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Physical Review A

Coherent cancellation of geometric phase for the OH molecule in external fields

Mishkatul Bhattacharya, Stefano Marin, Michaela Kleinert

Published May 6, 2014• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physreva.89.052503

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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.
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.
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.
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.
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.
We derive an effective Hamiltonian to account for the geometric phase that occurs in the adiabatic separation of center-of-mass and internal motion of a molecule moving in external fields. We then apply this Hamiltonian to the determination of the coherence time of molecules confined in a region of space by an anisotropic electric field. We show that the coherence time is expected to scale as the load temperature of the molecules squared and that milli-K temperatures are likely to be required for a trapped molecule experiment to compete with a more conventional Ramsey beam resonance experiment.
The hydroxyl radical (the OH molecule) carries both electric and magnetic dipole moments and, as a diatomic molecule, admits a comparatively simple and accurate model. This makes it a natural quantum probe for the joint estimation of electric and magnetic fields. Here we study simultaneous estimation of both fields using the tools of multiparameter quantum estimation theory, explicitly accounting for the performance loss caused by measurement incompatibility. We analyze and optimize both stationary and dynamical estimation strategies. In the stationary regime we consider ground and thermal states of the Stark-Zeeman Hamiltonian and identify optimal operating points. For thermal probes we find a nontrivial multiparameter effect: Increasing the temperature can reduce the overall estimation error by weakening parameter correlations. In the dynamical regime we study both pure and thermal initial states, illustrating nontrivial manifestations of incompatibility for mixed probes. Finally, we show that an optimal sequential control protocol can overcome limitations due to noncommutativity, and we assess its robustness in the multiparameter setting.