Engineering Photon Statistics in a Spinor Polariton Condensate

S. Baryshev, A. Zasedatelev, H. Sigurdsson, I. Gnusov, J. D. Töpfer, A. Askitopoulos, and P. G. Lagoudakis

Phys. Rev. Lett. 128, 087402 – Published 23 February 2022

Abstract

We implement full polarization tomography on photon correlations in a spinor exciton-polariton condensate. Our measurements reveal condensate pseudospin mean-field dynamics spanning from stochastic switching between linear polarization components, limit cycles, and stable fixed points, and their intrinsic relation to the condensate photon statistics. We optically harness the cavity birefringence, polariton interactions, and the optical orientation of an incoherent exciton reservoir to engineer photon statistics with precise control. Our results demonstrate a smooth transition from a highly coherent to a super-thermal state of the condensate polarization components.

Received 7 December 2020
Revised 9 August 2021
Accepted 7 January 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.087402

Physics Subject Headings (PhySH)

Exciton polariton Optical lattices & traps Spin coherence Spin dynamics

Polariton condensate Quantum wells Spinor Bose-Einstein condensates

Coherent control Dynamical mean field theory Laser techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

S. Baryshev ¹, A. Zasedatelev ^1,2,*, H. Sigurdsson ^3,2, I. Gnusov ¹, J. D. Töpfer ², A. Askitopoulos¹, and P. G. Lagoudakis ^1,2

¹Hybrid Photonics Laboratory, Skolkovo Institute of Science and Technology, Territory of Innovation Center Skolkovo, Bolshoy Boulevard 30, building 1, 121205 Moscow, Russia
²School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom
³Science Institute, University of Iceland, Dunhagi 3, IS-107, Reykjavik, Iceland

^*A.Zasedatelev@skoltech.ru

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Issue

Vol. 128, Iss. 8 — 25 February 2022

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Images

Figure 1
(a) Schematic presentation of the annular optical trap (upper panel) and condensate emission (lower panel). White dashed line outlines the optical trap. (b) Poincaré sphere showing three sets of the condensate pseudospin projections onto Stokes parameters. (c) HBT interferometers $I_{1}$ (black box) and $I_{2}$ (red box) are dedicated to measure intensity autocorrelation for orthogonal pseudospin projections indicated by black and red arrows, respectively [e.g., $I_{1}$ measures $g_{H, H}^{(2)} (τ)$ and $I_{2}$ measures $g_{V, V}^{(2)} (τ)$ ]. At the same time $I_{3}$ (green box) measures cross-correlation between these projections [i.e., $g_{H, V}^{(2)} (τ)$ ]. APD refers to Avalanche photo diode.
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Figure 2
(a) Second order correlation function of the condensate, measured without polarization filtering at $P = P_{th}$ and $P = 1.31 P_{th}$ . Blue line is a Gaussian fit. (b)–(d) $g_{i, i}^{(2)} (τ)$ , $g_{j, j}^{(2)} (τ)$ , and $g_{i, j}^{(2)} (τ)$ at $P = 1.31 P_{th}$ for LC-RC, $H − V$ , and D-AD polarizations, respectively (letter “ $x$ ” denoting cross correlation).
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Figure 3
(a) Measured (circles) and theoretical (solid lines) $g_{H, H}^{(2)} (0)$ (black), $g_{V, V}^{(2)} (0)$ (red), and $g_{H, V}^{(2)} (0)$ (green) power dependencies for linearly polarized excitation. Error bars for the experimental data are smaller than the size of the circled markers. (b) Schematic representation of the in-plane magnetic field (orange arrow denoted as $Ω_{∥}$ ) and the polarization of different photon occurrences (black transparent arrows). When pinned, the pseudospin is dominantly orientated parallel $Ω_{∥}$ (indicated by big number of co-oriented arrows) whereas random switching events change the pseudospin to antiparallel direction (indicated as few antiparallel arrows), corresponding to anticorrelated event between linear polarization components. Color scale represents total correlation photon count rate.
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Figure 4
Photon statistics engineering with excitation ellipticity. $g_{H, H}^{(2)} (τ)$ at pump power $P = 3.5 P_{th}$ for a range of ellipticities $ε$ . Data for $ε = 0$ and 0.007 are fitted by an exponential function (red line) $g_{H, H}^{(2)} (τ) = 1 + [g_{H, H}^{(2)} (0) - 1] e^{- 2 | τ | / τ_{c}}$ , data for higher ellipticity are fitted with a product of a Gaussian function and a cosine function $g_{H, H}^{(2)} (τ) = 1 + \cos (ω τ) [g_{H, H}^{(2)} (0) - 1] e^{- π (τ / τ_{c})^{2}}$ where $τ_{c}$ is correlation (i.e., dephasing) time.
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Figure 5
(a) $g_{H, H}^{(2)} (τ)$ (black), $g_{V, V}^{(2)} (τ)$ (red), and $g_{H, V}^{(2)} (τ)$ (green) at $P = 3.5 P_{th}$ , $ε = 0.028$ . (b) Calculated normalized pseudospin precession trajectory and its projection into equatorial plane of the Poincaré sphere. (c) Oscillation frequency of $g_{i, j}^{(2)} (τ)$ (blue triangles) plotted alongside with energy splitting (green circles) between LC and RC polarized condensate. Solid red line represents simulated results. (d) Experimental (triangles) and simulated (solid line) $g_{H, H}^{(2)} (0)$ (black) and $g_{V, V}^{(2)} (0)$ (red) for different pump ellipticities.
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