Download - PT transitions in dissipative Floquet system
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.
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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.
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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?
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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.
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H = �JSx
+ i�(t)Sz
exceptional point of order (2S+1)
Cold atoms in the TAILab (Le Luo Group)
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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
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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.
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Floquet PT phase diagram for dissipative case