Quantum Rydberg Central Spin Model

We consider dynamics of a Rydberg impurity in a cloud of ultracold bosonic atoms in which the Rydberg electron undergoes spin-changing collisions with surrounding atoms. This system realizes a new type of quantum impurity problems that compounds essential features of the Kondo model, the Bose polaron, and the central spin model. To capture the interplay of the Rydberg-electron spin dynamics and the orbital motion of atoms, we employ a new variational method that combines an impurity-decoupling transformation with a Gaussian ansatz for the bath particles. We find several unexpected features of this model that are not present in traditional impurity problems, including interaction-induced renormalization of the absorption spectrum that eludes simple explanations from molecular bound states, and long-lasting oscillations of the Rydberg-electron spin. We discuss generalizations of our analysis to other systems in atomic physics and quantum chemistry, where an electron excitation of high orbital quantum number interacts with a spinful quantum bath.

Figure 1

A photoexcited Rydberg electron undergoes spin-changing collisions in ultracold atoms. The interaction between the Rydberg electron and bosonic atoms includes both motional and Kondo-type components. Many-body effect manifests itself as interaction-induced renormalization of the absorption spectrum (top left). The central spin exhibits long-lasting oscillations that depend on the external magnetic field (top right).

Figure 2

(a), (c) Absorption spectra $A(\omega )$ at different densities $\rho$ of (a) mobile and (c) immobile environmental atoms. Dashed lines indicate the mean-field shifts ${\mathrm{\Delta }}_{\mathrm{MF}}$ of the spectra. (b), (d) Central spin dynamics $m_z(t)=⟨{\widehat{\sigma }}_e(t)⟩$ after a quench with (b) mobile and (d) immobile environmental spins. We set the magnetic field to be zero $h_z=0$.

Figure 3

Correlation $C(\nu )$ of the absorption spectrum with detuning $\nu$ (main panel). The blue solid and dashed curves (red dotted curve) show the results obtained by quenching the full interacting Hamiltonian $\widehat{H}$ (the quadratic Hamiltonian ${\widehat{H}}_{\parallel }$). The red dashed vertical lines indicate multiple values of the dominant bound-state energy ${\omega }_b$ of $V_{\text{mean}}$ (left inset), which match with the peak positions of the quadratic result. The many-body features appear as deviations of the interacting results from the single-particle energies and their sensitivity to environmental density (right inset). We set $h_z=0$.

Figure 4

The Fourier spectra ${\tilde{m}}_z(\omega )$ of the central spin dynamics $m_z(t)$ (a) at different particle densities $\rho$ with a zero magnetic field and (b) at different magnetic fields $h_z$ with $\rho =1.8\times {10}^{12}{\mathrm{cm}}^{-3}$. The black dashed curve and line at the bottom planes indicate the square root scaling $\omega \propto \sqrt{\rho }$ in (a) and the linear relation $\delta \omega =-h_z$ in (b), respectively. The circles in the bottom planes indicate the mean frequencies of the spectra around the peak values.

Figure 5

The mean frequencies of the central spin dynamics with the anisotropic spin interaction at (a) different densities $\rho$ with zero magnetic field and at (b) different magnetic fields $h_z$ with $\rho =6\times {10}^{11}{\mathrm{cm}}^{-3}$. The black dashed curve and line indicate the scalings $\omega \propto \sqrt{\rho }$ in (a) and $\delta \omega =-h_z$ in (b), respectively.