PT symmetry via electromagnetically induced transparency

Li, Huijun; Dou, Jian-Peng; Huang, Guoxiang

doi:10.1364/oe.21.032053

Cited by 54 publications

(36 citation statements)

References 25 publications

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“…Multistable solitons in PTsymmetric lattices in the presence of cubic-quintic nonlinearity F (x, |Ψ| 2 ) = g 1 |Ψ| 2 + g 2 |Ψ| 4 were reported by Li, Liu, and Dong (2012). He and Mihalache (2013) studied soliton propagation in the cubic-quintic Ginzburg-Landau model with a PT -symmetric lattice.…”

Section: E Solitons In Generalized Lattice Modelsmentioning

confidence: 99%

Nonlinear waves inPT-symmetric systems

2016

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Recent progress on nonlinear properties of parity-time (PT -) symmetric systems is comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying PT symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a PT -symmetric system. The natural inclusion of nonlinearity into these PT systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above PTsymmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear PT -symmetric systems arising from various physical disciplines are presented; nonlinear properties of these systems are thoroughly elucidated; and relevant experimental results are described. In addition, emerging applications of PT symmetry are pointed out.

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Section: E Solitons In Generalized Lattice Modelsmentioning

confidence: 99%

Nonlinear waves inPT-symmetric systems

2016

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“…PT-symmetric metamaterials require a delicate balance of gain and loss whereby the complex refraction index satisfies nðzÞ ¼ n Ã ð−zÞ and are typically made of periodic solid microstructures. Homogeneous atomic vapors driven into three-level [17,18] or four-level [19] configurations have also been proposed to realize PT-symmetric optical potentials via rather complicated spatial modulations of two driving fields. Such proposals have obvious advantages of real-time all-optical reconfigurable capabilities and implicit disadvantages of intractable field modulations and considerable symmetry errors.…”

mentioning

confidence: 99%

“…A probe susceptibility χ p ðzÞ with its real (imaginary) part being an even (odd) function of the lattice position z can be implemented by spatially modulating at least two critical parameters of atom-field interaction in distinct elaborate ways [17][18][19]. Since the atomic density distribution N j ðzÞ is here an even function of the lattice position z, we now try to engineer the dynamic frequency shift as an odd function of the lattice position.…”

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confidence: 99%

Non-Hermitian Degeneracies and Unidirectional Reflectionless Atomic Lattices

2014

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Light propagation in optical lattices of driven cold atoms exhibits non-Hermitian degeneracies when the first-order modulation amplitudes of real and imaginary parts of the probe susceptibility are manipulated to be balanced. At these degeneracies, one may observe complete unidirectional reflectionless light propagation. This strictly occurs with no gain and can be easily tuned and fully reversed as supported by the transfer-matrix calculations and explained via a coupled-mode analysis. DOI: 10.1103/PhysRevLett.113.123004 PACS numbers: 37.10.Jk, 11.30.Er, 42.25.Bs, 42.50.Gy Much attention has been devoted to the development of artificial metamaterials for achieving optical functionalities not available in nature. Photonic crystals [1] and lefthanded materials [2] are prominent instances tailored to stretch the rules of light propagation and interaction. Such metamaterials have seeded new paradigms in optical, optoelectronic, and optomechanical devices [3][4][5][6]. Nevertheless, some tasks are more difficult than others with unidirectional light transport being a most pronounced example. Significant progress has been made in recent years by developing optical materials with parity-time (PT) symmetry to attain unidirectional light invisibility [7][8][9][10][11][12][13][14][15][16]. PT-symmetric metamaterials require a delicate balance of gain and loss whereby the complex refraction index satisfies nðzÞ ¼ n Ã ð−zÞ and are typically made of periodic solid microstructures. Homogeneous atomic vapors driven into three-level [17,18] or four-level [19] configurations have also been proposed to realize PT-symmetric optical potentials via rather complicated spatial modulations of two driving fields. Such proposals have obvious advantages of real-time all-optical reconfigurable capabilities and implicit disadvantages of intractable field modulations and considerable symmetry errors. Large optical nonreciprocities may also be achieved by exploiting the asymmetric Doppler shift in moving atomic Bragg mirrors [20], and proofof-principle experiments have been carried out [21].The great interest in PT-symmetric complex media stemmed, however, from the non-Hermitian extensions of quantum mechanics and quantum field theories [22,23], and it is perhaps worth going back to the essential nonHermitian behavior of light transport to get a broader picture on reciprocity violations and unidirectional reflectionlessness. Take, e.g., a typical one-dimensional (1D) light scattering process as shown in Fig. 1(a) where the outgoing field amplitudes fE − L ; E þ R g are related to the incoming field amplitudes fE − R ; E þ L g by a scattering matrix S [24], the eigenvectors of which are defined byThe complex amplitudes t, r L , and r R of the (S) matrix in Eq.(1) denote, as usual, the reciprocal transmission and the reflection for incidence from the left and from the right. In general, the matrix S is non-Hermitian, its eigenvalues λ AE s ¼ t AE ffiffiffiffiffiffiffiffiffi ffi r L r R p are complex, and its eigenvectors ðAE ffiffiffiffiff...

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“…So far most even P T -symmetric materials are solid-state systems that consist of periodically arranged microstructures bearing on the whole balanced gain and loss. Homogeneous vapors of multilevel ultracold atoms can further be used to attain even P Tsymmetric optical potentials though via rather complicated spatial modulations of the driving fields [26][27][28]. These atomic proposals have the obvious advantages of real-time all-optical tunable and reconfigurable capabilities.…”

Section: Introductionmentioning

confidence: 99%

Parity-time-antisymmetric atomic lattices without gain

Artoni

Rocca

2015

Phys. Rev. A

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Lossy atomic photonic crystals can be suitably tailored so that the real and imaginary parts of the susceptibility are, respectively, an odd and an even function of position. Such a parity-time (P T ) space antisymmetry in the susceptibility requires neither optical gain nor negative refraction, but is rather attained by a combined control of the spatial modulation of both the atomic density and their dynamic level shift. These passive photonic crystals made of dressed atoms are characterized by a tunable unidirectional reflectionlessness accompanied by an appreciable degree of transmission. Interestingly, such peculiar properties are associated with non-Hermitian degeneracies of the crystal scattering matrix, which can then be directly observed through reflectivity measurements via a straightforward phase modulation of the atomic dynamic level shift and even off resonance.

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PT symmetry via electromagnetically induced transparency

Cited by 54 publications

References 25 publications

Nonlinear waves inPT-symmetric systems

Nonlinear waves inPT-symmetric systems

Non-Hermitian Degeneracies and Unidirectional Reflectionless Atomic Lattices

Parity-time-antisymmetric atomic lattices without gain

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