Collective-Coordinate Dynamics and Radiative Decoherence in a Driven-Dissipative Polariton Condensate

Collective-Coordinate Dynamics and Radiative Decoherence in a Driven-Dissipative Polariton CondensateGeometric constraints on centre-of-mass path coherence and a numerical test of self-confinement This paper asks whether a room-temperature driven-dissipative exciton-polariton condensate can supply a localized collective coordinate able to occupy a resolvable two-path superposition. For the platform considered and for ordinary radiative coupling, the answer is negative for two independent reasons, and the paper states precisely where the formal construction holds and where its physical realization fails. Radiative which-path decoherence. Treating the condensate as an open system with a mode-resolved loss channel, the coherence between two localized branch states decays at ΓCOM = Nγ[1 − Re χ(d)], where χ(d) is the overlap of the photon states emitted by the two branches. The controlling variable is environmental distinguishability rather than mechanical recoil: a photon that displaces the centre of mass by a negligible amount can still record, at full strength, which branch the emitter occupied. Where ordinary out-coupling preserves transverse-mode information, two requirements act on the same length scale and conflict — branch resolvability requires a separation of several core widths, indistinguishability requires a separation well below one — so that, for a sech profile and the working convention d ≳ 3ξ, the dimensionless ratio ΓCOM/(Nγ) is bounded below by about 0.7. The coefficient is geometric; the absolute rate retains its dependence on N and γ. Numerical test of self-confinement. The operating point inferred from the measured group velocity on the CsPbBr3 microwire platform lies in the positive-effective-mass regime, where repulsive polariton interactions do not support a bright soliton. A free-propagation integration anchored to that regime shows a packet seeded at the analytic width broadening from 2.2 µm to 25.8 µm over 6 ps, so the proposed self-confined realization is not present there. A negative-mass run is retained only as a control of the propagation solver. Corrected collective wavelength. The de Broglie wavelength of the collective coordinate follows from the aggregate mass M* = N mLP, not from the single-polariton value: λCOM = h/(M*vg) = λLP/N ≈ 0.11 nm. The corresponding Fraunhofer scale far exceeds the demonstrated 60 µm propagation length, so no far-field centre-of-mass double-slit geometry is proposed for this platform. Supporting these results, the collective-coordinate construction is retained as a conditional formal sector for a rigid bright soliton: translational symmetry protects free motion exactly, the Kohn conditions protect harmonic centre-of-mass motion, and a hydrodynamic Madelung cross-check reproduces the same statement independently. In the aperture region the adiabaticity parameter is of order unity on the platform considered, so no perturbative mass-renormalization coefficient is assigned there. The paper distinguishes first-order field coherence, which a driven condensate can maintain and which is experimentally measured, from coherence between two centre-of-mass configurations, which the radiative channel destroys. The argument is independent of any interpretation of quantum mechanics. Engineering of the output reservoir so that the two branches emit into nearly indistinguishable environmental modes is identified as the route by which radiative which-path decoherence could be suppressed. Changes in version 2.0 Version 2.0 revises the central claim of version 1.0 and should be read in place of it. The title and the subject of the paper have both changed. Retracted. The suppressed decoherence rate of version 1.0 and the 1/N estimate on which it rested. That estimate measures the back-action of a quantum jump on the mean position; it does not measure the which-path information deposited in the environment, which scales with the number of constituents rather than against it. The coherence time reported in version 1.0, and the transit-time margin derived from it, do not hold. Withdrawn. The claim that the structure traverses a double slit in a coherent superposition of paths; the claim that a transition between interpretations of quantum mechanics emerges as a necessary structure of the dynamics; the reduced fringe visibility previously advanced as the primary experimental signature, which is a property of the order parameter rather than of a path superposition; and the self-confinement property, shown numerically not to hold at the operating point of the platform. The acronym under which the construction was introduced is not used further. Removed from scope. The admissibility layer and the interpretive material associated with it. This version is self-contained within condensed-matter physics and quantum decoherence, and its results depend on no unpublished work. Corrected. Parameter provenance. Version 1.0 combined quantities measured on four distinct platforms and conflated the cavity photon lifetime, the polariton lifetime and the first-order coherence time. All platform inputs are now drawn from one system and tabulated with operational definition, origin and status as measured, derived or chosen. The de Broglie wavelength of the collective coordinate is corrected. The description of the soliton solution set as a symplectic manifold is weakened to a finite-dimensional collective-coordinate manifold, and the claim to a first explicit formulation of the mapping as an identity is withdrawn; the Ehrenfest theorem is stated as a consistency check rather than as the derivation. Retained. The strong-coupling analysis, the conditional collective-coordinate reduction, the exact symmetry sectors with their hydrodynamic cross-check, and the parametric relation between mass and nonlinearity, the last now confirmed against a measurement on the platform.