Atomic Interferometry D1 Report
Brief Overview of Related Theory
The principle behind Atom Interferometry is to cool atoms to subkelvin temperatures where they
behave as atomic waves. Similar to light waves, atomic waves can interfere and produce
interference patterns. Thus, through the use of light gratings, we can create atomic beam splitters
and mirrors analogous to beam splitters and mirrors used in light interferometers.
For our interferometer, we will first trap in the atoms in a Magnetic Optical Trap (MOT) through the
use of 3 pairs counterpropagating σ+ and σ- laser beams1 aimed at the center of between two antihelmholtz coils. The counterpropagating beams address typically a closed cycling transition in the
atoms. After the MOT is formed, the magnetic field is shut off and the atoms are subjected to
further cooling through the rotating linear polarization gradients created by the 3 pairs
counterpropagating σ+ and σ- laser beams. The atoms are thus cooled into an Optical Molass.
State preparation of the atoms then ensue, where the atoms are prepared in one of the ground
hyperfine states, typically the |j, m = 0> state where the atoms are less susceptible to magnetic
fluctuations. The atoms will then be allowed to drop under the influence of gravity. We will then use
a sequence Raman pulses to perform our interferometery and state selection. Raman transitions
place the atoms in a superposition of the two ground hyperfine states of the alkali atoms. These
hyperfine states are typically ordinarily separated by a few GHz. We will use a sequence of π/2- ππ/2 pulses which is analogous to the Mach-Zehnder inferometer. The first π/2 pulse acts as a beam
splitter cube to split the atom wave into a superposition of two states. The π pulse acts as a mirror
to flip the states of the atom, while the last π/2 pulse acts as a beam splitter to recombine the two
atomic waves and produce the interference fringes.
For our experiment, we plan to use Rubidium 87 and Cesium 133. At the moment, we are focusing
on interferometry of Rubidium 87 and the report will focus on the laser systems built to accomplish
this.
Current Progress
MOT Laser system
The MOT Laser system is shown in Fig. XX. The MOT Laser system consists of the cooling laser and
the repumper laser and is designed to cool and trap Rubidium atoms. The cooling laser consists of a
Master Oscillator Power Amplifier (MOPA) system that consists of an Extended Cavity Diode Laser
and a Tapered Amplifier, while the repumper laser simply consists of a Distributed Feedback Laser
(DFB). The wavelength of the two lasers is approximately 780.024nm, but the frequency of the
cooling laser is separated from the repumper laser by 6.834GHz. The role of the cooling laser is to
trap and cool the atoms. It is tuned to near the F = 2 → F′ = 3 transition which is the cycling transition
used for cooling and trapping the Rubidium 87 atoms. The cooling laser is also used to image the
1
σ- and σ+ laser beams refer to left and right circular polarized laser beams respectively.
atoms, by tuning the laser frequency to be resonant to the F = 2 → F′ = 3 transition. In addition, it is
also used to optically pump the atoms, for state selection.
The role of the repumper laser is to repump atoms that have decayed outside the cycling transition
back into the relevant hyperfine levels. The cooling laser is frequency stabilized using a Doppler free
saturation spectroscopy setup the crossover transition between the F = 2 → F′ = 3 and the F = 2 → F′
= 1 transition. The two lasers are then frequency locked using a trombone phase lock. The laser
frequency beat note is shown in Fig. XX.
Raman Laser system
The Raman Laser system and the related feedback mechanism are shown in Fig. XX. The Raman
Laser system consists of two MOPA systems similar to the MOPA in the MOT Laser system. The
purpose of the Raman Laser system is to produce the Raman pulses to initiate the Raman transitions
for state selection and interferometry. To that end, the two laser systems must be phased locked to
each other such that they are approximately 6.84GHz apart, which is approximately the frequency
separation between the hyperfine levels of Rubidium-87. The two lasers are phased locked to each
other by heterodyning them and focusing the two laser beams onto a fast photodiode. This
generates a 6.8-6.84GHz laser beat frequency. This laser beat frequency will be then further downconverted by mixing the laser beat frequency with a 7GHz frequency generated either by using an RF
signal generator or by using a RF signal generator that produces a 1GHz frequency and then
frequency multiplied by 7 times through the use of a step recovery diode. The resulting downconverted laser beat frequency and comparing it against a 160-200MHz frequency reference
through a phase frequency detector, we generate an error signal that is shaped by a proportionalintegrator controller which is then fed into the master laser current through a phase lag lead and a
bias-tee. The laser beat frequency is shown in Fig. XX and Fig. XX
The measured laser beat frequency linewidth is 4.63283Hz ± 0.03397Hz. This compares against the
original linewidth of a few hundred KHz. The servo bumps at the two sides give a rough ballpark
figure for the servo bandwidth of the phase lock. Thus far, our servo bandwidth has shown to be
approximately 500KHz-1MHz.
Computer Control
The various Acoustic Optic Modulators and shutters used in the optical setups are controlled using
National Instruments LabView Data Acquisition (DAQ) Cards that are PCI cards installed in two
computers. A Labview program was written to control the AOMs and the shutters to switch on and
off the laser beams as appropriate. A camera is used to image the atoms, which are made to
fluoresce using the imaging beam. The camera image is acquired by a computer using a LabView
program and then we use Matlab to measure and calculate the number of atoms that are in the
cloud of cold atoms.
Outlook
Vacuum system
At the moment, we have a vacuum system set up to accomplish the interferometry. The system will
eventually be placed on a vibration isolation stage to reduce vibrations throughout the setup. A
seismometer will be used to detect vibrations and used in a feedback loop together with the
vibration isolation stage to compensate for any vibrations which would otherwise affect the
accuracy of our measurements.
Laser system
At the moment, two signal generators are used to provide the frequency references required to
down-convert and serve as a frequency reference to phase stabilize the lasers. In the future, we will
use a single ultra stable frequency to generate the necessary frequencies to accomplish the same
task. We will also frequency lock the master Raman laser to the cooling laser using another
trombone phase lock.