Transport measurement, which applies an electric field and studies the migration of charged particles, i.e., the current, is the most widely used technique in condensed matter studies. It is generally assumed that the quantum phase remains unchanged when it hosts a sufficiently small probing current, which is, surprisingly, rarely examined experimentally. In this Letter, we study the ultra-high-mobility two-dimensional electron system using a propagating surface acoustic wave, whose traveling speed is affected by the electrons' compressibility. The acoustic power used in our Letter is several orders of magnitude lower than previous reports, and its induced perturbation to the system is smaller than the transport current. Therefore we are able to observe the quantum phases become more incompressible when hosting a perturbative current.