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Physical Review A

Spin depolarization of N2+ (Σ2+) in collisions with H3e and H4e in a magnetic field

Grégoire Guillon, Thierry Stoecklin, A. Voronin

Published Apr 22, 2008• 13 citations
Publisher

Abstract

We study the effect of a magnetic field on the spin-depolarization cross sections of $\text{N}_{2}{}^{+}(^{2}\ensuremath{\Sigma})$ in collisions with $^{3}\text{H}\text{e}$ and $^{4}\text{H}\text{e}$ at very low collision energy. The fundamental states of the two nuclear spin isomers of $\text{N}_{2}{}^{+}$ are shown to respond quite differently to the application of the field. When the applied magnetic filed increases, the spin-depolarization cross sections are found to monotonously decrease for the fundamental paralevel $N=0$ of $\text{N}_{2}{}^{+}$ whereas they monotonously increase for the fundamental ortholevel $N=1$ of $\text{N}_{2}{}^{+}$. This effect is found to be amplified around the resonances and an explanation based on the different mechanism of spin flipping acting for these two levels is proposed. We discuss the sensitivity of the results on the change of relative mass when $^{3}\text{H}\text{e}$ is replaced by $^{4}\text{H}\text{e}$. We also explore the tuning of the inelastic cross sections by examining the variation of the scattering length as a function of the magnetic field and locate several narrow Feshbach resonances.

DOI
10.1103/physreva.77.042718

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We present an accurate quantum mechanical study of molecule–molecule collisions in the presence of a magnetic field. The work focuses on the analysis of elastic scattering and spin relaxation in collisions of O 2 ( 3 Σ g – ) molecules at cold (∼0.1 K) and ultracold (∼10 –6 K) temperatures. Our calculations show that magnetic spin relaxation in molecule–molecule collisions is extremely efficient except at magnetic fields below 1 mT. The rate constant for spin relaxation at T =0.1 K and a magnetic field of 0.1 T is found to be as large as 6.1 × 10 –11 cm –3 s –1 . The magnetic field dependence of elastic and inelastic scattering cross sections at ultracold temperatures is dominated by a manifold of Feshbach resonances with the density of ∼100 resonances per Tesla for collisions of molecules in the absolute ground state. This suggests that the scattering length of ultracold molecules in the absolute ground state can be effectively tuned in a very wide range of magnetic fields. Our calculations demonstrate that the number and properties of the magnetic Feshbach resonances are dramatically different for molecules in the absolute ground and excited spin states. The density of Feshbach resonances for molecule–molecule scattering in the low-field-seeking Zeeman state is reduced by a factor of 10.

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We study the effect of a magnetic field on the spin-depolarization cross sections of N2+(2\ensuremathΣ)\text{N}_{2}{}^{+}(^{2}\ensuremath{\Sigma})N2​+(2\ensuremathΣ) in collisions with 3He^{3}\text{H}\text{e}3He and 4He^{4}\text{H}\text{e}4He at very low collision energy. The fundamental states of the two nuclear spin isomers of N2+\text{N}_{2}{}^{+}N2​+ are shown to respond quite differently to the application of the field. When the applied magnetic filed increases, the spin-depolarization cross sections are found to monotonously decrease for the fundamental paralevel N=0N=0N=0 of N2+\text{N}_{2}{}^{+}N2​+ whereas they monotonously increase for the fundamental ortholevel N=1N=1N=1 of N2+\text{N}_{2}{}^{+}N2​+. This effect is found to be amplified around the resonances and an explanation based on the different mechanism of spin flipping acting for these two levels is proposed. We discuss the sensitivity of the results on the change of relative mass when 3He^{3}\text{H}\text{e}3He is replaced by 4He^{4}\text{H}\text{e}4He. We also explore the tuning of the inelastic cross sections by examining the variation of the scattering length as a function of the magnetic field and locate several narrow Feshbach resonances.
We give a brief account of the effect of a magnetic field on the spin-depolarization cross sections of N2 +(2Σ) in collisions with 3He at very low collision energy. The fundamental states of the two nuclear spin isomers of N2 + are shown to respond quite differently to the application of the field. When the applied magnetic field increases, the spin depolarization cross sections are found to monotonously decrease for the fundamental para level N=0 of N2 +, whereas they monotonously increase for the fundamental ortho level N=1 of N2 +. This effect is found to be amplified around the resonances and an explanation based on the different mechanism of spin flipping acting for these two levels is proposed. We also explore the tuning of zero energy Feshbach resonances by examining the variation of the scattering length as a function of the magnetic field. We use the Smith Q matrix to calculate the lifetimes of the complexes associated with these resonances and discuss the law of variation as a function of the magnetic field of the Q matrix eigenvalues across such resonances.
We have carried out bound-state and low-energy quantum scattering calculations on He + NH (triplet Sigma) in magnetic fields, with the NH molecule in its n=1 rotationally excited states. We have explored the pattern of levels as a function of magnetic field and identified the nearly good quantum numbers in different regimes. We have used the bound-state calculations to locate low-energy Feshbach resonances. When the magnetic field is used to tune across such a resonance, the real and imaginary part of the scattering length show asymmetric oscillations and peaks with amplitude between 1 and 3 Angstroms. The scattering length does not pass through a pole at resonance. The resonant behavior is characterized by a complex resonant scattering length a_res. The corresponding inelastic cross sections show troughs as well as peaks near resonance. This may be important for efforts to achieve evaporative and sympathetic cooling for molecules, because it offers the hope that inelastic trap losses can be reduced by tuning close to a Feshbach resonance.
We have generalized the BOUND and MOLSCAT packages to allow calculations in basis sets where the monomer Hamiltonians are off diagonal and used this capability to carry out bound-state and scattering calculations on $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$ and $^{4}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$ as a function of magnetic field. Following the bound-state energies to the point where they cross thresholds gives very precise predictions of the magnetic fields at which zero-energy Feshbach resonances occur. We have used this to locate and characterize two very narrow Feshbach resonances in $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$. Such resonances can be used to tune elastic and inelastic collision cross sections, and sweeping the magnetic field across them will allow a form of quantum control in which separated atoms and molecules are associated to form complexes. For the first resonance, where only elastic scattering is possible, the scattering length shows a pole as a function of magnetic field and there is a very large peak in the elastic cross section. For the second resonance, however, inelastic scattering is also possible. In this case the pole in the scattering length is dramatically suppressed and the cross sections show relatively small peaks. The peak suppression is expected to be even larger in systems with stronger inelasticity. The results suggest that calculations on ultracold molecular inelastic collisions may be much less sensitive to details of the potential energy surface than has been believed.
Cross sections for relaxation of circular and linear polarization of 62P326^{2}P_{\frac{3}{2}}62P23​​ cesium atoms, induced in collisions with ground-state He, Ne, Ar, and Xe, have been determined by Zeeman scanning techniques. A fluorescence cell containing low-pressure cesium vapor together with a buffer gas was irradiated with circularly or linearly polarized 8521-\AA{} Cs resonance radiation, producing excited and polarized Cs atoms which became depolarized in subsequent collisions with the buffer-gas atoms. The resulting depolarization of the cesium resonance fluorescence was monitored in relation to buffer-gas pressure (0-10 Torr) and to the strength of the ambient magnetic field (0-10 kG). At low fields at which the nuclear spin $\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}$ is coupled to the electronic angular momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$, the measurements yielded depolarization cross sections Q(circ.)Q(\mathrm{circ}.)Q(circ.) and Q(lin.)Q(\mathrm{lin}.)Q(lin.), which agree within experimental error with theoretical values calculated for spin-coupled conditions. At kilogauss fields with $\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}$ and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$ decoupled, the experiments produced cross sections for disorientation and disalignment, which are also in satisfactory agreement with the appropriate theoretical predictions. The results indicate that the nuclear spin has a more pronounced effect on the collisional relaxation of the atomic dipole than of the quadrupole.
We investigate the effect of hyperfine interactions on ultracold molecular collisions in magnetic fields, using 24{}^{24}24Mg(1S)+14{}^{1}S){+}^{14}1S)+14NH(${}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}}$) as a prototype system. We explore the energy and magnetic-field dependence of the cross sections, comparing the results with previous calculations that neglected hyperfine interactions [A.O.G. Wallis and J. M. Hutson, Phys. Rev. Lett. 103, 183201 (2009)]. The main effect of hyperfine interactions for spin relaxation cross sections is that the kinetic energy release of the dominant outgoing channels does not reduce to zero at low fields. This results in reduced centrifugal suppression of the cross sections and increased inelastic cross sections at low energy and low field. We also analyze state-to-state cross sections, for various initial states, and show that hyperfine interactions introduce additional mechanisms for spin relaxation. In particular, there are hyperfine-mediated collisions to outgoing channels that are not centrifugally suppressed. However, for Mg+NH\mathrm{Mg}+\mathit{NH}Mg+NH these unsuppressed channels make only small contributions to the total cross sections. We consider the implications of our results for sympathetic cooling of NH by Mg and conclude that the ratio of elastic to inelastic cross sections remains high enough for sympathetic cooling to proceed.
We present an accurate quantum mechanical study of molecule–molecule collisions in the presence of a magnetic field. The work focuses on the analysis of elastic scattering and spin relaxation in collisions of O 2 ( 3 Σ g – ) molecules at cold (∼0.1 K) and ultracold (∼10 –6 K) temperatures. Our calculations show that magnetic spin relaxation in molecule–molecule collisions is extremely efficient except at magnetic fields below 1 mT. The rate constant for spin relaxation at T =0.1 K and a magnetic field of 0.1 T is found to be as large as 6.1 × 10 –11 cm –3 s –1 . The magnetic field dependence of elastic and inelastic scattering cross sections at ultracold temperatures is dominated by a manifold of Feshbach resonances with the density of ∼100 resonances per Tesla for collisions of molecules in the absolute ground state. This suggests that the scattering length of ultracold molecules in the absolute ground state can be effectively tuned in a very wide range of magnetic fields. Our calculations demonstrate that the number and properties of the magnetic Feshbach resonances are dramatically different for molecules in the absolute ground and excited spin states. The density of Feshbach resonances for molecule–molecule scattering in the low-field-seeking Zeeman state is reduced by a factor of 10.