Quantum Dynamics of Ultracold Bose Polarons

We analyze the dynamics of Bose polarons in the vicinity of a Feshbach resonance between the impurity and host atoms. We compute the radio-frequency absorption spectra for the case when the initial state of the impurity is noninteracting and the final state is strongly interacting with the host atoms. We compare results of different theoretical approaches including a single excitation expansion, a self-consistent $T$-matrix method, and a time-dependent coherent state approach. Our analysis reveals sharp spectral features arising from metastable states with several Bogoliubov excitations bound to the impurity atom. This surprising result of the interplay of many-body and few-body Efimov type bound state physics can only be obtained by going beyond the commonly used Fröhlich model and including quasiparticle scattering processes. Close to the resonance we find that strong fluctuations lead to a broad, incoherent absorption spectrum where no quasiparticle peak can be assigned.

Figure 1

Absorption spectra $A(\omega )$ of a single impurity immersed in a BEC as a function of the inverse interaction strength $1/(n^{1/3}{a}_{\mathrm{IB}})$. The polaron (4) and bound state (7) energies are shown as solid and dashed lines. For $1/(n^{1/3}{a}_{\mathrm{IB}})\gg 1$ the energy of the first bound state approaches the dimer binding energy (dash-dotted line). The spectrum is shown for a momentum cutoff $\mathrm{\Lambda }{n}^{-1/3}=20$, Bose scattering length $a_{BB}{n}^{1/3}=0.05$, and mass-balanced system $m_I=m_B$.

Figure 2

Ramsey contrast $|S(t)|$ and impurity absorption spectra $A(\omega )$ for fixed scattering lengths $1/(n^{1/3}{a}_{\mathrm{IB}})$. For negative scattering length, panels (a),(b), the spectrum reveals the attractive polaron. At unitarity, panels (c),(d), the spectrum shows a broad spectral feature and no quasiparticle peak can be assigned. For positive scattering lengths, panels (e),(f), a series of bound states emerges. Away from the resonance, panels (g),(h), their binding energy increases while at positive frequencies a long-lived repulsive polaron becomes the dominant excitation. As for Fig. 1 we broadened the spectrum to make sharp features visible.

Figure 3

Time evolution of the phonons number $N_{\mathrm{ph}}$ for (a) attractive $1/(n^{1/3}{a}_{\mathrm{IB}})=-2$ and (b) repulsive $1/(n^{1/3}{a}_{\mathrm{IB}})=4$ interactions, obtained by the coherent state approach (3) and the single-excitation expansion (8) (yellow solid and red dashed lines, respectively).