TY  - JOUR
AU  - Bruschi, David Edward
AU  - Xuereb, André
AU  - Zeier, Robert
TI  - Deciding finiteness of bosonic dynamics with tunable interactions
JO  - Journal of physics / A
VL  - 58
IS  - 2
SN  - 1751-8113
CY  - Bristol
PB  - IOP Publishing
M1  - FZJ-2025-00937
SP  - 025204 -
PY  - 2025
AB  - We are motivated by factorization of bosonic quantum dynamics and we study the corresponding Lie algebras, which can potentially be infinite dimensional. To characterize such factorization, we identify conditions for these Lie algebras to be finite dimensional. We consider cases where each free Hamiltonian term is itself an element of the generated Lie algebra. In our approach, we develop new tools to systematically divide skew-hermitian bosonic operators into appropriate subspaces, and construct specific sequences of skew-hermitian operators that are used to gauge the dimensionality of the Lie algebras themselves. The significance of our result relies on conditions that constrain only the independently controlled generators in a particular Hamiltonian, thereby providing an effective algorithm for verifying the finiteness of the generated Lie algebra. In addition, our results are tightly connected to mathematical work where the polynomials of creation and annihilation operators are known as the Weyl algebra. Our work paves the way for better understanding factorization of bosonic dynamics relevant to quantum control and quantum technology.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:001382139400001
DO  - DOI:10.1088/1751-8121/ad91fc
UR  - https://juser.fz-juelich.de/record/1037785
ER  -