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Physical Review A

Magnetic Feshbach resonances and Zeeman relaxation in bosonic chromium gas with anisotropic interaction

Zoran Miroslav Pavlovic, Roman V. Krems, Robin Côté, H. R. Sadeghpour

Published Jun 6, 2005• 38 citations
Publisher

Abstract

Rigorous calculations of magnetic Feshbach resonances and Zeeman relaxation cross sections in an ultracold and cold chromium gas are reported. This work presents the calculation of such inelastic processes in collisions of atoms with large magnetic moments. Using our recently constructed accurate interaction potentials for the chromium dimer, we compute the positions and widths of magnetically tuned resonances in an optically trapped ultracold Cr gas. We find good agreement with recent experimental data and report that spin-change collision cross sections quickly increase with decreasing collision energy and magnetic-field strength at energies below 1 K and magnetic fields larger than 40 G.

DOI
10.1103/physreva.71.061402

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In this dissertation, I present ab initio theoretical results on cold and ultra-cold collision of atomic and molecular systems with magnetic and electric dipole moments. The collisions of different isotopes of maximally spin-polarized chromium atoms (52Cr and 53Cr), alkali-metal atom (Rb) - chromium atom, and magnetically trapped hydroxide (OH) with cold supersonic helium beam are considered in this thesis. Spin-changing cross sections and rate constants in Cr-Cr isotopic collision in the presence of a magnetic field are calculated by propagating a set of multichannel equations in the field. The coupling between dipole-dipole allowed and hyperfine channels are included. The short range electrostatic interactions between atoms and atom-molecule are represented with highly-accurate Born-Oppenheimer (BO) potential energy curves. Due to the large spin multiplicity in Cr-Cr and Rb-Cr interactions, more than the usual singlet and triplet channels are obtained. The long-range van der Waals (vdW) interactions between atoms are calculated, for Cr, by including accurate transition frequencies, discrete dipole matrix elements, and photoionization continuum oscillator strengths, and for Rb, using published dynamic polarizabilities. The vdW coefficients for Cr-Cr and Rb-Cr are obtained. In the cold collision regime, I investigate the influence of angular momentum shape resonances on the elastic and inelastic (loss channel) rate coefficients, and when the Zeeman relaxation, resulting in the loss of atoms from the trap, dominates elastic collision. Dipolar collisions are crucial to achieving quantum degeneracy. Magnetically tuned Fano-Feshbach closed-channel resonances are used to obtain zero-energy scattering lengths in comparison with observation of trap loss. In bosonic chromium collisions, resonances appear due only to dipolar interaction. The interplay between hyperfine and dipolar resonances in mixed-species Cr-Cr and Rb-Cr collisions is studied. In Rb-Cr, it is found that the molecule has broken symmetry and therefore contains a large permanent electric dipole moment in the ground state. A recent collisional experiment at JILA of a supersonic helium beam with a magnetically trapped OH radical found the onset of a quantum threshold in the total OH loss rate. Using ab initio BO energy surfaces, I calculated the spin-changing collisions which removed OH from the trap. Only after including the effect of the trapping potential on the collision dynamics, some agreement with observation was found. ^

•Jan 1, 2011•1 citation
Rigorous calculations of magnetic Feshbach resonances and Zeeman relaxation cross sections in an ultracold and cold chromium gas are reported. This work presents the calculation of such inelastic processes in collisions of atoms with large magnetic moments. Using our recently constructed accurate interaction potentials for the chromium dimer, we compute the positions and widths of magnetically tuned resonances in an optically trapped ultracold Cr gas. We find good agreement with recent experimental data and report that spin-change collision cross sections quickly increase with decreasing collision energy and magnetic-field strength at energies below 1 K and magnetic fields larger than 40 G.
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.
We report on experiments with ultracold chromium atoms. Preparing a cloud of 52Cr atoms in a crossed optical dipole trap (CODT) and applying magnetic fields between 4 and 600 G, we observe 14 Feshbach resonances by the occurrence of increased atom loss at distinct magnetic field values. A comparison with theory taking only dipole–dipole coupling into account shows very good agreement between experimental and theoretical resonance positions and allows us to extract the s-wave scattering lengths a 6=112(14) a 0, a 4= 58(6) a 0, a 2=−7(20) a 0 of the involved molecular potentials as well as the dispersion coefficients C 6= 733(70) au and au. The strongest resonance at 589 G has a calculated width of 1.7 G and reveals a three-body loss coefficient below L 3, max∼3×10−36 m6 s−1. Further evaporative cooling within the CODT leads to the formation of a Bose–Einstein condensate (BEC) with up to 100 000 condensed atoms. The magnetic dipole–dipole interaction between the Cr atoms is so strong that, as a first mechanical manifestation of dipole–dipole interaction, we observe a modification of the condensate expansion which depends on the alignment of the atomic magnetic dipoles with respect to the axis of the CODT. This magnetostrictive effect is in very good agreement with the theory of dipolar quantum gases and shows that a Cr-BEC is an excellent model system to study dipole–dipole interactions in degenerate quantum gases.
We report on calculations of the elastic cross section and thermalization rate for collision between two maximally spin-polarized chromium atoms in the cold and ultracold regimes, relevant to buffer-gas and magneto-optical cooling. We calculate ab initio potential-energy curves for Cr2{\text{Cr}}_{2}Cr2​ and the van der Waals coefficient C6{C}_{6}C6​, and construct interaction potentials between two colliding Cr atoms. We explore the effect of shape resonances on the elastic cross section, and find that they dramatically affect the thermalization rate. Our calculated value for the sss-wave scattering length is compared in magnitude with a recent measurement. We propose that a dip in the elastic rate coefficient could be experimentally exploited to obtain an accurate value for the scattering length.
In this work a gas of ultra-cold chromium atoms in a magnetic trap has been prepared and its elastic and inelastic scattering properties have been investigated with regard to Bose-Einstein condensation. Bose-Einstein condensation of dilute atomic gases is achieved using different cooling and trapping techniques. Deviating from the standard way we were able to devise a continuous loading mechanism for a magnetic trap as a result of the spectroscopic properties and the large magnetic dipole moment of chromium. It not only allows us to trap more atoms but also facilitates the subsequent preparation steps. After loading, the magnetic trap is compressed to increase the atomic density. In doing so we also increases the temperature of the atomic cloud. Doppler cooling of the atoms in the compressed trap reduces the temperature and increases the density. Subsequent evaporative cooling further reduces the temperature. The efficiency of the cooling mechanism is determined by the elastic and inelastic scattering properties of atomic species. Ultra-cold collisions between ground state atoms are dominated by s-wave collisions. They are characterized by a single parameter, the scattering length a. We were able to determine the temperature dependence of the elastic collision rate for the two bosonic isotopes 52Cr and 50Cr in a relaxation experiment. Comparing our results with the effective range theory allowed us not only to extract the magnitude of the scattering length, but also its sign. The sign of the scattering length is important since only condensates with a positive scattering length are stable. Our efforts to achieve Bose-Einstein condensation in chromium by evaporative cooling in a magnetic trap resulted in a maximum phase space density of 0.04. Further cooling reduced the phase space density due to increased loss of atoms from dipolar relaxation. We were able to obtain preliminary results on the magnetic field dependence of dipolar relaxation. Our experimental data is in excellent agreement with theory. These experiments confirm the theoretical prediction that the dipolar relaxation rate is independent from the details of the interaction potential but rather scales with the magnetic offset field and the magnetic dipole moment of the atoms. The findings of this work mark an important step towards the realization of a Bose-Einstein condensate with chromium atoms. Especially the knowledge of the elastic and inelastic scattering properties allow now to devise a successful strategy.
Temperature dependence of the cross-section for elastic ground-state collisions of /sup 52/Cr- and /sup 50/Cr-atoms using the method of cross-dimensional relaxation, respectively is determined. The corresponding absolute values of the scattering length are on the order of 100a/sub 0/ for /sup 52/Cr and /sup 50/a/sub 0/ for /sup 50/Cr, respectively. However, to use evaporative cooling to increase the phase space density and achieve Bose-Einstein condensation with chromium atoms, have been limited to values below 10/sup -2/. Unusuually high inelastic collisio rates due to dipolar relaxation cause atom loss and heating of the sample. These losses are investigated and found similar magnetic-field-dependent rate coefficients (/spl ap/10/sup -11/ cm/sup 3//s @ 50 G offset field) for the two isotopes /sup 50/Cr and /sup 52/Cr indicating that the strongly enhanced dipolar relaxation is a generic feature of the dipole-dipole interaction. This conclusion is supported by theoretical calculations. To circumvent these losses, an optical dipole trap is currently being set up. Here, chromium can be trapped in the energetically lowest state where dipolar relaxation is absent.
In this dissertation, I present ab initio theoretical results on cold and ultra-cold collision of atomic and molecular systems with magnetic and electric dipole moments. The collisions of different isotopes of maximally spin-polarized chromium atoms (52Cr and 53Cr), alkali-metal atom (Rb) - chromium atom, and magnetically trapped hydroxide (OH) with cold supersonic helium beam are considered in this thesis. Spin-changing cross sections and rate constants in Cr-Cr isotopic collision in the presence of a magnetic field are calculated by propagating a set of multichannel equations in the field. The coupling between dipole-dipole allowed and hyperfine channels are included. The short range electrostatic interactions between atoms and atom-molecule are represented with highly-accurate Born-Oppenheimer (BO) potential energy curves. Due to the large spin multiplicity in Cr-Cr and Rb-Cr interactions, more than the usual singlet and triplet channels are obtained. The long-range van der Waals (vdW) interactions between atoms are calculated, for Cr, by including accurate transition frequencies, discrete dipole matrix elements, and photoionization continuum oscillator strengths, and for Rb, using published dynamic polarizabilities. The vdW coefficients for Cr-Cr and Rb-Cr are obtained. In the cold collision regime, I investigate the influence of angular momentum shape resonances on the elastic and inelastic (loss channel) rate coefficients, and when the Zeeman relaxation, resulting in the loss of atoms from the trap, dominates elastic collision. Dipolar collisions are crucial to achieving quantum degeneracy. Magnetically tuned Fano-Feshbach closed-channel resonances are used to obtain zero-energy scattering lengths in comparison with observation of trap loss. In bosonic chromium collisions, resonances appear due only to dipolar interaction. The interplay between hyperfine and dipolar resonances in mixed-species Cr-Cr and Rb-Cr collisions is studied. In Rb-Cr, it is found that the molecule has broken symmetry and therefore contains a large permanent electric dipole moment in the ground state. A recent collisional experiment at JILA of a supersonic helium beam with a magnetically trapped OH radical found the onset of a quantum threshold in the total OH loss rate. Using ab initio BO energy surfaces, I calculated the spin-changing collisions which removed OH from the trap. Only after including the effect of the trapping potential on the collision dynamics, some agreement with observation was found. ^