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
DPT_2_Setup.jpg
3. system Overview
Eq. of motion of atom in the modulating Magneto-optical trap
DPT_3_Overview_1.jpg
1) Parametric Resonance: dynamic bistable states when DPT_3_Overview_2.jpg
* Discrete time translation symmetry
DPT_3_Overview_3.jpg
DPT_3_Overview_4.jpg
* 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)

DPT_3_Overview_6.jpg

* 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”
DPT_3_Overview_9.jpg
DPT_3_Overview_10.jpg
4. Dynamic Response
* system response to sinusoidal additional bias field
Linear response regime (small bias field) : AC susceptibility
DPT_4_Response_1.jpg
DPT_4_Response_2.jpg
DPT_4_Response_3.jpg
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
DPT_4_Response_4.jpg
DPT_4_Response_5.jpg
* Dynamic order parameter
DPT_4_Response_6.jpg
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.

DPT_5_DPT_1.jpg

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
DPT_5_DPT_5.jpg
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
 
DPT_5_DPT_6.jpg
      :Observing the  tricritical point and coexistence region (first observation)