Stability of PT and anti- PT -symmetric Hamiltonians with multiple harmonics

Cen, Julia; Joglekar, Yogesh N.; Saxena, Avadh

doi:10.1103/PhysRevResearch.6.013167

Title: Stability of $PT$ and anti- $PT$ -symmetric Hamiltonians with multiple harmonics

Journal Article · 14 February 2024 · Physical Review Research

DOI: https://doi.org/10.1103/PhysRevResearch.6.013167 · OSTI ID:2305420

;

Hermitian Hamiltonians with time-periodic coefficients can be analyzed via Floquet theory, and have been extensively used for engineering Floquet Hamiltonians in standard quantum simulators. Generalized to non-Hermitian Hamiltonians, time periodicity offers avenues to engineer the landscape of Floquet quasienergies across the complex plane. We investigate two-level non-Hermitian $PT$ and anti- $PT$ -symmetric Hamiltonians with coefficients that have multiple harmonics using Floquet theory. By analytical and numerical calculations, we obtain their regions of stability, defined by real Floquet quasienergies, and contours of exceptional point (EP) degeneracies. We extend our analysis to study the phases that accompany these cyclic changes with the biorthogonality approach. Our results demonstrate that these time-periodic Hamiltonians generate a rich landscape of stable (real) and unstable (complex) regions. Published by the American Physical Society 2024

View Journal Article

Cite

Export

Save

Sponsoring Organization:: USDOE

OSTI ID:: 2305420

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Vol. 6 Journal Issue: 1; ISSN 2643-1564

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (62)

Observation of PT phase transition in a simple mechanical system Bender, Carl M.; Berntson, Bjorn K.; Parker, David American Journal of Physics, Vol. 81, Issue 3 https://doi.org/10.1119/1.4789549	journal	March 2013
Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators Chang, Long; Jiang, Xiaoshun; Hua, Shiyue Nature Photonics, Vol. 8, Issue 7 https://doi.org/10.1038/nphoton.2014.133	journal	June 2014
Modern Quantum Mechanics Sakurai, J. J.; Napolitano, Jim https://doi.org/10.1017/9781108499996	book	January 2017
Topological characterization of periodically driven quantum systems Kitagawa, Takuya; Berg, Erez; Rudner, Mark Physical Review B, Vol. 82, Issue 23 https://doi.org/10.1103/PhysRevB.82.235114	journal	December 2010
Unidirectional Invisibility Induced by P T -Symmetric Periodic Structures Lin, Zin; Ramezani, Hamidreza; Eichelkraut, Toni Physical Review Letters, Vol. 106, Issue 21 https://doi.org/10.1103/PhysRevLett.106.213901	journal	May 2011
Experimental Determination of PT -Symmetric Exceptional Points in a Single Trapped Ion Ding, Liangyu; Shi, Kaiye; Zhang, Qiuxin Physical Review Letters, Vol. 126, Issue 8 https://doi.org/10.1103/PhysRevLett.126.083604	journal	February 2021
PT spectroscopy of the Rabi problem Joglekar, Yogesh N.; Marathe, Rahul; Durganandini, P. Physical Review A, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevA.90.040101	journal	October 2014
Maximal quantum entanglement at exceptional points via unitary and thermal dynamics Kumar, Akhil; Murch, Kater W.; Joglekar, Yogesh N. Physical Review A, Vol. 105, Issue 1 https://doi.org/10.1103/PhysRevA.105.012422	journal	January 2022
Floquet topological insulator in semiconductor quantum wells Lindner, Netanel H.; Refael, Gil; Galitski, Victor Nature Physics, Vol. 7, Issue 6 https://doi.org/10.1038/nphys1926	journal	March 2011
Controllable Floquet edge modes in a multifrequency driving system Park, HaRu K.; Jeon, Junmo; Cho, Gil Young Physical Review B, Vol. 107, Issue 8 https://doi.org/10.1103/PhysRevB.107.085141	journal	February 2023
Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time Shirley, Jon H. Physical Review, Vol. 138, Issue 4B https://doi.org/10.1103/PhysRev.138.B979	journal	May 1965
Geometric phase for non-Hermitian Hamiltonian evolution as anholonomy of a parallel transport along a curve Sinitsyn, N. A.; Saxena, Avadh Journal of Physics A: Mathematical and Theoretical, Vol. 41, Issue 39 https://doi.org/10.1088/1751-8113/41/39/392002	journal	September 2008
Dynamical Control of Matter-Wave Tunneling in Periodic Potentials Lignier, H.; Sias, C.; Ciampini, D. Physical Review Letters, Vol. 99, Issue 22 https://doi.org/10.1103/PhysRevLett.99.220403	journal	November 2007
Exact PT -symmetry is equivalent to Hermiticity Mostafazadeh, Ali Journal of Physics A: Mathematical and General, Vol. 36, Issue 25 https://doi.org/10.1088/0305-4470/36/25/312	journal	June 2003
Anti–parity-time symmetry in diffusive systems Li, Ying; Peng, Yu-Gui; Han, Lei Science, Vol. 364, Issue 6436 https://doi.org/10.1126/science.aaw6259	journal	April 2019
Observation of slowly decaying eigenmodes without exceptional points in Floquet dissipative synthetic circuits León-Montiel, Roberto de J.; Quiroz-Juárez, Mario A.; Domínguez-Juárez, Jorge L. Communications Physics, Vol. 1, Issue 1 https://doi.org/10.1038/s42005-018-0087-3	journal	December 2018
Berry phase in an anti-PT symmetric metal-semiconductor complex system Lu, Bo; Liu, Xiao-Fei; Gao, Yong-Pan Optics Express, Vol. 27, Issue 16 https://doi.org/10.1364/OE.27.022237	journal	July 2019
Optical waveguide arrays: quantum effects and PT symmetry breaking Joglekar, Yogesh N.; Thompson, Clinton; Scott, Derek D. The European Physical Journal Applied Physics, Vol. 63, Issue 3 https://doi.org/10.1051/epjap/2013130240	journal	September 2013
Dynamically encircling an exceptional point in anti-parity-time symmetric systems: asymmetric mode switching for symmetry-broken modes Zhang, Xu-Lin; Jiang, Tianshu; Chan, C. T. Light: Science & Applications, Vol. 8, Issue 1 https://doi.org/10.1038/s41377-019-0200-8	journal	October 2019
Real Spectra in Non-Hermitian Hamiltonians Having P T Symmetry Bender, Carl M.; Boettcher, Stefan Physical Review Letters, Vol. 80, Issue 24 https://doi.org/10.1103/PhysRevLett.80.5243	journal	June 1998
Complex Extension of Quantum Mechanics Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F. Physical Review Letters, Vol. 89, Issue 27 https://doi.org/10.1103/PhysRevLett.89.270401	journal	December 2002
Pseudo-Parity-Time Symmetry in Optical Systems Luo, Xiaobing; Huang, Jiahao; Zhong, Honghua Physical Review Letters, Vol. 110, Issue 24 https://doi.org/10.1103/PhysRevLett.110.243902	journal	June 2013
Dynamically Encircling an Exceptional Point in a Real Quantum System Liu, Wenquan; Wu, Yang; Duan, Chang-Kui Physical Review Letters, Vol. 126, Issue 17 https://doi.org/10.1103/PhysRevLett.126.170506	journal	April 2021
Floquet Engineering of Quantum Materials Oka, Takashi; Kitamura, Sota Annual Review of Condensed Matter Physics, Vol. 10, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031218-013423	journal	March 2019
Localization Transitions in Non-Hermitian Quantum Mechanics Hatano, Naomichi; Nelson, David R. Physical Review Letters, Vol. 77, Issue 3 https://doi.org/10.1103/PhysRevLett.77.570	journal	July 1996
Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian Mostafazadeh, Ali Journal of Mathematical Physics, Vol. 43, Issue 1 https://doi.org/10.1063/1.1418246	journal	January 2002
Nonlinear Anti-(Parity-Time) Symmetric Dimer Rodrigues, A. S.; Ross, R. M.; Konotop, V. V. Frontiers in Physics, Vol. 10 https://doi.org/10.3389/fphy.2022.865910	journal	April 2022
Quantum state tomography across the exceptional point in a single dissipative qubit Naghiloo, M.; Abbasi, M.; Joglekar, Yogesh N. Nature Physics, Vol. 15, Issue 12 https://doi.org/10.1038/s41567-019-0652-z	journal	October 2019
Exceptional points of any order in a single, lossy waveguide beam splitter by photon-number-resolved detection Quiroz-Juárez, Mario A.; Perez-Leija, Armando; Tschernig, Konrad Photonics Research, Vol. 7, Issue 8 https://doi.org/10.1364/PRJ.7.000862	journal	January 2019
Observation of parity-time symmetry breaking in a single-spin system Wu, Yang; Liu, Wenquan; Geng, Jianpei Science, Vol. 364, Issue 6443 https://doi.org/10.1126/science.aaw8205	journal	May 2019
Conserved quantities in parity-time symmetric systems Bian, Zhihao; Xiao, Lei; Wang, Kunkun Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.022039	journal	May 2020
On-Demand Parity-Time Symmetry in a Lone Oscillator through Complex Synthetic Gauge Fields Quiroz-Juárez, Mario A.; Agarwal, Kaustubh S.; Cochran, Zachary A. Physical Review Applied, Vol. 18, Issue 5 https://doi.org/10.1103/PhysRevApplied.18.054034	journal	November 2022
Decoherence-Induced Exceptional Points in a Dissipative Superconducting Qubit Chen, Weijian; Abbasi, Maryam; Ha, Byung Physical Review Letters, Vol. 128, Issue 11 https://doi.org/10.1103/PhysRevLett.128.110402	journal	March 2022
PT-symmetric quantum mechanics Bender, Carl M.; Boettcher, Stefan; Meisinger, Peter N. Journal of Mathematical Physics, Vol. 40, Issue 5 https://doi.org/10.1063/1.532860	journal	May 1999
Floquet engineering of individual band gaps in an optical lattice using a two-tone drive Sandholzer, Kilian; Walter, Anne-Sophie; Minguzzi, Joaquín Physical Review Research, Vol. 4, Issue 1 https://doi.org/10.1103/PhysRevResearch.4.013056	journal	January 2022
Connecting active and passive $\mathcal{PT}$-symmetric Floquet modulation models Harter, Andrew K.; Joglekar, Yogesh N. Progress of Theoretical and Experimental Physics, Vol. 2020, Issue 12 https://doi.org/10.1093/ptep/ptaa181	journal	December 2020
Experimental demonstration of exceptional points of degeneracy in linear time periodic systems and exceptional sensitivity Kazemi, Hamidreza; Nada, Mohamed Y.; Nikzamir, Alireza Journal of Applied Physics, Vol. 131, Issue 14 https://doi.org/10.1063/5.0084849	journal	April 2022
Information retrieval and eigenstate coalescence in a non-Hermitian quantum system with anti- PT symmetry Ding, Liangyu; Shi, Kaiye; Wang, Yuxin Physical Review A, Vol. 105, Issue 1 https://doi.org/10.1103/PhysRevA.105.L010204	journal	January 2022
Observation of P T -Symmetry Breaking in Complex Optical Potentials Guo, A.; Salamo, G. J.; Duchesne, D. Physical Review Letters, Vol. 103, Issue 9 https://doi.org/10.1103/PhysRevLett.103.093902	journal	August 2009
PT -symmetric Rabi model: Perturbation theory Lee, Tony E.; Joglekar, Yogesh N. Physical Review A, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevA.92.042103	journal	October 2015
Quantum Jumps in the Non-Hermitian Dynamics of a Superconducting Qubit Chen, Weijian; Abbasi, Maryam; Joglekar, Yogesh N. Physical Review Letters, Vol. 127, Issue 14 https://doi.org/10.1103/PhysRevLett.127.140504	journal	September 2021
Experimental study of active LRC circuits with PT symmetries Schindler, Joseph; Li, Ang; Zheng, Mei C. Physical Review A, Vol. 84, Issue 4 https://doi.org/10.1103/PhysRevA.84.040101	journal	October 2011
Antisymmetric PT -photonic structures with balanced positive- and negative-index materials Ge, Li; Türeci, Hakan E. Physical Review A, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevA.88.053810	journal	November 2013
Photonic Floquet topological insulators Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan Nature, Vol. 496, Issue 7444 https://doi.org/10.1038/nature12066	journal	April 2013
Observation of parity–time symmetry in optics Rüter, Christian E.; Makris, Konstantinos G.; El-Ganainy, Ramy Nature Physics, Vol. 6, Issue 3 https://doi.org/10.1038/nphys1515	journal	January 2010
Berry's Phase Zwanziger, J. W.; Koenig, M.; Pines, A. Annual Review of Physical Chemistry, Vol. 41, Issue 1 https://doi.org/10.1146/annurev.pc.41.100190.003125	journal	October 1990
Theory of coupled optical PT-symmetric structures El-Ganainy, R.; Makris, K. G.; Christodoulides, D. N. Optics Letters, Vol. 32, Issue 17 https://doi.org/10.1364/OL.32.002632	journal	January 2007
Complex Berry phase dynamics in PT -symmetric coupled waveguides Hayward, Rosie; Biancalana, Fabio Physical Review A, Vol. 98, Issue 5 https://doi.org/10.1103/PhysRevA.98.053833	journal	November 2018
Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms Li, Jiaming; Harter, Andrew K.; Liu, Ji Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-08596-1	journal	February 2019
Geometrical phase in the cyclic evolution of non-Hermitian systems Dattoli, G.; Mignani, R.; Torre, A. Journal of Physics A: Mathematical and General, Vol. 23, Issue 24 https://doi.org/10.1088/0305-4470/23/24/020	journal	December 1990
Quantal Phase Factors Accompanying Adiabatic Changes Berry, M. V. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 392, Issue 1802 https://doi.org/10.1098/rspa.1984.0023	journal	March 1984
Topological Quantum State Control through Exceptional-Point Proximity Abbasi, Maryam; Chen, Weijian; Naghiloo, Mahdi Physical Review Letters, Vol. 128, Issue 16 https://doi.org/10.1103/PhysRevLett.128.160401	journal	April 2022
Quantum simulation of a general anti-PT-symmetric Hamiltonian with a trapped ion qubit Bian, Ji; Lu, Pengfei; Liu, Teng Fundamental Research, Vol. 3, Issue 6 https://doi.org/10.1016/j.fmre.2022.05.019	journal	November 2023
Anti-Parity-Time Symmetric Optical Four-Wave Mixing in Cold Atoms Jiang, Yue; Mei, Yefeng; Zuo, Ying Physical Review Letters, Vol. 123, Issue 19 https://doi.org/10.1103/PhysRevLett.123.193604	journal	November 2019
Parity–time synthetic photonic lattices Regensburger, Alois; Bersch, Christoph; Miri, Mohammad-Ali Nature, Vol. 488, Issue 7410 https://doi.org/10.1038/nature11298	journal	August 2012
Observation of two 𝓟𝓣 transitions in an electric circuit with balanced gain and loss Wang, Tishuo; Fang, Jianxiong; Xie, Zhongyi The European Physical Journal D, Vol. 74, Issue 8 https://doi.org/10.1140/epjd/e2020-10131-7	journal	August 2020
Exceptional Points of Degeneracy Induced by Linear Time-Periodic Variation Kazemi, Hamidreza; Nada, Mohamed Y.; Mealy, Tarek Physical Review Applied, Vol. 11, Issue 1 https://doi.org/10.1103/PhysRevApplied.11.014007	journal	January 2019
Floquet maser Jiang, Min; Su, Haowen; Wu, Ze Science Advances, Vol. 7, Issue 8 https://doi.org/10.1126/sciadv.abe0719	journal	February 2021
Special Issue “Pseudo-Hermitian Hamiltonians in Quantum Physics in 2014” Znojil, Miloslav International Journal of Theoretical Physics, Vol. 54, Issue 11 https://doi.org/10.1007/s10773-014-2501-2	journal	January 2015
Space Quantization in a Gyrating Magnetic Field Rabi, I. I. Physical Review, Vol. 51, Issue 8 https://doi.org/10.1103/PhysRev.51.652	journal	April 1937
Anti-parity–time symmetry with flying atoms Peng, Peng; Cao, Wanxia; Shen, Ce Nature Physics, Vol. 12, Issue 12 https://doi.org/10.1038/nphys3842	journal	August 2016
Visualization of Branch Points in P T -Symmetric Waveguides Klaiman, Shachar; Günther, Uwe; Moiseyev, Nimrod Physical Review Letters, Vol. 101, Issue 8 https://doi.org/10.1103/PhysRevLett.101.080402	journal	August 2008