Ultracold atoms have emerged as powerful and versatile platforms for simulating quantum many-body systems. Yet, there remain several obstacles preventing them from unleashing their full potential. One major bottleneck is the limited available methods for reading out information from the simulators. In this talk, I will focus on a pair of low-dimensional (1D and 2D) quantum gases, whereby spatial correlation of the phase fields can be extracted from matter-wave interference. I will start by examining the reliability of the standard method to extract relative phase profiles from density interference patterns [1]. Then, I will present a new method to extract the total phase, i.e. the sum rather than the difference of phase fields, from density ripples after time of flight [2]. Lastly, I will discuss applications of this new measurement towards pushing quantum simulators to new regimes previously unexplored, such as probing anharmonic correction to Luttinger liquid and non-equilibrium dynamics of sine-Gordon field theory.

[1] Murtadho, T., Gluza, M., Arifa, K. Z., Erne, S., Schmiedmayer, J., & Ng, N.H. (2024). Systematic analysis of relative phase extraction in one-dimensional Bose gases interferometry. https://arxiv.org/abs/2403.05528v2
[2] Murtadho, T., Cataldini, F., Erne, S., Gluza, M., Schmiedmayer, J., & Ng, N. H. (2024). Measurement of total phase fluctuation in cold-atomic quantum simulator. https://arxiv.org/abs/2408.03736