Ramsey Interference in One-Dimensional Systems: The Full Distribution Function of Fringe Contrast as a Probe of Many-Body Dynamics

We theoretically analyze Ramsey interference experiments in one-dimensional quasicondensates and obtain explicit expressions for the time evolution of full distribution functions of fringe contrast. We show that distribution functions contain unique signatures of the many-body mechanism of decoherence. We argue that Ramsey interference experiments provide a powerful tool for analyzing strongly correlated nature of 1D interacting systems.

Figure 1

(a),(c) Evolution of joint FDF $P_l^{x,y}$ with short integration length $l/{\xi }_s=10$ [top, (a)] and long integration length $l/{\xi }_s=30$ [bottom, (c)]. (b),(d) Corresponding FDF for spin $x$, $P_l^x$ with short integration length $l/{\xi }_s=10$ [top, (b)] and long integration length $l/{\xi }_s=10$ [bottom, (d)]. Here $L/{\xi }_s=200$, $K_s=20$. Time is measured in units of ${\xi }_s/c_s$.

Figure 2

(a) Time evolution of the distribution $P_l^{\perp }$ for the magnitude of spin $(S_l^{\perp }{)}^2$. (b) time evolution of $⟨S_l^x⟩$ and $\sqrt{⟨(S_l^{\perp }{)}^2⟩}$ with various integration length $l/{\xi }_s=10$, 30, 50. Here we set $K_s=20$, $L/{\xi }_s=200$.