It is important to consider heating effects within dipole traps and guides. These heating effects fall into two categories: heating due to scattering and viscous heat- ing effects.
Heating due to scattering
An important consideration for atoms held within an optical potential is the effect of resonant scattering. Although resonant scattering is intentionally exploited to cool and trap atoms before they are loaded into the trap, scattering acts to heat the cooled atoms once they are within the guide or trap.
For dipole traps, the momentum kick from both the absorption and spontaneous emission of photons will cause heating. As a result of the cooling cycle, the heating effect is more pronounced in the longitudinal direction, as the atoms will accumulate momentum in the direction of the beam’skvector for each absorption. We can approximate this change in momentum as a 1-D change in temperature for
nscattering events, given by,
T = n~
2k2
mkB
(2.25)
wheremis the mass of the atom, which for rubidium-85 is1.4114×10−25kg. Although this longitudinal heating can be extremely detrimental to dipole traps, where the atom is confined in 3-D, it can be less of an issue in optical guides, where the atom is only confined in 2-D. In guide experiments, the k vector of the guide is usually in the same plane as the desired direction of motion of the atoms, so the momentum push may be exploited to accelerate or decelerate atoms through the guide.
Heating due to the spontaneous emission part of the cooling cycle can also be an issue for shallow guides. Although the spontaneous emission will be in a ran-
dom direction, and as a result the net change in momentum due to spontaneous emission for many absorption/spontaneous emission cycles will tend to zero, the magnitude of the individual recoils may be enough to impart enough energy to kick an atom out of a shallow guide. Each spontaneous emission will change the atoms temperature by Trecoil = ~2k2/mkB so we can neglect spontaneous emis-
sion heating effects for guides and traps with a potential depthUdipole ≫Trecoil.
Viscous heating
Another source of heating in the transverse direction is from an effect known as viscous heating and is explained in figure 2.10. Viscous heating results from the difference in sign of the AC-Stark shift for the ground state and the excited state. Consequently, a ground state atom will be attracted to the intensity maximum of the beam whereas an excited atom will be repelled from the intensity maximum of the beam. Therefore, if a ground state atom initially at rest at the centre of the beam is excited to an excited state, it will be then be repelled from the region of high intensity gaining kinetic energy. The atom will then undergo a spontaneous emission returning to the ground state and then be attracted to the region of high intensity again, gaining kinetic energy.
Minimising heating effects
While both the depth of the dipole trap and the scattering rate are proportional to the intensity of the light, the dependency on laser detuning is different. The scattering rate, a resonant effect, has a dependency 1/δ2 while the dipole force however has a dependency of1/δ. Consequently heating effects can be minimised by choosing a laser frequency far away from resonance. Neglecting any other factors, for a desired optical potential depth, it is beneficial to choose the furthest detuningδthat still yields a large enough potential well. In practice the magnitude of δ will be limited by the available power of the laser. In some cases, where a radiation pressure force may be required to push atoms along a guide, the detuning may be kept deliberately low.
∆KE=−∆Udipole Absorption of photon Ee Eg E n er g y (a rb . u n it s)
Position (arb. units)
Spontaneous emission of photon Eg
Ee
∆KE=−∆Udipole
Kinetic energy of atom at start isKE
Kinetic energy of atom at end is Ee Eg E n er g y (a rb . u n it s) Eg Ee
Position (arb. units)
KE+ 2∆KE=KE+ 2|∆Udipole|
Position (arb. units)
B ea m in te n si ty (a rb . u n it
s) Gaussian intensity profile
Figure 2.10: A graphical representation of viscous heating. Proportional to the intensity of light, the AC-Stark shift acts to lower the potential energy of the atom in the ground state and raise the potential energy of an atom in the excited state. The potential energy shift is given in equation 2.9. A ground state atom situated in the centre of the beam will be at the bottom of the potential well. If the atom enters an excited state by absorbing a photon, it will find itself now at the top of a potential hill. The atom will move down the hill away from the region of high optical intensity, gaining kinetic energy equal to−∆Udipole, until it returns to the ground state by a spontaneous emission. Once in the ground state, the atom will roll down the potential well towards the region of high intensity. Once it reaches its original position it will have gained kinetic energy equal to−2∆Udipole. In the worst case scenario, the atom will gain the full potential of the excited state as kinetic energy before decaying to the ground state and gaining the full potential of the ground state. The kinetic energy of the atom will now be twice the potential energy of the guide and will escape the guide.
Chapter 3
L
ASER
,
SPECTROSCOPY AND
VACUUM SYSTEMS
3.1
Chapter synopsis
This chapter details the laser systems and vacuum procedures used as part of the atom guiding experiments described in chapters 4, 5 and 6. The extended cavity diode lasers, Doppler-free saturated absorption spectroscopy setup and frequency locking technique used to create a magneto-optical trap of rubidium-85 are de- scribed. A master-slave configuration is detailed which was used to increase the power available for the cooling transition. The Ti:sapphire laser that was used for the optical guides is detailed. I then explain briefly the vacuum requirements and how our ultra-high vacuum systems were prepared and evacuated.