[Paper Review] Decoherence in quantum open systems revisited

Robert Alicki|ArXiv.org|May 28, 2002

Quantum Information and Cryptography4 references3 citations

TL;DR

This paper challenges widely held beliefs in quantum decoherence theory by proving that linear coupling to a harmonic oscillator bath cannot produce pure decoherence due to energy non-conservation, and shows that chaotic environments are less efficient decoherers than regular ones. Using exact solutions of the spin-boson model and Markovian approximations, it demonstrates that decoherence rates depend critically on environmental spectral properties, not chaos, and introduces a framework where finite decoherence rates can be achieved without infinite boson clouds or unstable states.

ABSTRACT

The following statements belonging to the folklore of the theory of environmental decoherence are shown to be incorrect: 1) linear coupling to harmonic oscillator bath is a universal model of decoherence, 2) chaotic environments are more efficient decoherers.

Motivation & Objective

• To challenge the folklore that linear coupling to harmonic oscillator baths universally models pure decoherence.
• To clarify the misconception that chaotic environments enhance decoherence efficiency.
• To establish rigorous conditions under which pure decoherence can occur without energy exchange.
• To resolve inconsistencies in existing models of decoherence by analyzing exact solutions of the spin-boson Hamiltonian.
• To demonstrate that finite decoherence rates can be achieved in realistic models without divergent boson populations or unstable states.

Proposed method

• Analyzes the spin-boson Hamiltonian with a formfactor g in L²[0,∞), using coherent states and Weyl operators to diagonalize the Hamiltonian.
• Applies unitary transformation W(g) to decouple the system and environment, revealing the ground state structure and energy shift Eg.
• Uses the Markovian low-density Born approximation to derive a decoherence rate formula γ ≈ π∫|f(ω)|⁴n(ω)dω for a thermal bath.
• Introduces a mean-field model of N M-level chaotic systems coupled to a spin, with reservoir observables treated as Gaussian noise.
• Applies the fluctuation-dissipation relation to compute the decoherence rate γ = ½ limω→0 R̂(ω), with R̂(ω) derived from level spacing statistics.
• Uses Wigner’s level spacing distribution for chaotic systems and Poisson statistics for regular systems to compare decoherence rates.

Experimental results

Research questions

• RQ1 Can pure decoherence be consistently described by linear coupling to a harmonic oscillator bath?
• RQ2 Why do some models claim to show pure decoherence despite the energy non-conservation implied by linear coupling?
• RQ3 Does a chaotic environment enhance the rate of pure decoherence compared to a regular one?
• RQ4 Can finite decoherence rates be achieved without infinite boson clouds or unstable states in the reservoir?
• RQ5 What is the role of environmental spectral properties—such as level spacing statistics—in determining the decoherence rate?

Key findings

• The no-go theorem proves that linear coupling to a harmonic oscillator bath cannot produce pure decoherence because it inevitably alters the environment’s energy, violating the requirement of energy conservation.
• False decoherence arises in models where the environment’s energy is not conserved, leading to unphysical results such as infinite virtual boson populations.
• Chaotic environments are less efficient decoherers than regular ones because their energy levels are non-degenerate due to level repulsion, which hinders irreversible state perturbation without energy cost.
• For regular systems with Poisson-distributed level spacings, the decoherence rate γ is finite and non-zero, while for chaotic systems with Wigner statistics, γ → 0 in the low-frequency limit.
• The decoherence rate γ ≈ π∫|f(ω)|⁴n(ω)dω can be made finite and adjustable by choosing appropriate formfactors f(ω), even with small ‖f‖, avoiding divergences.
• In the mean-field limit of N identical M-level systems, the decoherence rate γ is proportional to the level spacing distribution p(ω), yielding γ ∼ ω for chaotic systems, hence γ → 0 as ω → 0.