Many-body interferometry of magnetic polaron dynamics

The physics of quantum impurities coupled to a many-body environment is among the most important paradigms of condensed-matter physics. In particular, the formation of polarons, quasiparticles dressed by the polarization cloud, is key to the understanding of transport, optical response, and induced interactions in a variety of materials. Despite recent remarkable developments in ultracold atoms and solid-state materials, the direct measurement of their ultimate building block, the polaron cloud, has remained a fundamental challenge. We propose and analyze a platform to probe time-resolved dynamics of polaron-cloud formation with an interferometric protocol. We consider an impurity atom immersed in a two-component Bose-Einstein condensate where the impurity generates spin-wave excitations that can be directly measured by the Ramsey interference of surrounding atoms. The dressing by spin waves leads to the formation of magnetic polarons and reveals a unique interplay between few- and many-body physics that is signified by single- and multi-frequency oscillatory dynamics corresponding to the formation of many-body bound states. Finally, we discuss concrete experimental implementations in ultracold atoms.

Figure 1

(a) Illustration of an impurity atom immersed in a two-component BEC. The arrows indicate the internal pseudospin states of BEC atoms. By applying a $\pi /2$ pulse, the host bosons are initially prepared in an equal superposition of spin-$\uparrow$ and spin-$\downarrow$ states. The interaction between the impurity and the host atoms induces spin dephasing, which is measurable by Ramsey interferometry. (b) Depending on the impurity-boson scattering lengths $a_{\mathrm{IB},\uparrow \downarrow }$, the system is characterized by the existence of zero, one, and two many-body bound states (regions I–III). The diagram is plotted for a boson-boson scattering length $a_{\mathrm{BB}}{n}_{\mathrm{B}}^{1/3}=0.05$, and $m_{\mathrm{I}}/m_{\mathrm{B}}=0.95$ as appropriate for a mixture of ${}^{41}\mathrm{K}-{}^{39}\mathrm{K}$ atoms. (c) The BEC spin dephasing dynamics exhibits (I) monotone relaxation, (II) single-, and (III) multi-frequency oscillations reflecting the existence of bound states. The dephasing signal is proportional to the number of impurities, which fixes the scale of the vertical axis.

Figure 2

Quantum dynamics of bath spin (red solid line) and charge (blue dashed line) excitations for a single impurity immersed in a two-component BEC. The impurity-boson scattering lengths are $n_{\mathrm{B}}^{1/3}(a_{\mathrm{IB},\uparrow },a_{\mathrm{IB},\downarrow })=(-1,-10)\mathrm{in}\mathrm{I},(3.5,-5)\mathrm{in}\mathrm{II},\mathrm{and}(3.5,5)\mathrm{in}\mathrm{III}$. The inset in I shows the long-time behavior of spin excitations approaching an asymptotic $\sqrt{t}$ scaling. The insets in II and III show the Fourier spectra of $N^s\left(t\right)$. The energies of the underlying bound states and their difference, calculated from Eq. (8), are shown as black dotted lines and green dashed lines, respectively.

Figure 3

The magnetic bound-state energy ${\omega }_{\mathrm{bound}}$ (the solid line) calculated from Eq. (8) and the bare dimer energy ${\epsilon }_{\dim }={\hslash }^2/\left(2m_{\mathrm{red}}{a}_{\mathrm{IB},\uparrow }^2\right)$ (the dashed line) are plotted against the inverse impurity-bath scattering length $1/a_{\mathrm{IB},\uparrow }$. The inset shows the dynamics of spin excitations at $1/\left(a_{\mathrm{IB},\uparrow }{n}_{\mathrm{B}}^{1/3}\right)=2$ where we assume a homogeneous density $n_{\mathrm{B}}={10}^{14}{\mathrm{cm}}^{-3}$ and a finite impurity density $n_{\mathrm{I}}/n_{\mathrm{B}}=0.1$. We choose $a_{\mathrm{BB}}{n}_{\mathrm{B}}^{1/3}=0.05$ and set $1/\left(a_{\mathrm{IB},\downarrow }{n}_{\mathrm{B}}^{1/3}\right)=15$ and $m_{\mathrm{I}}/m_{\mathrm{B}}=0.95$ as appropriate for a ${}^{41}\mathrm{K}-{}^{39}\mathrm{K}$ mixture.