The fundamental limits of ground state metrology have been recently established as F\u03b8 \u2a7d N^2\/\u2206^2, where F\u03b8 is the Quantum Fisher Information, N is the number of particles, and \u2206 is the spectral gap. This bound defines the maximum achievable precision for estimating an unknown Hamiltonian parameter \u03b8 using the ground-state of a general N -body Hamiltonian. In this talk, we will discuss the saturability of this bound by realistic many-body probes, as well as the associated preparation\/sensing time. We focus on two distinct classes: short-range critical systems and all-to-all interacting models. First, for critical probes, we derive a universal condition on the critical exponents necessary to saturate the static ground-state bound\u2014a condition satisfied, for instance, by the XXZ model. We also argue that the bound can be saturated by gapped long-range interacting systems. We then address the sensing time \u03c4 , in particular the possibility to reach Heisenberg scaling (F\u03b8 \u223c N^2\u03c4^2) for optimised adiabatic protocols. We demonstrate that all-to-all interacting systems can effectively reach both the ground-state and Heisenberg bounds, and discuss the possibility of reaching it in the short-range XXZ model. Our results are supported by analytical and numerical calculations for four paradigmatic systems: the 1D Ising model, the XXZ chain, the two-axis twisting Hamiltonian, and the two-mode Bose-Hubbard model.<\/p>\n","protected":false},"excerpt":{"rendered":"
The fundamental limits of ground state metrology have been recently established as F\u03b8 \u2a7d N^2\/\u2206^2, where F\u03b8 is the Quantum Fisher Information, N is the number of particles, and \u2206 is the spectral gap. This bound defines the maximum achievable precision for estimating an unknown Hamiltonian parameter \u03b8 using the ground-state of a general N […]<\/p>\n","protected":false},"author":3002,"featured_media":0,"template":"","class_list":["post-2522","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/2522","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar"}],"about":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/types\/seminar"}],"author":[{"embeddable":true,"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/users\/3002"}],"wp:attachment":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/media?parent=2522"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}