**1. Introduction**

Periodically modulated system is one of the most important class of nonequilibrium systems.

Measuring the response of a system to an externally applied field is important tool for characterizing the system properties.

: Generalized susceptibility, fluctuation-dissipation theorem, …

We use cold atoms to reveal and explore critical behaviour and dynamic feature far from equilibrium system.

**2. Experimental Setup**

**3. system Overview**

Eq. of motion of atom in the modulating Magneto-optical trap

**1) Parametric Resonance: dynamic bistable states when**

* Discrete time translation symmetry

* Fluctuation-induced transition rate between two attractors: most important quantity for characterizing the system

Similar as Kramer’s equation: W ~ exp(-S/D) |

* References:

1. Kihwan Kim, Heung-Ryoul Noh, and Wonho Jhe, “Parametric resonance in an intensity-modulated magneto-optical trap”, Optics Comm.

**236**, 349 (2004) [Link]2. Kihwan Kim, Myoung-Sun Heo, Ki-Hwan Lee, Hyoun-Jee Ha, Kiyoub Jang, Heung-Ryoul Noh, and Wonho Jhe, “Noise-induced transition of atoms between dynamic phase-space attractors in a parametrically excited atomic trap”, Phys. Rev. A

**72**, 053402 (2005) [Link]**2) Time-translational Symmetry Breaking**

Light-induced interaction : shadow effect

Mean-field behavior : experimental data (critical exponents) and theory

* References:

1. Kihwan Kim, Myoung-Sun Heo, Ki-Hwan Lee, Kiyoub Jang, Heung-Ryoul Noh, Doochul Kim, and Wonho Jhe, “Spontaneous Symmetry Breaking of Population in a Nonadiabatically Driven atomic Trap: An Ising-Class Phase Transition”, Phys. Rev. Lett.

**96**, 150601 (2006) [Link]2. Myoung-Sun Heo, Yonghee Kim, Kihwan Kim, Geol Moon, Junhyun Lee, Heung-Ryoul Noh, M. I. Dykman, and Wonho Jhe, “Ideal mean-field transition in a modulated cold atom system”, Phys. Rev. E.

**82**, 031134 (2010) [Link]**3) Realization of Additional Bias Field: Parametric driving signal (ω**

_{F}

**) + small (ω**

_{F}

**/2) signal**

additional field frequency = atomic motional frequency => “effective bias field”

**4. Dynamic Response**

* system response to sinusoidal additional bias field

Linear response regime (small bias field) :

**AC susceptibility**Reference: Myoung-Sun Heo, Yonghee Kim, Kihwan Kim, Geol Moon, Junhyun Lee, Heung-Ryoul Noh, M. I. Dykman, and Wonho Jhe, “Ideal mean-field transition in a modulated cold atom system”, Phys. Rev. E.

**82**, 031134 (2010) [Link]* General case

* Dynamic order parameter

**5. Dynamic Phase Transition**

* **Dynamic Phase Transition (DPT)**: Dynamical behavior of a nonequilibrium system changes in a singular way at a critical value of a system parameter

* Competition between two dynamical time scale: bias field frequency vs. system relaxation(response) time

* Describes by simple mean-field type eq.

where : transition rate between two state without bias, : control parameter(number of atoms) and : bias field strength

* Phase map

Q vs. N vs. Ω

Fluctuation of <Q> has divergent behavior near critical point

– evidence to the criticality of DPT

Scaling exponents near dynamic critical point are still open questions

Q vs. N vs. h

_{0} :Observing the tricritical point and coexistence region (first observation)