Hamiltonian Hopping for Efficient Chiral Mode Switching in Encircling Exceptional Points

Li, Aodong; Dong, Jianji; Wang, Jian; Cheng, Zhengxing; Ho, John S.; Zhang, Dawei; Wen, Jing; Zhang, Xu‐Lin; Chan, Che Ting; Alù, Andrea; Qiu, Cheng‐Wei; Chen, Lin

doi:10.1103/physrevlett.125.187403

Cited by 76 publications

(40 citation statements)

References 36 publications

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“…For conventional chiral mode converters realized based on these principles, the chiral transmission efficiencies are quite low owing to significant energy dissipation for the eigenstates near EPs, with the maximum efficiency experimentally reported so far being 46% 11 . Recent theoretical studies have demonstrated the ability to realize high-efficiency chiral mode transmission by using a discontinuous encircling protocol via Hamiltonian hopping 22 . The physics behind the Hamiltonian hopping is that the eigenstates of the system Hamiltonian converge as its parameters approach infinity, and the hopping is accessible by transitioning between these states.…”

Section: Introductionmentioning

confidence: 99%

Fast encirclement of an exceptional point for highly efficient and compact chiral mode converters

Shu

et al. 2022

Nat Commun

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Exceptional points (EPs) are degeneracies at which two or more eigenvalues and eigenstates of a physical system coalesce. Dynamically encircling EPs by varying the parameters of a non-Hermitian system enables chiral mode switching, that is, the final state of the system upon a closed loop in parameter space depends on the encircling handedness. In conventional schemes, the parametric evolution during the encircling process has to be sufficiently slow to ensure adiabaticity. Here, we show that fast parametric evolution along the parameter space boundary of the system Hamiltonian can relax this constraint. The proposed scheme enables highly efficient transmission and more compact footprint for asymmetric mode converters. We experimentally demonstrate these principles in a 57 μm-long double-coupled silicon waveguide system, enabling chiral mode switching with near-unity transmission efficiency at 1550 nm. This demonstration paves the way towards high-efficiency and highly integrated chiral mode switching for a wide range of practical applications.

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Section: Introductionmentioning

confidence: 99%

Fast encirclement of an exceptional point for highly efficient and compact chiral mode converters

Shu

et al. 2022

Nat Commun

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“…In order to achieve this, we combine our strategy of variable postselection rate q with the strategy of parameter hopping proposed by Li et al in Ref. [36] for nHH dynamics.…”

Section: Hybrid-liouvillian Exceptionalmentioning

confidence: 99%

“…Introduction.-Over the past few years, exceptional points (EPs) of non-Hermitian Hamiltonians [1][2][3][4] have become an object of intense study in a number of distinct contexts. From rather abstract studies involving PT -symmetric nHHs [5][6][7][8], adiabatic nHH evolution [9][10][11][12][13][14][15][16][17], topological manifestations [18][19][20][21][22][23], exotic band structures [24], and properties of non-equilibrium phase transitions [25,26] to more practically-oriented proposals of loss-induced transparency and lasing [27][28][29][30][31][32], on-demand directional emission [33][34][35][36], optimal energy transfer [37,38], and enhanced sensing [39][40][41].…”

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confidence: 99%

“…We note, though, that even with the protocol where q is varied during the adiabatic evolution, the two desired goals: (i) perfect values of unit fidelity and (ii) no loss due to postselection, are unattainable simultaneously. To achieve these two goals together, we further employ a "hopping strategy", developed recently in the context of nHH dynamics [36]: we replace parts of the adiabatic encircling trajectory by abrupt hops. We demonstrate that combining the hopping strategy with a controlled postselection parameter, q, facilitates achieving both goals mentioned above, cf.…”

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Near-unit efficiency of chiral state conversion via hybrid-Liouvillian dynamics

Kumar,

Snizhko,

Gefen

2021

Preprint

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Following evolution under a non-Hermitian Hamiltonian (nHH) involves significant probability loss. This makes various nHH effects impractical in the quantum realm. In contrast, Lindbladian evolution conserves probability, facilitating observation and application of exotic effects characteristic of open quantum systems. Here we are concerned with the effect of chiral state conversion: encircling an exceptional point, multiple system states are converted into a single system eigenmode. While for nHH the possible converted-into eigenmodes are pure states, for Lindbladians these are typically mixed states. We consider hybrid-Liouvillian evolution, which interpolates between a Lindbladian and a nHH and enables combining the best of the two worlds. We design adiabatic evolution protocols that give rise to chiral state conversion with pure final states, no probability loss, and high fidelity. Furthermore, extending beyond continuous adiabatic evolution, we design a protocol that facilitates conversion to pure states with fidelity 1 and, at the same time, no probability loss. Employing recently developed experimental techniques, our proposal can be implemented with superconducting qubit platforms.

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“…EB states are predicted to exist in critical non-Hermitian fermionic systems containing exceptional points (EPs) [51][52][53][54][55]. Unlike ordinary gapless points, EPs are also branch points of the complex energy Riemann surface [56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72], and host unusual quantum critical, fractal and thermodynamic behavior as well as potential applications in sensing, multi-mode laser manipulation and topological energy transfer [47,60,61,[73][74][75][76][77][78][79][80][81][82][83][84][85]. Exceptional Boundary states around EPs are physically distinguished by their anomalously large occupation probabilities, which can be detected long after their host EPs are quenched.…”

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confidence: 99%

Exceptional Bound States and negative Entanglement Entropy

Lee¹

2020

Preprint

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This work introduces a new class of robust states known as Exceptional Boundary (EB) states, which are distinct from the well-known topological and non-Hermitian skin boundary states. EB states occur in the presence of exceptional points, which are non-Hermitian critical points where eigenstates coalesce and fail to span the Hilbert space. This eigenspace defectiveness not only limits the accessibility of state information, but also interplays with long-range order to give rise to singular propagators only possible in non-Hermitian settings. Their resultant EB eigenstates are characterized by robust anomalously large or negative occupation probabilities, unlike ordinary Fermi sea states whose probabilities lie between zero and one. EB states remain robust after a variety of quantum quenches and give rise to enigmatic negative entanglement entropy contributions. Through suitable perturbations, the coefficient of the logarithmic entanglement entropy scaling can be continuously tuned. EB states represent a new avenue for robustness arising from geometric defectiveness, independent of topological protection or non-reciprocal pumping.

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Hamiltonian Hopping for Efficient Chiral Mode Switching in Encircling Exceptional Points

Cited by 76 publications

References 36 publications

Fast encirclement of an exceptional point for highly efficient and compact chiral mode converters

Fast encirclement of an exceptional point for highly efficient and compact chiral mode converters

Near-unit efficiency of chiral state conversion via hybrid-Liouvillian dynamics

Exceptional Bound States and negative Entanglement Entropy

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