# Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks

## Abstract

Quantum walks often provide telling insights about the structure of the system on which they are performed. Here, in PT-symmetric and lossy dimer lattices, the topological properties of the band structure manifest themselves in the quantization of the mean displacement of such a walker. We investigate the fragile aspects of a topological transition in these two dimer models. We find that the transition is sensitive to the initial state of the walker on the Bloch sphere, and the resultant mean displacement has a robust topological component and a quasiclassical component. In PT symmetric dimer lattices, we also show that the transition is smeared by nonlinear effects that become important in the PT-symmetry broken region. By carrying out consistency checks via analytical calculations, tight-binding results, and beam-propagation-method simulations, we show that our predictions are easily testable in today’s experimental systems.

- Authors:

- Indiana Univ. - Purdue Univ. Indianapolis (IUPUI), Indianapolis, IN (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 1481974

- Report Number(s):
- LA-UR-18-20269

Journal ID: ISSN 2045-2322

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Scientific Reports

- Additional Journal Information:
- Journal Volume: 8; Journal Issue: 1; Journal ID: ISSN 2045-2322

- Publisher:
- Nature Publishing Group

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics

### Citation Formats

```
Harter, Andrew K., Saxena, Avadh, and Joglekar, Yogesh N. Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks. United States: N. p., 2018.
Web. doi:10.1038/s41598-018-30344-6.
```

```
Harter, Andrew K., Saxena, Avadh, & Joglekar, Yogesh N. Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks. United States. doi:10.1038/s41598-018-30344-6.
```

```
Harter, Andrew K., Saxena, Avadh, and Joglekar, Yogesh N. Mon .
"Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks". United States. doi:10.1038/s41598-018-30344-6. https://www.osti.gov/servlets/purl/1481974.
```

```
@article{osti_1481974,
```

title = {Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks},

author = {Harter, Andrew K. and Saxena, Avadh and Joglekar, Yogesh N.},

abstractNote = {Quantum walks often provide telling insights about the structure of the system on which they are performed. Here, in PT-symmetric and lossy dimer lattices, the topological properties of the band structure manifest themselves in the quantization of the mean displacement of such a walker. We investigate the fragile aspects of a topological transition in these two dimer models. We find that the transition is sensitive to the initial state of the walker on the Bloch sphere, and the resultant mean displacement has a robust topological component and a quasiclassical component. In PT symmetric dimer lattices, we also show that the transition is smeared by nonlinear effects that become important in the PT-symmetry broken region. By carrying out consistency checks via analytical calculations, tight-binding results, and beam-propagation-method simulations, we show that our predictions are easily testable in today’s experimental systems.},

doi = {10.1038/s41598-018-30344-6},

journal = {Scientific Reports},

number = 1,

volume = 8,

place = {United States},

year = {2018},

month = {8}

}

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Works referenced in this record:

##
Observation of Topological Phase Transitions in Photonic Quasicrystals

journal, February 2013

- Verbin, Mor; Zilberberg, Oded; Kraus, Yaacov E.
- Physical Review Letters, Vol. 110, Issue 7

##
Unidirectional Invisibility Induced by $\mathcal{P}\mathcal{T}$ -Symmetric Periodic Structures

journal, May 2011

- Lin, Zin; Ramezani, Hamidreza; Eichelkraut, Toni
- Physical Review Letters, Vol. 106, Issue 21

##
Observation of $\mathcal{P}\mathcal{T}$ -Symmetry Breaking in Complex Optical Potentials

journal, August 2009

- Guo, A.; Salamo, G. J.; Duchesne, D.
- Physical Review Letters, Vol. 103, Issue 9

##
Single-mode laser by parity-time symmetry breaking

journal, October 2014

- Feng, L.; Wong, Z. J.; Ma, R. -M.
- Science, Vol. 346, Issue 6212

##
Solitons in Polyacetylene

journal, June 1979

- Su, W. P.; Schrieffer, J. R.; Heeger, A. J.
- Physical Review Letters, Vol. 42, Issue 25

##
Topological States and Adiabatic Pumping in Quasicrystals

journal, September 2012

- Kraus, Yaacov E.; Lahini, Yoav; Ringel, Zohar
- Physical Review Letters, Vol. 109, Issue 10

##
Observation of parity–time symmetry in optics

journal, January 2010

- Rüter, Christian E.; Makris, Konstantinos G.; El-Ganainy, Ramy
- Nature Physics, Vol. 6, Issue 3

##
Nonreciprocal Light Propagation in a Silicon Photonic Circuit

journal, August 2011

- Feng, L.; Ayache, M.; Huang, J.
- Science, Vol. 333, Issue 6043

##
Theory of coupled optical PT-symmetric structures

journal, January 2007

- El-Ganainy, R.; Makris, K. G.; Christodoulides, D. N.
- Optics Letters, Vol. 32, Issue 17

##
Optical waveguide arrays: quantum effects and PT symmetry breaking

journal, September 2013

- Joglekar, Yogesh N.; Thompson, Clinton; Scott, Derek D.
- The European Physical Journal Applied Physics, Vol. 63, Issue 3

##
Non-Hermitian physics and PT symmetry

journal, January 2018

- El-Ganainy, Ramy; Makris, Konstantinos G.; Khajavikhan, Mercedeh
- Nature Physics, Vol. 14, Issue 1

##
Real Spectra in Non-Hermitian Hamiltonians Having $\mathcal{P}\mathcal{T}$ Symmetry

journal, June 1998

- Bender, Carl M.; Boettcher, Stefan
- Physical Review Letters, Vol. 80, Issue 24

##
Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models

journal, May 2013

- Ganeshan, Sriram; Sun, Kai; Das Sarma, S.
- Physical Review Letters, Vol. 110, Issue 18

##
Complex Extension of Quantum Mechanics

journal, December 2002

- Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.
- Physical Review Letters, Vol. 89, Issue 27

##
Local $\mathcal{P}\mathcal{T}$ Symmetry Violates the No-Signaling Principle

journal, April 2014

- Lee, Yi-Chan; Hsieh, Min-Hsiu; Flammia, Steven T.
- Physical Review Letters, Vol. 112, Issue 13

##
Observation of a Topological Transition in the Bulk of a Non-Hermitian System

journal, July 2015

- Zeuner, Julia M.; Rechtsman, Mikael C.; Plotnik, Yonatan
- Physical Review Letters, Vol. 115, Issue 4

##
Topologically protected bound states in photonic parity–time-symmetric crystals

journal, December 2016

- Weimann, S.; Kremer, M.; Plotnik, Y.
- Nature Materials, Vol. 16, Issue 4

##
Parity-time-symmetric microring lasers

journal, October 2014

- Hodaei, H.; Miri, M. -A.; Heinrich, M.
- Science, Vol. 346, Issue 6212

##
$\mathcal{PT}$ -breaking threshold in spatially asymmetric Aubry-André and Harper models: Hidden symmetry and topological states

journal, June 2016

- Harter, Andrew K.; Lee, Tony E.; Joglekar, Yogesh N.
- Physical Review A, Vol. 93, Issue 6

##
Parity–time synthetic photonic lattices

journal, August 2012

- Regensburger, Alois; Bersch, Christoph; Miri, Mohammad-Ali
- Nature, Vol. 488, Issue 7410

##
Loss-induced suppression and revival of lasing

journal, October 2014

- Peng, B.; Ozdemir, . K.; Rotter, S.
- Science, Vol. 346, Issue 6207

##
Topological phases of generalized Su-Schrieffer-Heeger models

journal, February 2014

- Li, Linhu; Xu, Zhihao; Chen, Shu
- Physical Review B, Vol. 89, Issue 8

##
Topologically protected midgap states in complex photonic lattices

journal, January 2013

- Schomerus, Henning
- Optics Letters, Vol. 38, Issue 11

##
Topological Transition in a Non-Hermitian Quantum Walk

journal, February 2009

- Rudner, M. S.; Levitov, L. S.
- Physical Review Letters, Vol. 102, Issue 6

##
Visualization of Branch Points in $\mathcal{P}\mathcal{T}$ -Symmetric Waveguides

journal, August 2008

- Klaiman, Shachar; Günther, Uwe; Moiseyev, Nimrod
- Physical Review Letters, Vol. 101, Issue 8

##
Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies

journal, November 2012

- Feng, Liang; Xu, Ye-Long; Fegadolli, William S.
- Nature Materials, Vol. 12, Issue 2

##
Quasi $\mathcal{P}\mathcal{T}$-symmetry in passive photonic lattices

journal, May 2014

- Ornigotti, Marco; Szameit, Alexander
- Journal of Optics, Vol. 16, Issue 6

##
Solitons in conducting polymers

journal, July 1988

- Heeger, A. J.; Kivelson, S.; Schrieffer, J. R.
- Reviews of Modern Physics, Vol. 60, Issue 3