Side pumped atom array in optical cavity: Dicke phase transition in optomechanics and Spin optodynamics*

The Dicke phase transition of atomic spin coupled to a global cavity field is known as an example of bifurcation behavior of quantum phase transition of an open system. We realize Dicke phase transition of N~20 atoms in a optical cavity in two different ways: 1. Atoms as mechanical harmonic oscillators; 2. Atoms as spins. 

First, we show the optomechanical Dicke phase transition of the atom position when the atoms are tweezed at the cavity field antinodes, and illuminated from the side with a uniform-phase pump light. The Dicke phase transition occurs when the atomic center of mass position bifurcates, which is couple to the bifurcation of the cavity field sign. 

Second, we study the spin-optomechanics, where the atoms are tightly tweezed by a 1D optical tweezer array at the antinode of the cavity field, and illuminated from the side with a uniform-phase pump light. Such system can be effectively described by a Dicke-type Hamiltonian with a  Z_2/U(1) symmetry, depending on if it is coupled to one or both polarizations of the cavity mode. At pump intensity beyond the Dicke phase transition, we observe spontaneous symmetry breaking of the cavity field phase (polarization) for the Z_2/U(1) model, accordingly. We measure the real-time dynamics of the system by performing phase-resolved heterodyne detection on both polarization of the cavity emission. We measure the final state of the atoms by performing a state-selective imaging of the atom array in the end.

 

One important question we are trying to answer in both case is: how does the stability of a quantum phase transition scale with system size, especially for a mesoscopic system that is sensitive to quantum fluctuations.