Probing BCS pairing and quasiparticle formation in ultracold gases by Rydberg atom spectroscopy

TL;DR

This work proposes using a heavy Rydberg impurity as a local spectroscopic sensor to probe BCS pairing in ultracold two-component Fermi gases. By extending the functional determinant approach to anomalous (BCS) baths and computing the absorption spectrum from the Ramsey signal, the authors show that dimer and trimer bound-state peaks encode the superconducting gap $\Delta$, revealing whether Cooper pairs are broken or trapped intact. The analysis also demonstrates suppression of the orthogonality catastrophe by the gap, leading to a well-defined quasiparticle peak and a Bogoliubov two-branch spectrum, with peak shifts directly measuring $\Delta$ locally. This method provides high spatial and temporal resolution for mapping pairing properties in strongly correlated matter and can be extended to finite temperature, imbalanced mixtures, or mobile impurities.

Abstract

Locally probing pairing in fermionic superfluids, ranging from micro- to macroscopic scales, has been a long-standing challenge. Here, we investigate a new approach that uses Rydberg impurities as a spectroscopic sensor of the surrounding strongly correlated state of ultracold paired fermions. The extended wavefunction of the Rydberg electron induces a finite-range potential that can bind atoms from the BCS medium, forming molecular states. As a consequence, the optical absorption spectrum of the impurity encodes key many-body properties. Using the functional determinant approach, we provide a direct measure of the superfluid gap through frequency shifts of dimer and trimer peaks. The spectra also reveal whether the Cooper pairs are broken or trapped intact. For static Rydberg atoms, we relate this signature of pairing to the suppression of the orthogonality catastrophe due to the superconducting gap resulting in the formation of well-defined polaron quasiparticles. Our work establishes Rydberg atom spectroscopy as a powerful local probe of strongly correlated matter.

Figures (9)

• Figure 1: Illustration of a Rydberg atom immersed in a BCS superfluid. The Rydberg potential $V_\mathrm{R}(\bm{r})$, Eq. \ref{['eq:potential']}, is depicted by the green curve and Cooper pairs by red and blue circles connected by a wiggly purple line. A dimer (a) is formed after breaking a Cooper pair with the energy cost of the gap $\Delta$. A trimer is formed by either (b) binding a whole Cooper pair or (c) breaking two Cooper pairs with an energy cost of $2\Delta$.
• Figure 2: Rydberg atom spectroscopy. (a) Absorption spectrum for $\Delta=0$, where each peak corresponds to the occupation of a bound state in the Rydberg potential. The energy scale is shifted such that the bare atomic Rydberg peak is at the origin. Figures (b-d) study the dependence of the spectrum on the gap parameter $\Delta$ (light blue to red curves): (b) Magnification of the trimer state, i.e., the double occupation of the bound state. Dashed lines mark the energies of different angular-momentum states of the bound state, denoted by $\ell=(\ell_1,\ell_2)$. Peaks with mixed angular momentum feature a shift of $2\Delta$, indicating the rupture of two Cooper pairs. Peaks with the same angular momentum do not show such a shift indicating intact trapping of the Cooper pair. (c) Dimer State: Single occupation of the bound state for different angular momenta (dashed lines). All peaks shift proportional to the gap strength $\Delta$, resulting in a direct measure of the superfluid gap, $\Delta=|E^{(\Delta)}_D-E_D|$. (d) Atomic Rydberg peak (repulsive branch): For $\Delta=0$ the orthogonality catastrophe is present as seen from the power-law decay of the spectrum. This feature deforms into a $\delta$-like peak structure for increasing gap strength accompanied by the appearance of a secondary branch corresponding to a Bogoliubov excitation. Inset: Ramsey signal for each gap strength showing the emergence of quasiparticle behavior.
• Figure 3: Orthogonality catastrophe. Ramsey signal for different gap strengths showing the OC for $\Delta=0$ and the emergence of a quasiparticle weight for $\Delta>0$ where the signal is fitted (thick lines) to Eq. \ref{['eq:fit']} at times $t\gtrsim1/\Delta$ (dashed lines). Inset: Quasiparticle weights of the bath and Bogoliubov excitation, where $Z_B$ follows a power-law relation with scaling given by the scattering shift exponent [Eq. \ref{['eq:exp']}].
• Figure S1: Bogoliubov dispersion for a balanced system, i.e., $m_{\uparrow}=m_{\downarrow}=m$, $\mu_{\uparrow}=\mu_{\downarrow}=\mu$ and $\omega_{\uparrow\bm{n}}=-\omega_{\downarrow\bm{n}}$, for ${\Delta/\epsilon_{\mathrm{F}}=0.5}$. At $T=0$ only the lower branch ($\downarrow$) is occupied, there can be a Bogoliubov excitation of $2\Delta/\epsilon_\mathrm{F}$ from the lower to the upper branch.
• Figure S2: Ramsey signal decomposed by contributions for different angular-momentum channels; $\ell_{\max}\approx5$. As the gap increases, higher angular-momentum channels will contribute to the oscillations in the total signal. The dashed line represents the onset of system size effects at time $t_{\max}\approx R/2$.