Relevance of "on" and "off" transitions in quantum pair production experiments

TL;DR

The paper addresses how inevitable 'on' and 'off' transitions in finite-time experiments affect quantum pair production in cosmological and electromagnetic contexts. It analyzes a real scalar field in a $(1+D)$-dimensional FLRW background, showing that particle production depends sensitively on the transition dynamics and the field-gravity coupling, with Bogoliubov coefficients $\beta_k$ governing the per-mode occupation and total density. The key finding is that abrupt transitions can dominate the spectra for nonconformal coupling, while conformal coupling suppresses this effect; in the Schwinger setup, the intermediate regime can dominate for long field durations due to anisotropy, though transitions remain influential. These results imply that experimental spectra in analog gravity systems require careful interpretation, particularly when simulating nonconformal cosmologies or inflation-to-reheating scenarios.

Abstract

Analog gravity experiments, such as those realized in Bose-Einstein condensates, often aim at simulating cosmological pair production due to the dynamical expansion of the Universe. However, these experiments have a start and an end, which introduces unavoidable transitions out of and into static regimes that alter the intended expansion profile. We show that the resulting particle spectra can be overwhelmingly dominated by these transition periods, which calls for a careful interpretation of experimental outcomes. In prospective Schwinger effect experiments, by contrast, transition effects do not dominate particle production, and such a reinterpretation may not be necessary.

Figures (5)

• Figure 1: Expansion rate in Eq. \ref{['eq:DerivativeScale']} as function of conformal time, for different transition durations $\delta$, with $\Delta\eta = \eta_{\text{off}} - \eta_{\text{on}}$.
• Figure 2: Total number density of produced particles $n$ as a function of $\eta_{\text{off}}$ ($\eta_{\text{on}}=0$), in the case of two and three spatial dimensions. Results are shown for different values of the coupling $\xi$, where the red continuous lines correspond to the conformal coupling case. 'On' and 'off' transitions are chosen sufficiently fast ($\delta=0.1$) to guarantee convergence to the limiting behavior as the product $\delta a_0^\prime$ becomes small. We also consider slower transition rates, comparable to the expansion rate in the intermediate region ($\delta=1$). Here, $\delta$ and $\eta_{\text{off}}$ are expressed in units of $m^{-1}$, while the number density $n$ is given in units of $m^3$.
• Figure 3: Function $\mathcal{C}_k$ for $D=3$ dimensional universe expansion with $\Delta \eta=3$, for different transition durations $\delta$, fixed $k=1$. The left panel illustrates the conformal coupling case ($\xi=1/6$) while the right panel corresponds to a nonconformal coupling case ($\xi= 1$). Here, $\eta$ and $k$ are expressed in units of $m^{-1}$ and $m$, respectively.
• Figure 4: Function $\mathcal{C}_k$ for a typical analog gravity experiment in quasi-two-dimensional BECs for $k=0.5 \, \mu\text{m}^{-1}$ and transitions of different abruptness characterized by $\delta$. The values are normalized with respect to $\bar{\mathcal{C}}_k \simeq 5 \times 10^{-11}$, assuming an intermediate region of duration $\Delta t = 3 \, \text{ms}$. The BEC parameters correspond to the expansion linear in $t$ presented in Ref. Viermann2022.
• Figure 5: Total number density of produced particles $n$ as function of $t_{\text{off}}$ ($t_{\text{on}}=0$) in the Schwinger effect for electric potentials of the form \ref{['eq:DerivativeScale']}, with an intermediate electric strength equal to the Schwinger limit, $-\dot{A}_0 = m^2/q^2$, and fast switch-on and switch-off transitions ($\delta=0.1$). Time variables are expressed in units of $m^{-1}$, and the number density in units of $m^3$.