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, high energy and black-hole 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), which is itself a non-local feature and a pattern of long-range entanglement. 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 spin/photon mode 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 spin. We show that this protocol can be implemented with state-of-the-art techniques in cold atom and circuit-QED experiments. In particular we show how the required conditional swap gate can be implemented with cold atoms using Rydberg interactions and with superconducting qubits using Jaynes-Cummings interactions. 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 of the entanglement and physical spectrum. Our protocol can also be extended to other experimental systems, such as trapped ions or materials coupled to cavity.
Guanyu Zhu is currently a postdoc associate at Joint Quantum Institute (NIST-University of Maryland), started from Sep. 2015 after spending a quarter as visiting scholar at Kavli Institute of Theoretical Physics at University of California, Santa Barbara. He works at the interface of quantum information, condensed matter theory and quantum optics. The focus of his research is on the relation between entanglement and many-body physics such as topological orders and thermalization, as will be presented in his talk. Besides, he also studies fault-tolerant quantum computation and many-body physics in synthetic materials with light-matter interactions, involving platforms such as Rydberg atoms, superconducting qubits, cavity-QED systems and ion traps. A common feature of these systems is that light or spins can be coupled to the many-body systems non-locally, allowing manipulation and detection of non-local properties of the systems, such as topological orders and entanglement patterns.
He received his Ph.D. from Northwestern University in 2015 where he worked with Jens Koch on quantum simulation with interacting photons and quantum information processing in circuit-QED systems. He finished his undergraduate education in the Department of Physics at Shanghai Jiao-Tong University in 2009.
Host: Ying Liu yingl@sjtu.edu.cn