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arXiv:0909.3644 · New Journal of Physics

Hyperfine structure in the microwave spectra of ultracold polar molecules

Hong Ran, J. Aldegunde, Jeremy M. Hutson

Published Apr 13, 2010• 24 citations
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Abstract

We investigate the microwave spectra of ultracold alkali metal dimers in magnetic, electric and combined fields taking into account the hyperfine structure due to nuclear spins. We consider the molecules 41 K 87 Rb and 7 Li 133 Cs, which are the targets of current experiments, and demonstrate two extremes of large and small nuclear quadrupole couplings. We calculate the frequencies and intensities of transitions that may be used to transfer ultracold molecules between hyperfine states in a magnetic field, employing different polarizations of microwave radiation. In an electric field, the hyperfine levels display narrow avoided crossings at specific fields that we explain in terms of molecular alignment. The hyperfine splittings that arise in electric fields may hinder individual addressing in schemes that use ultracold molecules in quantum computation, but the structure of the spectra is suppressed in combined fields.

DOI
10.1088/1367-2630/12/4/043015

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We investigate the microwave spectra of ultracold alkali metal dimers in magnetic, electric and combined fields taking into account the hyperfine structure due to nuclear spins. We consider the molecules 41 K 87 Rb and 7 Li 133 Cs, which are the targets of current experiments, and demonstrate two extremes of large and small nuclear quadrupole couplings. We calculate the frequencies and intensities of transitions that may be used to transfer ultracold molecules between hyperfine states in a magnetic field, employing different polarizations of microwave radiation. In an electric field, the hyperfine levels display narrow avoided crossings at specific fields that we explain in terms of molecular alignment. The hyperfine splittings that arise in electric fields may hinder individual addressing in schemes that use ultracold molecules in quantum computation, but the structure of the spectra is suppressed in combined fields.
We calculate the microwave spectra of ultracold 40K87Rb^{40}\text{K}^{87}\text{R}\text{b}40K87Rb alkali-metal dimers, including hyperfine interactions and in the presence of electric and magnetic fields. We show that microwave transitions may be used to transfer molecules between different hyperfine states, but only because of the presence of nuclear quadrupole interactions. Hyperfine splittings may also complicate the use of ultracold molecules for quantum computing. The spectrum of molecules oriented in electric fields may be simplified dramatically by applying a simultaneous magnetic field.
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We investigate the hyperfine energy levels and Zeeman splittings for homonuclear alkali-metal dimers in low-lying rotational and vibrational states, which are important for experiments designed to produce quantum gases of deeply bound molecules. We carry out density-functional theory calculations of the nuclear hyperfine coupling constants. For nonrotating states, the zero-field splittings are determined almost entirely by the scalar nuclear spin-spin coupling constant. By contrast with the heteronuclear case, the total nuclear spin remains a good quantum number in a magnetic field. We also investigate levels with rotational quantum number N=1N=1N=1, which have long-range anisotropic quadrupole-quadrupole interactions and may be collisionally stable. For these states the splitting is dominated by nuclear quadrupole coupling for most of the alkali-metal dimers and the Zeeman splittings are considerably more complicated.
Mixing of 0+{0}^{+}0+ and 0−{0}^{-}0− observed in the hyperfine and Zeeman structure of ultracold Rb2{\mathrm{Rb}}_{2}Rb2​ molecules
We study the combination of the hyperfine and Zeeman structure in the spin–orbit coupled complex of . For this purpose, absorption spectroscopy at a magnetic field around G is carried out. We drive optical dipole transitions from the lowest rotational state of an ultracold Feshbach molecule to various vibrational levels with symmetry of the complex. In contrast to previous measurements with rotationally excited alkali-dimers, we do not observe equal spacings of the hyperfine levels. In addition, the spectra vary substantially for different vibrational quantum numbers, and exhibit large splittings of up to MHz, unexpected for states. The level structure is explained to be a result of the repulsion between the states and of , coupled via hyperfine and Zeeman interactions. In general, and have a spin–orbit induced energy spacing Δ , that is different for the individual vibrational states. From each measured spectrum we are able to extract Δ , which otherwise is not easily accessible in conventional spectroscopy schemes. We obtain values of Δ in the range of GHz which can be described by coupled channel calculations if a spin–orbit coupling is introduced that is different for and of .
We demonstrate coherent control of the rotational and hyperfine state of ultracold, chemically stable 87Rb133Cs^{87}\mathrm{Rb}^{133}\mathrm{Cs}87Rb133Cs molecules with external microwave fields. We create a sample of $\ensuremath{\sim}2000$ molecules in the lowest hyperfine level of the rovibronic ground state N=0N=0N=0. We measure the transition frequencies to eight different hyperfine levels of the N=1N=1N=1 state at two magnetic fields $\ensuremath{\sim}23$ G apart. We determine accurate values of rotational and hyperfine coupling constants that agree well with previous calculations. We observe Rabi oscillations on each transition, allowing complete population transfer to a selected hyperfine level of N=1N=1N=1. Subsequent application of a second microwave pulse allows the transfer of molecules back to a different hyperfine level of N=0N=0N=0.
We demonstrate coherent microwave control of rotational and hyperfine states of trapped, ultracold, and chemically stable 23 Na 40 K molecules.Starting with all molecules in the absolute rovibrational and hyperfine ground state, we study rotational transitions in combined magnetic and electric fields and explain the rich hyperfine structure.Following the transfer of the entire molecular ensemble into a single hyperfine level of the first rotationally excited state, J ¼ 1, we observe lifetimes of more than 3 s, comparable to those in the rovibrational ground state, J ¼ 0. Long-lived ensembles and full quantum state control are prerequisites for the use of ultracold molecules in quantum simulation, precision measurements, and quantum information processing.