Amplitude control of a quantum state in a non-Hermitian Rice-Mele model driven by an external field

Sun, Liwei; Zhang, X. Z.; Song, Z.

doi:10.1103/physreva.92.012117

Cited by 7 publications

(7 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, the non-Hermitian version can be achieved in a zigzag array of optical waveguides with alternating optical gain and loss [49]. It is worth mentioning that this non-Hermitian Hamiltonian can be also utilized to control the wavepacket dynamics [50,51]. Now we consider the periodical boundary condition, that is c j ≡ c j+2N , to obtain the exact solution.…”

Section: Model Hamiltonian and Solutionmentioning

confidence: 99%

Classical correspondence of the exceptional points in the finite non-Hermitian system

Zhang

Song

2019

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We systematically study the topology of the exceptional point (EP) in the finite non-Hermitian system. Based on the concrete form of the Berry connection, we demonstrate that the exceptional line (EL), at which the eigenstates coalesce, can act as a vortex filament. The direction of the EL can be identified by the corresponding Berry curvature. In this context, such a correspondence makes the topology of the EL clear at a glance. As an example, we apply this finding to the non-Hermitian Rice-Mele (RM) model, the non-Hermiticity of which arises from the staggered on-site complex potential. The boundary ELs are topological, but the non-boundary ELs are not. Each non-boundary EL corresponds to two critical momenta that make opposite contributions to the Berry connection. Therefore, the Berry connection of the many-particle quantum state can have classical correspondence, which is determined merely by the boundary ELs. Furthermore, the non-zero Berry phase, which experiences a closed path in the parameter space, is dependent on how the curve surrounds the boundary EL. This also provides an alternative way to investigate the topology of the EP and its physical correspondence in a finite non-Hermitian system.

show abstract

Section: Model Hamiltonian and Solutionmentioning

confidence: 99%

Classical correspondence of the exceptional points in the finite non-Hermitian system

Zhang

Song

2019

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…The concept of the geometric phase can be generalized to non-Hermitian systems, providing a geometrical description of the quantum evolution of non-Hermitian systems under a cyclic variation of the parameters [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]. Compared to Hermitian systems, different forms of Berry phases have been introduced.…”

Section: Introductionmentioning

confidence: 99%

Complex Berry phase and imperfect non-Hermitian phase transitions

Longhi

Feng

2023

Phys. Rev. B

View full text Add to dashboard Cite

In many classical and quantum systems described by an effective non-Hermitian Hamiltonian, spectral phase transitions, from an entirely real-energy spectrum to a complex spectrum, can be observed as a non-Hermitian parameter in the system is increased above a critical value. A paradigmatic example is provided by systems possessing parity-time (PT ) symmetry, where the energy spectrum remains entirely real in the unbroken PT phase while a transition to complex energies is observed in the broken PT phase. Such spectral phase transitions are universally sharp. However, when the system is slowly and periodically cycled, the phase transition can become smooth, i.e., imperfect, owing to the complex Berry phase associated to the cyclic adiabatic evolution of the system. This remarkable phenomenon is illustrated by considering the spectral phase transition of the Wannier-Stark ladders in a PT -symmetric class of two-band non-Hermitian lattices subjected to an external dc field, revealing that a nonvanishing imaginary part of the Zak phase-the Berry phase picked up by a Bloch eigenstate evolving across the entire Brillouin zone-is responsible for imperfect spectral phase transitions.

show abstract

“…exceptional points [51][52][53] or spectral singularities [54][55][56], at the critical point. The concept of geometric phase can be generalized to non-Hermitian systems, providing a geometrical description of the quantum evolution of non-Hermitian systems under cyclic variation of parameters [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]. As compared to Hermitian systems, different forms of Berry phases have been introduced.…”

Section: Introductionmentioning

confidence: 99%

“…Zak phase, naturally arises under an external dc force or a time-varying magnetic flux [81], so that a Bloch eigenstate adiabatically evolves across the entire Brillouin zone accumulating a complex geometric phase. While the related phenomena of Bloch oscillations and Zener tunneling have been investigated at some extent in non-Hermitian lattices [90][91][92][93][94][95][96][97][98][99][100], physical signatures of the complex Zak phase have received so far little attention and mostly restricted to some specific lattice models [66,81].…”

Section: Introductionmentioning

confidence: 99%

Complex Berry phase and imperfect non-Hermitian phase transitions

Longhi¹,

Li²

2023

Preprint

View full text Add to dashboard Cite

In many classical and quantum systems described by an effective non-Hermitian Hamiltonian, spectral phase transitions, from an entirely real energy spectrum to a complex spectrum, can be observed as a non-Hermitian parameter in the system is increased above a critical value. A paradigmatic example is provided by systems possessing parity-time (PT ) symmetry, where the energy spectrum remains entirely real in the unbroken PT phase while a transition to complex energies is observed in the unbroken PT phase. Such spectral phase transitions are universally sharp. However, when the system is slowly and periodically cycled, the phase transition can become smooth, i.e. imperfect, owing to the complex Berry phase associated to the cyclic adiabatic evolution of the system. This remarkable phenomenon is illustrated by considering the spectral phase transition of the Wannier-Stark ladders in a PT -symmetric class of two-band non-Hermitian lattices subjected to an external dc field, unraveling that a non-vanishing imaginary part of the Zak phase -the Berry phase picked up by a Bloch eigenstate evolving across the entire Brillouin zone-is responsible for imperfect spectral phase transitions.

show abstract

Amplitude control of a quantum state in a non-Hermitian Rice-Mele model driven by an external field

Cited by 7 publications

References 47 publications

Classical correspondence of the exceptional points in the finite non-Hermitian system

Classical correspondence of the exceptional points in the finite non-Hermitian system

Complex Berry phase and imperfect non-Hermitian phase transitions

Complex Berry phase and imperfect non-Hermitian phase transitions

Contact Info

Product

Resources

About