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arXiv:2501.12328 · Comptes Rendus Physique

Decoherence of Schrödinger cat states in light of wave/particle duality

Th. K. Mavrogordatos

Published Dec 22, 2025• 0 citations
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Abstract

We challenge the standard picture of decohering Schrödinger cat states as an ensemble average obeying a Lindblad master equation, brought about locally from an irreversible interaction with an environment. We generate self-consistent collections of pure system states correlated with specific environmental records, corresponding to the function of the wave-particle correlator first introduced in Carmichael et al. [ Phys. Rev. Lett. 85 (2000)]. In the spirit of Carmichael et al. [in Coherent States: Past, Present and Future , World Scientific, 1994], we find that the complementary unravelings evince a pronounced disparity when the “position” and “momentum” of the damped cavity mode — an explicitly open quantum system — are measured. Intensity-field correlations may largely deviate from a monotonic decay, while Wigner functions of the cavity state display contrasting manifestations of quantum interference when conditioned on photon counts sampling a continuous photocurrent. In turn, the conditional photodetection events mark the contextual diffusion of both the net charge generated at the homodyne detector, and the electromagnetic field amplitude in the resonator.

DOI
10.5802/crphys.271

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We challenge the standard picture of decohering Schrödinger cat states as an ensemble average obeying a Lindblad master equation, brought about locally from an irreversible interaction with an environment. We generate self-consistent collections of pure system states correlated with specific environmental records, corresponding to the function of the wave-particle correlator first introduced in Carmichael et al. [ Phys. Rev. Lett. 85 (2000)]. In the spirit of Carmichael et al. [in Coherent States: Past, Present and Future , World Scientific, 1994], we find that the complementary unravelings evince a pronounced disparity when the “position” and “momentum” of the damped cavity mode — an explicitly open quantum system — are measured. Intensity-field correlations may largely deviate from a monotonic decay, while Wigner functions of the cavity state display contrasting manifestations of quantum interference when conditioned on photon counts sampling a continuous photocurrent. In turn, the conditional photodetection events mark the contextual diffusion of both the net charge generated at the homodyne detector, and the electromagnetic field amplitude in the resonator.
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Schrödinger cat states, representing coherent superpositions of macroscopically distinguishable states, are indispensable nonclassical resources for continuous-variable quantum information processing. Existing generation protocols typically rely on strong nonlinear interactions, complicated control techniques, or engineered dissipation, posing challenges for experimental implementation. Here, we propose a simple measurement-based protocol for generating Schrödinger cat states in a cavity-QED system by combining coherent driving, dispersive atom--cavity interactions, and atomic postselection. The atom--cavity interaction establishes coherent correlations between the atomic and photonic degrees of freedom, while the subsequent atomic postselection projects the cavity field onto a non-Gaussian superposition state with pronounced Wigner negativity. Numerical simulations based on the Lindblad master equation show that the generated Schrödinger cat states remain robust against moderate cavity dissipation. Our results demonstrate that conditional atomic measurements provide an effective and experimentally accessible approach for preparing nonclassical cavity states without relying on strong optical nonlinearities or engineered dissipation.
Application of the quantum nondemolition (QND) method to Schrodinger cat states is described. Phase cat states of trapped light is generated by QND measurement of the photon number parity of a coherent field initially injected into the cavity. The measured Wigner function of a cat state at four different delays between preparation and measurement is presented. The Wigner function exhibits two positive, ideally Gaussian, peaks corresponding to the two classical components of the state. Quantitative analysis of the decoherence process is also presented. Generalization of this experiment to the preparation of non-local cat states located at the same time between two different cavities is discussed.
The Schrödinger equation describes a quantum system that does not interact with anything outside itself. The participation measure evolves unitarily; the norm is preserved; coherent superpositions are maintained indefinitely. This is a useful idealization but it is not what real quantum systems do. Every real quantum system is in contact with its environment — thermal photons, lattice vibrations, stray fields, gas‑phase collisions, observation by experimenters. Coherent superpositions decay; populations relax toward thermal equilibrium; entanglement with the environment proliferates. The closed‑system Schrödinger equation cannot describe these phenomena because, by construction, it has no environment. In 1976, Lindblad — and independently Gorini, Kossakowski, and Sudarshan — proved that the most general Markovian dynamics for a quantum density operator that preserves Hermiticity, trace, and complete positivity has a specific functional form: ∂ₜ ρ̂ = −(i/ℏ)[Ĥ, ρ̂] + ∑_α ( L̂_α ρ̂ L̂_α† − ½{ L̂_α† L̂_α , ρ̂ } ) The first term is the von Neumann equation. The sum is the “dissipator” — jump operators L̂_α mediating environmental coupling. This is the master equation of decoherence theory: qubits coupled to reservoirs, atoms in optical cavities, mesoscopic conductors with electron‑phonon coupling, open‑system everything. The standard derivation traces out the environment and applies the Born–Markov approximation. It works empirically but leaves open: why is Markov valid? Why is Born valid? What is the substrate‑level meaning of the jump operators? This walkthrough shows how the Event Density framework forces the Lindblad form at substrate level rather than deriving it from approximations. The density‑operator description is forced by environmental phase‑independence, derived from substrate primitives, rather than postulated as the natural object after partial‑tracing. Between commitment events, the density operator evolves unitarily — U3 in density‑operator form. The jump operators are the substrate‑level representation of Primitive 11 commitment events: discrete, channel‑selective updates triggered when environmental coupling drives the chain’s individuation. The Markov property is forced by P11’s locality (commitment events do not carry long‑range memory). The anti‑commutator normalization is forced by P04 (bandwidth conservation) plus trace preservation. Complete positivity is automatic from the projector structure of commitment events. The structural payoff: decoherence is not approximate physics derived from a Born–Markov simplification of a more fundamental closed‑system theory. It is what U3 plus substrate primitives produces directly when the chain is non‑isolated. The Lindblad form is forced rather than approximate. Complete positivity, trace preservation, and the Markovian property — usually justified by appeals to physical reasonableness — are forced consequences of bandwidth conservation, environmental phase‑independence, and commitment‑event locality respectively.
The cover page shows snapshots of a decaying Schrödinger cat Wigner function. This is a quasi-probability distribution for the amplitude of a microwave field stored in an ultra-high quality superconducting cavity. A single circular Rydberg atom interacting with a coherent state produces a quantum superposition of two fields with different phases. The two positive peaks in the Wigner function (front) are centered on the classical amplitudes of these components. The interference pattern in-between indicates the quantum nature of the superposition. As time proceeds (from front to rear), the interference pattern vanishes, revealing the rapid decoherence of a mesoscopic quantum state superposition.
The cover page shows snapshots of a decaying Schrödinger cat Wigner function. This is a quasi-probability distribution for the amplitude of a microwave field stored in an ultra-high quality superconducting cavity. A single circular Rydberg atom interacting with a coherent state produces a quantum superposition of two fields with different phases. The two positive peaks in the Wigner function (front) are centered on the classical amplitudes of these components. The interference pattern in-between indicates the quantum nature of the superposition. As time proceeds (from front to rear), the interference pattern vanishes, revealing the rapid decoherence of a mesoscopic quantum state superposition.