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Quantum state tomography across the exceptional point in a single dissipative qubit


Open physical systems can be described by effective non-Hermitian Hamiltonians that characterize the gain or loss of energy or particle numbers from the system. Experimental realization of optical1,2,3,4,5,6,7 and mechanical8,9,10,11,12,13 non-Hermitian systems has been reported, demonstrating functionalities such as lasing14,15,16, topological features7,17,18,19, optimal energy transfer20,21 and enhanced sensing22,23. Such realizations have been limited to classical (wave) systems in which only the amplitude information, not the phase, is measured. Thus, the effects of a systems’s proximity to an exceptional point—a degeneracy of such non-Hermitian Hamiltonians where the eigenvalues and corresponding eigenmodes coalesce24,25,26,27,28,29—on its quantum evolution remain unexplored. Here, we use post-selection on a three-level superconducting transmon circuit to carry out quantum state tomography of a single dissipative qubit in the vicinity of its exceptional point. We observe the spacetime reflection symmetry-breaking transition30,31 at zero detuning, decoherence enhancement at finite detuning and a quantum signature of the exceptional point in the qubit relaxation state. Our experiments show phenomena associated with non-Hermitian physics such as non-orthogonality of eigenstates in a fully quantum regime, which could provide a route to the exploration and harnessing of exceptional point degeneracies for quantum information processing.

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Fig. 1: Experimental overview.
Fig. 2: \({\cal{P}}{\cal{T}}\) symmetry-breaking transition in a single dissipative qubit.
Fig. 3: Non-orthogonality of eigenstates in the vicinity of the EP.
Fig. 4: Coherence damping and steady state of a single dissipative qubit.

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Data availability

The data that support the plots within this paper and other findings of this study are available from K.W.M. on reasonable request.


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We thank P. M. Harrington for preliminary contributions, D. Tan for sample fabrication and K. Mølmer and C. Bender for discussions. K.W.M. acknowledges research support from the NSF (grant nos. PHY-1607156 and PHY-1752844 (CAREER)), and Y.N.J. acknowledges NSF grant no. DMR-1054020 (CAREER). This research used facilities at the Institute of Materials Science and Engineering at Washington University.

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Authors and Affiliations



K.W.M., M.N. and Y.N.J. conceived the project. K.W.M., M.A. and M.N. performed the experiments and analysed the data. Y.N.J. provided theory support. K.W.M., M.N. and Y.N.J. wrote the manuscript.

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Correspondence to Yogesh N. Joglekar or K. W. Murch.

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Naghiloo, M., Abbasi, M., Joglekar, Y.N. et al. Quantum state tomography across the exceptional point in a single dissipative qubit. Nat. Phys. 15, 1232–1236 (2019).

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