Nonequilibrium Phenomena in the Cold Atomic System

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 DPT_3_Overview_2.jpg
* Discrete time translation symmetry
* Fluctuation-induced transition rate between two attractors: most important quantity for characterizing the system
DPT_3_Overview_5.jpg 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
DPT_3_Overview_7.jpg DPT_3_Overview_8.jpg
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 (ωF) + small (ωF/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 DPT_5_DPT_2.jpg : transition rate between two state without bias, DPT_5_DPT_3.jpg: control parameter(number of atoms) and DPT_5_DPT_4.jpg: 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. h0
      :Observing the  tricritical point and coexistence region (first observation)