Quantum coherence of a long-lifetime exciton-polariton condensate

TL;DR

This work addresses how to maximize quantum coherence in long-lived exciton-polariton condensates. By spatially separating the condensate from the incoherent reservoir with an annular optical trap and modeling the state as a displaced thermal state, the authors quantify coherence using the metric $C$ and show that coherence increases significantly as the system crosses the condensation threshold. They demonstrate a coexistence of condensed and uncondensed populations near threshold and observe a rapid approach of $g^{(2)}(0)$ toward 1 at higher pump powers, with $C$ reaching ~0.6–0.7, about three times higher than prior reports. The results suggest that long polariton lifetimes enabling thermalization, combined with reduced reservoir fluctuations, are key to achieving robust quantum coherence, offering a pathway to integrating polariton condensates into hybrid quantum devices.

Abstract

In recent years, quantum information science has made significant progress, leading to a multitude of quantum protocols for the most diverse applications. States carrying resources such as quantum coherence are a key component for these protocols. In this study, we optimize the quantum coherence of a nonresonantly excited exciton-polariton condensate of long living polaritons by minimizing the condensate's interaction with the surrounding reservoir of excitons and free carriers. By combining experimental phase space data with a displaced thermal state model, we observe how quantum coherence builds up as the system is driven above the condensation threshold. Our findings demonstrate that a spatial separation between the condensate and the reservoir enhances the state's maximum quantum coherence directly beyond the threshold. These insights pave the way for integrating polariton systems into hybrid quantum devices and advancing applications in quantum technologies.

Figures (5)

• Figure 1: Spectroscopic analysis of the power dependent polariton emission. Polariton PL in momentum (a) and real space (b), at three different pump powers: $0.57\,P_\text{th}$ (I), $1.00\,P_\text{th}$ (II), and $1.35\,P_\text{th}$ (III). The images for case II are a superposition of consecutive images acquired under identical external conditions. In that case, the system shows a critical mode competition over time, switching between polariton emission within the circular barrier and a strong spontaneous condensate emission.
• Figure 2: Polariton condensation signatures. (a) PL intensity and linewith as a function of P/P$_{th}$. (b) Corresponding blueshift extracted from the momentum-resolved emissions at $k=0$. LPB denotes spectra where the polariton system only occupies the ground state of the lower polariton branch. BEC denotes spectra where the system displays a polariton condensate state.
• Figure 3: Long scale time-resolved emission properties. Long scale time resolved (a) second order correlation function $g^{(2)}(0)$ and (b) photon number of the polariton emission for the powers $1.05\,P_\text{th}$, $1.10\,P_\text{th}$ and $1.35\, P_\text{th}$. In the case of $1.05,P_\text{th}$ the system shows switching between an uncondensed state and a polariton condensate. For clarity, the uncondensed state photon number is greyed out and its $g^{(2)}(0)$-values are omitted.
• Figure 4: Evolution of the polariton state in phase space. (a)-(d) Phase averaged Husimi distributions for excitation powers of $0.77\,P_\text{th}$, $1.05\,P_\text{th}$, $1.15\,P_\text{th}$ and $1.35\,P_\text{th}$, displaying the transition from a vacuum state, characterized by a Gaussian probability distribution, to a displaced thermal state with a ring-like distribution. In case (b), the main figure only shows the condensate state distribution, the distribution of the whole recorded data set is given in the corresponding inset. (e) Coherent and thermal photon numbers extracted from the Husimi representations at different excitation powers. (f) Corresponding $g^{(2)}(0)$ as a function of the excitation power. (g) Calculated quantum coherence in dependence of the excitation power.
• Figure 5: Scheme of the experimental setup. The sample is non resonantly excited in reflection geometry by a cw laser, spatially reshaped to an annular trap. The emission is then either analyzed using a combination of spectrometer and CCD or a two-channel homodyne detection setup. (SLM: spatial light modulator; PBS: polarized beam splitter; MO: microscope objective; FM: flip mirror; $\lambda/2$: half waveplate; $\lambda/4$: quarter waveplate)