Topological Quantum Fluctuations and Traveling Wave Amplifiers

Abstract

It is now well established that photonic systems can exhibit topological energy bands. Similar to their electronic counterparts, this leads to the formation of chiral edge modes which can be used to transmit light in a manner that is protected against backscattering. While it is understood how classical signals can propagate under these conditions, it is an outstanding important question how the quantum vacuum fluctuations of the electromagnetic field get modified in the presence of a topological band structure. We address this challenge by exploring a setting where a nonzero topological invariant guarantees the presence of a parametrically unstable chiral edge mode in a system with boundaries, even though there are no bulkmode instabilities. We show that one can exploit this to realize a topologically protected, quantum-limited traveling wave parametric amplifier. The device is naturally protected against both internal losses and backscattering; the latter feature is in stark contrast to standard traveling wave amplifiers. This adds a new example to the list of potential quantum devices that profit from topological transport.

Snowflake phononic topological insulator at the nanoscale

“…These new helical phonon networks could also contain optically tunable nonreciprocal elements [46], as well as quantum-limited chiral traveling wave amplifiers of phononic signals (adapting the scheme presented in Ref. [47]). …”

L lines, C points and Chern numbers: understanding band structure topology using polarization fields

“…Besides the mechanical arrays of pendula and nanopillars mentioned above, we will also explain how our method can be applied in general to arbitrary mechanical structures (e. g. phononic crystals), and also to the electromagnetic fields in photonic structures. It is, thus, applicable in principle to a large class of the recently proposed or implemented topological devices for sound waves [1,2,[33][34][35][36][37][38][39][40][41][42][43][44], light waves [45][46][47][48][49][50][51][52][53][54][55][56][57], ultracold atoms [58,59], or magnons [60][61][62][63][64]. These include Chern insulators, as well as time-reversal preserving topological insulators whose Hamiltonian can be decomposed into a pair of Chern insulator Hamiltonians with opposite Chern numbers.…”

Nonlinear dynamics of weakly dissipative optomechanical systems

“…Panels (c) and (d) illustrate the evolution of the fixed points with increasing P. Stable and unstable fixed points are represented by black and red dashed lines, respectively. 5 In a saddle-node bifurcation a pair of stable-unstable fixed points approach each other as a parameter η is varied (for simplicity and without loss of generality, let us suppose that we are increasing η). At h h = * the two fixed points merge and form one single stable fixed point; if h h > * the fixed points cease to exist.…”

“…For an extended review we refer the reader to [1]. In the past few years, a range of impressive achievements has been observed, which includes topological transport in optomechanical arrays [4,5], the engineering of nonreciprocal interactions [6][7][8][9][10][11], the generation of single phonon states using optical control [12], the generation of mechanical squeezed states [13], measurement-based quantum control of mechanical motion [14], conversion of quantum information to mechanical motion [15], conversion between light in the microwave and optical range [16], single photon frequency shifters [17], force measurements using cold-atom optomechanics [18], and the use of unconventional mechanical modes, like high frequency bulk modes of crystals [19], multilayer graphene [20], and the modes of superfluid helium [21].…”