Self-normal and biorthogonal dynamical quantum phase transitions in non-Hermitian quantum walks

Area of Science:

• Quantum Physics
• Condensed Matter Physics
• Non-Hermitian Systems

Background:

• Dynamical quantum phase transitions (DQPTs) are characterized by non-analytic behavior in rate functions and abrupt changes in dynamic topological order parameters (DTOPs).
• Defining DQPTs in non-Hermitian systems is complex due to the biorthogonality of bases.

Purpose of the Study:

• To comprehensively investigate and compare self-normal DQPTs with their biorthogonal counterparts in non-Hermitian quantum walks (QWs).
• To analyze the behaviors of Loschmidt rate functions and DTOPs under these two distinct theoretical approaches.

Main Methods:

• Analysis of Loschmidt rate functions and dynamic topological order parameters (DTOPs).
• Theoretical comparison of self-normal and biorthogonal approaches for DQPT detection.
• Investigation of Fisher zeros and fixed points to define critical momenta and times.
• Experimental observation using one-dimensional discrete-time quantum walks with single photons.

Main Results:

• Both self-normal and biorthogonal methods can detect DQPTs in non-Hermitian QWs during quench dynamics.
• Theoretical differences in the definition of critical momenta and critical times were identified between the two methods.
• Experimental verification of both self-normal and biorthogonal DQPTs was achieved.

Conclusions:

• The study clarifies the application and distinctions of self-normal and biorthogonal approaches for DQPTs in non-Hermitian systems.
• The findings provide a framework for understanding and detecting DQPTs in a broader range of quantum systems.
• The experimental realization validates the theoretical predictions and opens avenues for future research.