Quantum Transients and Hanbury Brown-Twiss Correlations in Identical Particles

The Moshinsky quantum-shutter model is extended to the case of two identical particles in free fall under a linear gravitational potential, with the aim of describing the time evolution of the joint probability density and the emergence of Hanbury Brown–Twiss–type correlations. The study proposes to examine how bunching and antibunching signals depend on time and space according to the initial state, and how the quantum predictions relate to classical free fall. These questions seek to connect the theoretical formalism with observables in experiments with ultracold atomic clouds.

Analytical and semi-analytical expressions are derived for the time evolution of the two-particle wavefunction in the presence of gravity, considering factorizable and entangled initial states. In parallel, numerical computations are implemented to evaluate the joint probability density, generate temporal and spatial maps, and compute correlation statistics for a wide set of initial conditions (separations, packet widths, and momentum differences). The zero-gravity limit is checked and the agreement of the mean displacement with the classical free-fall equations is verified. Visualizations and statistical analyses allow identification of the regimes in which bunching and antibunching signatures are most detectable.

The generalization of the Moshinsky shutter to two particles in the presence of gravity reproduces transients in the joint probability density associated with bunching and antibunching, whose spatial and temporal localization depends strongly on the initial conditions; the mean displacement follows classical free fall while the fine structure is of quantum origin. These results are robust against small variations, provide observable measures to maximize the experimental detectability of HBT correlations, and motivate extensions including interactions, additional fields, and more realistic detection models.