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arXiv:0705.2472

Non-Markovian decoherence dynamics of entangled coherent states

Jun‐Hong An, Mang Feng, Zhang, Wei-Min

Published May 17, 2007• 8 citations
arXivHTMLPDF

Abstract

We microscopically model the decoherence dynamics of entangled coherent states under the influence of vacuum fluctuation. We derive an exact master equation with time-dependent coefficients reflecting the memory effect of the environment, by using the Feynman-Vernon influence functional theory in the coherent-state representation. Under the Markovian approximation, our master equation recovers the widely used Lindblad equation in quantum optics. We then investigate the non-Markovian entanglement dynamics of the quantum channel in terms of the entangled coherent states under noise. Compared with the results in Markovian limit, it shows that the non-Markovian effect enhances the disentanglement to the initially entangled coherent state. Our analysis also shows that the decoherence behaviors of the entangled coherent states depend sensitively on the symmetrical properties of the entangled coherent states as well as the interactions between the system and the environment.

DOI
10.48550/arxiv.0705.2472

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FINDING: Exact non-Markovian master equation for entangled coherent states via Feynman-Vernon influence functional yields time-dependent memory coefficients; other sources are pedagogical (PSD definitions, spectral approaches to friction). | MATH: The core result (arXiv:0705.2472v3) derives an exact master equation of the form: \[ \frac{d\rho}{dt} = -i[H_S(t),\rho] + \gamma(t)\mathcal{L}[\rho] + \Delta(t)\mathcal{D}[\rho] \] where \(\gamma(t)\) and \(\Delta(t)\) are non-local, time-dependent coefficients encoding the spectral density \(J(\omega)\) of the vacuum environment. Specifically, these coefficients involve integrals over \(J(\omega)\coth(\hbar\omega/2k_BT)\sin(\omega t)/\omega\) and \(J(\omega)\cos(\omega t)\) — the memory kernel. For a Lorentzian spectral density \(J(\omega) = \lambda \gamma_0^2/((\omega-\omega_0)^2+\gamma_0^2)\), the coefficients become exponential/oscillatory: \(\gamma(t) \propto e^{-\gamma_0 t}\cos(\omega_0 t)\), \(\Delta(t) \propto e^{-\gamma_0 t}\sin( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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We microscopically model the decoherence dynamics of entangled coherent states under the influence of vacuum fluctuation. We derive an exact master equation with time-dependent coefficients reflecting the memory effect of the environment, by using the Feynman-Vernon influence functional theory in the coherent-state representation. Under the Markovian approximation, our master equation recovers the widely used Lindblad equation in quantum optics. We then investigate the non-Markovian entanglement dynamics of the quantum channel in terms of the entangled coherent states under noise. Compared with the results in Markovian limit, it shows that the non-Markovian effect enhances the disentanglement to the initially entangled coherent state. Our analysis also shows that the decoherence behaviors of the entangled coherent states depend sensitively on the symmetrical properties of the entangled coherent states as well as the interactions between the system and the environment.
We investigate the entanglement dynamics of continuous-variable quantum channels in terms of an entangled squeezed state of two cavity fields in a general non-Markovian environment. Using the Feynman-Vernon influence functional theory in the coherent-state representation, we derive an exact master equation with time-dependent coefficients reflecting the non-Markovian influence of the environment. The influence of environments with different spectral densities, e.g., Ohmic, sub-Ohmic, and super-Ohmic, is numerically studied. The non-Markovian process shows its remarkable influence on the entanglement dynamics due to the sensitive time dependence of the dissipation and noise functions within the typical time scale of the environment. The Ohmic environment shows a weak dissipation-noise effect on the entanglement dynamics, while the sub-Ohmic and super-Ohmic environments induce much more severe noise. In particular, the memory of the system interacting with the environment contributes a strong decoherence effect to the entanglement dynamics in the super-Ohmic case.
We study the non-Markovian decoherence and disentanglement dynamics of dissipative quantum systems with special emphasis on non-Gaussian continuous variable systems. The dynamics are described by the Hu-Paz-Zhang master equation of quantum Brownian motion. The time evolution of the decoherence function of a single-mode superposition is compared to the concurrence of a two-mode entangled state. It is verified that moderate non-Markovian influences slow down the decay of interference fringes and quantum correlations, while strong non-Markovian effects resulting from an out-of-resonance bath can even accelerate the loss of coherence, compared to predictions of Markovian approximations. Qualitatively different scenarios including exponential, Gaussian or algebraic decay of the decoherence function are analyzed. It is shown that partial revivals of coherence can occur in case of non-Lindblad-type dynamics.
FINDING: Exact non-Markovian master equation for entangled coherent states via Feynman-Vernon influence functional yields time-dependent memory coefficients; other sources are pedagogical (PSD definitions, spectral approaches to friction). | MATH: The core result (arXiv:0705.2472v3) derives an exact master equation of the form: dρdt=−i[HS(t),ρ]+γ(t)L[ρ]+Δ(t)D[ρ] \frac{d\rho}{dt} = -i[H_S(t),\rho] + \gamma(t)\mathcal{L}[\rho] + \Delta(t)\mathcal{D}[\rho] dtdρ​=−i[HS​(t),ρ]+γ(t)L[ρ]+Δ(t)D[ρ] where γ(t)\gamma(t)γ(t) and Δ(t)\Delta(t)Δ(t) are non-local, time-dependent coefficients encoding the spectral density J(ω)J(\omega)J(ω) of the vacuum environment. Specifically, these coefficients involve integrals over J(ω)coth⁡(ℏω/2kBT)sin⁡(ωt)/ωJ(\omega)\coth(\hbar\omega/2k_BT)\sin(\omega t)/\omegaJ(ω)coth(ℏω/2kB​T)sin(ωt)/ω and J(ω)cos⁡(ωt)J(\omega)\cos(\omega t)J(ω)cos(ωt) — the memory kernel. For a Lorentzian spectral density J(ω)=λγ02/((ω−ω0)2+γ02)J(\omega) = \lambda \gamma_0^2/((\omega-\omega_0)^2+\gamma_0^2)J(ω)=λγ02​/((ω−ω0​)2+γ02​), the coefficients become exponential/oscillatory: γ(t)∝e−γ0tcos⁡(ω0t)\gamma(t) \propto e^{-\gamma_0 t}\cos(\omega_0 t)γ(t)∝e−γ0​tcos(ω0​t), \(\Delta(t) \propto e^{-\gamma_0 t}\sin( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
We study the non-Markovian decoherence and disentanglement dynamics of dissipative quantum systems with special emphasis on non-Gaussian continuous variable systems. The dynamics are described by the Hu–Paz–Zhang master equation of quantum Brownian motion. The time evolution of the decoherence function of a single-mode superposition is compared to the concurrence of a two-mode entangled state. It is verified that moderate non-Markovian influences slow down the decay of interference fringes and quantum correlations, while strong non-Markovian effects resulting from an out-of-resonance bath can even accelerate the loss of coherence, compared to predictions of Markovian approximations. Qualitatively different scenarios including exponential, Gaussian or algebraic decay of the decoherence function are analyzed. It is shown that partial revivals of coherence can occur in case of non-Lindblad-type dynamics.
FINDING: The search results are dominated by generic kernel methods (KDE, GP regression) with only one relevant physics paper on non-Markovian decoherence of entangled coherent states via exact master equations. | MATH: The relevant paper derives an exact master equation with time-dependent coefficients from the Feynman-Vernon influence functional — the memory kernel K(t,t′)K(t,t')K(t,t′) is non-local in time, encoding spectral density J(ω)J(\omega)J(ω) of the vacuum environment. No explicit golden angle or golden ratio appears in the retrieved abstracts; the spectral density is not specified as J(ω)∝ωse−ω/ωcJ(\omega) \propto \omega^s e^{-\omega/\omega_c}J(ω)∝ωse−ω/ωc​ (Ohmic/super-Ohmic) in the visible text. | CONNECTION: No direct geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 or crystallographic symmetry is present in the search results. The only structural link is the mathematical form of non-Markovian kernels — which in certain integrable spectral densities (e.g., Lorentzian) yield exponential memor Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com