Quantum 2025 – scientific programme

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FRI: Friday Contributed Sessions

FRI 1: Quantum Information: Concepts and Methods II

FRI 1.2: Talk

Friday, September 12, 2025, 11:00–11:15, ZHG001

From bosons and fermions to spins: A multi-mode extension of the Jordan-Schwinger map — Benoît Dubus¹, •Tobias Haas^1,2, and Nicolas J. Cerf¹ — ¹Centre for Quantum Information and Communication, Université libre de Bruxelles — ²Institut für Theoretische Physik, Universität Ulm

The Jordan-Schwinger map is widely employed to switch between bosonic or fermionic mode operators and spin observables, with numerous applications ranging from quantum simulation and ultracold quantum gases to quantum optics. While the construction of observables obeying the algebra of spin operators across multiple modes is straightforward, a mapping between bosonic or fermionic Fock states and spin states has remained elusive beyond the two-mode case. Here, we generalize the Jordan-Schwinger map by algorithmically constructing complete sets of spin states over several bosonic or fermionic modes, allowing one to describe arbitrary multi-mode systems faithfully in terms of spins. We discuss our method's potential for efficiently simulating complex many-body dynamics with spin systems.

Keywords: Quantum Simulation; Many-body systems; Bosons, Fermions, Spins; Jordan-Schwinger map