Experimental Realization of Floquet PT -Symmetric Systems

Abstract

We provide an experimental framework where periodically driven PT -symmetric systems can be investigated. The set-up, consisting of two UHF oscillators coupled by a time-dependent capacitance, demonstrates a cascade of PT -symmetric broken domains bounded by exceptional point degeneracies. These domains are analyzed and understood using an equivalent Floquet frequency lattice with local PT -symmetry. Management of these PT -phase transition domains is achieved through the amplitude and frequency of the drive.PACS numbers: 42.25.Bs, 11.30.Er Introduction -Non-Hermitian Hamiltonians H which commute with the joint parity-time (PT ) symmetry might have real spectrum when some parameter γ, that controls the degree of non-hermiticity, is below a critical value γ PT [1]. In this parameter domain, termed exact PT -phase the eigenfunctions of H are also eigenfunctions of the PT -symmetric operator. In the opposite limit, coined the broken PT -phase, the spectrum consists (partially or completely) of pairs of complex conjugate eigenvalues while the eigenfunctions cease to be eigenfunctions of the PT operator. The transition point γ = γ PT shows all the characteristic features of an exceptional point (EP) singularity where both eigenfunctions and eigenvalues coalesce.Although originally the interest on PT -symmetric systems was driven by a mathematical curiosity [1], during the last five years the field has blossomed and many applications in areas of physics, ranging from optics [2-18], matter waves [19,20] and magnonics [21,22] [4, 9, 10, 12-14, 17, 18, 24-26]. Importantly, the existence of the PT phase transition and specifically of the EP singularity played a prominent role in many of these studies, and subsequent technological applications.Though the exploitation of PT -symmetric systems has been prolific, most of the attention has been devoted to static (i.e. time-independent) potentials. Recently, however, a parallel activity associated with time-dependent PT -symmetric systems has started to attract increasing attention [29][30][31][32][33][34][35][36][37][38][39]. The excitement for this line of research stems from two reasons: the first one is fundamental and it is associated with the expectation that new pathways in the PT -arena can lead to new exciting phenomena. This expectation is further supported by the fact that the investigation of time-dependent Hermitian counterparts led to a plethora of novel phenomena-examples include Rabi oscillations [40], Autler-Townes splitting [41], dynamical localization [42], dynamical Anderson localization [43], and coherent destruction of tunneling [44,45] (for a review see [46]). The second reason is technological and it is associated with the possibility to use driving schemes as a flexible experimental knob to realize new forms of reconfigurable synthetic matter [47,48]. Specif-

Optical Pulling and Pushing Forces in Bilayer PT -Symmetric Structures

“…The asymmetric forces can be understood from the fact that the system is not invariant under space inversion [38,39]. We use the wellknown PT phase-transition parameters, i.e., n 0 d=λ and n 00 =n 0 [35,[40][41][42], to conduct a detailed study concerning their influence on the optical forces, transmission, and eigenvalues of the scattering matrix:…”

Parametric amplification and bidirectional invisibility in PT -symmetric time-Floquet systems

“…So far, nonHermitian PT -symmetric devices have been observed in very different physical systems, from optics to acoustics [13][14][15][16][17][18][19][20][21][22]. Different methods have been exploited to induce the required gain, e.g., the use of optical gain media (in optics) [23,24], amplifiers (in electronics and electroacoustics) [25][26][27], or coupling with hydrodynamic instabilities or heat sources (in flow acoustics and thermoacoustics, respectively) [28,29].…”

Parity‐Time‐Symmetric Optical Lattice with Alternating Gain and Loss Atomic Configurations

“…[5] Given that a single PT cell (one pair of gain-loss elements) can exhibit many unconventional optical properties, [6][7][8][9][10][11][12][13] interesting, exotic features are expected in non-Hermitian optical lattices. [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] The proposed behaviors for light travelling through non-Hermitian lattices include non-Hermitian optical solitons, [15,16] non-Hermitian Bloch oscillation, [17,18] unidirectional invisibility, [20] and PTsymmetric Talbot effect. [25] Studying these novel effects in periodic non-Hermitian optical settings may provide new routes for exploring useful applications in non-Hermitian synthetic materials and further constructing on-chip optical integrated devices.…”