Optical trapping techniques are an efficient way to probe limited quantities of rare isotopes. In order to achieve the highest possible measurement precision, it is critical to optimize the optical trapping efficiency. This work presents the development of a three-dimensional semi-classical Monte Carlo simulation of the optical trapping process and its application to optimizing the optical trapping efficiency of Radium for use in the search of the permanent electric dipole moment of $^{225}$ Ra. The simulation includes an effusive-oven atomic beam source, transverse cooling and Zeeman slowing of an atomic beam, a three-dimensional magneto-optical trap, and additional processes such as collisions with residual gas molecules. We benchmark the simulation against a well-characterized $^{88}$ Sr optical trap before applying it to the $^{225}$ Ra optical trap. The simulation reproduces the relative gains in optical trapping efficiency measured in both the $^{88}$ Sr and $^{225}$ Ra optical traps. The measured and simulated values of the overall optical trapping efficiencies for $^{88}$ Sr are in agreement; however, they differ by a factor of $30$ for $^{225}$ Ra. Studies of several potential imperfections in the apparatus or systematic effects, such as atomic beam source misalignment and laser frequency noise, show only limited effects on the simulated trapping efficiency for $^{225}$ Ra. We rule out any one systematic effect as the sole cause of the discrepancy between the simulated and measured $^{225}$ Ra optical trapping efficiencies; but, we do expect that a combination of systematic effects contribute to this discrepancy. The accurate relative gains predicted by the simulation prove that it is useful for testing planned upgrades to the apparatus.Optical trapping techniques are an efficient way to probe limited quantities of rare isotopes. In order to achieve the highest possible measurement precision, it is critical to optimize the optical trapping efficiency. This work presents the development of a three-dimensional semi-classical Monte Carlo simulation of the optical trapping process and its application to optimizing the optical trapping efficiency of Radium for use in the search of the permanent electric dipole moment of $^{225}$Ra. The simulation includes an effusive-oven atomic beam source, transverse cooling and Zeeman slowing of an atomic beam, a three-dimensional magneto-optical trap, and additional processes such as collisions with residual gas molecules. We benchmark the simulation against a well-characterized $^{88}$Sr optical trap before applying it to the $^{225}$Ra optical trap. The simulation reproduces the relative gains in optical trapping efficiency measured in both the $^{88}$Sr and $^{225}$Ra optical traps. The measured and simulated values of the overall optical trapping efficiencies for $^{88}$Sr are in agreement; however, they differ by a factor of $30$ for $^{225}$Ra. Studies of several potential imperfections in the apparatus or systematic effects, such as atomic beam source misalignment and laser frequency noise, show only limited effects on the simulated trapping efficiency for $^{225}$Ra. We rule out any one systematic effect as the sole cause of the discrepancy between the simulated and measured $^{225}$Ra optical trapping efficiencies; but, we do expect that a combination of systematic effects contribute to this discrepancy. The accurate relative gains predicted by the simulation prove that it is useful for testing planned upgrades to the apparatus.

arXiv:1903.07798Mar 19, 20192 citations

The one dimensional Ising model with a transverse field

Annals of PhysicsFeb 1, 197063 citations

Initial State Encoding via Reverse Quantum Annealing and H-Gain Features

Elijah Pelofske, Georg Hahn, Hristo N. Djidjev

Quantum annealing is a specialized type of quantum computation that aims to use quantum fluctuations in order to obtain global minimum solutions of combinatorial optimization problems. Programmable D-Wave quantum annealers are available as cloud computing resources which allow users low level access to quantum annealing control features. In this paper, we are interested in improving the quality of the solutions returned by a quantum annealer by encoding an initial state into the annealing process. We explore two D-Wave features allowing one to encode such an initial state: the reverse annealing and the h-gain features. Reverse annealing (RA) aims to refine a known solution following an anneal path starting with a classical state representing a good solution, going backwards to a point where a transverse field is present, and then finishing the annealing process with a forward anneal. The h-gain (HG) feature allows one to put a time-dependent weighting scheme on linear ( $h$ ) biases of the Hamiltonian, and we demonstrate that this feature likewise can be used to bias the annealing to start from an initial state. We also consider a hybrid method consisting of a backward phase resembling RA, and a forward phase using the HG initial state encoding. Importantly, we investigate the idea of iteratively applying RA and HG to a problem, with the goal of monotonically improving on an initial state that is not optimal. The HG encoding technique is evaluated on a variety of input problems including the edge-weighted Maximum Cut problem and the vertex-weighted Maximum Clique problem, demonstrating that the HG technique is a viable alternative to RA for some problems. We also investigate how the iterative procedures perform for both RA and HG initial state encoding on random whole-chip spin glasses with the native hardware connectivity of the D-Wave Chimera and Pegasus chips.Quantum annealing is a specialized type of quantum computation that aims to use quantum fluctuations in order to obtain global minimum solutions of combinatorial optimization problems. Programmable D-Wave quantum annealers are available as cloud computing resources which allow users low level access to quantum annealing control features. In this paper, we are interested in improving the quality of the solutions returned by a quantum annealer by encoding an initial state into the annealing process. We explore two D-Wave features allowing one to encode such an initial state: the reverse annealing and the h-gain features. Reverse annealing (RA) aims to refine a known solution following an anneal path starting with a classical state representing a good solution, going backwards to a point where a transverse field is present, and then finishing the annealing process with a forward anneal. The h-gain (HG) feature allows one to put a time-dependent weighting scheme on linear ($h$) biases of the Hamiltonian, and we demonstrate that this feature likewise can be used to bias the annealing to start from an initial state. We also consider a hybrid method consisting of a backward phase resembling RA, and a forward phase using the HG initial state encoding. Importantly, we investigate the idea of iteratively applying RA and HG to a problem, with the goal of monotonically improving on an initial state that is not optimal. The HG encoding technique is evaluated on a variety of input problems including the edge-weighted Maximum Cut problem and the vertex-weighted Maximum Clique problem, demonstrating that the HG technique is a viable alternative to RA for some problems. We also investigate how the iterative procedures perform for both RA and HG initial state encoding on random whole-chip spin glasses with the native hardware connectivity of the D-Wave Chimera and Pegasus chips.

arXiv:2303.13748IEEE Transactions on Quantum EngineeringJan 1, 202312 citations

The transverse spin-1 Ising model with random interactions

Touria Bouziane, M. Saber

Journal of Magnetism and Magnetic MaterialsJul 31, 200810 citations

^{225}

Ra. The simulation includes an effusive-oven atomic beam source, transverse cooling and Zeeman slowing of an atomic beam, a three-dimensional magneto-optical trap, and additional processes such as collisions with residual gas molecules. We benchmark the simulation against a well-characterized

^{88}

Sr optical trap before applying it to the

^{225}

Ra optical trap. The simulation reproduces the relative gains in optical trapping efficiency measured in both the

^{88}

Sr and

^{225}

Ra optical traps. The measured and simulated values of the overall optical trapping efficiencies for

^{88}

Sr are in agreement; however, they differ by a factor of

30

for

^{225}

Ra. Studies of several potential imperfections in the apparatus or systematic effects, such as atomic beam source misalignment and laser frequency noise, show only limited effects on the simulated trapping efficiency for

^{225}

Ra. We rule out any one systematic effect as the sole cause of the discrepancy between the simulated and measured

^{225}

Ra optical trapping efficiencies; but, we do expect that a combination of systematic effects contribute to this discrepancy. The accurate relative gains predicted by the simulation prove that it is useful for testing planned upgrades to the apparatus.

h

) biases of the Hamiltonian, and we demonstrate that this feature likewise can be used to bias the annealing to start from an initial state. We also consider a hybrid method consisting of a backward phase resembling RA, and a forward phase using the HG initial state encoding. Importantly, we investigate the idea of iteratively applying RA and HG to a problem, with the goal of monotonically improving on an initial state that is not optimal. The HG encoding technique is evaluated on a variety of input problems including the edge-weighted Maximum Cut problem and the vertex-weighted Maximum Clique problem, demonstrating that the HG technique is a viable alternative to RA for some problems. We also investigate how the iterative procedures perform for both RA and HG initial state encoding on random whole-chip spin glasses with the native hardware connectivity of the D-Wave Chimera and Pegasus chips.