Competition of light- and phonon-dressing in microwave-dressed Bose polarons

TL;DR

This work develops and validates an extended effective Hamiltonian to describe a microwave-dressed, spin-1/2 impurity immersed in a one-dimensional Bose gas. By combining ab initio ML-MCTDHX simulations with a progressively richer effective description, the authors show that light dressing can enhance the polaron residue and suppress phonon dressing, while strong dressing stabilizes repulsive polarons even in regimes susceptible to temporal orthogonality catastrophe. The framework yields impurity energy, residue, and an effective mass, and captures the interplay between light and phonon dressing across attractive and repulsive polaron regimes. These results provide a practical, tunable route to exploring strongly interacting polaronic systems and guide forthcoming experiments.

Abstract

We theoretically investigate the stationary properties of a spin-1/2 impurity immersed in a one-dimensional confined Bose gas. In particular, we consider coherently coupled spin states with an external field, where only one spin component interacts with the bath, enabling light dressing of the impurity and spin-dependent bath-impurity interactions. Through detailed comparisons with ab-initio many-body simulations, we demonstrate that the composite system is accurately described by a simplified effective Hamiltonian. The latter builds upon previously developed effective potential approaches in the absence of light dressing. It can be used to extract the impurity energy, residue, effective mass, and anharmonicity induced by the phononic dressing. Light-dressing is shown to increase the polaron residue, undressing the impurity from phononic excitations because of strong spin coupling. For strong repulsions-previously shown to trigger dynamical Bose polaron decay (a phenomenon called temporal orthogonality catastrophe), it is explained that strong light-dressing stabilizes a repulsive polaron-dressed state. Our results establish the effective Hamiltonian framework as a powerful tool for exploring strongly interacting polaronic systems and corroborating forthcoming experimental realizations.

Figures (6)

• Figure 1: Description of Rabi-coupled polarons in terms of a two level model and its limitations. Ground state energies of Eq. (\ref{['eq:hamilt']}) for (a) $N_I=1$ and (b) $N_I=2$ impurities with $g_{BI}=-g_{BB}=-0.5~\sqrt{\hbar^3 \omega_B /m_B}$ and varying $\Omega_{{\rm R}0}$ (see legend). The dashed lines indicate the lowest in energy eigenstates for different $S_z$ and $\Omega_R=0$. The important energy scales, $E_{1 \uparrow}$, $E_{2 \uparrow}$ and $\Delta_0$ are also schematically illustrated. (c) Population of the spin-$\uparrow$ and spin-$\downarrow$ states and (d) expectation values of the spin-magnitude $|\langle \hat{S}_{\mu}\rangle|$ for varying detuning $\Delta$ and for $N_I = 1$ at different Rabi-couplings $\Omega_{{\rm R}0}$ (see legend). The polaronic (non-interacting) impurity states are reproduced for $\Delta \to -\infty$ ($\Delta \to \infty$). For $\Delta \approx - E_{1 \uparrow}/\hbar$, a correlated superposition state is created.
• Figure 2: Deviations from the two-level system description of microwave polaron-dressing captured by the effective-potential model. (a) The energy shift owing to the spin-orbit coupling term $\propto \Lambda$ within second order perturbation theory to the effective potential of Eq. \ref{['Heff_2']}. (b) The minimum value of $|\langle \hat{\bm S}\rangle|$ within the same approximation. In both cases we consider $\Omega_{{\rm R}0} = 1~\omega_I$ and $Z_{\rm eff} = 1$. (c) The $\Omega_{{\rm R} 0}$ dependence of the minimum of $|\langle \hat{\bm S}\rangle|$ for different values of $Z_{\rm eff}$, $m_I^*$ and $\frac{g_{BI} m_I \omega_I^2}{g_{BB} m_B \omega_B^2}$ (see legend). Notice that only the region $\Omega_{{\rm R} 0} > 0.5 \omega_{I}$ is presented to avoid issues associated with the breakdown of perturbation theory.
• Figure 3: (a$_i$) The momentum, $\Delta p_{I}$ and position, $\Delta x_{I}$ uncertainties for the impurity species with varying detuning, $\Delta$. The results are provided for different $\Omega_{R 0}$ (see inset labels for $i = 1,2,3$) and within the effective potential and ML-MCTDHX approach (see legend). Excellent agreement between the two methods is observed. (b$_{i}$) The deviation of the product $\Delta x_{I} \Delta p_{I}$ from the bound set by the Heisenberg uncertainty principle. In all cases, $g_{BI} = - g_{BB} = -0.5 \sqrt{\hbar^{3} \omega_B /m_B}$, $N_{B} = 100$ and $m_{I} = m_{B}$. Small deviations between the ML-MCTDHX and effective potential models occur for $\Delta < - E_{1 \uparrow}/\hbar$ due to the correlated character of the polaronic state.
• Figure 4: The effective potential, $V_{\rm eff}(x) = \frac{1}{2} m_I \omega_I^2 x^2 +g_{BI} \rho_B^{(1)}(x)$, for $\Omega_{{\rm R} 0} = 0$, alongside its single-particle eigenstates. Here, we assume a Thomas-Fermi profile, Eq. \ref{['thomas_fermi_profile']}. $V_{\rm eff}(x)$ at (a) the critical interaction strength for phase-separation $g_{BI} = g_{BB} = 0.5~\sqrt{\frac{\hbar^3 \omega_B}{m_B}}$ and (b) within the temporal orthogonality catastrophe regime $g_{BI} = 3 g_{BB} = 1.5~\sqrt{\frac{\hbar^3 \omega_B}{m_B}}$. In panel (b) we schematically assign the stable phase-separated eigenstates and the metastable polaronic ones mistakidis20_pump_probe_spect_bose_polar. For more details on the $\Omega_{{\rm R}0} = 0$ effective potential, see Ref. mistakidis2019b.
• Figure 5: Behavior of the bath and impurity densities in the repulsive polaron case. (a$_i$) Density fluctuations of the BEC background, $\delta\rho^{(1)}_B(x)$ with respect to $\Delta/\omega_B$. Spatially resolved expectation values of the spin operators (b$_i$) $\hat{S}_x(x)$ and (c$_i$) $\hat{S}_z(x)$ for varying $\Delta$. (d$_i$) The total (spin-unresolved) impurity density $\rho^{(1)}_I(x)$ in terms of $\Delta$. In all cases, the index $i = 1$ refers to $g_{BI}= g_{BB} = 0.5~\sqrt{\hbar^3 \omega_B/m_B}$ and $\Omega_{{\rm R}0}= \omega_B$, whilst $i = 2$ corresponds to $g_{BI} = 3 g_{BB} = 1.5~\sqrt{\hbar^3 \omega_B/m_B}$ and $\Omega_{{\rm R}0} = 40~\omega_B$. Superposition states of the impurity manifest by the $\langle \hat{S}_x(x) \rangle < 0$ regions in (b$_i$). The dashed lines mark the Thomas-Fermi radius of the BEC.