We use laser-cooled cesium atoms in atomic fountains to perform precision measurements. Efforts have been ongoing for about a decade to measure the fine structure constant a and local gravity g with sensitivity and accuracy higher than any previous method.
Atoms in magneto-optic traps are launched in moving optical molasses with a temperature of about 2 mK. The temperature can further be reduced through Raman sideband cooling in a moving optical lattice to about 150 nK. These atoms then enter a magnetically well-shielded region where atom interferometry is performed.
Beamsplitters and mirrors for the interferometer are formed by pulses of laser light which drive velocity selective stimulated Raman transitions between magnetic field insensitive hyperfine ground states. The use of ultra-cold atoms, atomic fountains and hyperfine ground states allow interrogation time of up to 1 second thereby improving the precision of such measurements by orders of magnitude. [Top]
We use a four optical pulse atom interferometer (p/2-p/2-p/2-p/2) to precisely measure the momentum change of a cesium atom when it absorbs a photon. Since we know precisely the wavelength of the photon, a measurement of this "photon recoil" gives us a value for h/Mcs, where h is Planck's constant and Mcs is the mass of the cesium atom. With independent measurements of the Rydberg constant, the proton-electron mass ratio, and the proton-Cesium mass ratio, a value of h/Mcs can lead to an improved value of a, the fine structure constant.
Four pulse interferometer to measure photon recoil. The difference in phase between the two interferometers is used to measure h/m.
In our experiment, we increase our sensitivity by sandwiching p-pulses between the pairs of p/2-pulses. Using adiabatic passage, each pulse has an efficiency of about 94% in transferring atoms from one state to the other. This results in our ability to add up to 30 p-pulses, and obtain a 30-fold increase in sensitivity as illustrated below.
Sandwiching N (2 here) p-pulses between the four p/2-pulses results in increased sensitivity
Currently, the most accurate determinations of a come from the quantum Hall effect (20 ppb), the ac Josephson effect (56 ppb), neutron interferometry (39 ppb), and an experimental measurement plus a QED estimation of the g-2 value for the electron (4.2 ppb). Our measurement, which depends only weakly on QED through the Rydberg constant, will measure a to less than one part in 109 (=1 ppb).
In our latest measurement, we have determined a to an accuracy of about 7.4 ppb (see figure). Many systematic effects have been investigated thoroughly.
Comparing some of the experimental determined value of a with our results.
Work is in progress to increase the sensitivity by minimizing some of the largest noise sources such as vibration noise through common mode noise reduction, and increase in the interrogation time of the interferometer. [Top]
We have built an atom interferometer to measure g, the local acceleration due to gravity. Laser cooled cesium atoms in an atomic fountain provide us with a suitable sample of atoms. The p/2-p-p/2 sequence of Raman pulses that we apply leads to a Mach-Zehnder type interferometer configuration.
Setup for gravity measurement
The combination of cold atoms in an atomic fountain and the use of an active vibration isolation system with an effective resonance frequency of 1/100 Hz allow us to achieve a long time between the interferometer pulses. This is of great importance, since the gravity sensitivity of the interferometer scales quadratically with this time.
We improve our performance by mounting some critical pieces of optics on an active feedback low frequency vibration isolator. The graph indicates the performance of our vibration isolator. The dotted line is the spectrum when sensor is resting on floor; thin line when it is suspended by springs on floated optical table; and the thick line when feedback is turned on. Vibrations in the critical regimes of 0.1 to 10 seconds is reduced by up to a factor of 10 - 1000. The insert shows the response of our system to an external step function disturbance.
Our standard time of 400 ms between pulses means that a single fringe corresponds to a gravity change of 270 ppb (2.7 x 10-7). Under typical conditions, a single launch lasting 1.6 second measurement determines gravity to 8 ppb and sufficient averaging can give us a resolution approaching 60 ppt (6 x 10-11) before we run into limitations due to geophysical effects and environmental background.
The absolute gravity value obtained in this measurement is referenced directly to atomic standards. We have compared our results with an official NOAA (Nation Oceanic & Atmospheric Administration) gravity measurement taken in our lab and found that they agree to within 7 ppb, limited mainly by the uncertainty in comparing g at slightly different locations.
We have also used the atom interferometer to monitor geophysical phenomena, such as tides and ocean loading effects, for extended periods of time. The quality of the data has been high enough to compare with some commonly used theoretical ocean loading models.
Data obtained from a 2 day continuous monitoring of gravity. The variation observed in the measured value of g is due mainly to the tidal effect of up to 3 x 10-6 m/s2. A smaller effect of about 2 x 10-7 m/s2 is caused by the loading of ocean. Each experimental data point is obtained by measuring the phase over a minute. The blue line in the upper graph is the theoretical prediction that takes into account both the tidal and ocean loading effects. In the lower graph, the difference of our experimental data from the tidal correction is compared with two different models of ocean loading effects. (Notice that the usual unit used here is mGal = 10-8 m/s2, and 1 mGal is the difference of g between two points separated vertically by 3 mm due solely to the 1/r2 dependence of gravity due to the earth.)
More recent works include using a pulse sequences of p/2-p-p-p/2 and p/2-p-p-p-p/2 to measure gradient of gravity directly with a single cloud of atoms. Multiple loops of interferometers are formed with these sequences. Appropriate time between the pulses allows the huge phase shift due to g to cancel in different loops resulting in the measurement of the minute differences of g in these loops due to gradient. Resolution is high enough to compare the value with that obtained by other methods.
The configuration to measure gravity gradient with multiple loops.
Further improvements of the apparatus are still possible and future development might lead to portable instruments, measurements of the gravitational constant G, or to new tests of the equivalence principle. [Top]
Precision Measurement of the Photon Recoil of an Atom Using Atom Interferometry
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Precision Measurement ofBased on Photon Recoil Using Laser-cooled Atoms and Atomic Interferometry
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Atom Manipulation Based on Delayed Laser Pulses in Three- and Four-level Systems: Light Shifts and Transfer Efficiencies
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Precision Atom Interferometry
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The Manipulation of Neutral Particles
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Active Low Frequency Vertical Vibration Isolation
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A. Peters, K. Y. Chung, and S. Chu, Nature 400, 849 (1999) PDF
High-precision Gravity Measurements Using Atom Interferometry
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High-brightness Atom Source for Atomic Fountains
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Active sub-Rayleigh alignment of parallel or antiparallel laser beams
H. Müller, S.-w. Chiow, Q. Long, C. Vo, and S. Chu, Opt. Lett. 30, 3323 (2005). PDF
Phase-locked, low-noise, frequency agile titanium:sapphire lasers for simultaneous atom interferometers
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A new photon recoil experiment: towards a determination of the fine structure constant
H. Müller, S.-w. Chiow, Q. Long, C. Vo, and S. Chu, Appl. Phys. B 84, 633 (2006). PDF
Extended-cavity diode lasers with tracked resonances
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Nanosecond electro-optical switching with a repetition rate above 20 MHz
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Atom-interferometry tests of the isotropy of post-Newtonian gravity
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Atom-wave diffraction between the Raman-Nath and the Bragg regime: Effective Rabi frequency, losses, and phase shifts
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Atom interferometry with up to 24-photon-momentum-transfer beam splitters
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Last modified 01/13/2009 by Sheng-wey Chiow
