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.

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