Anomalous Behavior of Dark States in Quantum Gases of ${}^6\mathrm{Li}$

We create atom-molecule dark states in a degenerate Fermi gas of ${}^6\mathrm{Li}$ in both weakly and strongly interacting regimes using two-photon Raman scattering to couple fermion pairs to bound molecular states in the ground singlet and triplet potential. Near the unitarity point in the BEC-BCS crossover regime, the atom number revival height associated with the dark state abruptly and unexpectedly decreases and remains low for magnetic fields below the Feshbach resonance center at 832.2 G. With a weakly interacting Fermi gas at 0 G, we perform precision dark-state spectroscopy of the least-bound vibrational levels of the lowest singlet and triplet potentials. From these spectra, we obtain binding energies of the $v^{\prime \prime }=9$, $N^{\prime \prime }=0$ level of the $a(1^3{\mathrm{\Sigma }}_u^{+})$ potential and the $v^{\prime \prime }=38$, $N^{\prime \prime }=0$ level of the $X(1^1{\mathrm{\Sigma }}_g^{+})$ potential with absolute uncertainty as low as 20 kHz. For the triplet potential, we resolve the molecular hyperfine structure.

Figure 1

Energy levels relevant to the experiments presented here. At $B=0$, the initial unbound two-atom state is $|i_0⟩=\sqrt{1/3}|00000⟩+\sqrt{2/3}|01110⟩$, a linear combination of the singlet and triplet states shown lying $2a_{2S}$ below the $2S_{1/2}+2S_{1/2}$ asymptote. The levels are labeled with the quantum numbers $|NSIJF⟩$, where $\overrightarrow{N}$ is the molecular rotational angular momentum, $\overrightarrow{S}(\overrightarrow{I})$ is total electronic (nuclear) spin, $\overrightarrow{J}$ is total angular momentum apart from nuclear spin, and $\overrightarrow{F}=\overrightarrow{J}+\overrightarrow{I}$. Here, ${\mathrm{\Omega }}_1$ and ${\mathrm{\Omega }}_2$ are Rabi frequencies of transitions driven by the lasers $L_1$ and $L_2$, respectively, and $a_{2S}=152.137\mathrm{MHz}$ is the atomic magnetic dipole hyperfine constant of $2^2{S}_{1/2}$.

Figure 2

Dark states in a Fermi gas at 0 G. The atom number is plotted versus the detuning of the probe frequency from the two-photon resonance, where the photon energy difference $h({\nu }_2-{\nu }_1)$ equals the difference between the energy of the initial free atom state and a bound molecular level and the atom number exhibits a maximum revival. (a)–(c) Corresponding different molecular hyperfine levels ($F^{\prime \prime }=2,1,0$) of the $v^{\prime \prime }=9$, $N^{\prime \prime }=0$ level in the $a(1^3{\mathrm{\Sigma }}_u^{+})$ potential. We were not able to find parameters that would improve the revival of $F^{\prime \prime }=1$ to above 50%. Spectrum (d) corresponds to the $v^{\prime \prime }=38$, $N^{\prime \prime }=I^{\prime \prime }=F^{\prime \prime }=0$ level of the $X(1^1{\mathrm{\Sigma }}_g^{+})$ potential.

Figure 3

(top) The revival height of the dark state defined as a ratio of the suppression amplitude to the loss amplitude, measured on both sides of the Feshbach resonance (dashed vertical line). The states involved are Feshbach molecules or BCS-like pairs ($|i_{\mathrm{c}}⟩$), $v^{\prime }=31$ in the $A(1^1{\mathrm{\Sigma }}_u^{+})$ excited molecular potential ($|e⟩$) and $v^{\prime \prime }=37$ in the $X(1^1{\mathrm{\Sigma }}_g^{+})$ ground-state potential ($|g⟩$). For magnetic fields above 829 G, we observe near complete revival on the two-photon resonance. Insets: spectra at selected magnetic fields. (bottom) Full circles represent the probability $Z$ of the dressed molecule to be in the closed channel. Squares (red) show $Z$ measured in Ref. [33] where the excited state $|e⟩$ is $v^{\prime }=68$ [$A(1^1{\mathrm{\Sigma }}_u^{+})$ potential]. Dash-dotted line shows theoretical prediction for $Z$ taken from Ref. [34]. The gray region corresponds to $k_F|a|>1$. For these data, $T/T_F=0.4\pm 0.15$, $E_F/h=11\mathrm{kHz}$, ${\mathrm{\Omega }}_1=200\mathrm{kHz}$, and ${\mathrm{\Omega }}_2\simeq 2\mathrm{MHz}$.