Abstract
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.
Highlights
In this work we show that both approaches allow to unambiguously distinguish the crystal from independent collective scattering as it occurs in matter wave super-radiance
A dilute cold atomic gas illuminated by a laser far off any optical resonance experiences an optical potential with the particles drawn to high or low intensity regions depending on the sign of their linear polarizability
As due to losses time was limited in our setup, we introduced a sudden switch of the laser and the resulting quench dynamics of the crystallization process has been studied in detail in [4]
Summary
A dilute cold atomic gas illuminated by a laser far off any optical resonance experiences an optical potential with the particles drawn to high or low intensity regions depending on the sign of their linear polarizability. One possible signature includes a careful analysis of the instability threshold of a homogeneous density for single side versus symmetric pumping In this respect we perform very detailed studies of the the short time dynamics, varying the pump geometry from symmetric pumping for ideal crystallization via asymmetric pumping towards the single side pump case as the standard configuration where matter wave super-radiance is usually observed. The two electromagnetic fields Stark shift the atomic ground state and create an optical potential for the BEC atoms, which in turn modify the field propagation as they constitute an effective density dependent index of refraction The dynamics of this setup can be efficiently described by a coupled system of mean field equations. The system’s properties described above lead to the fact that the phase transition from a homogeneous BEC to a spontaneously formed crystal can be non-destructively observed by measuring the light reflected from the atomic cloud. As one can see from figure 5b), this dephasing is getting smaller for growing intensities until it reaches a certain constant value
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