Quasi-energies, parametric resonances, and stability limits in ac-driven PT-symmetric systems

D'Ambroise, Jennie; Malomed, Boris A.; Kevrekidis, P. G.

doi:10.1063/1.4883715

Cited by 15 publications

(15 citation statements)

References 71 publications

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“…In the simplest case of two sites (N = 2), the instability arises from an ordinary parametric resonance, which for a nonHermitian PT symmetric dimer has been recently studied in Ref. [25]. For a larger number of lattice sites in the chain, instability arises from multiple parametric resonances, which can be captured by a secular perturbation theory in the h → 0 limit.…”

Section: Multiple Parametric Resonance In a Tight-binding Linearmentioning

confidence: 99%

Tight-binding lattices with an oscillating imaginary gauge field

Longhi

2016

Phys. Rev. A

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We consider non-Hermitian dynamics of a quantum particle hopping on a one-dimensional tightbinding lattice made of N sites with asymmetric hopping rates induced by a time-periodic oscillating imaginary gauge field. A deeply different behavior is found depending on the lattice topology. While in a linear chain (open boundary conditions) an oscillating field can lead to a complex quasi energy spectrum via a multiple parametric resonance, in a ring topology (Born-von Karman periodic boundary conditions) an entirely real quasi energy spectrum can be found and the dynamics is pseudo-Hermitian. In the large N limit, parametric instability and pseudo-Hermitian dynamics in the two different lattice topologies are physically explained on the basis of a simple picture of wave packet propagation.

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Section: Multiple Parametric Resonance In a Tight-binding Linearmentioning

confidence: 99%

Tight-binding lattices with an oscillating imaginary gauge field

Longhi

2016

Phys. Rev. A

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“…Modulation of structure parameters along the propagation direction of coupled optical waveguides with gain and loss can open new opportunities for optical signal control in both linear [178][179][180] and nonlinear [67,82,[181][182][183][184][185] regimes.…”

Section: Modulated Waveguide Couplersmentioning

confidence: 99%

“…Parameters correspond to nonlinear stabilisation in a linearly unstable system, adopted fromFig. 8in Ref [183]…”

mentioning

confidence: 99%

Nonlinear switching and solitons in PT‐symmetric photonic systems

Suchkov

Sukhorukov

Huang

et al. 2016

Laser & Photonics Reviews

345

263

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One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested ParityTime (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT-symmetric photonic systems with an intensitydependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly-induced PT-symmetry breaking, and all-optical switching. Nonlinear PT-symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control.

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“…time-independent) potentials. Recently, however, a parallel activity associated with time-dependent PT -symmetric systems has started to attract increasing attention [29][30][31][32][33][34][35][36][37][38][39]. The excitement for this line of research stems from two reasons: the first one is fundamental and it is associated with the expectation that new pathways in the PT -arena can lead to new exciting phenomena.…”

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confidence: 99%

Experimental Realization of Floquet PT -Symmetric Systems

2017

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We provide an experimental framework where periodically driven PT -symmetric systems can be investigated. The set-up, consisting of two UHF oscillators coupled by a time-dependent capacitance, demonstrates a cascade of PT -symmetric broken domains bounded by exceptional point degeneracies. These domains are analyzed and understood using an equivalent Floquet frequency lattice with local PT -symmetry. Management of these PT -phase transition domains is achieved through the amplitude and frequency of the drive.PACS numbers: 42.25.Bs, 11.30.Er Introduction -Non-Hermitian Hamiltonians H which commute with the joint parity-time (PT ) symmetry might have real spectrum when some parameter γ, that controls the degree of non-hermiticity, is below a critical value γ PT [1]. In this parameter domain, termed exact PT -phase the eigenfunctions of H are also eigenfunctions of the PT -symmetric operator. In the opposite limit, coined the broken PT -phase, the spectrum consists (partially or completely) of pairs of complex conjugate eigenvalues while the eigenfunctions cease to be eigenfunctions of the PT operator. The transition point γ = γ PT shows all the characteristic features of an exceptional point (EP) singularity where both eigenfunctions and eigenvalues coalesce.Although originally the interest on PT -symmetric systems was driven by a mathematical curiosity [1], during the last five years the field has blossomed and many applications in areas of physics, ranging from optics [2-18], matter waves [19,20] and magnonics [21,22] [4, 9, 10, 12-14, 17, 18, 24-26]. Importantly, the existence of the PT phase transition and specifically of the EP singularity played a prominent role in many of these studies, and subsequent technological applications.Though the exploitation of PT -symmetric systems has been prolific, most of the attention has been devoted to static (i.e. time-independent) potentials. Recently, however, a parallel activity associated with time-dependent PT -symmetric systems has started to attract increasing attention [29][30][31][32][33][34][35][36][37][38][39]. The excitement for this line of research stems from two reasons: the first one is fundamental and it is associated with the expectation that new pathways in the PT -arena can lead to new exciting phenomena. This expectation is further supported by the fact that the investigation of time-dependent Hermitian counterparts led to a plethora of novel phenomena-examples include Rabi oscillations [40], Autler-Townes splitting [41], dynamical localization [42], dynamical Anderson localization [43], and coherent destruction of tunneling [44,45] (for a review see [46]). The second reason is technological and it is associated with the possibility to use driving schemes as a flexible experimental knob to realize new forms of reconfigurable synthetic matter [47,48]. Specif-

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Quasi-energies, parametric resonances, and stability limits in ac-driven PT-symmetric systems

Cited by 15 publications

References 71 publications

Tight-binding lattices with an oscillating imaginary gauge field

Tight-binding lattices with an oscillating imaginary gauge field

Nonlinear switching and solitons in PT‐symmetric photonic systems

Experimental Realization of Floquet PT -Symmetric Systems

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