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Bulletin of the American Physical Society

The ground state OH molecule in combined electric and magnetic fields: exact solution of the effective Hamiltonian

Mishkatul Bhattacharya, Zachary Howard, Michaela Kleinert

Published Jun 6, 2013• 0 citations
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Abstract

Department of Physics, Willamette University, 900 State Street, Salem, OR 97301, USA(Dated: September 12, 2013)The OH molecule is currently of great interest from the perspective of ultracold chemistry, quan-tum fluids, precision measurement and quantum computation. Crucial to these applications arethe slowing, guiding, confinement and state control of OH, using electric and magnetic fields. Inthis article, we show that the corresponding eight-dimensional effective ground state Stark-ZeemanHamiltonian is exactly solvable and explicitly identify the underlying chiral symmetry. Our analyt-ical solution opens the way to insightful characterization of the magnetoelectrostatic manipulationof ground state OH. Based on our results, we also discuss a possible application to the quantumsimulation of an imbalanced Ising magnet.

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Ground-state OH molecule in combined electric and magnetic fields: Analytic solution of the effective Hamiltonian

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The OH molecule is currently of great interest from the perspective of ultracold chemistry, quantum fluids, precision measurement, and quantum computation. Crucial to these applications are the slowing, guiding, confinement, and state control of OH, using electric and magnetic fields. In this article, we show that the corresponding eight-dimensional effective ground-state Stark-Zeeman Hamiltonian is exactly solvable and explicitly identify the underlying chiral symmetry. Our analytical solution opens the way to insightful characterization of the magnetoelectrostatic manipulation of ground-state OH. Based on our results, we also discuss a possible application to the quantum simulation of an imbalanced Ising magnet.

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The OH molecule in its ground state presents a versatile platform for precision measurement and quantum information processing. These applications vitally depend on the accurate measurement of transition energies between the OH levels. Significant sources of systematic errors in these measurements are shifts based on the geometric phase arising from the magnetic and electric fields used for manipulating OH. In this article, we present these geometric phases for fields that vary harmonically in time, as in the Ramsey technique. Our calculation of the phases is exact within the description provided by our recent analytic solution of an effective Stark-Zeeman Hamiltonian for the OH ground state. This Hamiltonian has been shown to model experimental data accurately. We find that the OH geometric phases exhibit rich structure as a function of the field rotation rate. Remarkably, we find rotation rates where the geometric phase accumulated by a specific state is zero, or where the relative geometric phase between two states vanishes. We expect these findings to be of importance to precision experiments on OH involving time-varying fields. More specifically, our analysis quantitatively characterizes an important item in the error budget for precision spectroscopy of ground-state OH.

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OH Trapped by Magnets

Confining atoms with a combination of optical and magnetic fields has led to the formation of new states of matter and provided a tunable test bed to explore many-body atomic and electronic interactions; however, its extension to molecules has been slow. Ultracold molecules (milikelvin temperatures and below) are of interest for a number of additional applications, including studies of quantum phase transitions and precision spectroscopy. One approach to confining polar molecules has relied on inhomogeneous electric fields. Sawyer et al. present an alternative method that traps molecules magnetically. They demonstrate the technique on hydroxyl (OH) radicals, which have appreciable magnetic as well as electric dipole moments. Lifetimes in the magnetoelectrostatic trap ranged from 20 to 500 ms, depending on the background pressure. The technique allows the additional degree of freedom of an electrical field to be superimposed onto the trapped molecules and should facilitate further studies in the direction of controlled molecular collisions and chemical reactions. — ISO

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The OH molecule in its ground state presents a versatile platform for precision measurement and quantum information processing. These applications depend vitally on the accurate measurement of transition energies between the OH levels. Significant sources of systematic errors in these measurements are shifts based on the geometric phase arising from the magnetic and electric fields used for manipulating OH. In this article, we present these geometric phases for fields that vary harmonically in time, as in the Ramsey technique. Our calculation of the phases is exact within the description provided by our recent analytic solution of an effective Stark-Zeeman Hamiltonian for the OH ground state. This Hamiltonian has earlier been shown to model experimental data accurately. We find that the OH geometric phases exhibit rich structure as a function of the field rotation rate. Remarkably, we find rotation rates where the geometric phase accumulated by a specific state is zero, or where the relative geometric phase between two states vanishes. We expect these findings to be of importance to precision experiments on OH involving time-varying fields. More specifically, our analysis quantitatively characterizes an important item in the error budget for precision spectroscopy of ground state OH.

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Microwave state transfer and adiabatic dynamics of magnetically trapped polar molecules

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Cold and ultracold polar molecules with nonzero electronic angular momenta are of great interest for studies in quantum chemistry and control, investigations of novel quantum systems, and precision measurement. However, in mixed electric and magnetic fields, these molecules are generically subject to a large set of avoided crossings among their Zeeman sublevels; in magnetic traps, these crossings lead to distorted potentials and trap loss from electric bias fields. We have characterized these crossings in OH by microwave-transferring trapped OH molecules from the upper $|f;\phantom{\rule{0.16em}{0ex}}M=+\frac{3}{2}\ensuremath{\rangle}$ parity state to the lower $|e;\phantom{\rule{0.16em}{0ex}}+\frac{3}{2}\ensuremath{\rangle}$ state and observing their trap dynamics under an applied electric bias field. Our observations are very well fit by a simple Landau-Zener model, yielding insight to the rich spectra and dynamics of polar radicals in mixed external fields.

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Department of Physics, Willamette University, 900 State Street, Salem, OR 97301, USA(Dated: September 12, 2013)The OH molecule is currently of great interest from the perspective of ultracold chemistry, quan-tum fluids, precision measurement and quantum computation. Crucial to these applications arethe slowing, guiding, confinement and state control of OH, using electric and magnetic fields. Inthis article, we show that the corresponding eight-dimensional effective ground state Stark-ZeemanHamiltonian is exactly solvable and explicitly identify the underlying chiral symmetry. Our analyt-ical solution opens the way to insightful characterization of the magnetoelectrostatic manipulationof ground state OH. Based on our results, we also discuss a possible application to the quantumsimulation of an imbalanced Ising magnet.
The OH molecule is currently of great interest from the perspective of ultracold chemistry, quantum fluids, precision measurement, and quantum computation. Crucial to these applications are the slowing, guiding, confinement, and state control of OH, using electric and magnetic fields. In this article, we show that the corresponding eight-dimensional effective ground-state Stark-Zeeman Hamiltonian is exactly solvable and explicitly identify the underlying chiral symmetry. Our analytical solution opens the way to insightful characterization of the magnetoelectrostatic manipulation of ground-state OH. Based on our results, we also discuss a possible application to the quantum simulation of an imbalanced Ising magnet.
The OH molecule in its ground state presents a versatile platform for precision measurement and quantum information processing. These applications vitally depend on the accurate measurement of transition energies between the OH levels. Significant sources of systematic errors in these measurements are shifts based on the geometric phase arising from the magnetic and electric fields used for manipulating OH. In this article, we present these geometric phases for fields that vary harmonically in time, as in the Ramsey technique. Our calculation of the phases is exact within the description provided by our recent analytic solution of an effective Stark-Zeeman Hamiltonian for the OH ground state. This Hamiltonian has been shown to model experimental data accurately. We find that the OH geometric phases exhibit rich structure as a function of the field rotation rate. Remarkably, we find rotation rates where the geometric phase accumulated by a specific state is zero, or where the relative geometric phase between two states vanishes. We expect these findings to be of importance to precision experiments on OH involving time-varying fields. More specifically, our analysis quantitatively characterizes an important item in the error budget for precision spectroscopy of ground-state OH.
We report magnetic confinement of neutral, ground state OH at a density of approximately 3 x 10(3) cm(-3) and temperature of approximately 30 mK. An adjustable electric field sufficiently large to polarize the OH is superimposed on the trap in various geometries, making an overall potential arising from both Zeeman and Stark effects. An effective molecular Hamiltonian is constructed, with Monte Carlo simulations accurately modeling the observed single-molecule dynamics in various trap configurations. Magnetic trapping of cold polar molecules under adjustable electric fields may enable study of low energy dipolar interactions.
Confining atoms with a combination of optical and magnetic fields has led to the formation of new states of matter and provided a tunable test bed to explore many-body atomic and electronic interactions; however, its extension to molecules has been slow. Ultracold molecules (milikelvin temperatures and below) are of interest for a number of additional applications, including studies of quantum phase transitions and precision spectroscopy. One approach to confining polar molecules has relied on inhomogeneous electric fields. Sawyer et al. present an alternative method that traps molecules magnetically. They demonstrate the technique on hydroxyl (OH) radicals, which have appreciable magnetic as well as electric dipole moments. Lifetimes in the magnetoelectrostatic trap ranged from 20 to 500 ms, depending on the background pressure. The technique allows the additional degree of freedom of an electrical field to be superimposed onto the trapped molecules and should facilitate further studies in the direction of controlled molecular collisions and chemical reactions. — ISO
The OH molecule in its ground state presents a versatile platform for precision measurement and quantum information processing. These applications depend vitally on the accurate measurement of transition energies between the OH levels. Significant sources of systematic errors in these measurements are shifts based on the geometric phase arising from the magnetic and electric fields used for manipulating OH. In this article, we present these geometric phases for fields that vary harmonically in time, as in the Ramsey technique. Our calculation of the phases is exact within the description provided by our recent analytic solution of an effective Stark-Zeeman Hamiltonian for the OH ground state. This Hamiltonian has earlier been shown to model experimental data accurately. We find that the OH geometric phases exhibit rich structure as a function of the field rotation rate. Remarkably, we find rotation rates where the geometric phase accumulated by a specific state is zero, or where the relative geometric phase between two states vanishes. We expect these findings to be of importance to precision experiments on OH involving time-varying fields. More specifically, our analysis quantitatively characterizes an important item in the error budget for precision spectroscopy of ground state OH.
Cold and ultracold polar molecules with nonzero electronic angular momenta are of great interest for studies in quantum chemistry and control, investigations of novel quantum systems, and precision measurement. However, in mixed electric and magnetic fields, these molecules are generically subject to a large set of avoided crossings among their Zeeman sublevels; in magnetic traps, these crossings lead to distorted potentials and trap loss from electric bias fields. We have characterized these crossings in OH by microwave-transferring trapped OH molecules from the upper $|f;\phantom{\rule{0.16em}{0ex}}M=+\frac{3}{2}\ensuremath{\rangle}$ parity state to the lower $|e;\phantom{\rule{0.16em}{0ex}}+\frac{3}{2}\ensuremath{\rangle}$ state and observing their trap dynamics under an applied electric bias field. Our observations are very well fit by a simple Landau-Zener model, yielding insight to the rich spectra and dynamics of polar radicals in mixed external fields.