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Abstract
Quantum phase fluctuations prevent true long range phase order from forming in interacting low dimensional condensates at any finite temperature. Nevertheless, by dynamically splitting a condensate into two the system can be prepared with a macroscopic relative phase, facilitating interferometric measurement. Here we describe a new dephasing mechanism whereby the quantum phase fluctuations, which are so effective in equilibrium, act to destroy the macroscopic relative phase that was imposed as a non equilibrium initial condition. We show that for one dimensional systems the phase coherence between the condensates decays exponentially with a dephasing time that depends on intrinsic parameters: the interaction strength, sound velocity and density as well as on the splitting rate of the original condensate. Interestingly, significant temperature dependence appears only above a crossover scale T*. For two dimensional systems the coherence decays in time as a power-law. In contrast to the usual phase diffusion, which is essentially an effect of confinement, the dephasing due to quantum fluctuations is a bulk effect that survives the thermodynamic limit.
Even after the coherence completely decayed the system remains out of equilibrium. To characterize the system at this stage we study the two point correlation function of one of the condensates comprising it. We find that the system approaches a non thermal quasi-steady state.
We then turn to study number squeezed interferometers i.e. interferometers created by a slow split. We find that a slow splitting process has two counteracting effects on the coherence. On the one hand a slow split decreases the dephasing rate, on the other hand it entails a weaker initial coherence immediately following the split. In particular, the initial coherence of a one dimensional system has a power law dependence on the splitting rate with a power that depends solely on the Luttinger parameter.