arXiv:quant-ph/0303069 · Physical Review Letters

Determination of the s -Wave Scattering Length of Chromium

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

Published Nov 3, 2003• 49 citations

Abstract

We have measured the deca-triplet $s$-wave scattering length of the bosonic chromium isotopes $^{52}\mathrm{C}\mathrm{r}$ and $^{50}\mathrm{C}\mathrm{r}$. From the time constants for cross-dimensional thermalization in ultracold atomic samples, we have determined the magnitudes $|a(^{52}\mathrm{C}\mathrm{r})|=(170\ifmmode\pm\else\textpm\fi{}39){a}_{0}$ and $|a(^{50}\mathrm{C}\mathrm{r})|=(40\ifmmode\pm\else\textpm\fi{}15){a}_{0}$, where ${a}_{0}=0.053\text{ }\mathrm{n}\mathrm{m}$. By measuring the rethermalization rate of $^{52}\mathrm{C}\mathrm{r}$ over a wide temperature range and comparing the temperature dependence with the effective-range theory and numerical single-channel calculations, we have obtained strong evidence that the sign of $a(^{52}\mathrm{C}\mathrm{r})$ is positive. Rescaling our $^{52}\mathrm{C}\mathrm{r}$ model potential to $^{50}\mathrm{C}\mathrm{r}$ strongly suggests that $a(^{50}\mathrm{C}\mathrm{r})$ is positive also.

DOI: 10.1103/physrevlett.91.193201

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arXiv:quant-ph/0303069 · Physical Review Letters

Determination of the s -Wave Scattering Length of Chromium

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

Published Nov 3, 2003• 49 citations

arXiv HTML PDF

Abstract

We have measured the deca-triplet

s

-wave scattering length of the bosonic chromium isotopes

^{52}\mathrm{C}\mathrm{r}

and

^{50}\mathrm{C}\mathrm{r}

. From the time constants for cross-dimensional thermalization in ultracold atomic samples, we have determined the magnitudes

|a(^{52}\mathrm{C}\mathrm{r})|=(170\ifmmode\pm\else\textpm\fi{}39){a}_{0}

and

|a(^{50}\mathrm{C}\mathrm{r})|=(40\ifmmode\pm\else\textpm\fi{}15){a}_{0}

, where

{a}_{0}=0.053\text{ }\mathrm{n}\mathrm{m}

. By measuring the rethermalization rate of

^{52}\mathrm{C}\mathrm{r}

over a wide temperature range and comparing the temperature dependence with the effective-range theory and numerical single-channel calculations, we have obtained strong evidence that the sign of

a(^{52}\mathrm{C}\mathrm{r})

is positive. Rescaling our

^{52}\mathrm{C}\mathrm{r}

model potential to

^{50}\mathrm{C}\mathrm{r}

strongly suggests that

a(^{50}\mathrm{C}\mathrm{r})

is positive also.

DOI: 10.1103/physrevlett.91.193201

Related papers

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Scattering properties of ultra-cold chromium atoms

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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. 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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.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.

Jan 1, 20035 citations

Collisional properties of trapped cold chromium atoms

Zoran Miroslav Pavlovic, Björn Olof Roos, Robin Côté +1 more

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.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.

arXiv:physics/0309076Physical Review AMar 22, 200422 citations

We have measured the deca-triplet

s

-wave scattering length of the bosonic chromium isotopes

^{52}\mathrm{C}\mathrm{r}

and

^{50}\mathrm{C}\mathrm{r}

. From the time constants for cross-dimensional thermalization in ultracold atomic samples, we have determined the magnitudes

|a(^{52}\mathrm{C}\mathrm{r})|=(170\ifmmode\pm\else\textpm\fi{}39){a}_{0}

and

|a(^{50}\mathrm{C}\mathrm{r})|=(40\ifmmode\pm\else\textpm\fi{}15){a}_{0}

, where

{a}_{0}=0.053\text{ }\mathrm{n}\mathrm{m}

. By measuring the rethermalization rate of

^{52}\mathrm{C}\mathrm{r}

over a wide temperature range and comparing the temperature dependence with the effective-range theory and numerical single-channel calculations, we have obtained strong evidence that the sign of

a(^{52}\mathrm{C}\mathrm{r})

is positive. Rescaling our

^{52}\mathrm{C}\mathrm{r}

model potential to

^{50}\mathrm{C}\mathrm{r}

strongly suggests that

a(^{50}\mathrm{C}\mathrm{r})

is positive also.

s

-wave scattering length

{a}_{\mathrm{s}}

for the four highest-abundance isotopes of erbium, in the magnetic field range from 0 to 5 G. We report on cross-dimensional thermalization measurements and apply the Enskog equations of change to numerically simulate the thermalization process and to analytically extract an expression for the so-called number of collisions per rethermalization (NCPR) to obtain

{a}_{\mathrm{s}}

from our experimental data. We benchmark the applied cross-dimensional thermalization technique with the experimentally more demanding lattice modulation spectroscopy and find good agreement for our parameter regime. Our experiments are compatible with a dependence of the NCPR with

{a}_{\mathrm{s}}

, as theoretically expected in the case of strongly dipolar gases. Surprisingly, we experimentally observe a dependency of the NCPR on the density, which might arise due to deviations from an ideal harmonic trapping configuration. Finally, we apply a model for the dependency of the background scattering length with the isotope mass, allowing us to estimate the number of bound states of erbium.

We report the measurement of the deca-heptuplet

s

-partial-wave scattering length

a

of two bosonic isotopes of the highly magnetic element dysprosium:

a=112(10){a}_{0}

for

^{162}\mathrm{Dy}

and

a=92(8){a}_{0}

for

^{164}\mathrm{Dy}

, where

{a}_{0}

is the Bohr radius. The scattering lengths are determined by the cross-dimensional relaxation of ultracold gases of these Dy isotopes at temperatures above quantum degeneracy. In this temperature regime, the measured rethermalization dynamics can be compared to simulations of the Boltzmann equation using a direct-simulation Monte Carlo method employing the anisotropic differential scattering cross section of dipolar particles.

We determine the interspecies

s

-wave triplet scattering length

{a}_{3}

for all K-Rb isotopic mixtures by measuring the elastic cross section for collisions between

^{\mathrm{41}}\mathrm{K}

and

^{87}\mathrm{R}\mathrm{b}

in different temperature regimes. The positive value ${a}_{3}=+{163}_{\ensuremath{-}12}^{+57}{a}_{0}$ ensures the stability against collapse of binary $^{41}\mathrm{K}\ensuremath{-}^{87}\mathrm{R}\mathrm{b}$ Bose-Einstein condensates. For the fermion-boson mixture $^{40}\mathrm{K}\ensuremath{-}^{87}\mathrm{R}\mathrm{b}$, we obtain a large and negative scattering length which implies an efficient sympathetic cooling of the fermionic species down to the degenerate regime.

{940a}_{0}.

{\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.