Controlling the Hyperfine State of Rovibronic Ground-State Polar Molecules

We report the preparation of a rovibronic ground-state molecular quantum gas in a single hyperfine state and, in particular, the absolute lowest quantum state. This addresses the last internal degree of freedom remaining after the recent production of a near quantum degenerate gas of molecules in their rovibronic ground state, and provides a crucial step towards full control over molecular quantum gases. We demonstrate a scheme that is general for bialkali polar molecules and allows the preparation of molecules in a single hyperfine state or in an arbitrary coherent superposition of hyperfine states. The scheme relies on electric-dipole, two-photon microwave transitions through rotationally excited states and makes use of electric nuclear quadrupole interactions to transfer molecular population between different hyperfine states.

Figure 1

(a) Hyperfine structure of ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$ molecules in their rotational ($N=0$) and vibrational ($v=0$) ground state of the electronic ground molecular potential ($X{}^1\Sigma ^{+}$) at $B=545.9\mathrm{G}$ (see text). The circled quantum states can be directly populated via STIRAP in our experiment. (b) Optical two-photon spectroscopy of the rovibrational ground-state manifold of ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$ molecules (see text). We observe three hyperfine states, which are characterized by $m_F=-7/2$ (black points) and $m_F=-11/2$ (blue open points). Here, $\Delta E_B$ is the binding energy of the hyperfine states at $B=546.9\mathrm{G}$ relative to the binding energy of the rovibrational ground state at zero magnetic field. Negative $\Delta E_B$ indicates a more deeply bound state and positive $\Delta E_B$ a less deeply bound state.

Figure 2

(a) Electric-dipole transitions between the rotational ground state $N=0$ and the first rotationally excited state $N=1$. To first order, electric-dipole transitions will keep the hyperfine state unchanged $\Delta m_I=0$. (b) Controlling the hyperfine state within the rotational and vibrational ground state. The interaction between the nuclear electric-quadrupole moment of ${}^{40}\mathrm{K}/{}^{87}\mathrm{Rb}$ and the electric-field gradient of the electronic cloud mixes quantum states with different nuclear spin quantum number $m_I^{\mathrm{K}/\mathrm{Rb}}$ in $N=1$. This allows the implementation of a two-photon scheme to transfer molecules between different hyperfine states within the rovibrational ground state ($\Delta m_I^{\mathrm{K}/\mathrm{Rb}}=\pm 1$). To simplify the notation, we abbreviate $|N,m_N,m_I^{\mathrm{K}},m_I^{\mathrm{Rb}}⟩$ by $N$ $|m_N,m_I⟩$. Here $m_I$ refers to the changing hyperfine quantum number $m_I$ of K or Rb.

Figure 3

Rabi oscillations on a (a) hyperfine preserving microwave transition $|0,0,-4,1/2⟩\to |1,1,-4,1/2⟩$; (b) Rb hyperfine changing transition $|0,0,-4,1/2⟩\to |1,0,-4,3/2⟩+\delta |1,1,-4,1/2⟩$; (c) K hyperfine changing transition $|0,0,-4,1/2⟩\to |1,0,-3,1/2⟩+\delta |1,1,-4,1/2⟩$. Note the different time axis in panel (a). The microwave power was reduced by a factor of 4 for the data in (a) resulting in an effective decrease of the Rabi frequency by a factor of 2.