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Three-Body Recombination in Cold Atomic Gases
PhD-defense by
Peder Klokmose Sørensen
Tuesday September 17th, 2013
|
Supervisors:
Dmitri V. Fedorov
Aksel S. Jensen
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Department of Physics
and Astronomy
Aarhus University
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Outline
-
Introduction
-
Hyperspherical description
-
Zero-range models
-
Three-body recombination rate
-
Finite temperature effects
-
Mass-imbalanced systems
Introduction
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The problem:
- System of cold atoms in a trap
- Interactions lead to losses
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The question:
- How to describe the interactions?
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The fun part:
- Three-body physics
- Efimov physics
|
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The guy:
Vitaly Efimov
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r12
r23
r13
1
2
3
x1
y1
x2
y2
x3
y3
Jacobi coordinates
Hyper-spherical coordinates
|
| Cartesian coordinates |
Jacobi coordinates |
|
|
\[
\rho^2=x_i^2+y_i^2\quad,\quad
\rho\sin(\alpha_i)=x_i\quad,\quad
\rho\cos(\alpha_i)=y_i
\]
Hyper-spherical coordinates II
\(\alpha\qquad\quad\;\pi\)
\(\rho\qquad\; r_0\)
Zero-range models
\(\psi=cx+d\)
\(=c\left(x+\dfrac{d}{c}\right)\)
\(\propto x-a\)
\(\dfrac{\psi'}{\psi\phantom{'}}\bigg\vert_{x\,=\,0}\)
\(=-\dfrac{1}{a}\)
\(+\dfrac{1}{2}Rk^2\)
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\(-\left\vert E_T^{(n)}\dfrac{2ma_0^{2}}{\hbar^2}\right\vert^{1/8}\)
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Efimov spectrum
|
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\(\textrm{sign}(a)\times\left\vert\dfrac{a_0^2}{a^2}\right\vert^{1/8}\)
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rvdW /a(-)
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Three-body parameter
|
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log10(sres)
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Three-body recombination
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Three particles collide...
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... and form a dimer and a free particle
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All particles are lost at a rate given by
\(\dot n = -\alpha_\text{rec}n^3\)
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αrec [cm6/s]
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Three-body recombination rate
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a[a0] |
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[1] Pollack et. al. Science vol. 326 [2009]
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\(\dfrac{\nu_1^2-\frac{1}{4}}{2(\rho/a)^2}\)
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Optical potential model
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ρ /|a| |
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αrec [cm6/s]
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Finite temperature effects
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a[a0] |
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[1] Pollack et. al. arXiv:1302.0281v2
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Mass-imbalanced systems
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-
For instance the system of
133Cs – 7Li
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Mass ratio of ~19 fairly large
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Scaling ratio reduced down to ~4.8
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This leads to almost twice as many interference features in any
given scattering length range for for the equal mass system
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αrec [ cm6/s ]
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Mass imbalanced recombination rate
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a [ a0 ]
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Thank you for your attention