The motivation for reducing the MOT size in the previous section was to confine the atoms to a region of strong coupling. However, as shown in Figure 5.8, reducing the MOT beam detuning alone is not enough to keep atoms in the coupling beam. We see the cloud either sagging to a position below the peak coupling beam intensity (when blue-detuned), or simply failing to trap (when red-detuned) for the desired coupling beam detunings. Several approaches have been considered to address this:
Increasing the magnetic field gradient to more tightly confine the cloud to the coupling beam region.
Using a larger coupling beam width, reducing the peak AC Stark shift and AC Stark shift gradient but sacrificing Rabi frequency and thus interaction strength. Smoothly increasing the coupling beam intensity over time. Whilst this does not
change the final resonance condition it avoids a step-change in resonance condition, allowing atoms to reach a new equilibrium rather than falling under gravity. Changing the MOT beam detuning when the coupling beam is turned on, to com-
pensate the AC Stark shift.
We prefer to keep our choice of Rydberg state based on the achievable coupling strength and interaction strength. However, we do note that going to higher n will reduce our coupling strength, reducing the perturbation due to the AC Stark shift, but also increasing
the interaction length scale, allowing us to move beyond the two-body dressed interactions case.
The most effective technique that we have used to keep atoms in the coupling beam when using blue-detuned coupling light is to compensate the AC Stark shift by changing the MOT beam detuning when we turn the coupling laser on. This is shown in Figure 5.9. Parameters used are the same as in Figure 5.8 but with a shorter dressing time of 5 ms and a coupling beam detuning fixed at +12 MHz. We change the MOT beam detuning by a compensation amount δCOMP, if we undercompensate the cloud still moves lower
and if we overcompensate the cloud will move and a fraction of the cloud will fall under gravity and be lost from the trap.
Vertical position/µm
Shift
/
µ
m
Position/µm Position/µm Position/µm Position/µm Position/µm
Figure 5.9: The dressed MOT (b) forms at a lower position than the undressed MOT (a). Changing the MOT beam detuning (c-e) when coupling reduces the position shift but excessively large changes result in atom loss. (g) shows the cloud movement (blue) and the atom number (red). The dashed line indicates the initial cloud vertical position. (f) shows the Zeeman shift (black, solid) and the combined Zeeman shift and AC Stark shift (blue) as a function of vertical position. Dotted lines indicate the four δMOT used in (b-e),
dashed lines indicate resonance for the undressed case. The shaded red areas illustrate the cloud position for the undressed MOT and the optimally compensated MOT.
This has been done with an initial MOT beam detuning of δMOT = −140 kHz. What
is particularly interesting about this is that optimum compensation occurs at δCOMP =
+280 kHz i.e. the compensated MOT is blue-detuned by +140 kHz from the bare state. Consequently, the trap can only work in the presence of the coupling laser, and only traps Rydberg dressed atoms.
A peak Rabi frequency of 3.7 MHz and a coupling beam detuning of +12 MHz gives rise to a peak AC Stark shift of 280 kHz, which matches the observed optimum compensation. Using this compensation technique we can successfully trap atoms at the centre of the coupling beam, where coupling is strongest. We will refer to MOTs formed using this technique as ‘compensated MOTs’.
In addition to reduced cloud movement and atom loss, compensation of the AC Stark shift minimises the perturbation to the MOT dynamics - the more the resonance condition changes between the dressed and the undressed MOT, the longer it will take for the cloud to reach a new equilibrium. Reducing the initial perturbation of the cloud when we begin dressing will make it easier to eliminate effects due to atoms reaching a new equilibrium position that may make the effect of Rydberg dressed interactions less clear. Cloud dynamics are considered more later in this chapter.
This technique is effective at keeping atoms trapped at the quadrupole field centre for blue-detuned dressing experiments, but is less effective when red-detuned, as illustrated in Figure 5.10. When blue-detuned the Zeeman shift and AC Stark shift both cause the 5s5p3P1mJ = −1 state to fall in energy with increasing distance from the quadrupole and
coupling beam centre, referred to as the trap centre. This means that there will always be a MOT beam detuning for which the cloud can form at the trap centre, illustrated in Figure 5.10(a).
When red-detuned the Zeeman shift and AC Stark shift compete, shifting the 5s5p3P
1mJ =
−1 state down and up in energy respectively. The two effects both have different gra- dients in the vertical and horizontal direction, the Zeeman shift because of the nature of the quadrupole field and the AC Stark shift because of the ellipticity of the coupling beam spatial profile. We can therefore identify three possibilities when coupling with red-detuned light:
In regions where the AC Stark shift gradient is stronger than the Zeeman shift gradient in both vertical and horizontal directions, the 5s5p 3P1 mJ = −1 state
In regions where the Zeeman shift gradient is stronger than the AC Stark shift gradient in the vertical direction but not in the horizontal direction, atoms will be trapped in the wings of the MOT rather than at the trap centre, illustrated in Figure 5.10(b).
Where the Zeeman shift gradient is stronger than the AC Stark shift gradient in both directions, the trap can form in the centre of the coupling beam.
Shift / MHz Shift / MHz Position/µm Position/µm P osition / µ m
Figure 5.10: Combined Zeeman and AC Stark shift for red- and blue-detuned Rydberg coupling of |δC| = 12 MHz, ΩC = 4 MHz, with resonance contours overlaid.
To compensate the AC Stark shift due to red-detuned coupling light, we must ensure that the Zeeman shift gradient is stronger than the AC Stark shift gradient in both the vertical and horizontal directions at the trap centre. This may involve increasing the quadrupole field strength, defocussing the coupling beam, using a lower Rabi frequency, coupling to a higher principal quantum number Rydberg state, or a combination of these techniques. There are also more novel techniques we can attempt, such as using a spatial light modulator to control the coupling beam spatial profile, or retroreflection of the coupling beam with a position offset to reduce the AC Stark shift gradient.
These techniques are being investigated as part of the ongoing work on Rydberg dressed MOTs in this group; however, this thesis will focus on compensated MOTs that are dressed with blue-detuned coupling light. Our ability to compensate the AC Stark shift caused by Rydberg dressing of the MOT allows us to keep atoms trapped at the centre of the coupling beam, where the Rydberg-mixed fraction is strongest, and reduces the equilibration time of the cloud by reducing the initial perturbation of the cloud when we couple the cloud to the Rydberg state.
In the above sections we have demonstrated techniques for coupling the MOT to the Rydberg state. We understand the role of the AC Stark shift in modifying the spatial distribution of the cloud, and we can confine atoms to regions of strong Rydberg coupling. A full characterisation of the Rydberg dressed MOT will demonstrate the Rydberg char- acter of the MOT, study the cloud dynamics, observing the cloud velocity and velocity distribution and measure loss from the Rydberg dressed MOT.