Contrast Interferometry using Bose-Einstein Condensates to Measureh/mandα

Abstract

The kinetic energy of an atom recoiling due to absorption of a photon was measured as a frequency, using an interferometric technique called "contrast interferometry." Optical standing wave pulses were used to create a symmetric three-path interferometer with a Bose-Einstein condensate. Its recoil phase, measurable with a single shot, varies quadratically with additional recoils and is insensitive to errors from vibrations and ac Stark shifts. We have measured the photon recoil frequency of sodium to 7 ppm precision, using a simple realization of this scheme. Plausible extensions should yield sufficient precision to attain a ppb-level determination of h/m and the fine structure constant alpha.

Squeezed-light-enhanced atom interferometry below the standard quantum limit

“…Assuming a beamsplitterlike coupling [such as described by Eqs. (10)], then N a 1 (t 1 ) = N t cos 2 ( dt eff (t )/2) = N t − N b (t 0 ) sin 2 (θ QST /2), where the final equality follows from conservation of atom number. Therefore, the total loss is…”

“…Since beamsplitting and mirror operations are implemented by strong coherent optical fields, we can approximate them as linear, and the complex amplitudes α 1 (t f ) and α 2 (t f ) can be directly evolved from α 1 (t 1 ) and α 2 (t 1 ) by repeated application of Eqs. (10). The mean Ŝ a and variance V (S a ) can then be computed using the relations,…”

“…Atom interferometry is a leading precision measurement technology, having demonstrated state-of-the-art measurements of accelerations and rotations [1][2][3][4][5][6], gravity gradients [7,8], magnetic fields [9], the fine structure constant (α) [10,11], and Newton's gravitational constant (G) [12][13][14][15]. Further increases to the sensitivity of atom interferometers would allow for some exciting science, such as improved tests of the weak equivalence principle [16][17][18], searches for quantum gravitational effects [19], and the measurement of gravitational waves [20,21].…”

Time-orbiting potential trap for Bose-Einstein condensate interferometry

“…Slow velocities and long coherence lengths allow condensates to exhibit greater sensitivity per atom than a thermal cloud with similar number of atoms. Though producing and working with condensates remains challenging, several groups have demonstrated Mach-Zehnder or Michelson interferometers using condensates [3,4,5,6,7,8,9,10]. However, all these experiments have been limited to measurement times of roughly ten milliseconds or less.…”

“…The simplest method is to orient the axis of the device vertically, allowing the atoms to fall freely under the influence of gravity [3,6,8]. While this technique introduces no additional fields or dephasing effects, the measurement time is limited by the speed at which the condensate falls.…”