Non-Hermitian topological quantum states in a reservoir-engineered transmon chain

Funding Information: We acknowledge the computational resources provided by the Aalto Science-IT project and the financial support from the Academy of Finland Projects No. 331094 and No. 316619. The work is supported by the Foundation for Polish Science through the IRA Programme co-financed by EU within SG OP. W.B. also acknowledges support by Narodowe Centrum Nauki (NCN, National Science Centre, Poland), Project No. 2019/34/E/ST3/00404. M.P. acknowledges the support of the Polish National Agency for Academic Exchange, the Bekker Programme No. PPN/BEK/2020/1/00317, and Ministerio de Ciencia y Innovation Agencia Estatal de Investigaciones (R&D Project No. CEX2019-000910-S, AEI/10.13039/501100011033, Plan National FIDEUA PID2019-106901GB-I00, FPI), Fundació Privada Cellex, Fundació Mir-Puig, and by Generalitat de Catalunya (AGAUR Grant No. 2017 SGR 1341, CERCA program). F.M. acknowledges financial support from the Research Council of Norway (Grant No. 333937) through participation in the QuantERA ERA-NET Cofund in Quantum Technologies (project MQSens) implemented within the European Union's Horizon 2020 Programme. Publisher Copyright: © 2023 American Physical Society.Dissipation in open systems enriches the possible symmetries of the Hamiltonians beyond the Hermitian framework, allowing the possibility of novel non-Hermitian topological phases which exhibit long-living end states that are protected against disorder. So far, non-Hermitian topology has been explored in settings where probing genuine quantum effects has been challenging. We theoretically show that a non-Hermitian topological quantum phase can be realized in a reservoir-engineered transmon chain. The spatial modulation of dissipation is obtained by coupling each transmon to a quantum circuit refrigerator, allowing in situ tuning of dissipation strength in a wide range. By solving the many-body Lindblad master equation using a combination of the density matrix renormalization group and Prosen-Seligman third quantization approaches, we show that the topological end modes and the associated phase transition are visible in simple reflection measurements with experimentally realistic parameters. Finally, we demonstrate that genuine quantum effects are observable in this system via robust and slowly decaying long-range quantum entanglement of the topological end modes, which can be generated passively starting from a locally excited transmon.Peer reviewe