Dynamical characterization of non-Hermitian Floquet topological phases in one dimension

Zhou, Longwen

doi:10.1103/physrevb.100.184314

Cited by 65 publications

(51 citation statements)

References 112 publications

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“…This thus greatly expands the scope by which ROs can be controlled or engineered, achieving Rabi frequencies that are orders of magnitudes higher than allowed by the bare dipole moments. More generally, our study sheds light on how non-Hermiticity further enriches the already vibrant field of Floquet dynamics [55][56][57] beyond merely causing gain or attenuation.…”

mentioning

confidence: 81%

Ultrafast and anharmonic Rabi oscillations between non-Bloch bands

Lee

Longhi

2020

Commun Phys

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Bloch band theory and bulk-boundary correspondence in non-Hermitian systems are attracting great attention in different areas of science. Interband transitions and Rabi flopping induced by emission or absorption of field quanta are fundamental and well-understood processes in Hermitian systems. However, they are challenged in a non-Hermitian system, where band theory is affected by system boundaries. Here we consider Rabi oscillations in non-Hermitian lattices exhibiting unbalanced non-Hermitian skin effect, and unveil an unprecedented scenario of Rabi flopping. The effective dipole moment of the transitionusually considered a bulk property-is however strongly dependent on boundary conditions. Rabi oscillations become anharmonic and transitions cease to be vertical in the energymomentum plane in systems with open boundaries. Remaining stable even in the presence of complex energies, Rabi oscillations provide a vivid illustration of how competition between non-Hermitian, non-local and Floquet effects can result in significant enhancements of physically measurable quantities.

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confidence: 81%

Ultrafast and anharmonic Rabi oscillations between non-Bloch bands

Lee

Longhi

2020

Commun Phys

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“…The mean chiral displacement (MCD) refers to the time-averaged chiral displacement

of a wavepacket in a lattice, where

is the sublattice symmetry operator and

is the position operator of the unit cell. The MCD was first introduced as a dynamical probe to the winding numbers of 1D topological insulators in the symmetry classes AIII and BDI [ 98 ], and later extended to Floquet systems [ 93 , 99 , 100 ], two-dimensional systems [ 101 ], many-body systems [ 102 ], systems in other symmetry classes [ 84 ], and recently also to non-Hermitian systems [ 50 , 51 , 53 ]. In the meantime, the MCD has also been measured experimentally in photonic [ 98 , 103 ] and cold atom [ 104 , 105 ] setups.…”

Section: Dynamical Probe To the Topological Phasesmentioning

confidence: 99%

“…Recently, the study of non-Hermitian physics has been extended to Floquet systems, in which the interplay between time-periodic driving fields and gains/losses or nonreciprocal effects could potentially yield topological phases that are unique to driven non-Hermitian systems [ 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 ]. In early studies, various non-Hermitian Floquet topological phases and phenomena have been discovered, including non-Hermitian Floquet topological insulators [ 49 , 50 , 53 , 54 , 55 ], superconductors [ 52 ], semimetals [ 63 ], and skin effects [ 56 , 57 ].…”

Section: Introductionmentioning

confidence: 99%

“…In early studies, various non-Hermitian Floquet topological phases and phenomena have been discovered, including non-Hermitian Floquet topological insulators [ 49 , 50 , 53 , 54 , 55 ], superconductors [ 52 ], semimetals [ 63 ], and skin effects [ 56 , 57 ]. Meanwhile, the time-averaged spin texture and mean chiral displacement have been suggested as two dynamical tools to extract the topological invariants of non-Hermitian Floquet systems [ 49 , 50 , 51 , 53 ]. These discoveries extend the boundary of nonequilibrium phases of matter to driven non-Hermitian systems, and shed light on new approaches for the detection of their intriguing features.…”

Section: Introductionmentioning

confidence: 99%

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Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

Zhou

2020

Entropy

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Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical, and transport properties. In this work, we introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects, which belongs to an extended CII symmetry class. Due to the interplay between drivings and nonreciprocity, rich non-Hermitian Floquet topological phases emerge in the system, with each of them characterized by a pair of even-integer topological invariants ( w 0 , w π ) ∈ 2 Z × 2 Z . Under the open boundary condition, these invariants further predict the number of zero- and π -quasienergy modes localized around the edges of the system. We finally construct a generalized version of the mean chiral displacement, which could be employed as a dynamical probe to the topological invariants of non-Hermitian Floquet phases in the CII symmetry class. Our work thus introduces a new type of non-Hermitian Floquet topological matter, and further reveals the richness of topology and dynamics in driven open systems.

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“…Finding the dynamical signatures of these non-equilibrium topological matter has become a fascinating area for more experimental and theoretical research. In recent works, several dynamical probes to the topological invariants of non-Hermitian phases in one and two dimensions have been introduced, such as the non-Hermitian extension of dynamical winding numbers [61][62][63][64][65][66] and mean chiral displacements [67,68]. Further, the dynamical quantum phase transitions (DQPTs) following a quench across the EPs of a non-Hermitian lattice model is studied in Refs.…”

Section: Introductionmentioning

confidence: 99%

Dissipative Floquet Dynamical Quantum Phase Transition

Naji,

Jafari,

Jafari

et al. 2021

Preprint

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Non-Hermitian Hamiltonians provide a simple picture for inspecting dissipative systems with natural or induced gain and loss. We investigate the Floquet dynamical phase transition in the dissipative periodically time driven XY and extended XY models, where the imaginary terms represent the physical gain and loss during the interacting processes with the environment. The time-independent effective Floquet non-Hermitian Hamiltonians disclose three regions by analyzing the non-Hermitian gap: pure real gap (real eigenvalues), pure imaginary gap, and complex gap. We show that each region of the system can be distinguished by the complex geometrical non-adiabatic phase. We have discovered that in the presence of dissipation, the Floquet dynamical phase transitions (FDPTs) still exist in the region where the time-independent effective Floquet non-Hermitian Hamiltonians reveal real eigenvalues. Opposed to expectations based on earlier works on quenched systems, our findings show that the existence of the non-Hermitian topological phase is not an essential condition for dissipative FDPTs (DFDPTs). We also demonstrate the range of driven frequency, over which the DFDPTs occur, narrows down by increasing the dissipation coupling and shrinks to a single point at the critical value of dissipation. Moreover, quantization and jumps of the dynamical geometric phase reveals the topological characteristic feature of DFDPTs in the real gap region where confined to exceptional points.

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Dynamical characterization of non-Hermitian Floquet topological phases in one dimension

Cited by 65 publications

References 112 publications

Ultrafast and anharmonic Rabi oscillations between non-Bloch bands

Ultrafast and anharmonic Rabi oscillations between non-Bloch bands

Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

Dissipative Floquet Dynamical Quantum Phase Transition

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