The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization

Non-Hermitian systems distinguish themselves from Hermitian systems by exhibiting a phase transition point called an exceptional point (EP), which is the point at which two eigenstates coalesce under a system parameter variation. Many interesting EP phenomena such as level crossings/repulsions in nuclear/molecular and condensed matter physics, and unusual phenomena in optics such as loss-induced lasing and unidirectional transmission can be understood by considering a simple 2x2 non-Hermitian matrix. At a higher dimension, more complex EP physics not found in two-state systems arises. We consider the emergence and interaction of multiple EPs in a four-state system theoretically and realize the system experimentally using four coupled acoustic cavities with asymmetric losses. We find that multiple EPs can emerge and as the system parameters vary, these EPs can collide and merge, leading to higher order singularities and topological characteristics much richer than those seen in two-state systems.

[1]  D. Christodoulides,et al.  Parity-time–symmetric microring lasers , 2014, Science.

[2]  U. Peschel,et al.  Parity–time synthetic photonic lattices , 2012, Nature.

[3]  Open quantum systems and Dicke superradiance , 2013, 1305.2762.

[4]  Shiyue Hua,et al.  Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators , 2014, Nature Photonics.

[5]  Hui Cao,et al.  Unidirectional invisibility induced by PT-symmetric periodic structures. , 2011, Physical review letters.

[6]  C. Schneider,et al.  Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard , 2015, Nature.

[7]  Soo-Young Lee,et al.  Geometric phase around multiple exceptional points , 2012 .

[8]  J. P. Woerdman,et al.  Excess Quantum Noise Due to Nonorthogonal Polarization Modes , 1997, Technical Digest. 1998 EQEC. European Quantum Electronics Conference (Cat. No.98TH8326).

[9]  Shanhui Fan,et al.  Parity–time-symmetric whispering-gallery microcavities , 2013, Nature Physics.

[10]  H. Cartarius,et al.  Model of a PT-symmetric Bose-Einstein condensate in a δ-function double-well potential , 2012 .

[11]  W. Heiss,et al.  Resonance scattering at third-order exceptional points , 2015 .

[12]  Soo-Young Lee,et al.  Divergent Petermann factor of interacting resonances in a stadium-shaped microcavity , 2008 .

[13]  B. M. Fulk.  MATH , 1992 .

[14]  C. Bender,et al.  Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry , 1997, physics/9712001.

[15]  N. Rivolta,et al.  Symmetry recovery for coupled photonic modes with transversal PT symmetry. , 2015, Optics letters.

[16]  S. Longhi,et al.  Bloch oscillations in complex crystals with PT symmetry. , 2009, Physical review letters.

[17]  Z. Q. Zhang,et al.  Coalescence of exceptional points and phase diagrams for one-dimensional PT -symmetric photonic crystals , 2015, 1509.07948.

[18]  Xuefeng Zhu,et al.  PT-symmetric acoustics , 2015 .

[19]  J. Main,et al.  Coupling approach for the realization of a PT -symmetric potential for a Bose-Einstein condensate in a double well , 2014, 1409.7490.

[20]  R. Aguado,et al.  Majorana bound states from exceptional points in non-topological superconductors , 2014, Scientific Reports.

[21]  D. Vanderbilt,et al.  Smooth gauge for topological insulators , 2012, 1201.5356.

[22]  M. Berry,et al.  Diabolical points in the spectra of triangles , 1984, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[23]  H. Harney,et al.  Experimental observation of the topological structure of exceptional points. , 2001, Physical review letters.

[24]  M. Segev,et al.  Observation of parity–time symmetry in optics , 2010 .

[25]  Li Ge,et al.  PT-symmetry breaking and laser-absorber modes in optical scattering systems. , 2010, Physical review letters.

[26]  R. Morandotti,et al.  Observation of PT-symmetry breaking in complex optical potentials. , 2009, Physical review letters.

[27]  Vilson R. Almeida,et al.  Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies. , 2013, Nature materials.

[28]  Y. Wang,et al.  Single-mode laser by parity-time symmetry breaking , 2014, Science.

[29]  E. Graefe,et al.  Signatures of three coalescing eigenfunctions , 2011, 1110.1489.

[30]  Ling Lu,et al.  Spawning rings of exceptional points out of Dirac cones , 2015, Nature.

[31]  Heidelberg,et al.  Observation of a chiral state in a microwave cavity. , 2002, Physical review letters.

[32]  Xue-Feng Zhu,et al.  P T -Symmetric Acoustics , 2014 .

[33]  Z. Musslimani,et al.  Beam dynamics in PT symmetric optical lattices. , 2008, Physical review letters.

[34]  W. Heiss,et al.  The physics of exceptional points , 2012, 1210.7536.

[35]  Andrea Alù,et al.  An invisible acoustic sensor based on parity-time symmetry , 2015, Nature Communications.

[36]  Ingrid Rotter,et al.  A non-Hermitian Hamilton operator and the physics of open quantum systems , 2009 .

[37]  Hong Chen,et al.  Experimental demonstration of a coherent perfect absorber with PT phase transition. , 2014, Physical review letters.

[38]  M. Znojil,et al.  Three Solvable Matrix Models of a Quantum Catastrophe , 2014, 1403.0723.

[39]  H. Yilmaz,et al.  Loss-induced suppression and revival of lasing , 2014, Science.

[40]  Henri Benisty,et al.  Transverse periodic P T symmetry for modal demultiplexing in optical waveguides , 2015 .

[41]  G. Strasser,et al.  Reversing the pump dependence of a laser at an exceptional point , 2014, Nature Communications.

[42]  W. Heiss.  Chirality of wavefunctions for three coalescing levels , 2007, 0708.1392.