N. Bender, S. Factor, J. D. Bodyfelt, H. Ramezani, F. M. Ellis, T. Kottos
A mechanism for asymmetric transport based on the interplay between the fundamental symmetries of parity (P) and time (T) with nonlinearity is presented. We experimentally demonstrate and theoretically analyze the phenomenon using a pair of coupled van der Pol oscillators, as a reference system, one with anharmonic gain and the other with complementary anharmonic loss; connected to two transmission lines. An increase of the gain/loss strength or the number of PT-symmetric nonlinear dimers in a chain, can increase both the asymmetry and transmittance intensities.
http://arxiv.org//abs/1301.7337
Optics (physics.optics); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
J. Schindler, Z. Lin, J. M. Lee, Hamidreza Ramezani, F. M. Ellis, Tsampikos Kottos
We show both theoretically and experimentally that a pair of inductively coupled active LRC circuits (dimer), one with amplification and another with an equivalent amount of attenuation, display all the features which characterize a wide class of non-Hermitian systems which commute with the joint parity-time PT operator: typical normal modes, temporal evolution, and scattering processes. Utilizing a Liouvilian formulation, we can define an underlying PT-symmetric Hamiltonian, which provides important insight for understanding the behavior of the system. When the PT-dimer is coupled to transmission lines, the resulting scattering signal reveals novel features which reflect the PT-symmetry of the scattering target. Specifically we show that the device can show two different behaviors simultaneously, an amplifier or an absorber, depending on the direction and phase relation of the interrogating waves. Having an exact theory, and due to its relative experimental simplicity, PT-symmetric electronics offers new insights into the properties of PT-symmetric systems which are at the forefront of the research in mathematical physics and related fields.
http://arxiv.org/abs/1209.2347
Other Condensed Matter (cond-mat.other); Optics (physics.optics); Quantum Physics (quant-ph)
Hamidreza Ramezani, J. Schindler, F. M. Ellis, Uwe Guenther, Tsampikos Kottos
The beat time \({\tau}_{fpt}\) associated with the energy transfer between two coupled oscillators is dictated by the bandwidth theorem which sets a lower bound \({\tau}_{fpt}\sim 1/{\delta}{\omega}\). We show, both experimentally and theoretically, that two coupled active LRC electrical oscillators with parity-time (PT) symmetry, bypass the lower bound imposed by the bandwidth theorem, reducing the beat time to zero while retaining a real valued spectrum and fixed eigenfrequency difference \(\delta\omega\). Our results foster new design strategies which lead to (stable) pseudo-unitary wave evolution, and may allow for ultrafast computation, telecommunication, and signal processing.
http://arxiv.org/abs/1205.1847
Classical Physics (physics.class-ph)
Joseph Schindler, Ang Li, Mei C. Zheng, F. M. Ellis, Tsampikos Kottos
Mutually coupled modes of a pair of active LRC circuits, one with amplification and another with an equivalent amount of attenuation, provide an experimental realization of a wide class of systems where gain/loss mechanisms break the Hermiticity while preserving parity-time PT symmetry. For a value PT of the gain/loss strength parameter the eigen-frequencies undergo a spontaneous phase transition from real to complex values, while the normal modes coalesce acquiring a definite chirality. The consequences of the phase-transition in the spatiotemporal energy evolution are also presented.
http://arxiv.org/abs/1109.2913
Other Condensed Matter (cond-mat.other); Quantum Physics (quant-ph)