Tracking Quantum Coherence in Polariton Condensates with Time-Resolved Tomography

Carolin Lüders, Matthias Pukrop, Franziska Barkhausen, Elena Rozas, Christian Schneider, Sven Höfling, Jan Sperling, Stefan Schumacher, and Marc Aßmann

Phys. Rev. Lett. 130, 113601 – Published 13 March 2023

Abstract

Long-term quantum coherence constitutes one of the main challenges when engineering quantum devices. However, easily accessible means to quantify complex decoherence mechanisms are not readily available, nor are sufficiently stable systems. We harness novel phase-space methods—expressed through non-Gaussian convolutions of highly singular Glauber-Sudarshan quasiprobabilities—to dynamically monitor quantum coherence in polariton condensates with significantly enhanced coherence times. Via intensity- and time-resolved reconstructions of such phase-space functions from homodyne detection data, we probe the systems’ resourcefulness for quantum information processing up to the nanosecond regime. Our experimental findings are confirmed through numerical simulations, for which we develop an approach that renders established algorithms compatible with our methodology. In contrast to commonly applied phase-space functions, our distributions can be directly sampled from measured data, including uncertainties, and yield a simple operational measure of quantum coherence via the distribution’s variance in phase. Therefore, we present a broadly applicable framework and a platform to explore time-dependent quantum phenomena and resources.

Received 15 September 2022
Accepted 21 February 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.113601

Physics Subject Headings (PhySH)

Exciton polariton Quantum information with hybrid systems Quantum interference effects Quantum optics Resource theories Semiconductor quantum optics

Polariton condensate Semiconductor microcavities

Homodyne & heterodyne detection Phase space dynamics Phase space methods

Quantum Information, Science & TechnologyAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Carolin Lüders ^1,*, Matthias Pukrop ², Franziska Barkhausen ², Elena Rozas ¹, Christian Schneider³, Sven Höfling⁴, Jan Sperling ^5,†, Stefan Schumacher^2,6, and Marc Aßmann ¹

¹Experimentelle Physik 2, Technische Universität Dortmund, D-44221 Dortmund, Germany
²Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, 33098 Paderborn, Germany
³Institute of Physics, University of Oldenburg, D-26129 Oldenburg, Germany
⁴Technische Physik, Physikalisches Institut and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
⁵Theoretical Quantum Science, Institute for Photonic Quantum Systems (PhoQS), Paderborn University, Warburger Straße 100, 33098 Paderborn, Germany
⁶Wyant College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA

^*carolin.lueders@tu-dortmund.de
^†jan.sperling@upb.de

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Issue

Vol. 130, Iss. 11 — 17 March 2023

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Images

Figure 1
Experimental concept as conditional intensity spectroscopy. The signal is split into three homodyne detection channels. Two are used for intensity selection, delivering field quadratures $(q_{p s}, p_{p s})$ of a Husimi function $Q (α_{p s})$ , with $α_{p s} = q_{p s} + i p_{p s}$ . Thereby, a specific region with radius $s$ and width $w$ is chosen, fixing the signal’s mean intensity and its uncertainty. The third quadrature is the target channel for quadratures $q$ . Together with the corresponding phases, this allows us to directly sample $P_{Ω}$ . The time delay $τ$ determines the elapsed time of the system’s evolution.
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Figure 2
Temporal behavior of the mean amplitude $⟨ | α | ⟩$ and the circular phase variance $Var (ϕ)$ of reconstructed $P_{Ω}$ , depending on the selected intensity radius $s$ . A shaded area around the curves corresponds to a 1-standard-deviation error margin, directly derived from $P_{Ω}$ ’s uncertainty, but is mostly not visible. Lines depict exponential fits. Plots (a) and (b) are for $P_{exc} = 1.7 P_{thr}$ . The width $w$ of the selected phase-space region is 0.57. Plots (c) and (d) are for $P_{exc} = 0.8 P_{thr}$ . The width $w$ is 0.1, except for the two highest radii $s$ , where $w = 0.57$ . Insets in (a) and (c) show the Husimi functions from which the radius $s$ is selected, cf. Fig. 1. The inset in (d) displays a zoom of the region $τ \approx 0$ , revealing an oscillation of the mean amplitude. The right column exemplifies three $P_{Ω}$ for $P_{exc} = 1.7 P_{thr}$ and a selected radius $s = 9.9$ at time delays $τ = - 6 ps$ (top), $τ = 494 ps$ (middle), and $τ = 1214 ps$ (bottom).
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Figure 3
Decay times (a) $τ_{c}$ of $Var (ϕ)$ and (b) of the mean amplitude $⟨ | α | ⟩$ versus the selected radius $s$ for different excitation powers. Connecting lines are guides for the eye. Triangles indicate the mean radius averaged over the Husimi distribution—i.e., the stationary state. For the amplitude decay times, $s$ values too close to the mean radius are discarded, as fits are error prone due to the flat curve shape in those cases. (c) Decay time $τ_{c}$ , averaged over the radii $s$ , versus excitation power. For the average, the decay time for each radius has been weighted by the number of data points.
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Figure 4
Numerical results. Circular variance $Var (ϕ)$ from $P_{Ω}$ for the $k = 0$ condensate mode as a function of time for different excitation powers. Lines are the fitted exponential curves, color-coded to the excitation powers as defined in the inset; the inset shows the fitted coherence times $τ_{c}$ as a function of the excitation power, with error margins of 1 standard deviation. Additionally, the values of quantum coherence are given.
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