Chiral Modes at Exceptional Points in Exciton-Polariton Quantum Fluids

T. Gao, G. Li, E. Estrecho, T. C. H. Liew, D. Comber-Todd, A. Nalitov, M. Steger, K. West, L. Pfeiffer, D. W. Snoke, A. V. Kavokin, A. G. Truscott, and E. A. Ostrovskaya

Phys. Rev. Lett. 120, 065301 – Published 9 February 2018

Abstract

We demonstrate the generation of chiral modes–vortex flows with fixed handedness in exciton-polariton quantum fluids. The chiral modes arise in the vicinity of exceptional points (non-Hermitian spectral degeneracies) in an optically induced resonator for exciton polaritons. In particular, a vortex is generated by driving two dipole modes of the non-Hermitian ring resonator into degeneracy. Transition through the exceptional point in the space of the system’s parameters is enabled by precise manipulation of real and imaginary parts of the closed-wall potential forming the resonator. As the system is driven to the vicinity of the exceptional point, we observe the formation of a vortex state with a fixed orbital angular momentum (topological charge). This method can be extended to generate higher-order orbital angular momentum states through coalescence of multiple non-Hermitian spectral degeneracies. Our Letter demonstrates the possibility of exploiting nontrivial and counterintuitive properties of waves near exceptional points in macroscopic quantum systems.

Received 2 June 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.065301

Physics Subject Headings (PhySH)

Exciton polariton

Bose-Einstein condensates

Condensed Matter, Materials & Applied PhysicsGeneral Physics

Authors & Affiliations

T. Gao¹, G. Li², E. Estrecho^1,3, T. C. H. Liew⁴, D. Comber-Todd¹, A. Nalitov², M. Steger⁵, K. West⁶, L. Pfeiffer⁶, D. W. Snoke⁵, A. V. Kavokin^2,7,8, A. G. Truscott⁹, and E. A. Ostrovskaya^1,3

¹Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 2601, Australia
²School of Physics and Astronomy, University of Southampton, SO17 1BJ Southampton, United Kingdom
³ARC Centre of Excellence in Future Low-Energy Electronics Technologies
⁴Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371
⁵Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
⁶Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
⁷SPIN-CNR, Viale del Politecnico 1, I-00133 Rome, Italy
⁸Spin Optics Laboratory, St-Petersburg State University, 1 Ulianovskaya St., St-Petersburg 198504, Russia
⁹Laser Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 2601, Australia

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Vol. 120, Iss. 6 — 9 February 2018

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Images

Figure 1
(a) Experimental pump intensity distribution. The width of the left half-ring is $W = 9 μ m$ and is fixed; the width of the right half-ring is tuned between $w_{1} = 1.0 μ m$ and $w_{2} = 1.2 μ m$ with a step of $0.1 μ m$ . The inner ring diameter is $D = 15 μ m$ and is fixed. (b) Schematics of the DMD mirror mask shaping the pump spot (white), the direction of the gradient of the cavity wedge (yellow), and the corresponding dipole modes of the trapped exciton polaritons (blue and red).
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Figure 2
The (a) crossing of the real parts of the eigenenergies and (b) anticrossing of the imaginary parts of the eigenenergies (linewidths) corresponding to the dipole states for the changing detuning $Δ$ and fixed width of the right half-ring $w_{2} = 1.2 μ m$ . The variation of $Δ$ is produced by moving the excitation beam relative to the sample over the distance of approximately $60 μ m$ . Insets in (a) show the corresponding spatial density structure of eigenmodes observed in the energy-resolved tomography measurement (see Supplemental Material [34]). The (c) anticrossing of the energies and (d) crossing of the linewidths for the changing detuning $Δ$ and fixed width of the right half-ring $w_{1} = 1.0 μ m$ .
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Figure 3
Experimentally observed (a),(c),(e) probability density distribution of the exciton-polariton condensate and (b),(d),(f) the corresponding interference pattern for the dipole modes with (a),(b) near-vertical and (c),(d) near-horizontal nodal line, and (e),(f) for a charge one vortex state. In (b),(d), the nodal lines can be discerned by the relative shift in fringes. The fork in the fringes marked by the dot in (f) signifies a charge one vortex. Parameters are (a)–(d) $Δ = - 3.8 meV$ , $w \approx 1.1 μ m$ ; (e),(f) $Δ = - 3.6 meV$ , $w \approx 1.1 μ m$ .
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Figure 4
Approximate complex effective potential and the typical profiles of the dipole modes: (a) $V^{'} (r)$ , (d) $V^{''} (r)$ , (b) $| ψ_{2} |$ , (c) $| ψ_{2} + i ψ_{3} |$ , (e) $| ψ_{3} |$ . (f) The phase distribution corresponding to (c).
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Figure 5
Behavior of energy levels corresponding to the dipole modes with the change of the exciton-photon detuning $Δ$ . (a) $Re [\tilde{E}]$ crossing and (b) $Im [\tilde{E}]$ anticrossing at $w = w_{2}$ . (c) $Re [\tilde{E}]$ anticrossing and (d) $Im [\tilde{E}]$ crossing at $w = w_{1} < w_{2}$ . (a),(d) Two different $y$ axes accentuate the crossing. The real and imaginary parts of the ground state eigenvalues are subtracted from the absolute values in (a)–(d) [48].
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Figure 6
Experimentally measured (a) density and (b) interference image of the triple-vortex state. Theoretically calculated (c) modulus and (d) phase of the triple-vortex state $ψ = (ψ_{7} + i ψ_{8}) + (ψ_{9} + i ψ_{10})$ . The three dots in (b) mark the forks in the interference fringes.
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