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arXiv:1209.1214 · Physical Review A

Proposal for trapped-ion emulation of the electric dipole moment of neutral relativistic particles

Tihomir G. Tenev, Peter A. Ivanov, Nikolay V. Vitanov

Published Feb 4, 2013• 12 citations
arXivHTMLPDF

Abstract

The electric dipole moments of various neutral elementary particles, such as neutron, neutrinos, certain hypothetical dark matter particles, and others, are predicted to exist by the standard model of high-energy physics and various extensions of it. However, the predicted values are beyond the present experimental capabilities. We propose to simulate and emulate the electric dipole moment of neutral relativistic particles and the ensuing effects in the presence of an electrostatic field by emulation of an extended Dirac equation in ion traps.

DOI
10.1103/physreva.87.022103

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The electric dipole moments of various neutral elementary particles, such as neutron, neutrinos, certain hypothetical dark matter particles, and others, are predicted to exist by the standard model of high-energy physics and various extensions of it. However, the predicted values are beyond the present experimental capabilities. We propose to simulate and emulate the electric dipole moment of neutral relativistic particles and the ensuing effects in the presence of an electrostatic field by emulation of an extended Dirac equation in ion traps.
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Abstract A novel design for an electromagnetic trap is proposed for confinement of neutral particles having a permanent electric dipole moment. The device uses a combination of a sextupole electric and quadrupole magnetic fields superimposed with a strong constant electric field perfectly aligned along the z-axis. We use the extended dipole model to study the dynamics of particle in this position dependent electromagnetic field. The motion of the centre of mass of the dipole is nonlinearly coupled with its rotation. We find three families of particular solutions for which the orbits are periodic or quasiperiodic. They correspond to the particular cases when the whole energy is accumulated in either translational or rotational degrees of freedom. Stability analysis of chosen particular solutions provides trapping conditions. We present several numerical simulations which illustrate trapping and confinement of an electric dipole in the proposed trap. These simulations were performed for three kinds of polar particles and various fields selections. We hope that the proposed model allows experimental physicists to apply a wide variety of non-destructive methods for manipulation, detection and analysis of trapped particles.
We report on quantum simulations of relativistic scattering dynamics using trapped ions. The simulated state of a scattering particle is encoded in both the electronic and vibrational state of an ion, representing the discrete and continuous components of relativistic wave functions. Multiple laser fields and an auxiliary ion simulate the dynamics generated by the Dirac equation in the presence of a scattering potential. Measurement and reconstruction of the particle wave packet enables a frame-by-frame visualization of the scattering processes. By precisely engineering a range of external potentials we are able to simulate text book relativistic scattering experiments and study Klein tunneling in an analogue quantum simulator. We describe extensions to solve problems that are beyond current classical computing capabilities.
We propose the quantum simulation of the Dirac equation with potentials, allowing the study of relativistic scattering and Klein tunneling. This quantum relativistic effect permits a positive-energy Dirac particle to propagate through a repulsive potential via the population transfer to negative-energy components. We show how to engineer scalar, pseudoscalar, and other potentials in the 1+11+11+1 Dirac equation by manipulating two trapped ions. The Dirac spinor is represented by the internal states of one ion, while its position and momentum are described by those of a collective motional mode. The second ion is used to build the desired potentials with high spatial resolution.
A superposition of inhomogeneous static and rapidly oscillating electric fields is capable of trapping neutral particles with a permanent electric dipole moment. Detailed numerical simulations prove the validity and stability of our trapping scheme. Thin rods of barium titanate (BaTiO3{}_{3}3​) are presented as an example for trapping on the macroscale. HC17{}_{17}17​N, a polar molecule of astrophysical significance, is presented as an example for trapping on the microscale. For HC17{}_{17}17​N and the parameters chosen, the depth of the trap is $40 $mK.
Heavy polar molecules can be used to measure the electric dipole moment of the electron, which is a sensitive probe of physics beyond the Standard Model. The value is determined by measuring the precession of the molecule’s spin in a plane perpendicular to an applied electric field. The longer this precession evolves coherently, the higher the precision of the measurement. For molecules in a trap, this coherence time could be very long indeed. We evaluate the sensitivity of an experiment where neutral molecules are trapped electrically, and compare this to an equivalent measurement in a molecular beam. We consider the use of a Stark decelerator to load the trap from a supersonic source, and calculate the deceleration efficiency for YbF molecules in both strong-field seeking and weak-field seeking states. With a 1 s holding time in the trap, the statistical sensitivity could be ten times higher than it is in the beam experiment, and this could improve by a further factor of five if the trap can be loaded from a source of larger emittance. We study some effects due to field inhomogeneity in the trap and find that rotation of the electric field direction, leading to an inhomogeneous geometric phase shift, is the primary obstacle to a sensitive trap-based measurement. 1