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arXiv:2209.07129 · Physical Review Letters

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, Marc Aßmann

Published Mar 13, 2023• 16 citations
arXivHTMLPDF

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.

DOI
10.1103/physrevlett.130.113601

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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.
General quasiprobabilities are introduced to visualize time-dependent quantum correlations of light in phase space. They are based on the generalization of the Glauber-Sudarshan PPP function to a time-dependent PPP functional [W. Vogel, Phys. Rev. Lett. 100, 013605 (2008)], which fully describes temporal correlations of radiation fields on the basis of continuous phase-space distributions. This approach is nontrivial, as the PPP functional itself is highly singular for many quantum states and nonlinear processes. In general, it yields neither a well-behaved nor an experimentally accessible description of quantum stochastic processes. Our regularized version of this multitime-dependent quasiprobability is a smooth function and applies to stronger divergences compared to the single-time and multimode scenario. The technique is used to characterize an optical parametric process with frequency mismatch and a strongly nonlinear evolution of the quantized center-of-mass motion of a trapped ion. A measurement scheme, together with a sampling approach, is provided which yields direct experimental access to the regularized PPP functional from measured data.
This review examines the use of continuous-variable spectroscopy techniques for investigating quantum coherence and light-matter interactions in semiconductor systems with ultrafast dynamics. Special emphasis is placed on multichannel homodyne detection as a powerful tool to measure the quantum coherence and the full density matrix of a polariton system. Observations, such as coherence times that exceed the nanosecond scale obtained by monitoring the temporal decay of quantum coherence in a polariton condensate, are discussed. Proof-of-concept experiments and numerical simulations that demonstrate the enhanced resourcefulness of the produced system states for modern quantum protocols are assessed. The combination of tailored resource quantifiers and ultrafast spectroscopy techniques that have recently been demonstrated paves the way for future applications of quantum information technologies.
In this review, we discuss the use of continuous variable spectroscopy techniques for investigating quantum coherence and light-matter interactions in semiconductor systems with ultrafast dynamics. We focus on multichannel homodyne detection as a powerful tool to measure the quantum coherence and the full density matrix of a polariton system. By monitoring the temporal decay of quantum coherence in the polariton condensate, we observe coherence times exceeding the nanosecond scale. Our findings, supported by proof-of-concept experiments and numerical simulations, demonstrate the enhanced resourcefulness of the produced system states for modern quantum protocols. The combination of tailored resource quantifiers and ultrafast spectroscopy techniques presented here paves the way for future applications of quantum information technologies.
Polariton condensates provide a versatile platform for exploring non-equilibrium phase transitions and collective phenomena in open quantum systems. Near the condensation threshold, these systems are particularly sensitive to fluctuations and instabilities, yet how these dynamics govern the initial formation of the condensate remains poorly understood. To address this, we directly access the photon statistics and second-order correlation function g (2) (0) of the condensate by using optical trapping and homodyne detection. We show that polariton condensation near the threshold is not a purely static transition, but instead undergoes a dynamical regime characterized by stochastic hopping between condensed and non-condensed states. These intermittent dynamics are accompanied by a gradual reduction of g (2) (0) toward unity, revealing the progressive build-up of coherence even in the presence of strong temporal fluctuations. Numerical simulations, based on a stochastic truncated Wigner description of the driven-dissipative polariton field, reproduce these dynamics and capture the essential role of noise and reservoir interactions. This work demonstrates that the observed temporal hopping is an intrinsic feature of polariton condensation, challenging traditional static descriptions of phase transitions and offering a framework for controlling noise and coherence in driven-dissipative quantum technologies.
Polariton condensates provide a versatile platform for exploring non-equilibrium phase transitions and collective phenomena in open quantum systems. Near the condensation threshold, these systems are particularly sensitive to fluctuations and instabilities, which can strongly influence the condensate formation. Using optical trapping and homodyne detection, we directly access the photon statistics and second-order correlation function g(2)(0)g^{(2)}(0)g(2)(0) of the condensate. We show that polariton condensation near the threshold is not a purely static transition, but instead undergoes a dynamical regime characterized by stochastic hopping between condensed and non-condensed states. These intermittent dynamics are accompanied by a gradual reduction of g(2)(0)g^{(2)}(0)g(2)(0) towards unity, revealing the progressive build-up of coherence even in the presence of strong temporal fluctuations. Numerical simulations, based on a stochastic Truncated Wigner description of the driven-dissipative polariton field, reproduce these dynamics and capture the essential role of noise and reservoir interactions. This work demonstrates that the observed temporal hopping is an intrinsic feature of polariton condensation, providing a dynamical perspective that goes beyond static descriptions of the condensation phase transition.
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.