Bloch sphere like construction of SU(3) Hamiltonians using unitary integration

Details Bloch sphere like construction of SU(3) Hamiltonians using unitary integration Bloch sphere like construction of SU(3) Hamiltonians using unitary integration

2009-06-06

arxiv.org/abs/0906.1259v1

J. Phys. A: Math. Theor. 42 425303 (2009)

Physics

Quantum Physics

19 pages, 9 figures

Scientific paper

10.1088/1751-8113/42/42/425303

The Bloch sphere is a familiar and useful geometrical picture of the dynamics of a single spin or two-level system's quantum evolution. The analogous geometrical picture for three-level systems is presented, with several applications. The relevant SU(3) group and su(3) algebra are eight-dimensional objects and are realized in our picture as two four-dimensional manifolds describing the time evolution operator. The first, called the base manifold, is the counterpart of the S^2 Bloch sphere, whereas the second, called the fiber, generalizes the single U(1) phase of a single spin. Now four-dimensional, it breaks down further into smaller objects depending on alternative representations that we discuss. Geometrical phases are also developed and presented for specific applications. Arbitrary time-dependent couplings between three levels or between two spins (qubits) with SU(3) Hamiltonians can be conveniently handled through these geometrical objects.

Affiliated with

Also associated with

No associations

Rating

Bloch sphere like construction of SU(3) Hamiltonians using unitary integration does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bloch sphere like construction of SU(3) Hamiltonians using unitary integration, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bloch sphere like construction of SU(3) Hamiltonians using unitary integration will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-62008