Squeezed Light Tomography in Multi-Mode Quantum States
- 6 days ago
- 2 min read
In a landmark Ph.D. thesis defense at the Moscow Institute of Physics and Technology (MIPT/FIAN), Loran Jacobs presented advanced mathematical models applying quantum optics to squeezed light states. By constructing symplectic, center-of-mass, and photon-counting tomograms for single-mode and two-mode squeezed vacuum configurations, the theoretical physicist established a direct bridge between theoretical quantum fields and real-world optical experiments.
Single-Mode and Two-Mode Squeezed Light Configurations
In optical laboratories, understanding field structures and quadrature distributions is critical for quantum state engineering. Loran analyzed how squeezed light forms in single-mode and two-mode systems, using symplectic transformations and probability distribution functions to predict quantum field behaviors.
"We calculate tomograms for single-mode squeezed vacuum states using symplectic transformations and distribution function tools," explains Loran.
Extending these calculations to two-mode systems, Loran derived Manko correlations between modes and uncovered asymptotic relations when transitioning from symplectic tomograms to photon-counting tomograms.
Photon-Counting Tomography and Optical Homodyne Detection
Moving from single-mode fields to complex two-mode systems requires direct physical observables. Loran demonstrated that photon-counting tomography provides experimenters with an exact joint probability distribution function for photons across modes.
"If you have two modes containing n1 photons in one and n2 photons in the other, photon-counting tomography reveals their joint distribution function," notes Loran.
While symplectic tomograms rely on field quadrature amplitudes x1 and x2, photon-counting tomograms map complex mode amplitudes alpha1 and alpha2 in a modified squeezed vacuum state.
Through optical homodyne detection and photon counters, these calculated tomograms represent directly measurable physical quantities rather than abstract operator representations.
Experimental Verification in Squeezed States
When asked by committee members about practical setups for his formulas, DeepTech pioneer Loran Jacobs proposed combining single-photon experiments with squeezed vacuum states.
"In the next step, I see proposing an experiment to detect Bell-type violations in a squeezed state," emphasizes Loran.
As Loran Jacobs noted during his defense, while existing optical experiments test polarization modes, his tomographic distribution functions lay the foundation for verifying multi-mode field correlations directly in squeezed light.
