Open Access

S. Ostermann, Francesco Piazza, H. Ritsch

• The non-linear coupled particle light dynamics of an ultracold gas in the field of two independent counter-propagating laser beams can lead to the dynamical formation of a self-ordered lattice structure as presented in (2016) Phys. Rev. X 6 021026. Here we present new numerical studies on experimentally observable signatures to monitor the growth and properties of such a crystal in real time. While, at least theoretically, optimal non-destructive observation of the growth dynamics and the hallmarks of the crystalline phase can be performed by analyzing scattered light, monitoring the evolution of the particle's momentum distribution via time-of-flight probing is an experimentally more accessible choice. In this work we show that both approaches allow us to unambiguously distinguish the crystal from independent collective scattering as it occurs in matter wave super-radiance. As a clear crystallization signature, we identify spatial locking between the two emerging standing laser waves,The non-linear coupled particle light dynamics of an ultracold gas in the field of two independent counter-propagating laser beams can lead to the dynamical formation of a self-ordered lattice structure as presented in (2016) Phys. Rev. X 6 021026. Here we present new numerical studies on experimentally observable signatures to monitor the growth and properties of such a crystal in real time. While, at least theoretically, optimal non-destructive observation of the growth dynamics and the hallmarks of the crystalline phase can be performed by analyzing scattered light, monitoring the evolution of the particle's momentum distribution via time-of-flight probing is an experimentally more accessible choice. In this work we show that both approaches allow us to unambiguously distinguish the crystal from independent collective scattering as it occurs in matter wave super-radiance. As a clear crystallization signature, we identify spatial locking between the two emerging standing laser waves, together creating the crystal potential. For sufficiently large systems, the system allows reversible adiabatic ramping into the crystalline phase as an alternative to a quench across the phase transition and growth from fluctuations.…