Sympathetic rotational cooling of large trapped molecular ions

Abstract

We suggest a protocol for the sympathetic cooling of a molecular asymmetric top rotor co-trapped with laser-cooled atomic ions, based on resonant coupling between the molecular ion's electric dipole moment and a common normal mode of the trapped particles. By combining sympathetic sideband laser cooling with coherent microwave excitation, we demonstrate the efficient depopulation of arbitrary rotational subspaces and the ability to cool an incoherent distribution of rotational states into a single, well-defined quantum state. This capability opens the door to exploiting the rotational Hilbert space for applications in quantum information processing and high-precision spectroscopy.

Figures (3)

• Figure 1: (a) Trapping a polyatomic ion with intrinsic dipole moment $\bm \mu$ (here protonated 1,2-propanediol) together with two Yb$^+$ ions. The black arrows indicate the radial zig-zag normal mode. (b) Sympathetic rotational cooling of the molecule, modeled as an asymmetric top rotor, combines an effective decay of the $j_2$-level (wiggled gray arrows) with resonant microwave excitation depleting all other rotational states. Solid (dashed) blue arrows indicate transitions induced by $x$- and $z$-polarized pulses with selection rules $\Delta M= \pm 1$ and $\Delta M = 0$, respectively. The effective decay is due to sideband-cooling of the atoms and requires resonant dipole-phonon coupling. (c) Dipole-phonon coupling strength (see also SM) in kHz/D (contour lines) vs radial trap frequency $\omega_z$ and molecular mass (with axial trap frequency $\omega_x=1$ MHz). The horizontal lines indicate the masses of (i) protonated 1,2-propanediol, (ii) protonated glutamine (ii), and (iii) CHCaBrI$^+$; red stars point to dipole-allowed transitions between asymmetric top eigenstates $J_{K_a,K_c}$ and $J_{K_a,K_{c+1}}$ which are resonant to the frequency $\omega_p$ of the radial zig-zag mode. (d) Combined level scheme with $\ket{a,n_p,j} = \ket{a} \otimes \ket{n_p,j}$, where $a=g,e$ denotes the internal state of the atom (for simplicity, only the levels of one atom are depicted), $n_p$ the phonon excitation, and $j_{1/2}$ the rotational state. Dipole-phonon coupling induces a splitting $2 \Delta E_{n_p}$ of the states $\ket{a,n_p,j_1}$ and $\ket{a,n_p-1,j_2}$, cf. Eq. (\ref{['eq:dipole_splitting']}). The wiggled gray arrows indicate spontaneous emission on the atom, the red arrows show the transitions induced by the cooling laser.
• Figure 2: Sympathetic cooling of protonated 1,2-propanediol into the rotational level $3_{31}$, cf. Fig. \ref{['fig:trap']}(b), with repeated cycles of laser cooling and microwave population shuffling. (a) Total population of the states $\ket{2_{21},M}$, $\ket{3_{31},M}$ and $\ket{3_{30},M}$ with the atom in its ground state. (b,c) $M$-resolved populations for one step of laser cooling. The parameters for laser cooling are: Rabi frequency $\Omega = 2 \pi \times 200\,$kHz, effective decay rate $\gamma = 0.1\,$MHz, Lamb-Dicke parameter $\eta = 0.012$Kulosa_2023, see also SM SM. The blue, red and green curves correspond to $n_p=0,1,2$. (d) Cooling error, $1-\sum_M P_{3_{31},M}$, vs number of iterations for microwave pulses with perfect $x$-polarization (solid line), and with 25% (dashed line), 50% (dotted line), and 100% (dash-dotted line) $z$-polarization.
• Figure 3: Sympathetic rotational cooling to prepare a single quantum state of protonated 1,2-propanediol within a degenerate manifold: (a) Microwave excitation (blue and orange arrows) to prepare the state $\ket{3_{31},3}$, marked by the yellow box, with the same engineered decay from the states $\ket{3_{30},M}$ as in Fig. \ref{['fig:trap']}(b). (b) Cooling error vs number of iterations for microwave pulses with perfect $\sigma_+$-polarization (solid line) and pulses with 1% (dashed line), 5% (dash-dotted line), and 10% (dotted line) $\sigma_-$polarization. The inset shows the initial and target population distributions.