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Physical Review A

Infrared frequency standard based on magnetically trapped NH molecules

Masatoshi Kajita

Published Sep 27, 2006• 7 citations
Publisher

Abstract

An infrared frequency standard based on the NH $\ensuremath{\mid}{n}_{v}=0,{N}_{0}=0,J=1,{F}_{1}=3∕2,F=5∕2,{M}_{F}=5∕2⟩\ensuremath{\rightarrow}\ensuremath{\mid}{n}_{v}=1,{N}_{0}=0,J=1,{F}_{1}=3∕2,F=5∕2,{M}_{F}=5∕2⟩$ transition $(3\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m})$ is proposed. There is no Zeeman shift with this transition frequency, because the Zeeman coefficient is not dependent on the vibrational state. NH molecules, precooled by collisions with liquid $^{3}\mathrm{He}$ vapor, are trapped by an inhomogeneous magnetic field. The temperature of the trapped NH molecules holds the potential to be reduced down to several $\ensuremath{\mu}\mathrm{K}$ by evaporative cooling. The uncertainty of the clock transition can potentially be reduced to lower than ${10}^{\ensuremath{-}17}$.

DOI
10.1103/physreva.74.035403

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An infrared frequency standard based on the NH \ensuremath∣nv=0,N0=0,J=1,F1=3∕2,F=5∕2,MF=5∕2⟩\ensuremath→\ensuremath∣nv=1,N0=0,J=1,F1=3∕2,F=5∕2,MF=5∕2⟩\ensuremath{\mid}{n}_{v}=0,{N}_{0}=0,J=1,{F}_{1}=3∕2,F=5∕2,{M}_{F}=5∕2⟩\ensuremath{\rightarrow}\ensuremath{\mid}{n}_{v}=1,{N}_{0}=0,J=1,{F}_{1}=3∕2,F=5∕2,{M}_{F}=5∕2⟩\ensuremath∣nv​=0,N0​=0,J=1,F1​=3∕2,F=5∕2,MF​=5∕2⟩\ensuremath→\ensuremath∣nv​=1,N0​=0,J=1,F1​=3∕2,F=5∕2,MF​=5∕2⟩ transition (3\ensuremathμm)(3\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m})(3\ensuremathμm) is proposed. There is no Zeeman shift with this transition frequency, because the Zeeman coefficient is not dependent on the vibrational state. NH molecules, precooled by collisions with liquid 3He^{3}\mathrm{He}3He vapor, are trapped by an inhomogeneous magnetic field. The temperature of the trapped NH molecules holds the potential to be reduced down to several \ensuremathμK\ensuremath{\mu}\mathrm{K}\ensuremathμK by evaporative cooling. The uncertainty of the clock transition can potentially be reduced to lower than 10\ensuremath−17{10}^{\ensuremath{-}17}10\ensuremath−17.
NH radicals are magnetically trapped and their Zeeman relaxation and energy transport collision cross sections with helium are measured. Continuous buffer-gas loading of the trap is direct from a room-temperature molecular beam. The Zeeman relaxation (inelastic) cross section of magnetically trapped electronic, vibrational, and rotational ground state NH molecules in collisions with 3He^{3}\mathrm{He}3He is measured to be $3.8\ifmmode\pm\else\textpm\fi{}1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}\text{ }\text{ }{\mathrm{cm}}^{2}$ at 710 mK. The NH-He energy transport cross section is also measured, indicating a ratio of diffusive to inelastic cross sections of $\ensuremath{\gamma}=7\ifmmode\times\else\texttimes\fi{}{10}^{4}$, in agreement with recent theory [R. V. Krems, H. R. Sadeghpour, A. Dalgarno, D. Zgid, J. K\l{}os, and G. Cha\l{}asi\ifmmode \acute{n}\else \'{n}\fi{}ski, Phys. Rev. A 68, 051401 (2003)].
Recent advances in quantum technologies have enabled the precise control of single trapped molecules on the quantum level. Exploring the scope of these new technologies, we studied theoretically the implementation of qubits and clock transitions in the spin, rotational, and vibrational degrees of freedom of molecular nitrogen ions including the effects of magnetic fields. The relevant spectroscopic transitions span six orders of magnitude in frequency, illustrating the versatility of the molecular spectrum for encoding quantum information. We identified two types of magnetically insensitive qubits with very low ("stretched"-state qubits) or even zero ("magic" magnetic-field qubits) linear Zeeman shifts. The corresponding spectroscopic transitions are predicted to shift by as little as a few mHz for an amplitude of magnetic-field fluctuations on the order of a few mG, translating into Zeeman-limited coherence times of tens of minutes encoded in the rotations and vibrations of the molecule. We also found that the Q(0) line of the fundamental vibrational transition is magnetic-dipole allowed by interaction with the first excited electronic state of the molecule. The Q(0) transitions, which benefit from small systematic shifts for clock operation and is thus well suited for testing a possible variation in the proton-to-electron mass ratio, were so far not considered in single-photon spectra. Finally, we explored possibilities to coherently control the nuclear-spin configuration of N2+ through the magnetically enhanced mixing of nuclear-spin states.
Ab initio calculations of cross sections and rate constants for elastic scattering and Zeeman relaxation in collisions of $\mathrm{NH}(X{}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}})$ molecules with 3He{}^{3}\mathrm{He}3He atoms in a magnetic field are presented and the mechanism for Zeeman transitions in ground-state ${}^{3}\ensuremath{\Sigma}$ molecules is established. The potential surface for He-NH interaction is obtained using all-electron coupled-cluster calculations with single, double, and noniterative triple excitations in a basis set augmented by bond functions. The ratio of the rates for elastic energy transfer and Zeeman relaxation in NH-3He{}^{3}\mathrm{He}3He collisions exceeds 105{10}^{5}105 at temperatures between 0.50.50.5 and 1 K.
The laser cooling and trapping of molecules have recently been achieved. In this paper, the possibility of precisely measuring the vibrational transition frequencies of optically trapped 40Ca19F molecules is discussed. The quadratic Stark shift induced by the trap laser is eliminated using the trap laser frequencies where the Stark energy shifts at upper and lower states are equal (magic frequencies). At one value of the magic frequency, molecules are trapped at the positions where the power density is minimum, therefore, the measurement is not sensitive to the detuning of the trap laser frequency from the magic frequency. Measurement with an uncertainty of 10−17 appears to be possible using the (v,N,J,F,M)=(0,0,1/2,1,±1)→(1,0,1/2,1,±1)(v,N,J,F,M) = (0,0,1/2,1, \pm 1) \to (1,0,1/2,1, \pm 1)(v,N,J,F,M)=(0,0,1/2,1,±1)→(1,0,1/2,1,±1) transition frequency.
The problem of developing a thermal compensation system in quantum frequency standards based on the effect of coherent population trapping is considered. The development of such a system significantly reduces the temperature coefficient of frequency, the value of which is an order of magnitude higher than in rubidium frequency standards. One of the ways to reduce the temperature coefficient of frequency is temperature compensation. A method of thermal compensation based on the Zeeman effect for the shift of the actual frequency is proposed. A method for determining the minimum value of the magnetic field at which there is no influence of magnetosensitive resonances on the reference resonance is considered. The results of the operation of the quantum frequency standard before and after switching on the thermal compensation system are presented.
Elastic and inelastic collisions between NH\mathrm{NH}NH molecules in the (N=0,J=1)(N=0,J=1)(N=0,J=1) state were analyzed. These analyses showed that the elastic collision is caused mainly by electric dipole-induced dipole interaction, and the inelastic collision is caused mainly by the magnetic dipole-dipole interaction. The collision cross sections obtained by the quantum and classical methods are roughly in good agreement in the kinetic-energy region of 5−−500mK5--500\phantom{\rule{0.3em}{0ex}}\mathrm{mK}5−−500mK. Moreover, the ratio of the inelastic-collision rate to the elastic-collision rate is lower than 1/200. These results show that the NH\mathrm{NH}NH molecule is advantageous to perform evaporative cooling.