Calculating the spatial structures of ion crystals is important in ion-trapped quantum computation. Here we demonstrate that the simulated annealing method is a powerful tool to evaluate the structures of ion crystals. By calculating equilibrium positions of 10 ions under harmonic potential and those of 120 ions under anharmonic potential, both with the standard procedure and simulated annealing method, we find that the standard procedure to evaluate spatial structures is complicated and may be inefficient in some cases, and that the simulated annealing method is more favorable.
Calculating the spatial structures of ion crystals is important in ion-trapped quantum computation. Here we demonstrate that the simulated annealing method is a powerful tool to evaluate the structures of ion crystals. By calculating equilibrium positions of 10 ions under harmonic potential and those of 120 ions under anharmonic potential, both with the standard procedure and simulated annealing method, we find that the standard procedure to evaluate spatial structures is complicated and may be inefficient in some cases, and that the simulated annealing method is more favorable.
There is currently intensive research into creating a large-scale quantum computer with trapped ions. It is well known that for a linear ion crystal in a harmonic potential, the ions near the center are more closely spaced compared to the ions near the ends. This is problematic as the number of ions increases. Here, we consider a linear ion crystal in an anharmonic potential that is purely quartic in position. We find that the ions are more evenly spaced compared to the harmonic case. We develop a variational approach to calculate the properties of the ground state. We also characterize the zigzag transition in an anharmonic potential.
Coulomb crystals of cold trapped ions are a leading platform for the realization of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the standard model.For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state but also to be able to determine its temperature with a high accuracy.However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques.In this work, we present a new thermometry method tailored for ion crystals.The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals.We test the temperature estimate with two experiments, namely with a one-dimensional linear chain of four ions and a two-dimensional crystal of 19 ions and verify the results, where possible, using other methods.The results show that the new method is an accurate and efficient tool for thermometry of ion crystals.
Coulomb crystals of cold trapped ions are a leading platform for the realization of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the standard model. For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state but also to be able to determine its temperature with a high accuracy. However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques. In this work, we present a new thermometry method tailored for ion crystals. The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals. We test the temperature estimate with two experiments, namely with a one-dimensional linear chain of four ions and a two-dimensional crystal of 19 ions and verify the results, where possible, using other methods. The results show that the new method is an accurate and efficient tool for thermometry of ion crystals.
Coulomb crystal yields a wide range of applications including quantum computing and simulation, phase transitions, quantum logic spectroscopy, nonlinear dynamics and chaos, chemical reaction process, etc. The structure of the Coulomb crystal and the trajectory of each trapped ion are typically determined by the parameters of the trap and the ion species. However, dark ions are often inevitable in experiments, which introduces uncertainty to the desired crystal structures and ion trajectories. Few research has been conducted to investigate the configuration change of the crystal in the presence of dark ions and the influence of a dark ion on its surrounding ion trajectories in a multi-ion system. In this paper, we utilize the molecular dynamics simulation software LAMMPS and the (py)Lion package (modified to adapt the semi-classical theory of laser cooling) for the simulation of the 3D ion trajectories of Coulomb crystals. The formation process of 40Ca+ Coulomb crystals in a linear trap is simulated. With the micromotion and secular motion trajectories of each ion, we calculate the temperature of Coulomb crystal and the average velocity of specific ions. It’s observed that the crystal structure exhibits obvious layering phenomenon when the trapped ions yield a large difference in their charge-to-mass ratio (CMR), however, layering is not obvious with a small difference in the CMR. In addition, we simulate and compare the Coulomb crystal structure formed by pure 40Ca+ ions and that formed by 40Ca+ ions mixed with a small number of dark ions including isotopic ions (44Ca+) and impurity ions (CaH+). Three different cases are investigated, namely the 1D ion string, 2D plane structure and 3D helical structure. Results show that ions in the neighborhood of a dark ion exhibit around micron-order position changes compared to their positions before the dark ion is formed. Such a change can be measured in experiment through microscopic imaging, providing a way to identify dark ions in Column crystals with a large number of ions.
Coulomb crystals of cold trapped ions are a leading platform for the realisation of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the Standard Model. For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state, but also to be able to determine its temperature with a high accuracy. However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques. In this work we present a new thermometry method tailored for ion crystals. The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals. We test the temperature estimate with two experiments, namely with a 1D linear chain of 4 ions and a 2D crystal of 19 ions and verify the results, where possible, using other methods. The results show that the new method is an accurate and efficient tool for thermometry of ion crystals.
Coulomb crystals have applications in many areas such as quantum computing and simulation, quantum logic spectroscopy, nonlinear dynamics and chaos, phase transitions, and chemical reaction process. The structure of the Coulomb crystal and the trajectory of each trapped ion are typically determined by the parameters of the trap and the ion species. However, dark ions are often inevitable in experiment, which introduces uncertainty into the desired crystal structures and ion trajectories. Few researches have been conducted to investigate the configuration change of the crystal in the presence of dark ions and the influence of a dark ion on its surrounding ion trajectories in a multi-ion system. In this work, we utilize the molecular dynamics simulation software LAMMPS and the (py)LIon package (modified to adapt the semi-classical theory of laser cooling) for simulating the three-dimensional ion trajectories of Coulomb crystals. The formation process of 40Ca+ Coulomb crystal in a linear trap is simulated. With the micromotion and secular motion trajectories of each ion, we calculate the temperature of Coulomb crystal and the average velocity of specific ions. It is observed that the crystal structure exhibits obvious layering phenomenon when the trapped ions yield a large difference in their charge-to-mass ratio (CMR), however, layering is not obvious with a small difference in the CMR. In addition, we simulate and compare the Coulomb crystal structure formed by pure 40Ca+ ions with that formed by 40Ca+ ions mixed with a small number of dark ions including isotopic ions (44Ca+) and impurity ions (CaH+). Three different cases are investigated, namely the one-dimensional ion string, two-dimensional planar structure and three-dimensional helical structure. The results show that the ions in the neighborhood of a dark ion exhibit around micron-order position change compared with their positions before the dark ion is formed. Such a change can be measured in experiment through microscopic imaging, thereby providing a way to identify the formation of dark ions in Column crystals with a large ion number.