Dipole-Phonon Quantum Logic with Trapped Polar Molecular Ions

The interaction between the electric dipole moment of a trapped molecular ion and the phonon modes of the confined Coulomb crystal couples the orientation of the molecule to its motion. We consider the practical feasibility of harnessing this interaction to initialize, process, and read out quantum information encoded in molecular ion qubits without ever optically illuminating the molecules. We present two schemes wherein a molecular ion can be entangled with a cotrapped atomic ion qubit, providing, among other things, a means for molecular state preparation and measurement. We also show that virtual phonon exchange can significantly boost the range of the intermolecular dipole-dipole interaction, allowing strong coupling between widely separated molecular ion qubits.

Figure 1

Basic dipole-phonon coupling scheme. (a) Simplest realization of dipole-phonon quantum logic with trapped molecular and atomic ions. (b) Bare energy levels of one motional mode at a lower (solid) and higher (dashed) secular frequency and the molecule dipole state energy levels. (c) Energy levels of trapped molecular ion as a function of normal mode frequency ${\omega }_q$. State preparation can be accomplished by adiabatically increasing the trap frequency, which results in the conversion of $|e,0⟩$ to $|g,1⟩$. The $|g,1⟩$ state is detected by motional ground-state cooling via a cotrapped atomic ion. (d) Schematic of a chip-based, hybrid atomic and molecular ion quantum processor. Separate regions can be optimized for qubit SPAM, microwave-to-atom transduction, atomic ion quantum processing, and atom-molecule and molecule-molecule quantum operations. Ions can be shuttled between zones to allow individual molecule addressing.

Figure 2

Calculated strength of the phonon-mediated dipole-dipole interaction [absolute value of Eq. (8)] as a function of the distance between 10 ${\mathrm{CaO}}^{+}$ molecular ions in a chain. Circles show the calculation for ${\omega }_1/2\pi =(3.96,3.88,3.11,5.33,8.00)\mathrm{MHz}$ for the (red, orange, green, blue, purple) circles. The magenta curve is the direct, electromagnetic dipole-dipole interaction, illustrating that the phonon-mediated dipole-dipole interaction can be made longer range and orders of magnitude stronger.

Figure 3

Energy levels and couplings of a cotrapped atomic and molecular ion while driving the atomic ion with a laser at ${\omega }_L={\omega }_a^{\prime }+\mathrm{\Delta }$. Multiple pathways interfere to remove the $n$ dependence of the coupling between $|g_m,g_a,n⟩$ and $|e_m,e_a,n⟩$, allowing quantum control without the need for ground-state cooling.