Repeatedly readable state, spontaneous collapse, and quantum/classical boundary

• URL: http://arxiv.org/abs/2204.11656v1
• Date: Mon, 25 Apr 2022 13:48:27 GMT
• Title: Repeatedly readable state, spontaneous collapse, and quantum/classical boundary
• Authors: Xiao-Fu Peng, Yu-Hang Luo, Jiang Zhu, Bang-Hui Hua, Xue-Nan Chen, Dan-Dan Lian, Zi-Wei Chen, Xiang-Song Chen
• Abstract summary: The model introduces a spontaneous collapse of state superposition: $fracddt rho_ij =-fracihbar[H,rho]_ij-rho_ij/tau_ij$. For a "trapped Schr"odinger's cat", the superposition of $|rm here rangle$ and $| rm there rangle $ is forbidden if $E D gg 4pi hbar c$
• Score: 1.4907593787644957
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a model to identify the quantum/classical boundary. The model introduces a spontaneous collapse of state superposition: $\frac{d}{dt} \rho_{ij} =-\frac{i}{\hbar}[H,\rho]_{ij}-\rho_{ij}/\tau_{ij}$. Different from other collapse models, the collapsing scale $\tau_{ij}$ here does not contain a universal parameter, but is specified by the two states $| i\rangle $ and $ | j\rangle$: If each state is {\em in principle} repeatedly readable (typically by a QND measurement), then $\tau_{ij}$ is the {\em potentially} needed measuring time to discriminate the two states, and the collapse occurs spontaneously {\em without} any actual monitoring. Otherwise, $\tau_{ij}=\infty$, which means no collapse and everlasting superposition. This happens if one state is not repeatedly readable, or if the two states cannot possibly be discriminated in a particular circumstance (for example in the Rabi oscillation). Detailed analysis shows that for a "trapped Schr{\"o}dinger's cat", the superposition of $|{\rm here} \rangle$ and $| {\rm there} \rangle $ is forbidden if $E D \gg 4\pi \hbar c$, and allowed if $E D \le 4\pi \hbar c$, where $D$ is the trap separation and $ E$ is the energy gap, which can be estimated with $ M v^2$. The model also constrains a "free Schr{\"o}dinger's cat" to display double-slit interference if $p\theta D\ge 8\hbar$, where $p= Mv$, $\theta $ is the angle spanned by the two trajectories, and $D$ is the slit separation. In contrast, this model sets no limit on the coherent length of massless photon, thus the arm of a Michelson interferometer can be arbitrarily long. The spontaneous collapse which we propose can occur for an isolated system, and parallels the decoherence induced by interaction with environment.

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