Out of phase BEC

Factual Questions
1

Take 2 BEC’s (Bose Einstien Condensates) and place them half overlapping, except make one of the BEC’s have a matter wave that is 1 half wavelength off that of the first, thus they would have inverse overlapping wave patterns.

Would these two wave patterns cancel each other out, much like a wave and a trough of same wave height cancel each other out?

And if you had the two BECs pass through each other they would exist right up until they overlapped inwhich case they cancel each other out but continue to move through each other and once not overlapped they come back into existance.

While cancelled out would they lose mass and thus create no gravitational field, hence creating a faster than light change in mass within a given space (creating a gravity wave to propagate from that point at the speed of light to update the space curvature)?

2

I’m far from an expert on Bose-Einstein Condensates, but I suspect that it’d be impossible to get two to destructively interfere everywhere. You’d end up with cancelletion in some places and reinforcement in others, such that the total amount of mass would be unchanged. You would have, in effect, a net (non-instantaneous) motion of mass, which would cause a gravitational wave, but it’d be extremely weak and unnoticeable (you can also create gravitational waves by, say, waving your arms).