, independent of the excitation position, and the propagation in the opposite direction is suppressed. The system shows robustness against disorder and, using the bistable nature of polaritons to encode information, we show one-way information transfer. This paves the way for compact and robust feedback-free one-dimensional polariton transmission channels without the need for external magnetic field, which are compatible with proposals for polaritonic circuits.

Received 29 April 2020
Accepted 19 August 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.123902

Physics Subject Headings (PhySH)

Exciton polariton Nonlinear optics Optical pumping Skin effect Spin-orbit coupling

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsNonlinear Dynamics

Authors & Affiliations

S. Mandal ^1,*, R. Banerjee ¹, Elena A. Ostrovskaya ², and T. C. H. Liew ^1,†

¹Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
²ARC Centre of Excellence in Future Low-Energy Electronics Technologies and Nonlinear Physics Centre, Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia

^*Corresponding author. subhaska001@e.ntu.edu.sg
^†Corresponding author. tchliew@gmail.com

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Issue

Vol. 125, Iss. 12 — 18 September 2020

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Images

Figure 1
Scheme: (a) A pair of coupled elliptical micropillars of different sizes; their mutual orientation introduces the polarization splitting angle $θ$ . (b) Micropillar pairs are arranged in a 1D zigzag chain, where each micropillar is subjected to an incoherent excitation. (c) Effective coupling mechanism between the micropillars in the lattice. Each pair of micropillars indicated by the dashed boxes has nonreciprocal coupling. The unit cell of the 1D lattice is shown by the gray box.
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Figure 2
Spatial profiles of different modes as a function of site number for a trivial chain of 100 micropillars (left panel) and nonreciprocal chain of 100 micropillars (right panel) in the tight binding limit. Here the blue arrows correspond to bidirectional coupling and the red arrows correspond to nonreciprocal coupling. Because of the non-Hermitian skin effect all the modes for the nonreciprocal chain collapse to the left edge. The most localized modes for $n = 50$ and 51 correspond to the zero energy modes, similar to those in Ref. [56], but located at one edge. Parameter: $J = 0.5 meV$ .
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Figure 3
(a)–(b) The spatial profile of the incoherent pumps $P_{σ_{+}}$ and $P_{σ_{-}}$ , respectively, composed of Gaussians of width $2.1 μ m$ positioned at the center of the relevant micropillars. Such an arrangement is within the reach of experimental technology [58]. (c) Band structure of an infinite chain under incoherent excitation. The states shown in red correspond to the slow modes and decay slower than all other states shown in blue. (d) Spatial profile, $I_{x} = \sum_{σ_{\pm}} \int | ψ_{σ} (x, y) |^{2} d y$ , corresponding to the slow modes for the case of a finite chain. Here different colors denote different modes.
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Figure 4
(a),(c),(e) Density of the $σ_{+}$ polaritons under an incoherently pulsed excitation for 10, 90, and 180 ps, respectively. The same for the $σ_{-}$ polaritons are shown in (b),(d),(f). The nonreciprocal nature of the system is clear from the fact that the polaritons propagate only in one direction while the propagation in the opposite direction is suppressed. The width of the incoherent pulse is taken as $2.1 μ m$ and the peak power of the gain rate is taken as $14.2 γ$ .
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Figure 5
(a)–(b) Bistability curves of the pillars at the left and right end of the chain, respectively. The energy of the resonant pump $F$ is fixed at 1.38 meV. The gray line in the bistability curves represents the pump values ( $F = 4.1 meV μ m^{- 1}$ and $3.9 meV μ m^{- 1}$ , respectively, for left and right end pillars) used to demonstrate the switching. (c)–(d) Time dynamics of the end pillars when the incoherent pulse is positioned at the left and right end, respectively. Pulse positioned at the right end induces switching at both ends, whereas the pulse positioned at the left end does not switch the pillar at the right end. The spatial profile of the resonant pump and incoherent pulse are the same as the one in Fig 4. The peak value of the pulse is taken as $35 p_{0}$ . To visualize the switching effect the maximum density is cut at $10^{3} μ m^{- 2}$ .
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