Classical Quantization: Two Possible Approaches

P. B. Guest

P. Milman, Nicim Zagury

We study the interaction of an intense classical field with a two-level system coupled to a bosonic quantized field. We focus on the regime where the classical field and the two-level system characteristic frequencies are the same, while the quantized mode is set off resonance with both. We show that a parameter governing the dynamics of the system is the ratio between the classical field's intensity and the quantized mode detuning. Depending on this parameter, multiple excitations can be created in the quantized mode in a single cycle of the two-level system. Examples of physical setups allowing for the application of the presented ideas are superconducting circuits in strip-line resonators, laser cooled trapped ions, and neutral atoms coupled to the quantized field of a cavity. We focus on the latter in order to show that, with realistic experimental parameters, it is possible to generate up to four photons in a single Rabi cycle.

Karel V. Kuchař

Geoffrey Brooker

Abstract “Quantization of waves: the stretched string” discusses waves in one dimension, in order to display the quantization procedure without the complication of three dimensions and of two polarization possibilities. Quantization goes via classical Lagrangian mechanics. The waves travel in both directions along the string, and we face up to disentangling these. The quantization procedure yields raising and lowering operators, their commutation rules, and their matrix elements.

Hiroshi Kuratsuji

We investigate the restoration of the symmetry breakdown inherent to the ground state from a viewpoint of the classical quantization of time-dependent mean field. We take two examples of translational motion of nuclei and rotation of pseudo-spin in the degenerate BCS model. A possible extension is also suggested.

Yoshio Ohnuki, S. Kamefuchi