Multiple Quantum Mpemba Effect: Exceptional Points and Oscillations: Model and Protocol

Table of Links

• Introduction
• Model and Protocol
• Different Regimes in d˜− Γ˜ Plain and Multiple QMPE
• QMPE in Region (d): Second-order Ep
• QMPE in Region (a1): Oscillations
• Summary
• Appendix A: Eigenvectors of L in region (d)
• Appendix B: Eigenvectors of L in region (a1)
• Appendix C: QMPE in region (b): purely exponential relaxation
• Appendix D: QMPE in region (e): 3rd order EP
• References

II. MODEL AND PROTOCOL

We consider a two-level open quantum system, subjected to a periodic drive and dissipatively coupled to the environment. Following Ref. [95], we hereafter refer to this model as Hatano’s model in the present manuscript. In this paper, we adopt ~ = 1. The two levels of the system, ground state and excited state, have energies Eg and Ee, respectively. The gap between the two levels is denoted by ∆ := Ee − Eg. In Hatano’s model, the transfers between the energy levels are enabled by the external oscillatory electric field E = E0cos(ωt) and the dissipation of the system to the environment via coupling Γ. The parameter δ := ∆ −ω represents the detuning of the periodic drive with respect to the system and d := DE0, where D is the electric dipole moment, denotes the effective electric field. The tuning parameters in Hatano’s model are d, Γ and δ . However, one of them fixes the unit of energy, so we essentially have two free parameters ˜d := d/δ and Γ := Γ ˜ /δ.

Hatano’s model, within Markovian approximation, can be described by the Gorini-Kossakowski-SudarshanLindblad (GKSL) equation [101–104] (see [95] for the present context):