Ion Trap Group

We reflect on the prospect of exploiting the recoil associated with absorption and emission of photons to perform spectroscopy of a single molecular ion. For this recoil to be detectable, the molecular ion is sympathetically cooled by a laser-cooled atomic ion to near their common quantum mechanical ground state within a trapping potential. More specifically, we present a general framework for simulating the expected photon recoil spectra in regimes where either the natural transition linewidth $Γ_t$ of the molecular ion or the spectral width $Γ_L$ of the exciting light source exceeds the motional frequencies of the two-ion system. To exemplify the framework, we present two complementary cases: spectroscopy of the broad 3s $^2$S$_{1/2}$ - 3p $^2$P$_{3/2}$ electronic transition ($Γ_t/2π= 41.8$ MHz) of a single $^{24}$Mg$^+$ ion at $λ=279.6$ nm by a narrow laser source ($Γ_L/2π\lesssim 1$ MHz) and mid-infrared vibrational spectroscopy of the very narrow $|v=0,J=1\rangle$ - $|v'=1,J'=0\rangle$ transition ($Γ_t/2π= 2.50 $ Hz) at $λ=6.17$ $μ$m in the $^1Σ^+$ electronic ground state of $^{24}$MgH$^+$ by a broadband laser source ($Γ_L/2π\gtrsim$ 50 MHz). The atomic ion $^{24}$Mg$^+$ has been picked to introduce a simple system to make comparisons with experimental results while still capturing most of the physics involved in electronic excitations of molecular ions.

The family of $n$-bit Toffoli gates, with the two-bit Toffoli gate as the figurehead, are of great interest in quantum information as they can be used as universal gates and in quantum error correction, among other things. We present a single-step implementation of arbitrary $n$-bit Toffoli gates (up to a local change of basis), based on resonantly driving a single qubit that has a strong Ising coupling to $n$ other qubits. The setup in the two-qubit case turns out to be identical to the universal Barenco gate. The gate time and error are, in theory, independent of the number of control qubits, scaling better than conventional circuit decompositions. We note that our assumptions, namely strongly coupling $n+1$ qubits and a driving frequency that scales with $n$, may break down for large systems. Still, our protocol could enhance the capabilities of intermediate scale quantum computers, and we discuss the prospects of implementing our protocol on trapped ions, Rydberg atoms, and on superconducting circuits. Simulations of the latter platform show that the Toffoli gate with two control bits attains fidelities of above 0.98 even in the presence of decoherence. We also show how similar ideas can be used to make a series of controlled-\textsc{not}-gates in a single step. We show how these can speed up the implementation of quantum error correcting codes and we simulate the encoding steps of the three-qubit bit-flip code and the seven-qubit Steane code.

We present a method to measure the decay rate of the first excited vibrational state of simple polar molecular ions being part of a Coulomb crystal in a cryogenic linear Paul trap. Specifically, we have monitored the decay of the $|ν$=$1,J$=$1 \rangle_X$ towards the $|ν$=$0,J$=$0 \rangle_X$ level in MgH$^+$ by saturated laser excitation of the $|ν$=$0,J$=$2 \rangle_X$-$|ν$=$1,J$=$1 \rangle_X$ transition followed by state selective resonance enhanced two-photon dissociation out of the $|ν$=$0,J$=$2 \rangle_X$ level. The technique enables the determination of decay rates, and thus absorption strengths, with an accuracy at the few percent level.

We demonstrate resolved sideband laser cooling of a single 40Ca+ ion in a macroscopic linear radio frequency trap with a radial diagonal electrode spacing of 7 mm and an rf drive frequency of just 3.7 MHz. For an oscillation frequency of 585 kHz along the rf-field-free axis, a ground state population of 99+-1% has been achieved, corresponding to a temperature of only 6 microkelvin. For several oscillation frequencies in the range 285 - 585 kHz, heating rates below one motional quantum per second have been measured at room temperature. The lowest measured heating power is about an order of magnitude lower than reported previously in room temperature, as well as cryogenically cooled traps.

We provide several schemes to construct the continuous-variable SWAP gate and present a Hermitian generalized many-body continuous controlled^n-NOT gate. We introduce and study the hybrid controlled-NOT gate and controlled-SWAP gate, and physical realizations of them are discussed in trapped-ion systems. These continuous-variable and hybrid quantum gates may be used in the corresponding continuous-variable and hybrid quantum computations.

We investigate single ions of $^{40}Ca^+$ in Paul traps for quantum information processing. Superpositions of the S$_{1/2}$ electronic ground state and the metastable D$_{5/2}$ state are used to implement a qubit. Laser light on the S$_{1/2} \leftrightarrow$ D$_{5/2}$ transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state $|n=0>$, we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190 ms. We also report on ground state cooling of two ions.