- Open Access
Quantum Otto engine with field-decoupled idle levels in a non-Hermitian XY model
APS Open Sci. 1, 000154 – Published 29 September, 2026
DOI: https://doi.org/10.1103/vf26-wl4f
Abstract
We propose a microscopic realization of the idle-level quantum heat engine architecture based on a two-qubit non-Hermitian XY model with a staggered imaginary magnetic field. The energy spectrum naturally separates into two working levels coupled to the external field and two field-decoupled idle levels entirely independent of it. Tuning the non-Hermitian parameter drives the system from a dissipative accelerator regime into a genuine heat engine regime, while simultaneously enhancing both the net work output and the cycle efficiency. The efficiency enhancement originates from the compression of the idle-level gap, which redistributes level occupations and progressively suppresses the idle-level heat current, signaling the approach to the reverse heat-flow regime that underlies the idle-level engine principle. We map the full thermodynamic phase diagram identifying engine, refrigerator, accelerator, and heater regimes, and decompose the heat current into working-level and idle-level contributions to clarify the microscopic origin of the performance gain. The model is implementable in trapped-ion and NMR quantum simulators. These results establish non-Hermiticity as a versatile control knob for idle-level quantum thermal machines.
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References (43)
- R. Alicki, The quantum open system as a model of the heat engine, J. Phys. A: Math. Gen. 12, L103 (1979).
- R. Kosloff, A quantum mechanical open system as a model of a heat engine, J. Chem. Phys. 80, 1625 (1984).
- E. Geva and R. Kosloff, A quantum-mechanical heat engine operating in finite time: A model consisting of spin-1/2 systems as the working fluid, J. Chem. Phys. 96, 3054 (1992).
- O. Abah, J. Roßnagel, G. Jacob, S. Deffner, F. Schmidt-Kaler, K. Singer, and E. Lutz, Single-ion heat engine at maximum power, Phys. Rev. Lett. 109, 203006 (2012).
- J. Roßnagel, S. T. Dawkins, K. N. Tolazzi, O. Abah, E. Lutz, F. Schmidt-Kaler, and K. Singer, A single-atom heat engine, Science 352, 325 (2016).
- J. Klatzow, J. N. Becker, P. M. Ledingham, C. Weinzetl, K. T. Kaczmarek, D. J. Saunders, J. Nunn, I. A. Walmsley, R. Uzdin, and E. Poem, Experimental demonstration of quantum effects in the operation of microscopic heat engines, Phys. Rev. Lett. 122, 110601 (2019).
- J. P. S. Peterson, T. B. Batalhão, M. Herrera, A. M. Souza, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, Experimental characterization of a spin quantum heat engine, Phys. Rev. Lett. 123, 240601 (2019).
- H. T. Quan, Y. Liu, C. P. Sun, and F. Nori, Quantum thermodynamic cycles and quantum heat engines, Phys. Rev. E 76, 031105 (2007).
- R. Kosloff and Y. Rezek, The Quantum harmonic Otto cycle, Entropy 19, 136 (2017).
- J. Gemmer, M. Michel, and G. Mahler, Quantum Thermodynamics (Springer, Berlin, 2009).
- S. Vinjanampathy and J. Anders, Quantum thermodynamics, Contemp. Phys. 57, 545 (2016).
- J. Goold, M. Huber, A. Riera, L. del Rio, and P. Skrzypczyk, The role of quantum information in thermodynamics—A topical review, J. Phys. A: Math. Theor. 49, 143001 (2016).
- Thermodynamics in the Quantum Regime, edited by F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (Springer, Cham, 2018).
- C. M. Bender and S. Boettcher, Real spectra in non-Hermitian Hamiltonians having symmetry, Phys. Rev. Lett. 80, 5243 (1998).
- C. M. Bender, Making sense of non-Hermitian Hamiltonians, Rep. Prog. Phys. 70, 947 (2007).
- L. Feng, R. El-Ganainy, and L. Ge, Non-Hermitian photonics based on parity–time symmetry, Nat. Photon. 11, 752 (2017).
- Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, Parity–time symmetry and exceptional points in photonics, Nat. Mater. 18, 783 (2019).
- 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).
- V. V. Konotop, J. Yang, and D. A. Zezyulin, Nonlinear waves in -symmetric systems, Rev. Mod. Phys. 88, 035002 (2016).
- 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).
- Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys. 69, 249 (2020).
- S. Lin and Z. Song, Non-Hermitian heat engine with all-quantum-adiabatic-process cycle, J. Phys. A: Math. Theor. 49, 475301 (2016).
- A. Insinga, B. Andresen, P. Salamon, and R. Kosloff, Quantum heat engines: Limit cycles and exceptional points, Phys. Rev. E 97, 062153 (2018).
- J.-W. Zhang, J.-Q. Zhang, G.-Y. Ding, J.-C. Li, J.-T. Bu, B. Wang, L.-L. Yan, S.-L. Su, L. Chen, F. Nori, Ş. K. Özdemir, F. Zhou, H. Jing, and M. Feng, Dynamical control of quantum heat engines using exceptional points, Nat. Commun. 13, 6225 (2022).
- Z.-Y. Zhou, Z.-L. Xiang, J. Q. You, and F. Nori, Work statistics in non-Hermitian evolutions with Hermitian endpoints, Phys. Rev. E 104, 034107 (2021).
- S. Khandelwal, N. Brunner, and G. Haack, Signatures of Liouvillian exceptional points in a quantum thermal machine, PRX Quantum 2, 040346 (2021).
- T. R. de Oliveira and D. Jonathan, Efficiency gain and bidirectional operation of quantum engines with decoupled internal levels, Phys. Rev. E 104, 044133 (2021).
- M. F. Anka, T. R. de Oliveira, and D. Jonathan, Work and efficiency fluctuations in a quantum Otto cycle with idle levels, Phys. Rev. E 109, 064129 (2024).
- C. Cherubim, T. R. de Oliveira, and D. Jonathan, Nonadiabatic coupled-qubit Otto cycle with bidirectional operation and efficiency gains, Phys. Rev. E 105, 044120 (2022).
- Y. Li, P.-P. Zhang, L.-Z. Hu, Y.-L. Xu, and X.-M. Kong, Ground-state and thermal entanglements in non-Hermitian XY system with real and imaginary magnetic fields, Quantum Inf. Process. 22, 277 (2023).
- B. Gardas, S. Deffner, and A. Saxena, Non-Hermitian quantum thermodynamics, Sci. Rep. 6, 23408 (2016).
- A. Mostafazadeh, Pseudo-Hermitian representation of quantum mechanics, Int. J. Geom. Methods Mod. Phys. 07, 1191 (2010).
- C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, Trapped-ion quantum computing: Progress and challenges, Appl. Phys. Rev. 6, 021314 (2019).
- M. Campisi, P. Hänggi, and P. Talkner, Colloquium: Quantum fluctuation relations: Foundations and applications, Rev. Mod. Phys. 83, 771 (2011).
- U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
- C. Jarzynski, Nonequilibrium equality for free energy differences, Phys. Rev. Lett. 78, 2690 (1997).
- G. E. Crooks, Nonequilibrium measurements of free energy differences for microscopically reversible Markovian systems, J. Stat. Phys. 90, 1481 (1998).
- M. Esposito, U. Harbola, and S. Mukamel, Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems, Rev. Mod. Phys. 81, 1665 (2009).
- R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
- E. Chitambar and G. Gour, Quantum resource theories, Rev. Mod. Phys. 91, 025001 (2019).
- W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80, 2245 (1998).
- L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80, 517 (2008).
- A. Brollo, A. del Campo, and A. Bastianello, Universal efficiency boost in prethermal quantum heat engines at negative temperature, Nat. Commun. 16, 10593 (2025).