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.
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.
Although ion-ion sympathetic cooling is now commonly used to reduce speeds of trapped molecular ions to milliKelvin temperatures, cooling of the decoupled internal molecular modes remains a challenge. Here, we demonstrate that a single spectrally filtered femtosecond laser, tuned to the electronic A-X transition of trapped AlH+, can efficiently cool rotations from room temperature to the ground state. Since this single-laser technique simultaneously drives rotationally de-exciting electronic excitations from all initially populated states, each parity can be cooled as quickly as 100 μs. In our current implementation, full population collection into the N = 0 positive-parity level relies on vibrational relaxation on the timescale of 100 ms. Since this technique cools by step-wise rotational pumping, it is most readily applicable to “alkali-like” molecular species, such as AlH+, with semi-closed cycling transitions. Although we currently use a destructive two-photon state readout technique, these species are also promising candidates for single-molecule fluorescence detection. The ability to quickly cool molecular rotations is expected to be important for precision spectroscopy experiments, quantum information processing applications, and for ultracold chemistry studies.
Sympathetic cooling of molecular ions through the Coulomb interaction with laser-cooled atomic ions is an efficient tool to prepare translationally cold molecules without, ideally, affecting the internal state of the molecular ions. However, the electric field due to the Coulomb interaction may induce rotational transitions that change the purity of initially quantum state prepared molecules. Here, we use estimates of rotational state changes in single collisions of diatomic ions with atomic ions [J. M. Berglund, M. Drewsen, and C. P. Koch, ] to determine the overall rotational excitation accumulated over the sympathetic cooling. Considering two different experimental scenarios, that of a molecular ion cotrapped with a single atomic ion and a molecular ion immersed in a Coulomb crystal of atomic ions, we also estimate the cooling time.
Sympathetic cooling of molecular ions through the Coulomb interaction with laser-cooled atomic ions is an efficient tool to prepare translationally cold molecules without, ideally, affecting the internal state of the molecular ions. However, the electric field due to the Coulomb interaction may induce rotational transitions that change the purity of initially quantum state prepared molecules. Here, we use estimates of rotational state changes in single collisions of diatomic ions with atomic ions [J. M. Berglund, M. Drewsen, and C. P. Koch, Phys. Rev. A 113, 042816 (2026)] to determine the overall rotational excitation accumulated over the sympathetic cooling. Considering two different experimental scenarios, that of a molecular ion cotrapped with a single atomic ion and a molecular ion immersed in a Coulomb crystal of atomic ions, we also estimate the cooling time.
Laser-cooled atomic ions have led to an unprecedented amount of control over the quantum states of matter. The Coulombic interaction allows for information to be transferred between neighboring ions, and this interaction can be used to entangle qubits for logic operations in quantum information processors. The same procedure for logic operations can be used for high resolution atomic spectroscopy, and is the basis for the most accurate atomic optical clocks to date. This thesis describes how laser-cooled atomic ions can impact physical chemistry through the development of molecular ion spectroscopy techniques and the simulation of magnetic systems by ion trap quantum computers. \n\t \n\tA new technique developed for spectroscopy, Sympathetic Heating Spectroscopy (SHS), takes advantage of the Coulombic interaction between two trapped ions: the control ion and a spectroscopy ion. SHS uses the back action of the interrogating laser to map spectroscopy ion information onto the Doppler shift of the control ion for measurement. SHS only requires Doppler cooling of the ions and fluorescence measurement and represents a simplification of quantum logic spectroscopy. This technique is demonstrated on two individual isotopes of calcium: Ca-40(+) for cooling and Ca-44(+) as the spectroscopy ion. \n \n\tHaving demonstrated SHS with atomic ions, the next step was to extend the technique by loading and characterizing molecular ions. The identification of an unknown molecular ion is necessary and can be achieved by monitoring the change in motion of the two ion crystal, which is dependent on the molecular ion mass. The motion of two trapped ions is described by their normal modes, which can be accurately measured by performing resolved sideband spectroscopy of the S(1/2)-D(5/2) transition of calcium. The resolved sidebands can be used to identify unknown ions (atomic and molecular) by calculating the mass based on the observed value in axial normal mode frequencies. Again, the trapped molecular ion is sympathetically cooled via the Coulombic interaction between the Ca-40(+) and the unknown molecular ion. The sensitivity of SHS could be improved by implementing sympathetic sideband cooling and determining the heating by measuring single quanta of motion. \n\t \n\tThe ultimate limit of control would be the development of an ion trap quantum computer. Many theoretical quantum computing researchers have made bold claims of the exponential improvement a quantum computer would have over a classical computer for the simulation of physical systems such as molecules. These claims are true in principle for ideal systems, but given non-ideal components it is necessary to consider the scaling due to error correction. An estimate of the resource requirements, the total number of physical qubits and computational time, required to compute the ground state energy of a 1-D quantum Transverse Ising Model (TIM) of N spin-1/2 particles, as a function of the system size and the numerical precision, is presented. This estimate is based on analyzing the impact of fault-tolerant quantum error correction in the context of the quantum logic array architecture. The results show that a significant amount of error correction is required to implement the TIM problem due to the exponential scaling of the computational time with the desired precision of the energy. Comparison of this result to the resource requirements for a fault-tolerant implementation of Shor's quantum factoring algorithm reveals that the required logical qubit reliability is similar for both the TIM problem and the factoring problem.
We demonstrate rotational excitation of molecular ions that are sympathetically cooled by laser-cooled atomic ions to a temperature as low as approximately 10 mK. The molecular hydrogen ions HD+ and the fundamental rotational transition $(v=0,\phantom{\rule{0.16em}{0ex}}N=0)\ensuremath{\rightarrow}({v}^{\ensuremath{'}}=0,\phantom{\rule{0.16em}{0ex}}{N}^{\ensuremath{'}}=1)$ at 1.3 THz, the most fundamental dipole-allowed rotational transition of any molecule, are used as a test case. This transition has not been observed before. Rotational laser cooling was employed in order to increase the signal, and resonance-enhanced multiphoton dissociation was used as detection method. The black-body-radiation-induced rotational excitation is also observed. The extension of the method to other molecular species is briefly discussed.
We demonstrate sympathetic Doppler cooling and our progress towards sideband cooling of a CaH+ ion co-trapped with a Ca+ atomic ion in a linear Paul trap. Molecular ions are generally difficult to laser cool due to a lack of closed electronic transitions as a result of vibrational and rotational states. Despite this challenge, they can be cooled indirectly through their Coulombic interaction with a fluorescent atomic ion that is being directly laser cooled. Ions are firstly Doppler cooled to get to the Lamb-Dicke regime, where the ion motion is small relative to the excitation wavelength and then sideband cooled reaching temperatures below 1 μK. All the ions' axial modes (center of mass and breathing mode) and radial modes ( two center of mass and two tilt modes) are addressed, and the temperature is determined by examining the ratio of sidebands.