Deciding finiteness of bosonic dynamics with tunable interactions
arXiv:2401.00069 · doi:10.1088/1751-8121/ad91fc
Abstract
In this work 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.
arXiv comment32 pages, 5 figures. Comments welcome
References in corpus (44)
- Cavity Optomechanics
- Theory of Bose-Einstein condensation in trapped gases
- Quantum Computing
- Quantum Simulation
- Quantum Annealing in the Transverse Ising Model
- Quantum computation over continuous variables
- Continuous variable quantum information: Gaussian states and beyond
- Training Schrödinger's cat: quantum optimal control
- A short introduction to the Lindblad Master Equation
- Quantum control theory and applications: A survey
- Squeezing as an irreducible resource
- Perspectives of quantum annealing: Methods and implementations
- Preparation of Nonclassical States in Cavities with a Moving Mirror
- Non-standard Hubbard models in optical lattices: a review
- Spontaneous parametric down-conversion
- Controllability of quantum mechanical systems by root space decomposition of su(N)
- Tuneable hopping and nonlinear cross-Kerr interactions in a high-coherence superconducting circuit
- Time evolution techniques for detectors in relativistic quantum information
- Symmetry Principles in Quantum Systems Theory
- Combinatorics and Boson normal ordering: A gentle introduction
- Finite Controllability of Infinite-Dimensional Quantum Systems
- Ultrafast dynamics with the exact factorization
- Smooth Controllability of Infinite Dimensional Quantum Mechanical Systems
- Heat transport in harmonic oscillator systems with correlated baths: Application to optomechanical arrays
- Quantum Quench of the trap frequency in the harmonic Calogero model
- Analytic Controllability of Time-Dependent Quantum Control Systems
- A Dynamic Systems Approach to Fermions and Their Relation to Spins
- Controlling Several Atoms in a Cavity
- Universal extensions of restricted classes of quantum operations
- Time-evolution of nonlinear optomechanical systems: Interplay of mechanical squeezing and non-Gaussianity
- Dynamical Decoupling of Unbounded Hamiltonians
- Optimal estimation of time-dependent gravitational fields with quantum optomechanical systems
- Master-equation treatment of nonlinear optomechanical systems with optical loss
- "Mechano-optics": An optomechanical quantum simulator
- Enhanced continuous generation of non-Gaussianity through optomechanical modulation
- Time evolution of coupled multimode and multiresonator optomechanical systems
- Time evolution of two harmonic oscillators with cross-Kerr interactions
- Quantum state conversion by cross-Kerr interaction
- Compensating for non-linear distortions in controlled quantum systems
- Time-optimal polarization transfer from an electron spin to a nuclear spin
- Quantum Control of Infinite Dimensional Many-Body Systems
- Phase Spaces, Parity Operators, and the Born-Jordan Distribution
- A bounded version of bosonic creation and annihilation operators and their related quasi-coherent states
- Landau electron in a rotating environment: a general factorization of time evolution