Is the Conventional Picture of Coherence Time Complete? Dark Matter Recoherence

TL;DR

The paper investigates whether the conventional ULDM coherence time is complete by highlighting how a solar gravitational potential induces discrete bound states, leading to a generalized coherence time and the novel DM-recoherence phenomenon. It develops a formal framework for the generalized coherence time from the auto-correlation function and mode expansion, and analyzes three concrete scenarios (free gas in a 3D box, a ground-state solar halo, and a virialized halo) to show how discrete level structure alters coherence, decoherence, and recoherence timescales. These insights are then connected to experimental sensitivity, showing that long observation times can significantly boost the reach of clock-based DM searches via recoherence, with explicit SNR and coupling-sensitivity scaling relations and practical implications for solar and terrestrial halos. The work suggests that even small bound-state fractions of ULDM can materially improve discovery prospects for upcoming experiments, particularly those accumulating data over years to decades.

Abstract

The local solar gravitational potential forms a basin for ultralight dark matter (ULDM), with discrete energy levels. Even if barely populated, it introduces a new characteristic timescale in DM dynamics. This necessitates a generalization of the notion of coherence time. We find that, at long times, the phenomenon of recoherence emerges, whereby a subcomponent of ULDM exhibits a formally divergent coherence time. The fact that this generalized coherence time can significantly exceed the naive estimate implies an enhanced sensitivity for dark matter searches that accumulate data over extended observation periods.

Figures (5)

• Figure 1: Evolution of the sensitivity to the effective DM coupling in a broadband search as a function of observation time. The energy spread $\Delta E$ of states populated by DM leads to decoherence and a deterioration of the sensitivity. Bound states with finite energy spacing $\delta E$ eventually lead to recoherence and the same scaling as in the coherent regime is recovered.
• Figure 2: In the shaded regions, the solar halo dominates the detection prospects. This may even be the case if the halo is less dense than the galactic DM at the position of earth ($\rho^\odot<\rho^\mathrm{gal}$, region below horizontal black line). The vertical black line marks the DM mass $m$ for which the gravitational atoms Bohr radius equals 1 AU. Left: Halo populated only by the 1s ground state. The DM field is always coherent if the solar halo dominates (orange). If subdominant, it recoheres on timescales longer than the galactic halo coherence time $\sim 1/(m\sigma^2)$ such that even a subdominant halo can enhance the experimental significance for sufficiently long integration times (blue). Extrapolating the halo profile inward excludes the red region from Mercury's ephemeris Pitjev:2013sfa. Right: Virialized halo with all gravitational atom states populated. For Bohr radii larger than 1 AU (left of the black line), the 1s state dominates and the behavior matches the left panel. For smaller Bohr radii, multiple states contribute at earth, causing recoherence even when the galactic halo is negligible (light purple), and potentially multiple stages of de- and recoherence when it dominates (dark purple). The pink, vertical lines mark the mass at which for small observation times (2 days, month) the solar halo as a whole decoherse due to its finite width. The purple lines conversely give the mass where the halo recoherse after longer times (year, 10 years) due to the discrecte energies. The green line shows the expected solar-halo density if equilibrated with the galactic halo.
• Figure 3: Evolution of the coherence time for a free quantum gas in a 3D box case with temperature $\beta^{-1}$ and size of the box $L$ chosen such that $\frac{2 \pi^2 \beta}{m L^2}=0.05$ . We compare the case of a degenerate box with a non-degenerate one, where the ratios between lengths is chosen as described in the text. In the non-degenerate case the onset of recoherence is delayed.
• Figure 4: $1s$ solar halo: Coherence time evolution for solar halo ground state in background of galactic halo DM for the point in parameter space marked with a cross in Fig. \ref{['fig:Solar halo dominating detection prospects']}. The recoherence time is estimated as $T_\mathrm{obs}\sim (\rho_\mathrm{gal}/\rho^{\odot}_{\text{1s}})^2/(m\sigma^2)$. The vertical black dashed lines mark the de- and recoherence time, whereas the vertical thick black line correponds to $T_\text{obs}=1\,\text{year}$.
• Figure 5: Evolution of the coherence time for the virialized solar halo only with $r/a_0=25$. The spread of energies leads to a finite decoherence time $\sim 1/m v^2$, in agreement with the standard picture. The discrete nature of the bound states gives rise to recoherence at $T_\mathrm{obs} \sim \delta E^{-1} \sim (r/a_0)/m v^2$.