Sisyphus cooling

Sisyphus cooling (rarely also Sisyphos cooling ) or polarization gradient cooling is a special form of laser cooling in laser spectroscopy , with which temperatures lower than the Doppler temperature can be reached.

history

This cooling method was first proposed in 1989 by Claude Cohen-Tannoudji , for which he received the 1997 Nobel Prize in Physics . The name is derived from the Greek hero Sisyphus , who had to carry a stone up the same mountain over and over again, from where it rolled down again.

construction

To implement Sisyphus cooling, a linearly polarized laser is superimposed on itself in the opposite direction with the polarization rotated by 90 °. This creates a standing wave of laser light , the polarization of which changes periodically in space and alternates between -, - and - polarization. This state is also referred to as a lin lin arrangement ( linear-perpendicular-linear ). The atoms to be cooled must move in and along the laser beam. ${\ displaystyle \ sigma ^ {+}}$ ${\ displaystyle \ pi}$ ${\ displaystyle \ sigma ^ {-}}$ ${\ displaystyle \ bot}$

Physical basics

Basic process in Sisyphus cooling: The atoms run against the potential, are excited, fall back into a potential minimum and start over.
The transition from blue to red on the left corresponds a little later to the transition from red to blue on the right.

The areas of the laser with -light induce a transition with , whereas the -light causes a transition with . Since the spontaneous emission does not cause any change ( ) on average after the excitation , the atoms are thus sent from one degenerate state of the ground state to the other. Since the atom moves along the beam, it then reaches the other polarization and is returned to its original state. The state of the atom thus always oscillates between the two degeneracies of the ground state. ${\ displaystyle \ sigma ^ {+}}$ ${\ displaystyle \ Delta m = + 1}$ ${\ displaystyle \ sigma ^ {-}}$ ${\ displaystyle \ Delta m = -1}$ ${\ displaystyle \ Delta m = 0}$

Furthermore, the Stark effect , which is caused by the electric field of the laser on the atom, is dependent on the transition probability between the energy levels and the detuning . This means that the energy levels of the atom with a greater transition probability move further apart energetically than the levels with a lower transition probability. If the mood is red, the energy of the basic state drops. However, since the polarization also changes, the transition probability also changes - depending on which of the two basic states the atom is in.

An atom in the ground state moving along the laser must run against the potential of the standing wave (transition from the first to the second blue point, left in the adjacent drawing). In doing so, it gains potential energy , but loses kinetic energy , which corresponds to cooling. At the maximum of the wave crest, the absorption probability of -light is at its maximum, the atom is therefore very likely to be placed in the excited state with , through spontaneous emission it then goes into the ground state with and the process begins again, this time with -light. ${\ displaystyle m = -1 / 2}$ ${\ displaystyle \ sigma ^ {+}}$ ${\ displaystyle m = + 1/2}$ ${\ displaystyle m = + 1/2}$ ${\ displaystyle \ sigma ^ {-}}$

The theoretical limit of the temperature with Sisyphus cooling is in the one-dimensional case at the recoil temperature

{\ displaystyle T _ {\ text {recoil}} = {\ frac {(\ hbar k) ^ {2}} {2k _ {\ mathrm {B}} m}}}

with the momentum of the emitted photons , the Boltzmann constant and the atomic mass . These temperatures are in the microkelvin range . Since this temperature depends on the photon pulse, lower temperatures can be achieved by making the laser more red. However, the detuning must also not be selected too large, since otherwise the cooling performance will decrease overall, because the likelihood of excitation decreases with the detuning. ${\ displaystyle \ hbar k}$ ${\ displaystyle k _ {\ mathrm {B}}}$ ${\ displaystyle m}$

Further information

Wolfgang Demtröder: Laser Spectroscopy . 5th edition. Springer, Kaiserslautern 2007, ISBN 978-3-540-33792-8 .

Tobias Müther: Evaporative cooling in optical dipole potentials

Individual evidence

^ J. Dalibard, C. Cohen-Tannoudji: Laser cooling below the Doppler limit by polarization gradients: Simple theoretical model . In: J. Opt. Soc. At the. tape 6 , 1989, pp. 2023 .
^ Nobelprize.org: The Nobel Prize in Physics 1997

[1] J. Dalibard, C. Cohen-Tannoudji: Laser cooling below the Doppler limit by polarization gradients: Simple theoretical model . In: J. Opt. Soc. At the. tape 6 , 1989, pp. 2023 .

[2] Nobelprize.org: The Nobel Prize in Physics 1997