- Open Access
Nonlinear dynamics of one-dimensional bright solitonlike state in polariton condensates induced by a PT-symmetric periodic potential
Phys. Rev. Research 8, 023133 – Published 8 May, 2026
DOI: https://doi.org/10.1103/fsp4-cwh6
Abstract
We investigate the dynamics of one-dimensional bright solitonlike state in exciton-polariton condensates under a parity-time (PT) symmetric periodic potential. For the static potential case, we demonstrate the formation of stable gap solitonlike state arising from the combined action of the potential and a composite Gaussian pump. Notably, these gap solitonlike state differ from those in the conventional nonlinear Schrödinger equation in two key ways. First, their existence and stability depend not only on the balance between nonlinearity and dispersion but also critically on the system's gain-loss balance. Second, their profiles (e.g., main-peak amplitude) can be directly controlled by the intensity of the composite Gaussian pump. Furthermore, when the PT-symmetric potential is designed to include a barrier with exponentially varying intensity, we observe that a stable incident bright solitonlike state exhibits controllable switching dynamics, in stark contrast to the unidirectional transmission seen in conservative systems. During this process, the bright solitonlike state transforms into a polariton wave, temporarily disappears, and subsequently re-emerges. This behavior is governed by the interaction between the PT-symmetric barrier and the intrinsic gain-loss mechanism of the system. Additionally, we propose an active control scheme based on nonresonant optical Gaussian pump pulses to precisely manipulate the disappearance time of the bright solitonlike state. Our findings establish a promising platform for soliton-based photonic devices in nonequilibrium systems.
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References (81)
- C. M. Bender and S. Boettcher, Real spectra in non-Hermitian Hamiltonians having PT symmetry, Phys. Rev. Lett. 80, 5243 (1998).
- C. M. Bender, D. C. Brody, and H. F. Jones, Complex extension of quantum mechanics, Phys. Rev. Lett. 89, 270401 (2002).
- R. El-Ganainy, K. G. Makris, and D. N. Christodoulides, Theory of coupled optical PT-symmetric structures, Opt. Lett. 32, 2632 (2007).
- K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Beam dynamics in PT symmetric optical lattices, Phys. Rev. Lett. 100, 103904 (2008).
- K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, PT-symmetric optical lattices, Phys. Rev. A 81, 063807 (2010).
- A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Observation of PT-symmetry breaking in complex optical potentials, Phys. Rev. Lett. 103, 093902 (2009).
- C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Observation of parity-time symmetry in optics, Nat. Phys. 6, 192 (2010).
- Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Optical solitons in PT periodic potentials, Phys. Rev. Lett. 100, 030402 (2008).
- R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Non-Hermitian physics and PT symmetry, Nat. Phys. 14, 11 (2018).
- S. Hu, X. Ma, D. Lu, Z. Yang, Y. Zheng, and W. Hu, Solitons supported by complex PT-symmetric Gaussian potentials, Phys. Rev. A 84, 043818 (2011).
- J. Zeng and Y. Lan, Two-dimensional solitons in PT linear lattice potentials, Phys. Rev. E 85, 047601 (2012).
- S. Nixon, L. Ge, and J. Yang, Stability analysis for solitons in PT-symmetric optical lattices, Phys. Rev. A 85, 023822 (2012).
- C. Li, C. Huang, H. Liu, and L. Dong, Multipeaked gap solitons in PT-symmetric optical lattices, Opt. Lett. 37, 4543 (2012).
- X. Zhu, H. Wang, H. Li, W. He, and Y. He, Two-dimensional multipeak gap solitons supported by parity-time-symmetric periodic potentials, Opt. Lett. 38, 2723 (2013).
- H. Wang and J. Wang, Defect solitons in parity-time periodic potentials, Opt. Express 19, 4030 (2011).
- S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity, Phys. Rev. A 85, 043826 (2012).
- H. Li, X. Zhu, Z. Shi, B. A. Malomed, T. Lai, and C. Lee, Bulk vortices and half-vortex surface modes in parity-time-symmetric media, Phys. Rev. A 89, 053811 (2014).
- L. Dong and C. Huang, Vortex solitons in fractional systems with partially parity-time-symmetric azimuthal potentials, Nonlinear Dyn. 98, 1019 (2019).
- J. Yang, Symmetry breaking of solitons in one-dimensional parity-time-symmetric optical potentials, Opt. Lett. 39, 5547 (2014).
- Z. Yan, Z. Wen, and C. Hang, Spatial solitons and stability in self-focusing and defocusing Kerr nonlinear media with generalized parity-time-symmetric Scarff-II potentials, Phys. Rev. E 92, 022913 (2015).
- U. Al Khawaja, S. M. Al-Marzoug, H. Bahlouli, and Y. S. Kivshar, Unidirectional soliton flows in PT -symmetric potentials, Phys. Rev. A 88, 023830 (2013).
- Y. V. Kartashov, V. A. Vysloukh, V. V. Konotop, and L. Torner, Diffraction control in PT-symmetric photonic lattices: From beam rectification to dynamic localization, Phys. Rev. A 93, 013841 (2016).
- Y. Chen, Z. Yan, and X. Li, One- and two-dimensional gap solitons and dynamics in the PT-symmetric lattice potential and spatially-periodic momentum modulation, Commun. Nonlinear Sci. Numer. Simul. 55, 287 (2018).
- K. Zhou, T. Wei, H. Sun, Y. He, and S. Liu, Soliton dynamics in a PT-symmetric optical lattice with a longitudinal potential barrier, Opt. Express 23, 16903 (2015).
- V. Achilleos, Y. Aurégan, and V. Pagneux, Scattering by finite periodic PT-symmetric structures, Phys. Rev. Lett. 119, 243904 (2017).
- A. Govindarajan, A. K. Sarma, and M. Lakshmanan, Tailoring PT -symmetric soliton switch, Opt. Lett. 44, 663 (2019).
- A. Sahoo, D. K. Mahato, A. Govindarajan, and A. K. Sarma, Bistable soliton switching dynamics in a PT -symmetric coupler with saturable nonlinearity, Phys. Rev. A 105, 063503 (2022).
- H. Ramezani, J. Schindler, F. M. Ellis, U. Günther, and T. Kottos, Bypassing the bandwidth theorem with PT symmetry, Phys. Rev. A 85, 062122 (2012).
- Z. Lin, J. Schindler, F. M. Ellis, and T. Kottos, Experimental observation of the dual behavior of PT-symmetric scattering, Phys. Rev. A 85, 050101(R) (2012).
- M. Kang, F. Liu, and J. Li, Effective spontaneous PT-symmetry breaking in hybridized metamaterials, Phys. Rev. A 87, 053824 (2013).
- Y. Sun, W. Tan, H. Q. Li, J. Li, and H. Chen, Experimental demonstration of a coherent perfect absorber with PT phase transition, Phys. Rev. Lett. 112, 143903 (2014).
- J. Li, A. K. Harter, J. Liu, L. Melo, Y. N. Joglekar, and L. Luo, Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms, Nat. Commun. 10, 855 (2019).
- J. Sheng, M. A. Miri, D. N. Christodoulides, and M. Xiao, PT-symmetric optical potentials in a coherent atomic medium, Phys. Rev. A 88, 041803(R) (2013).
- C. Hang, G. Huang, and V. V. Konotop, PT symmetry with a system of three-level atoms, Phys. Rev. Lett. 110, 083604 (2013).
- L. Qin, C. Hang, H. Sun, J. Qian, X. Feng, J. Qian, Y. Zhang, S. Xia, W. Liu, and X. Zhao, Soliton molecules and their scattering by a localized PT-symmetric potential in atomic gases, Opt. Express 31, 11116 (2023).
- J. H. Wu, M. Artoni, and G. C. La Rocca, Non-Hermitian degeneracies and unidirectional reflectionless atomic lattices, Phys. Rev. Lett. 113, 123004 (2014).
- S. Weimann, M. Kremer, Y. Plotnik, Y. Lumer, K. G. Makris, M. Segev, M. C. Rechtsman, and A. Szameit, Topologically protected bound states in photonic parity-time-symmetric crystals, Nat. Mater. 16, 433 (2017).
- M. Kremer, T. Biesenthal, L. J. Maczewsky, M. Heinrich, R. Thomale, and A. Szameit, Demonstration of a two-dimensional PT-symmetric crystal, Nat. Commun. 10, 435 (2019).
- H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, Condensation of semiconductor microcavity exciton polaritons, Science 298, 199 (2002).
- J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, and J. L. Staehli, et al., Bose-Einstein condensation of exciton polaritons, Nature (London) 443, 409 (2006).
- R. Balil, D. Snoke, L. Pfeiffer, and K. West, Bose-Einstein condensation of microcavity polaritons in a trap, Science 316, 1007 (2007).
- H. Deng, H. Haug, and Y. Yamamoto, Exciton-polariton Bose-Einstein condensation, Rev. Mod. Phys. 82, 1489 (2010).
- T. Byrnes, N. Y. Kim, and Y. Yamamoto, Exciton-polariton condensates, Nat. Phys. 10, 803 (2014).
- S. Christopoulos, G. Baldassarri Höger von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F. Carlin, and N. Grandjean, Room-temperature polariton lasing in semiconductor microcavities, Phys. Rev. Lett. 98, 126405 (2007).
- J. J. Baumberg, A. V. Kavokin, S. Christopoulos, A. J. D. Grundy, R. Butté, G. Christmann, D. D. Solnyshkov, G. Malpuech, G. Baldassarri Höger von von Högersthal, E. Feltin, J.-F. Carlin, and N. Grandjean, Spontaneous polarization buildup in a room-temperature polariton laser, Phys. Rev. Lett. 101, 136409 (2008).
- M. Wouters and I. Carusotto, Excitations in a nonequilibrium Bose-Einstein condensate of exciton polaritons, Phys. Rev. Lett. 99, 140402 (2007).
- L. A. Smirnov, D. A. Smirnova, E. A. Ostrovskaya, and Y. S. Kivshar, Dynamics and stability of dark solitons in exciton-polariton condensates, Phys. Rev. B 89, 235310 (2014).
- Y. Xue, and M. Matuszewski, Creation and abrupt decay of a quasistationary dark soliton in a polariton condensate, Phys. Rev. Lett. 112, 216401 (2014).
- T. C. H. Liew, O. A. Egorov, M. Matuszewski, O. Kyriienko, X. Ma, and E. A. Ostrovskaya, Instability-induced formation and nonequilibrium dynamics of phase defects in polariton condensates, Phys. Rev. B 91, 085413 (2015).
- X. Ma, O. A. Egorov, and S. Schumacher, Creation and manipulation of stable dark solitons and vortices in microcavity polariton condensates, Phys. Rev. Lett. 118, 157401 (2017).
- H. Sigurdsson, T. C. H. Liew, and I. A. Shelykh, Parity solitons in nonresonantly driven-dissipative condensate channels, Phys. Rev. B 96, 205406 (2017).
- G. Li, Azimuthons and pattern formation in annularly confined exciton-polariton Bose-Einstein condensates, Phys. Rev. A 93, 013837 (2016).
- X. Ma and S. Schumacher, Vortex-vortex control in exciton-polariton condensates, Phys. Rev. B 95, 235301 (2017).
- E. A. Ostrovskaya, J. Abdullaev, A. S. Desyatnikov, M. D. Fraser, and Y. S. Kivshar, Dissipative solitons and vortices in polariton Bose-Einstein condensates, Phys. Rev. A 86, 013636 (2012).
- D. Tanese, H. Flayac, D. Solnyshkov, A. Amo, A. Lemaître, E. Galopin, R. Braive, P. Senellart, I. Sagnes, G. Malpuech, et al., Polariton condensation in solitonic gap states in a one-dimensional periodic potential, Nat. Commun. 4, 1749 (2013).
- E. A. Ostrovskaya, J. Abdullaev, M. D. Fraser, A. S. Desyatnikov, and Y. S. Kivshar, Self-localization of polariton condensates in periodic potentials, Phys. Rev. Lett. 110, 170407 (2013).
- A. V. Nalitov, H. Sigurdsson, S. Morina, Y. S. Krivosenko, I. V. Iorsh, Y. G. Rubo, A. V. Kavokin, and I. A. Shelykh, Optically trapped polariton condensates as semiclassical time crystals, Phys. Rev. A 99, 033830 (2019).
- F. Pinsker and H. Flayac, On-demand dark soliton train manipulation in a spinor polariton condensate, Phys. Rev. Lett. 112, 140405 (2014).
- K. Zhang, W. Wen, J. Lin, and H.-J. Li, Generation and stability of diversiform nonlinear localized modes in exciton-polariton condensates, New J. Phys. 23, 033011 (2021).
- K. Zhang, W. Wen, J. Lin, and H.-J. Li, Stability and controllability of various spatial solitons in exciton-polariton condensates by a composite pumping, Front. Phys. 10, 798562 (2022).
- J. Hu, K. Zhang, M. Idrees, H.-J. Li, J. Lin, and A. V. Kavokin, Dark soliton cloning in exciton-polariton condensates, Phys. Rev. B 110, 155112 (2024).
- J. Hu, M. Idrees, K. Zhang, H.-J. Li, J. Lin, and A. V. Kavokin, Gaussian potential driven dark soliton and their cloning in exciton-polariton condensates, Phys. Rev. B 111, 165142 (2025).
- M. Chen, M. Idrees, K. Zhang, H.-J. Li, J. Lin, and A. V. Kavokin, Pump-driven transitions between non- and near-PT-symmetric steady states in polariton condensates, Phys. Rev. B 112, 075153 (2025).
- I. Y. Chestnov, S. S. Demirchyan, A. P. Alodjants, Y. Rubo, and A. V. Kavokin, Permanent Rabi oscillations in coupled exciton-photon systems with PT-symmetry, Sci. Rep. 6, 19551 (2016).
- P. A. Kalozoumis and D. Petrosyan, Self-organized PT-symmetry of exciton-polariton condensate in a double-well potential, Appl. Sci. 11, 7372 (2021).
- P. A. Kalozoumis, G. M. Nikolopoulos, and D. Petrosyan, Coherent population oscillations and an effective spin-exchange interaction in a PT symmetric polariton mixture, Europhys. Lett. 129, 37003 (2020).
- I. J. Velazquez-Resendiz, and Y. G. Rubo, Polarization dynamics of trapped polariton condensates with PT symmetry, Phys. Rev. B 109, 085312 (2024).
- X. Ma, Y. Y. Kartashov, T. Gao, and S. Schumacher, Controllable high-speed polariton waves in a PT-symmetric lattice, New J. Phys. 21, 123008 (2019).
- C. Y. Jia and Z. X. Liang, Dark soliton of polariton condensates under nonresonant PT-symmetric pumping, Chin. Phys. Lett. 37, 040502 (2020).
- G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, Single vortex-antivortex pair in an exciton-polariton condensate, Nat. Phys. 7, 129 (2011).
- X. Liu and J. Zeng, Gap solitons in parity-time symmetric moiré optical lattices, Photon. Res. 11, 196 (2023).
- Y. Chen and Z. Yan, Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrödinger equation, Phys. Rev. E 95, 012205 (2017).
- E. Luz, V. Lutsky, E. Granot, and B. A. Malomed, Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity, Sci. Rep. 9, 4483 (2019).
- Y. del Valle Inclan Redondo, X. Xu, T. C. H. Liew, E. A. Ostrovskaya, A. Stegmaier, R. Thomale, C. Schneider, S. Dam, S. Klembt, S. Höfling, S. Tarucha, and M. D. Fraser, Non-reciprocal band structures in an exciton-polariton Floquet optical lattice, Nat. Photonics 18, 548 (2024).
- M. M. de Lima, Jr., M. van der Poel, P. V. Santos, and J. M. Hvam, Phonon-induced polariton superlattices, Phys. Rev. Lett. 97, 045501 (2006).
- C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Coherent zero-state and -state in an exciton-polariton condensate array, Nature (London) 450, 529 (2007).
- A. V. Nalitov, T. C. H. Liew, A. V. Kavokin, B. L. Altshuler, and Y. G. Rubo, Spontaneous polariton currents in periodic lateral chains, Phys. Rev. Lett. 119, 067406 (2017).
- I. Gnusov, S. Harrison, S. Alyatkin, K. Sitnik, J. Töpferpfer, H. Sigurdsson, and P. Lagoudakis, Quantum vortex formation in the “rotating bucket” experiment with polariton condensates, Sci. Adv. 9, eadd1299 (2023).
- E. Sedov and A. Kavokin, Reconfigurable polariton mode control in a liquid-crystal microcavity, Phys. Rev. A 112, 043517 (2025).
- E. Sedov and A. Kavokin, Engineering polariton states through liquid-crystal-induced anisotropy and topology optimization, Phys. Rev. A 112, 013504 (2025).
- J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, Philadelphia, PA, 2011).