Phenomenological model of decaying Bose polarons

Abstract

Cold atom experiments show that a mobile impurity particle immersed in a Bose-Einstein condensate forms a well-defined quasiparticle (Bose polaron) for weak to moderate impurity-boson interaction strengths, whereas a significant line broadening is consistently observed for strong interactions. Motivated by this, we introduce a phenomenological theory based on the assumption that the most relevant states are characterized by the impurity correlated with at most one boson, since they have the largest overlap with the uncorrelated states to which the most common experimental probes couple. These experimentally relevant states can however decay to lower energy states characterised by correlations involving multiple bosons, and we model this using a minimal variational wave function combined with a complex impurity-boson interaction strength. We first motivate this approach by comparing to a more elaborate theory that includes correlations with up to two bosons. Our phenomenological model is shown to recover the main results of two recent experiments probing both the spectral and the non-equilibrium properties of the Bose polaron. Our work offers an intuitive framework for analyzing experimental data and highlights the importance of understanding the complicated problem of the Bose polaron decay in a many-body setting.

Figures (6)

• Figure 1: The zero momentum impurity spectral function calculated using the ansatz in Eq. (\ref{['eq:ansatz']}) for $n_0^{1/3}a_- = -1$ and $n_0^{1/3}a_{\mathrm{B}} = 0.02$. The ground state energy is shown as a faint dotted curve, the dashed yellow curve shows the ground state energy within the ladder approximation, and the dotted curve shows the energy of the dimer, $-1/a^2$. We have defined $E_n = (6\pi^2n_0)^{2/3}/2$ and $1/k_n=1/\sqrt{2 E_n}$. Note that the spectral function is computed numerically for a discrete set of interaction strengths, which accounts for the apparently discontinuous behavior of the high‑energy branch in the repulsive regime.
• Figure 2: a) The zero momentum impurity spectral function from our phenomenological model. The black dotted curve shows the ladder approximation with real $g_I$, the green dashed curve is the molecular state, and the orange dots are the experimental data of Ref. etrych2024universal. b) Extracted widths $\Gamma_{pol}$ of the attractive polaron for $a<0$ and repulsive polaron for $a>0$. To match the experiment etrych2024universal, we use $n^{1/3} a_B = 0.005$, and for fitting the signal we use $\Gamma=0.12$ and $\gamma=2.2$. Inset: Extracted width $\Gamma_{Mol}$ of the attractive polaron for $a>0$.
• Figure 3: Time dynamics of the contrast $|A(t)|$ on the repulsive side of the Feshbach resonance for $(k_na)^{-1} = 0.6$ in panel $(a)$ and $(k_na)^{-1} = 1.0$ in $(b)$. Dotted purple curves correspond to the standard ladder approximation ($\gamma=\Gamma=0$); solid blue curves are calculated using our phenomenological model with $\Gamma=0.05, \gamma = 0.5$; red solid curves are from the ansatz Eq. \ref{['eq:ansatz']} in the two-channel Hamiltonian (\ref{['eq:two-channel-Hamiltonian']}) with $n^{1/3}a_- = -100, n^{1/3}a_B = 0.005$ similar to the experiment morgenQuantumBeatSpectroscopy2023. The orange dots represent experimental data morgenQuantumBeatSpectroscopy2023. We account for magnetic dephasing and three-body loss when computing the blue and red solid curves.
• Figure S1: Time dynamics of the contrast $|A(t)|$ on the repulsive side of the Feshbach resonance for $(k_na)^{-1} = 1.25$ in panel $(a)$ and $(k_na)^{-1} = 2.0$ in $(b)$. Same format and parameters used in Fig. 3 of the main text.
• Figure S2: Time dynamics of the contrast $|A(t)|$ on the repulsive side of the Feshbach resonance for $(k_na)^{-1} = -2.0.$