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European Quantum Electronics Conference (EQEC)

Collisional properties of a dipolar gas of ultracold chromium atoms

S. Hensler, Piet O. Schmidt, J. Werner, Axel Griesmaier, Axel Görlitz, Tilman Pfau

Published Jan 1, 2003• 0 citations
Publisher

Abstract

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.

DOI
10.1109/eqec.2003.1314133

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Scattering properties of ultra-cold chromium atoms

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•Jan 1, 2003•5 citations

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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

Collisional properties of trapped cold chromium atoms

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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 ${\text{Cr}}_{2}$ and the van der Waals coefficient ${C}_{6}$, 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 $s$-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.

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All-optical Bose-Einstein condensation of chromium atoms and rf spectroscopy of cold Cr{sub 2} molecules

Quentin Beaufils, Radu Chicireanu, T. Zanon-Willette +5 more

Full text: The study of quantum gases made of chromium atoms is compelling for several reasons. Being accessible to laser manipulation, chromium has a most abundant bosonic isotope {sup 52}Cr and a 9-percent abundant fermionic isotope {sup 53}Cr. Most importantly, Cr atoms carry an exceptionally large magnetic moment of 6 {mu}{sub B}. Consequently, Cr provides a valuable tool to study the physics of dipolar quantum gases as demonstrated elsewhere. We present our recent achievement of a chromium Bose-Einstein Condensation (Cr-BEC) using an all-optical procedure along with two innovative techniques: continuous accumulation of metastable {sup 52}Cr atoms in a mixed optical and magnetic trap; fast and intense rf sweeps to average to zero the magnetic potential and optimize the transfer efficiency from the Cr-MOT to the optical trap. We also report on the rf spectroscopy and association of weakly bound Cr{sub 2} molecules in the decatriplet {sup 13}{sigma}{sub g}{sup +} state. These latter experiments are performed in the vicinity of a d-wave Feshbach resonance at low magnetic field. Though the association rate is at present fairly low, we can study the spectroscopic properties of these cold trapped high-spin chromium molecules. (author)

•Jul 1, 2008•0 citations
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 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.
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.
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. ^
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.
Due to its large magnetic moment of 6 muB, atomic chromium is the only Bose-Einstein condensed species so far to show relatively large magnetic dipole-dipole interactions (MDDI) besides the usual s-wave contact interaction. The long-range (1/r3) and anisotropic character of the MDDI gives birth to unique properties for the Cr Bose-Einstein condensate obtained recently in our group. In particular, it leads to an anisotropic deformation of the expanding condensate which depends on the orientation of the atomic dipole moments (Giovanazzi et al., 2006). In these measurements the dominant interaction is the contact one. We used expansion dynamics measurements to quantify the ratio between dipolar and contact interactions to be epsivdd= 0.159 plusmn 0.034 . This in turn provides a new experimental determination of the chromium scattering length: a = (96 plusmn 20) a0with an accuracy which is not limited by errors in the measurement of the atom number.
Full text: The study of quantum gases made of chromium atoms is compelling for several reasons. Being accessible to laser manipulation, chromium has a most abundant bosonic isotope {sup 52}Cr and a 9-percent abundant fermionic isotope {sup 53}Cr. Most importantly, Cr atoms carry an exceptionally large magnetic moment of 6 {mu}{sub B}. Consequently, Cr provides a valuable tool to study the physics of dipolar quantum gases as demonstrated elsewhere. We present our recent achievement of a chromium Bose-Einstein Condensation (Cr-BEC) using an all-optical procedure along with two innovative techniques: continuous accumulation of metastable {sup 52}Cr atoms in a mixed optical and magnetic trap; fast and intense rf sweeps to average to zero the magnetic potential and optimize the transfer efficiency from the Cr-MOT to the optical trap. We also report on the rf spectroscopy and association of weakly bound Cr{sub 2} molecules in the decatriplet {sup 13}{sigma}{sub g}{sup +} state. These latter experiments are performed in the vicinity of a d-wave Feshbach resonance at low magnetic field. Though the association rate is at present fairly low, we can study the spectroscopic properties of these cold trapped high-spin chromium molecules. (author)