Non-Hermitian Absorption Spectroscopy

Abstract

While non-Hermitian Hamiltonians have been experimentally realized in cold atom systems, it remains an outstanding open question of how to experimentally measure their complex energy spectra in momentum space for a realistic system with boundaries. The existence of non-Hermitian skin effects may make the question even more difficult to address given the fact that energy spectra for a system with open boundaries are dramatically different from those in momentum space; the fact may even lead to the notion that momentum-space band structures are not experimentally accessible for a system with open boundaries. Here, we generalize the widely used radio-frequency spectroscopy to measure both real and imaginary parts of complex energy spectra of a non-Hermitian quantum system for either bosonic or fermionic atoms. By weakly coupling the energy levels of a non-Hermitian system to auxiliary energy levels, we theoretically derive a formula showing that the decay of atoms on the auxiliary energy levels reflects the real and imaginary parts of energy spectra in momentum space. We further prove that measurement outcomes are independent of boundary conditions in the thermodynamic limit, providing strong evidence that the energy spectrum in momentum space is experimentally measurable. We finally apply our non-Hermitian absorption spectroscopy protocol to the Hatano-Nelson model and non-Hermitian Weyl semimetals to demonstrate its feasibility.

30 pages including Supplemental Material, 16 figures

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• Anderson Delocalization in Strongly Coupled Disordered Non-Hermitian Chains
• Non-Hermitian Skin Effect in Periodically-Driven Dissipative Ultracold Atoms
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages
• Quantum tomography of a third-order exceptional point in a dissipative trapped ion
• Interaction-Induced Second-Order Skin Effect
• Linear Response for pseudo-Hermitian Hamiltonian Systems: Application to PT-Symmetric Qubits
• Kibble-Zurek scaling immune to anti-Kibble-Zurek behavior in driven open systems at the limit of loss difference
• $\mathcal{P}\mathcal{T}$-symmetric quantum Rabi model: Solutions and exceptional points
• Many-body Liouvillian dynamics with a non-Hermitian tensor-network kernel polynomial algorithm
• Topological extension including quantum jump
• Local Non-Hermitian Hamiltonian Formalism for Dissipative Fermionic Systems and Loss-Induced Population Increase in Fermi Superfluids
• $\mathcal{P}\mathcal{T}$-symmetric two-photon quantum Rabi models
• A spectrum-based shortcut method for topological systems
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Arbitrary Control of Non-Hermitian Skin Modes via Disorder and An Electric Field
• $\mathcal{P}\mathcal{T}$-Symmetric Spin--Boson Model with a Continuous Bosonic Spectrum: Exceptional Points and Dynamics