Single-photon time qubit: Quantum-vacuum control and complementarity of the arrow of time

Abstract

Treating the arrow of time as a controllable quantum variable rather than a fixed external parameter is a central challenge in quantum physics. Recently, Bloch~\cite{Bloch2025} proposed the theoretical concept of a \emph{time qubit}, a two-level control space ${\mathcal{H}}_T=\mathrm{span}\{|+⟩,|-⟩\}$ that selects between opposite Hamiltonian evolutions ${\hat{H}}_{\pm }={\hat{H}}_0\pm \hat{V}$, but this paradigm has remained experimentally unrealized. Here we formulate the quantum-optical theory of a single-photon time qubit---uncovering quantum-vacuum control and complementarity of the arrow of time---and experimentally probe and validate its predictions using phase-resolved single-photon interferometry from two coherently seeded entangled nonlinear biphoton sources~\cite{Lee2018,Yoon2021}. First, we show theoretically and verify experimentally that a controlled $\pi$ pump--seed phase inversion during pair creation from the quantum vacuum flips the stimulated displacement generator $\hat{V}\to -\hat{V}$ on top of the spontaneous two-mode squeezing background ${\hat{H}}_0$, reversing the stimulated evolution time [${\hat{U}}_{\mathrm{stim},-}(t)={\hat{U}}_{\mathrm{stim},+}(-t)$] and enabling universal single-qubit $\mathrm{SU}(2)$ control and postselection-free first-order tomography on the temporal Bloch sphere. Second, we prove that spontaneous idler vacuum fluctuations record complete which-branch (temporal-direction) information whereas the shared coherent seed erases it without cascading or aligning the idler beams, establishing an exact wave--particle complementarity law $|\mathbf{r}|=\mathcal{V}=|\alpha {|}^2/(1+|\alpha {|}^2)$ for the purity of the arrow of time and enabling direct first-order measurement of the Loschmidt time-reversal echo.

arXiv comment45 pages and 5 figures