Liouvillian and Hamiltonian exceptional points of atomic vapors: The spectral signatures of quantum jumps

Abstract

We investigate spectral singularities in an alkali-metal atomic vapor modeled using four and effectively three hyperfine states. By comparing the eigenvalue spectra of a non-Hermitian Hamiltonian (NHH) and a Liouvillian superoperator, we analyze the emergence and characteristics of both semiclassical and quantum exceptional points. Our results reveal that, for atomic systems, the NHH approach alone may be insufficient to fully capture the system's spectral properties. While NHHs can yield accurate predictions in certain regimes, a comprehensive description typically requires the Liouvillian formalism, which governs the Lindblad master equation and explicitly incorporates quantum jump processes responsible for repopulation dynamics. We demonstrate that the inclusion of quantum jumps fundamentally alters the spectral structure of the system. In particular, we present examples in which the existence, location in parameter space, or even the order of spectral degeneracies differ significantly between the two approaches, thereby highlighting the impact of quantum jumps and the limitations of the NHH method. Finally, using the hybrid-Liouvillian formalism, we show how quantum jumps reshape spectral features initially predicted by the NHH, ultimately determining the full Liouvillian spectrum.

References in corpus (22)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• PT-Symmetric Phonon Laser
• Optomechanically-Induced Transparency in partiy-time-symmetric microresonators
• Quantum memory for entangled two-mode squeezed states
• Analysis of quantum semigroups with GKS--Lindblad generators II. General
• Decoherence Induced Exceptional Points in a Dissipative Superconducting Qubit
• Dynamical Control of Quantum Heat Engines Using Exceptional Points
• Observation of Exceptional Points in Thermal Atomic Ensembles
• Dynamically crossing diabolic points while encircling exceptional curves: A programmable symmetric-asymmetric multimode switch
• Enhancement of quantum heat engine by encircling a Liouvillian exceptional point
• Exceptional points of the Lindblad operator of a two-level system
• Long-lived entanglement generation of nuclear spins using coherent light
• Non-Markovian Quantum Exceptional Points
• Experimental Liouvillian exceptional points in a quantum system without Hamiltonian singularities
• Emergent parallel transport and curvature in Hermitian and non-Hermitian quantum mechanics
• Chiral quantum heating and cooling with an optically controlled ion
• Anomalous noise spectra in a spin-exchange-relaxation-free alkali-metal vapor
• Constraining work fluctuations of non-Hermitian dynamics across the exceptional point of a superconducting qubit
• Optimized experimental optical tomography of quantum states of room-temperature alkali-metal vapor
• Heisenberg and Heisenberg-Like Representations via Hilbert Space Bundle Geometry in the Non-Hermitian Regime

Cited by in corpus (3)

• Quantum jumps in open cavity optomechanics and Liouvillian versus Hamiltonian exceptional points
• Higher-order Liouvillian exceptional points in the dissipative dynamics of quadratic fermions
• Characterizing Liouvillian Exceptional Points Through Newton Polygons and Tropical Geometry