Decoherence of a dissipative Brownian charged magneto-anharmonic oscillator: an information theoretic approach

TL;DR

This work analyzes decoherence in a charged, anisotropic anharmonic oscillator in a magnetic field, coupled to an Ohmic environment, using a non-Markovian, perturbative framework. A quantum Langevin equation is derived and solved to first order in the anharmonicity parameter $α$, leading to a non-Markovian master equation for the reduced density matrix and a heating function $F_H(t)$ that captures decoherence. The von Neumann entropy $S_{VN}$ is computed via Weyl/Wigner methods, revealing an $O(α^2)$ anharmonic correction that increases entropy and hence system–bath entanglement; information backflow is evidenced by oscillations in $h(t)$ in the non-Markovian regime. A Penning-trap experimental setup with optical molasses is proposed to test these predictions, highlighting potential applications for quantum technologies where decoherence limits performance.

Abstract

We study the decoherence of an anisotropic anharmonic oscillator in a magnetic field, coupled to a bath of harmonic oscillators at high and low temperatures. We solve the anharmonic oscillator problem using perturbative techniques and derive the non-Markovian master equation in the weak coupling limit. The anharmonicity parameter α enhances decoherence due to the deconfining effect of anharmonicity. The oscillatory nature of the time evolution of heating function indicates information backflow. The von-Neumann entropy is also calculated for the system, which increases with α, consistent with the deconfining effect noted in the decoherence analysis. We have also proposed a cold ion experimental set up for testing our theoretical predictions. The study is of relevance to the domain of quantum technology where decoherence significantly affects the performance of a quantum computer.

Figures (5)

• Figure 1: Proposed experimental setup for an anharmonically oscillating charged particle trapped in a Penning trap. The counter-propagating laser beams are used to cool the trapped ions and act as an optical molasses. There is an externally applied magnetic field in the $z$-direction as shown in the figure.
• Figure 2: Reduced density matrix $\rho_s/\rho_s(0)$ as a function of time for different values of the anharmonicity parameter $\alpha$ with $\omega_0=10$, $\omega_c=0.1$, $\gamma=10$, $x'=2$, $x=1$, $\Lambda=10^3$: (A) Low temperature ($\Omega=0.1$), (B) High temperature ($\Omega=10^4$).
• Figure 3: h(t) versus time for different values of the anharmonicity parameter $\alpha$ with $\omega_0=10$, $\omega_c=0.1$, $\gamma=10$, $x'=2$, $x=1$, $\Lambda=10^3$: (A) Low temperature ($\Omega=0.1$), (B) High temperature ($\Omega=10^4$).
• Figure 4: Heating function $F_H$ versus time for different values of the anharmonicity parameter $\alpha$ with $\omega_0=10$, $\omega_c=0.1$, $\gamma=10$, $x'=2$, $x=1$, $\Lambda=10^3$ for non-Markovian cases: (A) Low temperature ($\Omega=0.1$), (B) High temperature ($\Omega=10^4$); and Markovian cases: (C) Low temperature ($\Omega=0.1$), (D) High temperature ($\Omega=10^4$)
• Figure 5: Anharmonic part of the von Neumann entropy ($(S_{VN})_{Anh}=S_{VN}(\alpha,n_x)/S_{VN}(1/2,1)$)