Rabi oscillations in gravitational fields: Exact solution via path integral

Abstract

The movement of a two-level atom interacting with an electromagnetic wave and subject to gravitation is studied using the path-integral formalism. The propagator is first of all written in the standard form D(path) exp(i/ )S(path) by replacing the spin by two fermionic oscillators; then it is determined exactly due to the auxiliary equation which has a cylindric parabolic function as a solution.

A path integral formulation for particle detectors: the Unruh-DeWitt model as a line defect

“…Recalling that Cl 3 coincides with the even part of Cl 4 [see 31, Theorem 3.7], we can do this by considering the operators constructed with an even number of fields coming from two tuplets (θ,θ) and (η,η), whose quantizations form two anticommuting copies of (3.1). The model obtained has been used in [32][33][34][35] to study the behaviour of spin 1/2 particles in a magnetic field. One way of proceeding is to write the ground and excited states of the UDW model as fermionic creation operators acting in a spurious vacuum state |0 D .…”

A path integral formulation for particle detectors: the Unruh-DeWitt model as a line defect

“…Recalling that Cl 3 coincides with the even part of Cl 4 [see 31, Theorem 3.7], we can do this by considering the operators constructed with an even number of fields coming from two tuplets (θ, θ) and (η, η), whose quantizations form two anticommuting copies of (10). The model obtained has been used in [32][33][34][35] to study the behaviour of spin 1/2 particles in a magnetic field.…”

“…In this way, each building block will be bounded by either the initial point τ i , the end point τ f , or an energy gap vertex with some label λ. Due to the Heaviside functions in the propagators (33), the integrals in the interactions within a building block can be taken to be within the interval bounding it. As an example, consider the diagram…”

Rabi oscillation in a damped rotating magnetic field: A path integral approach

“…This last expression represents the path integral of the propagator which has been the purpose subject of previous papers ( [9], [10]), and has the advantage that it permits us to perform explicitly some concrete calculations.…”

“…However, it is known that the most relativistic interactions are those where the spin is taken into account which is a very useful and very important notion in physics. From a practical point of view, the explicit calculus of propagators for such interactions by the path-integral formalism, has been discussed by many authors previously ( [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14]). …”