Casus Irreducibilis in Atomic States
Standing
Undergraduate
Type of Proposal
Poster Presentation
Challenges Theme
Open Challenge
Faculty
Faculty of Science
Faculty Sponsor
Dr. Chitra Rangan
Proposal
In Quantum Computing, one must switch between two quantum states called a 'qubit'. A well-known method for switching between quantum states is known as Stimulated Raman Adiabatic Passage (STIRAP). This method utilizes a specific atomic structure known as a 3-Level Lambda System (3LLS). A numerical investigation of these atomic structures led to the apparent result that the Hamiltonian describing the structure has eigenvalues that are complex-valued. This is problematic because the Hamiltonian that describes this atomic structure is self-adjoint and its eigenvalues can only be real-valued. In this project, these numerically-found, complex eigenvalues were found to be the result of the 'Casus irreducibilis'; a special case when trying to solve polynomials of degree 3 or higher, in which real solutions must be represented as complex numbers, proven by Pierre Wantzel in 1843. The impact of this discovery is that special care must be taken when theoretically & numerically modeling the dynamics of quantum systems.
Casus Irreducibilis in Atomic States
In Quantum Computing, one must switch between two quantum states called a 'qubit'. A well-known method for switching between quantum states is known as Stimulated Raman Adiabatic Passage (STIRAP). This method utilizes a specific atomic structure known as a 3-Level Lambda System (3LLS). A numerical investigation of these atomic structures led to the apparent result that the Hamiltonian describing the structure has eigenvalues that are complex-valued. This is problematic because the Hamiltonian that describes this atomic structure is self-adjoint and its eigenvalues can only be real-valued. In this project, these numerically-found, complex eigenvalues were found to be the result of the 'Casus irreducibilis'; a special case when trying to solve polynomials of degree 3 or higher, in which real solutions must be represented as complex numbers, proven by Pierre Wantzel in 1843. The impact of this discovery is that special care must be taken when theoretically & numerically modeling the dynamics of quantum systems.