[Paper Review] Damping and Decoherence in Neutron Oscillations

B. O. Kerbikov, М. С. Лукашов+2 more|arXiv (Cornell University)|Dec 10, 2015

Nuclear Physics and Applications5 references3 citations

TL;DR

This paper develops a density matrix formalism to analyze neutron oscillations in the presence of residual gas, showing that collisions induce both a refraction-induced energy shift (analogous to a magnetic field) and strong decoherence. For neutron-antineutron oscillations, the decoherence rate from antineutron annihilation in residual gas exceeds the oscillation frequency, leading to overdamping that suppresses oscillations unless gas pressure is reduced by several orders of magnitude.

ABSTRACT

An analysis is made of the role played by the gas environment in neutron-mirror-neutron and neutron-antineutron oscillations. In the first process the interaction with the ambient medium induces a refraction energy shift which plays the role of an extra magnetic field. In the second process antineutron annihilation in practice might lead to strong decoherence, which should be taken into account in experiments with free neutrons looking for the neutron to antineutron transformation.

Motivation & Objective

• To investigate the impact of residual gas on neutron oscillation experiments, particularly for neutron-mirror-neutron and neutron-antineutron transitions.
• To identify and quantify two effects from gas interactions: a refraction-induced energy shift (analogous to a magnetic field) and decoherence from collisions.
• To demonstrate that decoherence from antineutron annihilation in residual gas can suppress oscillations, challenging the feasibility of current experimental setups.
• To provide a general formalism based on von Neumann-Liouville and Lindblad equations applicable to both disappearance and appearance processes.
• To guide future experiments—especially ESS-based n→n̄ searches—by quantifying required pressure thresholds to avoid damping.

Proposed method

• Uses the density matrix formalism with von Neumann-Liouville and Lindblad equations to describe open quantum systems interacting with a gas reservoir.
• Models the interaction with gas via a complex potential, deriving the effective Hamiltonian and damping/relaxation terms.
• Introduces a parameter Λ to describe the combined effect of refraction and decoherence, with its imaginary part (ImΛ) quantifying decoherence rate.
• Applies the formalism to two cases: neutron-mirror-neutron oscillations (with refraction effects) and neutron-antineutron oscillations (with strong decoherence).
• Solves the resulting second-order differential equation for the z-component of polarization (Rz), analyzing overdamped regimes.
• Estimates decoherence rates using known annihilation cross sections (e.g., vσa ≈ 50–55 mb for n̄p) and gas number densities (ν₂ ≈ 2.5×10¹³ cm⁻³).

Experimental results

Research questions

• RQ1 How do collisions with residual gas molecules affect the coherence and oscillation dynamics in neutron-antineutron and neutron-mirror-neutron systems?
• RQ2 To what extent does the decoherence rate from antineutron annihilation in residual gas exceed the oscillation frequency, potentially suppressing observable oscillations?
• RQ3 Can the refraction-induced energy shift from gas interactions be modeled as an effective magnetic field in neutron-mirror-neutron oscillations?
• RQ4 What pressure threshold is required to prevent overdamping in neutron-antineutron oscillation experiments?
• RQ5 How do the derived damping and decoherence rates compare with experimental limits from ILL and Super-K experiments?

Key findings

• The imaginary part of the effective interaction parameter Λ, representing decoherence, is estimated at (ImΛ)₂ ≈ 10⁻² s⁻¹ (10⁻¹⁷ eV) for ν₂ ≈ 2.5×10¹³ cm⁻³, indicating strong damping.
• For lower gas density (ν₃ ≈ 5×10¹⁰ cm⁻³), (ImΛ)₃ ≈ 10⁻⁵ s⁻¹ (10⁻²⁰ eV), still significantly exceeding the oscillation rate ε ≲ 10⁻²³ eV.
• The condition ImΛ ≫ 1/τₙₙ̄ ≈ ε (i.e., ImΛ ≫ 10⁻²³ eV) implies that decoherence dominates, leading to overdamped, non-oscillatory behavior.
• In the overdamped regime, the polarization Rz decays as exp(−(4ε²/ImΛ)t), suppressing oscillations entirely unless pressure is reduced by several orders of magnitude.
• The analysis shows that current experimental pressures (e.g., P ≈ 10⁻⁶ atm) are insufficient to avoid damping, necessitating much lower pressures for observable n→n̄ oscillations.
• The formalism is general and applicable to both disappearance (n→n′) and appearance (n→n̄) processes, with implications for future ESS-based experiments.