PT transitions in dissipative Floquet system
Yogesh N. Joglekar
Indiana University Purdue University Indianapolis (IUPUI)
Jiamin Li, Le Luo, ExperimentsAndrew Harter, Theory
AAMP XIIIPrague 2016
Outline
PT lattice systems = balanced gain and loss.
1. Two-site system: static or time-periodic gain and loss.
2. PT phase diagram of (dissipative) Floquet Hamiltonian.
3. Experimental realization in cold atoms.
2
PT systems = balanced gain and loss
Parity: exchange gain-loss locations.Time-reversal: change gain into loss.Loss only: PT over decaying background
PT symmetric phase: intensity oscillations with bounded amplification.PT boundary: power-law growth.PT broken phase: exponential growth.Single PT transition threshold.
3
What happens if we make loss periodic in time?
J+iγ -iγ
J
-2iγneutral
PT Floquet Hamiltonian
PT gain−loss strength a/J
PT m
odul
atio
n fre
quen
cy t
/J
0 0.25 0.5 0.75 1 1.25 1.5
0
0.5
1
1.5
2
2.5
3
3.5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
PT−broken phase
PT−symmetric phase
(a)
Static case: single PT transition.
High frequencies ⍵: no PT breaking. Resonance: PT breaking for vanishingly small gain-loss.
What about low ⍵ near the static threshold?
4
PRA 90, 040101(R) (2014)PRA 92, 042103 (2015)
H = �J�x
+ i�(t)�z
i�(t) = i�0 cos(!t)
No adiabatic picture at static threshold!
Infinite ladder of PT transitions.Breakdown of adiabatic approximation.
5
H = �JSx
+ i�(t)Sz
exceptional point of order (2S+1)
Cold atoms in the TAILab (Le Luo Group)
6
http://www.iupui.edu/~tailab/
• 6Li atoms• Tfinal = 10-6 K• N=1.6x105
• RF: Rabi coupling J.
• Resonant laser: loss 𝚪(t).
time (ms)
Static PT breaking in cold Fermi gas
7
8
Floquet PT breaking in cold Fermi gas
Conclusions
• PT Floquet models give lines of exceptional points.
• Weird behavior near static exceptional point.
• Experimental observation in a quantum system.
9
Floquet PT phase diagram for dissipative case