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Using non-destructive imaging we have been able to observe collective
excitations of a Bose-Einstein condensate in real time on a single condensate.
In past experiments, every 30 seconds a new condensate was produced, driven into a dynamic state, and then a single image was taken. By varying the time between the end of the drive and the time when the image was taken, information such as the frequency and damping rate of the excitation could be measured. But to determine these quantities precisely, images had to be taken of many different condensates, each at a different point in the oscillation, requiring several hours to take data on a single excitation. Furthermore, fluctuations in the experiment from shot to shot introduced errors into our analysis.
Using non-destructive dispersive imaging methods, we have been able to make the exploration of collective excitations quicker, easier, and more accurate. Taking many images of a single condensate allows us to measure the frequency of an excitation in a single shot. More accurate measurements can made by repeating the experiment and making several "movies," each starting at different times after the condensate is driven into the excited mode. We can typically take 20 or more pictures of a single condensate, allowing us to take the data 20 times faster. And by making sure that some of the frames in each sequence overlap with frames in the previous shot, we can compare the overlapping frames to make sure that shot to shot fluctuations don't introduce large errors in our analysis.
The picture on the left is made up of a series of images of an oscillating condensate. As you look down the column of images, each succeeding image was taken 5 milliseconds later than the one above it.
Only three condensates were used (one for every 16 frames), and the entire sequence was taken in less than three minutes. You can easily see two different modes in the oscillation. First, there is oscillation of the center of mass of the condensate (you can see that the condensate is moving back and forth from left to right as time passes). This oscillation has a frequency of 18.5 Hz. Secondly, there is a higher frequency oscillation in the aspect ratio of the condensate (the length of the condensate changes with time), which occurs at 29.3 Hz.
Phase contrast images of the dipole oscillation. Using non-destructive techniques, the dipole oscillation was observed directly for a single trapped condensate. This oscillation is a collective "sloshing" of the entire cloud back and forth in the trap. The frames were taken with a separation of 10 msec between frames. The length of the condensate was 200 mm. From these images, the frequency of the dipole motion was determined to be 19 Hz.
Phase contrast images of the quadrupole-type shape oscillation. In this mode, the radial width and the axial length of the condensate oscillate out of phase. The images were taken of a single condensate at a rate of 200 frames per second. From this data, the frequency of the shape oscillation was determined to be 30 Hz.
