Dephasing through Bremsstrahlung emission: insights from quantum Boltzmann equation

TL;DR

The paper addresses decoherence from Bremsstrahlung emission in Stern-Gerlach atom interferometers using a quantum Boltzmann equation (QBE) framework. It decomposes the interaction into non-spin and spin terms, derives a damping term within a Markovian QBE, and shows the off-diagonal density-matrix element evolves as $\rho_{12}(t_f)=\rho_{12}(0)e^{-\Gamma}$ with vacuum and thermal contributions $\Gamma_{\text{vac}}$ and $\Gamma_{\text{th}}$. The non-spin term yields dephasing without amplitude damping, while the spin term adds both dephasing and a small phase shift $\varphi_{\text{spin}}$, with the spin contribution becoming more pronounced at low velocities or for lighter test particles. The results align with the influence-functional approach and have direct implications for the sensitivity of atom interferometers and their use in probing new physics via precision quantum sensing.

Abstract

We investigate decoherence mechanisms in open quantum systems using quantum field theory techniques and the quantum Boltzmann equation. Specifically, we focus on decoherence through Bremsstrahlung emission, a fundamental process in quantum electrodynamics leading to coherence loss. By applying quantum field theory techniques and quantum Boltzmann equation, we model the fermion-photon interaction in the Stern-Gerlach interferometer and analyze the induced dephasing factor. Our approach offers significant advancements in understanding decoherence and its potential applications in quantum sensing and atomic interferometry. We demonstrate the accuracy of our method by comparing results to classical Bremsstrahlung.

Figures (4)

• Figure 1: The experimental setup involves a superposition of fermions interacting with Bremsstrahlung radiation. The thick black lines indicate the paths of the fermions. The initial state of the system is represented by $\mathinner{|{\uparrow}\rangle}+\mathinner{|{\downarrow}\rangle}$, while the final state is represented by $\mathinner{|{\uparrow}\rangle}+e^{i\varphi-\Gamma t}\mathinner{|{\downarrow}\rangle}$, where $\varphi$ is the induced phase and $\Gamma$ is the dephasing factor. The orange squiggly arrow indicates the emitted photon.
• Figure 2: The vacuum and thermal (at the temperature $1^{\circ}K$) dephasing factors of non-spin term (dashed lines) and spin term (solid lines) for the fixed maximum spacial distance $\zeta=O(10^{-3}m)$ of electrons is plotted. The dephasing factor of the spin term $\Gamma_{\textrm{spin-vac}}$ and $\Gamma_{\textrm{spin-th}}$ is calculated numerically.
• Figure 3: The plot illustrates the vacuum and thermal dephasing factor (at the temperature $1~\mathrm{K}$) of the non-spin term (dashed lines) and spin term (solid lines) for a fixed velocity $v/c=10^{-11}$ for electrons in (a) and Ag atoms in (b).
• Figure 4: The loop consists of two paths, each comprising four straight world-line segments with 4-velocities of $u_1$, $u_2$, $u_3$, and $u_4$. The loop spans a time period of $2t_f$, and the maximum spatial separation between the two paths, denoted as $\xi$, occurs at time $t_f$.