Tunnelling and Phase Locking of two 1d BEC
The RF double well allows exceptional control of the splitting parameters and the asymmetry in the potential. One can therefore build completely separated double wells and double wells where the two 1d BEC are coupled by tunnelling through the barrier.
On sees two distinct regimes:
If the double well is very well balanced, and one has a small atom number
in the BEC one observes fist the expected phase shift due to the asymmetry
and an increase in the phase spread. After a very short time (10-20 times
the transverse level spacing) the phase spread stabilises and the relative
phase settles around zero. This remains then nearly constant for as long as
one observes a BEC (seconds).
Experimental parameters:
Small splitting with a barrier height of ~ 5ћw
atom density n1d ~ 40at/µm µ
~ 0.3ћw
Short time behaviour: imbalance measured in by phase shift:
1.28 rad in 5 ms ~ 40 Hz ~ 1/80 ћw ~
1/25 µ imbalance from N1/2 ~ 25 Hz
Long time behaviour: stable phase with slow increase of phase spread
Interference pattern has a stable contrast of ~ 0.25
with a Gaussian distribution scontrast ~ 0.11
If the barrier between the two 1d BEC is very high, we observe that the phase of the interference pattern becomes very quickly random. Never the less there remains a stable contrast of about 20% as long as we observe the BEC.
Experimental parameters:
Larger splitting with a barrier height of > 15ћw
atom density n1d ~ 100at/µm µ
~ 0.7ћw
Short time behaviour: imbalance measured in by phase shift:
0.8 rad in 1 ms ~ 120 Hz ~ 1/25 ћw ~
1/17 µ imbalance from N1/2 ~ 40 Hz
Long time behaviour:after 3 ms interference pattern with a random phase
Interference pattern has a stable contrast of ~ 0.2
with a Gaussian distribution scontrast ~ 0.10
These observations are a clear signature for tunnel coupling between the two condensates and phase locking. To investigate these phenomena more carefully we have to change the observation direction and look at the interference along the 1d BEC.