Probing Many-Body Chern Number Through Randomized Measurement

Engineering and probing the topological order is an outstanding challenge in the current quantum simulators and of fundamental importance in the condensed matter physics. A great experimental efforts have been devoted to engineering strongly-correlated system and the topologically non-trivial band structure which makes the realization of the fractional quantum Hall liquid in the quantum simulators possible in the near future. However, the detection of the many-body topological invariant depends either on linear-response measurement which is not available in most quantum simulators or on the interferometric type measurement which requires an ancillary qubit that is highly entangled with the whole system. Here, we propose an experimental scheme for measuring the many-body Chern number, which characterizes the topological nature of the fractional quantum Hall system, without the aid of linear-response properties or any ancillary qubit. Our protocol only relies on the randomized measurement that can be implemented by either single qubit rotation or quenches dynamics with time-dependent disorder potentials. Our measurement scheme paves a realistic way for the detection the many-body topological invariant in the near-term quantum technology platform.
 
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