One-Dimensional Quantum Systems with Ground State of Jastrow Form Are Integrable

in Physical Review Letters (2022)

Exchange operator formalism describes many-body integrable systems using phase-space variables involving an exchange operator that acts on any pair of particles. We establish an equivalence between models ... [more ▼]

Exchange operator formalism describes many-body integrable systems using phase-space variables involving an exchange operator that acts on any pair of particles. We establish an equivalence between models described by exchange operator formalism and the complete infinite family of parent Hamiltonians describing quantum many-body models with ground states of Jastrow form. This makes it possible to identify the invariants of motion for any model in the family and establish its integrability, even in the presence of an external potential. Using this construction we establish the integrability of the long-range Lieb-Liniger model, describing bosons in a harmonic trap and subject to contact and Coulomb interactions in one dimension.We further identify a variety of models exemplifying the integrability of Hamiltonians in this family. [less ▲]

Variational principle for optimal quantum controls in quantum metrology

in Physical Review Letters (2022)

We develop a variational principle to determine the quantum controls and initial state that optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When ... [more ▼]

We develop a variational principle to determine the quantum controls and initial state that optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When the set of available controls is limited, the exact optimal initial state and the optimal controls are, in general, dependent on the probe time, a feature missing in the unrestricted case. Yet, for time-independent Hamiltonians with restricted controls, the problem can be approximately reduced to the unconstrained case via Floquet engineering. In particular, we find for magnetometry with a time-independent spin chain containing three-body interactions, even when the controls are restricted to one- and two-body interaction, that the Heisenberg scaling can still be approximately achieved. Our results open the door to investigate quantum metrology under a limited set of available controls, of relevance to many-body quantum metrology in realistic scenarios. [less ▲]