Topological Optical Parametric Oscillation

Abstract

Topological insulators possess protected boundary states which are robust against disorders and have immense implications in both fermionic and bosonic systems. Harnessing these topological effects in non-equilibrium scenarios is highly desirable and has led to the development of topological lasers. The topologically protected boundary states usually lie within the bulk bandgap, and selectively exciting them without inducing instability in the bulk modes of bosonic systems is challenging. Here, we consider topological parametrically driven nonlinear resonator arrays that possess complex eigenvalues only in the edge modes in spite of the uniform pumping. We show parametric oscillation occurs in the topological boundary modes of one and two dimensional systems as well as in the corner modes of a higher order topological insulator system. Furthermore, we demonstrate squeezing dynamics below the oscillation threshold, where the quantum properties of the topological edge modes are robust against certain disorders. Our work sheds light on the dynamics of weakly nonlinear topological systems driven out-of-equilibrium and reveals their intriguing behavior in the quantum regime.

Amplification of quantum signals by the non-Hermitian skin effect

“…This amplifying behavior is reminiscent of NHSE-induced amplification in classical or single-particle models [38], but we emphasize that the present analysis applies to a quantum nonlinear multiboson model with the NHSE entering directly via the BdG transformation. As all the BdG eigenenergies of the finite chain are real, the amplification comes from the existence of skin modes and not from any dynamical instability, unlike previously studied models of quantum amplifiers [56,60,64]. We also observe amplification if the input and output ports are interchanged, as there is another set of skin modes localized to the left.…”

“…This is noteworthy since the NHSE often (though not exclusively) arises in the presence of nonreciprocal couplings [20][21][22][23][25][26][27][28][29][30][31]. Previous authors have explored using BdG Hamiltonian dynamics for quantum amplification and related purposes [45,48,51,[53][54][55], including showing that BdG Hamiltonians can be made to exhibit distinct topological phases with unidirectional and/or amplified topological modes [56][57][58][59][60][61][62][63][64]. While most of these studies have been theoretical, simple quantum amplifiers have been implemented in quantum circuits [65][66][67].…”

Amplification of quantum signals by the non-Hermitian skin effect

“…This behavior is reminiscent of NHSE-induced amplification in classical or single-particle models [37], but the present analysis applies to a quantum nonlinear multiboson model with the NHSE entering directly via the BdG transformation. As all the BdG eigenenergies of the finite chain are real, the amplification comes from the existence of skin modes and not from any dynamical instability, unlike previously-studied models of quantum amplifiers [56,60,64]. We also observe amplification if the input and output ports are interchanged, as there is another set of skin modes localized to the left.…”

“…The quantum bosonic Hamiltonian lacks the nonreciprocal couplings commonly associated with the NHSE [20][21][22][24][25][26][27][28][29][30], but it can be mapped to a singleparticle Hamiltonian that is non-Hermitian and nonreciprocal via the Bogoliubov-de Gennes (BdG) transformation [50], a well-known procedure used in studying Majorana fermions [51] and topological superconductors [52]. Previous authors have explored using the dynamics of BdG Hamiltonians for quantum amplification and related purposes [42,50,[53][54][55], and BdG Hamiltonians can even be made to exhibit distinct topological phases, giving rise to unidirectional and/or amplified topological modes [56][57][58][59][60][61][62][63][64]. While most of these studies have been theoretical, quantum amplifiers have been successfully observed in simple quantum circuits [65][66][67].…”

Tensor Product States in the Synthetic Space of Quadratic Bosonic Systems: Emergent Interplay Between Diabolic and Exceptional Degeneracy

“…Both the EPs and DPs possess remarkable features. EPs have been predicted and observed in different platforms including: classical quantum electrodynamics (QED) [9][10][11][12], circuit QED [13][14][15][16][17], electronics [18], plasmonics [19,20], photonic lattices [21], hybrid metamaterials [22], acoustics [23][24][25][26], cavity optomechanics [24,[27][28][29], optoelectronics [30], spintronics [31][32][33], cavity magnonics [34][35][36][37][38], atom optics with Bose-Einstein condensates [39], trapped ions [40], and in the interaction of THz light with collective molecular vibrations [41]. EPs can induce counterintuitive effects such as: loss-induced optical transparency [42], loss-induced suppression and revival of lasing [43], anomalous absorption [44,45], unidirectional invisibility [46], topological chirality [13,28,30,47], topological insulator lasers [48], or state switchi...…”