Numerical Simulations of Matter Wave Interference
Monte Carlo wave function (MCWF)
simulations can be used to understand many interesting signatures of a single
state atom interferometer. Examples include the characteristics of the echo
signal from the interferometer, the relative population of momentum states, the
influence of spontaneous emission on the echo signal and the behaviour of the
interferometer in the Bragg regime. The MCWF method is a well-known approach
for solving dissipation problems in quantum optics. The method is equivalent to
a master equation approach, but the random nature of quantum jumps is simulated
more directly using a Monte Carlo treatment.
Key Papers
(a)
Evolution of the position space probability density as a function of time after
the first excitation pulse for a T ~ 10 nK sample. The pulse parameters are
Ω0 = 1 Γn, Δ =10 Γn and δt1 = 4 τn.
(b)
Evolution of 2kL Fourier component of density distribution shown in
(a), which represents the experimental signal. A fit to the signal, shown in
gray, gives a recoil frequency ωq = 2¹ × 15.430(1) kHz
and temperature T ~ 7 nK, which is consistent with the input temperature.
(a) Evolution of the position space
probability density after two sw excitation pulses for a T = 10 μK sample.
The pulse parameters are Ω0 = 2 Γn, Δ = 4
Γn, δt1 = δt2 = 4 τn
and T = 2 τq = 64.77 μs.
(b)
Evolution of 2kL Fourier component of density distribution shown in
(a). The signal decays exponentially after each excitation pulse due to Doppler
dephasing on a timescale consistent with tcoh ~ 4 μs. In the
vicinity of t = 2T, interference between momentum states creates a modulation
in the density distribution and the grating echo is formed.
Probabilities of momentum states associated with the ground state versus τDP; probabilities extracted from fits using gf (δT), Δ = 39 MHz and Ω ~ 18 MHz. The points are joined using a 5th order interpolation function.
b) MCWF simulations neglecting the effects of spontaneous emission and spatial profile showing probabilities versus τDP; Δ = 39 MHz and Ω = 18 MHz.
c) MCWF simulations including the effects of spontanoues emission and spatial profile for the same conditions as in b).