Entanglement Spectroscopy of Quantum Many-body Systems
** Note the special day and time for this talk, beginning on Monday, November 21 at 2:00 pm in 114 E. Bridge
Abstract: Entanglement spectrum, the full spectrum of the reduced density matrix of a subsystem, plays a major role in characterizing many-body quantum systems. In recent years, it has been widely studied in the fields of condensed matter physics, quantum information, and high energy physics. As first pointed out by Haldane and Li in the context of fractional quantum Hall effect, the entanglement spectrum can serve as fingerprint of topological order (TO). The correspondence between ES and TO has been further explored since then and the importance of ES has been extended to the context of quantum criticality, symmetry-breaking phases, tensor networks, eigenstate thermalization, and many-body localization.
While there has been a surge of theoretical works on the subject, no experimental measurement has been performed to this date, since the highly non-local ES is impossible to be extracted from local measurements. In this talk, I present a measurement protocol to access the entanglement spectrum of many-body states in experiments with cold atoms or cavity quantum electrodynamics, where non-local coupling between the many-body system and an ancilla qubit is possible. Our scheme effectively performs a Ramsey spectroscopy of the entanglement Hamiltonian, and is based on the ability to produce several copies of the state under investigation together with the possibility to perform a global swap gate between two copies conditioned on the state of the ancilla. We show that this protocol can be implemented with state-of-the-art techniques in cold atom and circuit-QED experiments. We illustrate these ideas on a simple (extended) Bose-Hubbard model where such a measurement protocol reveals topological features of the Haldane phase, and the bulk-edge correspondence between the entanglement and physical spectra. In addition, I also show how a modified scheme can also be used to measure the out-of-time-order correlator in many-body system, which features the scrambling of quantum information.