Quantum phase transition in a pseudo-Hermitian Dicke model

Area of Science:

• Quantum mechanics
• Quantum optics
• Condensed matter physics

Background:

• Non-Hermitian Hamiltonians are crucial for describing open quantum systems.
• The Dicke model describes light-matter interactions but typically uses Hermitian operators.
• Understanding quantum phase transitions in non-Hermitian systems is an active research area.

Purpose of the Study:

• To demonstrate that a specific non-Hermitian Hamiltonian can exhibit entirely real spectra.
• To establish a consistent quantum description for non-Hermitian systems with unitary time evolution.
• To investigate quantum phase transitions in nondissipative non-Hermitian quantum processes.

Main Methods:

• Employing a similarity transformation to map the non-Hermitian Hamiltonian to the dressed Dicke model.
• Identifying a positive-definite metric within the Hilbert space of the non-Hermitian Hamiltonian.
• Analyzing the spectral properties and time evolution of the transformed system.

Main Results:

• The non-Hermitian Hamiltonian is shown to possess entirely real energy spectra.
• A positive-definite metric ensures unitary time evolution, enabling a consistent quantum mechanical description.
• The non-Hermitian Hamiltonian undergoes a quantum phase transition, characteristic of nondissipative quantum processes.

Conclusions:

• The transformation to the dressed Dicke model provides a powerful method for analyzing non-Hermitian systems.
• Real spectra and unitary evolution confirm the physical applicability of this non-Hermitian Hamiltonian for nondissipative phenomena.
• The study highlights the potential for quantum phase transitions in these non-Hermitian quantum systems.