Generalized cold-atom simulators for vacuum decay

Abstract

Cold-atom analog experiments are a promising new tool for studying relativistic vacuum decay, enabling one to empirically probe early-Universe theories in the laboratory. However, existing proposals place stringent requirements on the atomic scattering lengths that are challenging to realize experimentally. Here we eliminate these restrictions and show that any stable mixture between two states of a bosonic isotope can be used as a faithful relativistic analog. This greatly expands the landscape of suitable experiments, and will expedite efforts to study vacuum decay with cold atoms.

Figures (4)

• Figure 1: Landscape of vacuum decay analogs in the $F=1$ hyperfine manifold of ${}^{41}\mathrm{K}$. The horizontal bars correspond to pairs of states $\ket{m_F}\in\{\ket{+1},\ket{0},\ket{-1}\}$. Shading indicates the viable parameter space for our asymmetric proposal (identified using scattering lengths from Ref. Lysebo:2010fesh), while dashed black lines show two points where the symmetric conditions hold Fialko:2014xbaFialko:2016gggJenkins:2023eez. (These lines are $\sim1000\times$ thicker than the actual symmetric regions.) As well as greatly expanding the parameter space for ${}^{41}\mathrm{K}$, our results enable analogs in isotopes with no symmetric options.
• Figure 2: Lattice simulation of a ${}^{39}\mathrm{K}$ analog, with time increasing from left to right and top to bottom. The metastable 'false vacuum' (blue) spontaneously decays via expanding bubbles of 'true vacuum' (red). We show a 2D analog here for illustration, while our main numerical results are in 1D.
• Figure 3: Dispersion relationship for $\varphi$ in the false vacuum. The blue heatmap shows the average of 32 simulations with parameters from Table \ref{['tab:parameters']} (with $\bar{n}_\varphi=100$, so no bubbles nucleate). This dispersion relation matches that of a relativistic scalar of mass $m_\mathrm{fv}$ (purple) on large scales but becomes nonrelativistic on small scales, agreeing with our theoretical prediction (red).
• Figure 4: Phase portraits of the asymmetric analog system with and without modulation, with parameters given in Table \ref{['tab:parameters']}. We obtain each curve by numerically integrating the mean-field equations of motion \ref{['eq:mean-field-equations-of-motion']} from different initial conditions. In the left panel, we see a family of trajectories corresponding to small oscillations around the false vacuum (red). In the right panel, we see that no such trajectories exist in the absence of modulation.