Splitting Reference
Fringe spacing formula (^{87}Rb):
(1)\begin{align} \Delta z = \frac{ h t}{m d} = 4.602 \frac{t [ms]}{d [\mu m]} \end{align}
Measurement of fringe spacing vs. dressing frequency
trap bottom = 773.0 kHz
Calculations of fringe spacing vs. detuning, various models
Joseph's calculations, from email 17 March 2009
 horizontal axis is detuning (kHz)
 Quotes from email:
 These calculations are done using the parameters you gave me a few weeks ago (44Hz optical, 1340Hz undressed osc frequ, 787kHz trap boot) and 1e4 atoms. For this set of parameters, the quartic point is 6.3kHz and the cloud is split at +4kHz.
 The method is to do 3d GPE imaginary time propagation to find the intrap distribution, and then do realtime propagation during time of flight. During TOF, the interaction energy converts to kinetic energy.
 Shown in the top graph is apparent doublewell separation in microns (as would be inferred by fringe spacing) versus dressing frequency. There are four lines plotted,




 "U" = the spacing between the minima in the potential
 "Guess" = the fringes in the Thomas Fermi trial wavefunction
 "GPE" = fringes in the wavefunction after GPE relaxation. This is the "real" in trap distribution.
 "TOF" = fringes after about 1ms TOF. In all cases, less than 3% of the energy was remaining as interaction energy.




How to calculate Rabi frequency of the dressing rf (or, how to do tickle spectroscopy):
 Dress your trap at some frequency, $\nu_{dress}$
 Find the resonance, $\nu_{res}$ (ie, trap bottom) at a number of different rf amplitudes
 Fit this function, as a function of rf current amplitude, to
\begin{align} \nu_{res} = \nu_{dress} + \sqrt{\Delta^2 + (\Omega(I) * I)^2} \end{align}
where $\Delta$ is the detuning of $\nu_{dress}$ from the undressed trap bottom, and $\Omega(I)$ is the Rabi frequency as a function of current, such that $\Omega_R = \Omega(I)*I$ is the Rabi frequency.
 To extract the magnetic field amplitude,
\begin{align} B_{rf, \perp} = \frac{4 h}{\mu_B} \Omega_R = 2.9 ~ \rm{G / MHz} * \Omega_R [MHz] \end{align}
(see Book 17, p 143)
page revision: 16, last edited: 22 Jul 2009 19:07