Star product and ordered moments of photon creation and annihilation operators
arXiv:1108.2244 · doi:10.1088/1751-8113/45/1/015305
Abstract
We develop a star-product scheme of symbols defined by the normally ordered powers of the creation and annihilation photon operators, (a†)^m a^n. The corresponding phase space is a two-dimensional lattice with nodes (m,n) given by pairs of nonnegative integers. The star-product kernel of symbols on the lattice and intertwining kernels to other schemes are found in explicit form. Analysis of peculiar properties of the star-product kernel results in new sum relations for factorials. Advantages of the developed star-product scheme for describing dynamics of quantum systems are discussed and time evolution equations in terms of the ordered moments are derived.
14 pages, 4 figures, some misprints are corrected, to appear in J. Phys. A
References in corpus (7)
- Quantum state tomography of an itinerant squeezed microwave field
- Experimental Tomographic State Reconstruction of Itinerant Microwave Photons
- Full characterization of Gaussian bipartite entangled states by a single homodyne detector
- Planck Spectroscopy and the Quantum Noise of Microwave Beam Splitters
- Star products, duality and double Lie algebras
- A tomographic setting for quasi-distribution functions
- Measuring microwave quantum states: tomogram and moments