AI 中文总结
研究物质波干涉测量中引力子诱导的路径信息退相干，通过对引力子求迹精确求解分支依赖演化，给出不同情况下退相干程度表达式，发现当前物质波干涉仪中辐射引力子诱导的退相干可忽略不计。
AI 中文摘要
我们推导了物质波干涉测量中由于对线性化量子引力的引力子进行求迹而产生的路径信息退相干。由于引力子由物质源线性驱动，分支依赖的演化可以精确求解，退相干程度由初始引力子态的特征函数给出，该函数在分支诱导的场位移之差处进行评估。在真空中，退相干指数等于由差分源辐射的引力子平均数量的一半。对于光滑高斯轨迹，退相干程度为 $\Gamma_{\rm vac}=(8/15)\,Gm^2d^4/(\hbar c^5\tau^4)$，在代表性物质波平台范围内从 $10^{-89}$ 到 $10^{-61}$。对于一般的压缩引力子真空，我们得到一个精确表达式，其中压缩根据压缩相位要么抑制要么增强真空响应。对于暴胀产生的强压缩态，该表达式变为 $\Gamma_{\rm inf}=(\pi/20)\,\Omega_{\rm inf}(md^2H_0/\hbar)^2$，对于乐观参数最多达到 $\sim10^{-27}$。因此，辐射引力子诱导的路径信息退相干在当前物质波干涉仪中可以忽略不计。
英文摘要
We derive which-path decoherence for matter-wave interferometry that arises from tracing out the gravitons of linearized quantum gravity. Because the gravitons are driven linearly by the matter source, the branch-dependent evolution can be solved exactly, and the reduced coherence is given by the characteristic function of the initial graviton state, evaluated at the difference of the branch-induced field displacements. In vacuum, the decoherence exponent equals half the mean number of gravitons radiated by the difference source. For a smooth Gaussian trajectory, it reduces to $Γ_{\rm vac}=(8/15)\,Gm^2d^4/(\hbar c^5τ^4)$, ranging from $10^{-89}$ to $10^{-61}$ across representative matter-wave platforms. For a general squeezed graviton vacuum, we obtain an exact expression in which squeezing either suppresses or enhances the vacuum response, depending on the squeezing phase. For the strongly squeezed state produced by inflation, this expression reduces to $Γ_{\rm inf}=(π/20)\,Ω_{\rm inf}(md^2H_0/\hbar)^2$ and reaches at most $\sim10^{-27}$ for optimistic parameters. Hence, the which-path decoherence induced by radiative gravitons is therefore negligible in current matter-wave interferometers.
Comments12 pages, 2 figures
