Synthetic Mechanical Lattices with Synthetic Interactions

Measuring the Adiabatic Non-Hermitian Berry Phase in Feedback-Coupled Oscillators

“…In this case, for fixed J, an exceptional point and PT symmetry-breaking phase transition are encountered at δJ = J, as previously demonstrated with this platform by spectral analysis in Ref. [20]. In the full (J,δJ) parameter space, there are two distinct regions of conserved and broken PT symmetry, denoted by white and grey in Fig.…”

“…Following its discovery, the Berry phase was generalised to systems with dissipation or gain, in which the Hamiltonian becomes non-Hermitian [4][5][6][7][8][9][10][11]. Interest in such problems has continued to grow, inspired by developments in non-Hermitian experimental platforms, including in photonics [12,13], mechanics [14][15][16][17][18][19][20], electric circuits [21,22], and cold atoms [23,24] amongst many others [25][26][27]. This progress has also been driven by interest in topological systems, in which non-Hermiticity leads to new topological classifications and unusual boundary phenomena [25,27].…”

“…In contrast, here we study a two-site PT -symmetric system, in a regime for which the eigenenergies are real and adiabatic evolution is possible. To realise our model, we employ a mapping between quantum evolution and the classical dynamics of a pair of oscillators coupled with real-time measurement-based feedback [20]. We evolve our system adiabatically and experimentally demonstrate that the imaginary part of the Berry phase leads to significant geometrical amplification and damping, which is intrinsically non-Hermitian.…”

“…To explore the two-site Hatano-Nelson model, we construct a synthetic mechanical lattice made up of two classical oscillators artificially coupled by real-time feedback measurements, based on our approach reported in Ref. [20]. The essential idea of this scheme is to map the Heisenberg equations for a desired tight-binding quantum Hamiltonian onto Newton's equations of motion for classical oscillators in phase-space within a rotating waveapproximation [43,44].…”

“…The essential idea of this scheme is to map the Heisenberg equations for a desired tight-binding quantum Hamiltonian onto Newton's equations of motion for classical oscillators in phase-space within a rotating waveapproximation [43,44]. As discussed in [20], the use of real-time feedback then means that many two level non-Hermitian Hamiltonian can be realized with this setup. Here, we use self-and cross-feedback between the oscillators to realize the Hamiltonian described in Eq.…”