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