Michelson Interferometer Analysis Method

WG1

WG2

(a) Returning in WG1 only.

WG1

WG2

(b) Returning in WG2 only.

Fig. 5.7 Two diagrams to show different configurations of a single arm Michelson interfer-ometer used to compare the output signal to a double arm interferinterfer-ometer. Figure 5.7a shows the position of atoms in a double transmission configuration. Similarly, Figure 5.7b shows a double reflection.

5.3 Michelson Interferometer Analysis Method

Understanding the dynamics of the atoms after recombination is essential to understanding the underlying process behind the lattice splitter. Full and separate control over the two waveguides intensities allows for a systematic approach to analysing any interference patterns produced by the recombination of two atomic clouds. To simplify the initial conditions, a single-arm Michelson interferometer is used where atoms are split as normal. One of the waveguides is momentarily switched off to deliberately remove all atoms in that waveguide.

The waveguide is returned to full power before remaining atoms re-enter the lattice from a single waveguide, forming a single arm Michelson atom interferometer.

The two configurations obtainable using this methodology are shown in Figure 5.7 where atoms can return from a single waveguide in either WG1 or WG2. Figure 5.7a shows atoms splitting as normal, the intensity in WG2 is reduced to zero before returning. Atoms only remain in WG1 and split in the lattice as normal when recombining. Figure 5.7b shows the opposite, where atoms in WG1 are selectively removed. This method does not excite atoms

96 Michelson Interferometer

in the remaining waveguide and provides a useful comparison to atoms returning in both waveguides simultaneously.

WG1

WG2

Fig. 5.8 A full Michelson interferometer. Atoms begin in a BEC in WG1 before splitting equally into WG1 and WG2. Applied magnetic fields in each arm reflect the atoms causing them to recombine.

By contrast, Figure 5.8 shows a diagram of a double arm Michelson atom interferometer where atoms are recombined from both waveguides simultaneously after splitting. Compar-ing splittCompar-ing results from the double and sCompar-ingle arm Michelson interferometer is useful to determine the level of interference generated between the two clouds of atoms.

Analysing the signal from the recombining atoms such as in Figure 5.6 can be achieved using a variety of methods. One such method analysed a single image taken a set time after the atoms have recombined. The atom cloud is then split along the axis of the waveguides into equal thin strips or bins 5 pixels in height and wide enough to encompass the oscillatory motion of the atoms. The number of atoms in each bin is calculated and plotted, giving an intensity profile as a function of distance to highlight the perceived peaks and troughs of intensity. This method was eventually not chosen due to difficulties in aligning the bins to the angle of the waveguides. The initial image is rotated to place one waveguide along the horizontal axis to fit the binning system better. However, the other waveguide will only be aligned along the vertical axis if they cross at 90°. As a result it becomes difficult to directly

5.3 Michelson Interferometer Analysis Method 97

compare atom number in one waveguide with the other using a single image. In addition, measuring a single image can accrue large noise fluctuations, whilst averaging over lots of images could remove finer details.

The preferred method used to analyse atoms after recombination is to create two equally sized regions of interest. They are equidistant from the lattice centre along the axis of the waveguides in the direction of travel. The distance between the lattice centre and the region of interest is deliberately chosen to be large enough to ignore any effect of the quasi-momentum peaks described in Chapter 4.11. These regions of interest are used to calculate the number of atoms in the small area. Figure 5.9 shows a sample image with the analysis method superimposed. A series of images are analysed with increasing time, essentially measuring the flux of atoms passing through a set point. The flux fluctuates as the returning atoms selectively favour one waveguide over the other. The chosen area of the region of interest affects the measurement greatly, with a large area blurring out variations in atom density whilst a small area is badly affected by fluctuations in background noise from picture to picture. Typically, images are taken sequentially, increasing the time atoms are in the waveguides by 0.2 ms scanning a total time frame of 20 ms for a total of 100 images. A full experiment cycle is completed every 18 s, resulting in a total time of 30 minutes to complete.

The time frame is set by the duration atoms are within the region of interest. The time separation between images is limited by the total time to complete a full sequence. Several sequences are required to provide good averaging and statistics. However, experimental conditions change from day to day, largely through temperature fluctuations or relaxation in mirror mounts affecting coupling to fibres. Therefore, minimising the sequence time is important to improve the overall reliability of results.

Taking subsequent images over a relatively long period also demonstrates the repeatability of the experiment and the deterministic nature of the splitter. By using a full sequence of images, the exact path of atoms in the waveguides is traced. Atom behaviour in the lattice remains constant throughout the image acquisition, and provides a good indication that the spatial and intensity stability of the waveguides described in Chapter 4.1 and Chapter 3.10 respectively is working as intended. It also provides good stability for several hours.

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Fig. 5.9 Explanation of the method used to analyse atoms after recombination. The flux of atoms through the red boxes equidistant from the lattice in each waveguide is calculated as a function of time. The distance d is sufficiently large to ignore effects from the quasi-momentum peaks from Figure 4.15.