Breaking Lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering

Abstract

A century-old tenet in physics and engineering asserts that any type of system, having bandwidth Δω, can interact with a wave over only a constrained time period Δ inversely proportional to the bandwidth (Δ·Δω ~ 2π). This law severely limits the generic capabilities of all types of resonant and wave-guiding systems in photonics, cavity quantum electrodynamics and optomechanics, acoustics, continuum mechanics, and atomic and optical physics but is thought to be completely fundamental, arising from basic Fourier reciprocity. We propose that this "fundamental" limit can be overcome in systems where Lorentz reciprocity is broken. As a system becomes more asymmetric in its transport properties, the degree to which the limit can be surpassed becomes greater. By way of example, we theoretically demonstrate how, in an astutely designed magnetized semiconductor heterostructure, the above limit can be exceeded by orders of magnitude by using realistic material parameters. Our findings revise prevailing paradigms for linear, time-invariant resonant systems, challenging the doctrine that high-quality resonances must invariably be narrowband and providing the possibility of developing devices with unprecedentedly high time-bandwidth performance.

Quantum limits on the time-bandwidth product of an optical resonator

“…[9], with its large input rate and arbitrarily small output rate, is analogous to a black hole that sucks energy in one direction. If there is no other neglected dissipation, extra noise akin to Hawking radiation must be present to uphold the second law.…”

“…A three-dimensional view of the silicon-indiumantimonide-silver (Si-InSb-Ag) system assumed in Ref. [9]. Their two-dimensional model with only the x and z dimensions neglect modes that have a nonzero wavevector component in the y dimension (k y ) and would miss any coupling of the SMPs at the Ag mirror to those modes.…”

“…The model in Ref. [9] relies crucially on the assumption that only a forward-propagating SMP mode exists and the back-propagating mode is forbidden, resulting in a net power transfer and energy build-up in one direction. Suppose that two baths, initially at the same temperature, are placed on the opposite ends of the system, exchanging energy via the SMPs only.…”

“…(3) in Ref. [9]). They defined the time-bandwidth product (TBP) as τγ 0 and claimed that their proposed device could make τγ 0 arbitrarily large.…”

“…While the main driver has been the practical desire to make on-chip isolators and circulators for integrated photonics, a recent proposal by Tsakmakidis et al [9] suggests that nonreciprocal optics can break a fundamental time-bandwidth limit to passive resonators. If true, the proposal promises an upheaval of fundamental physics, as well as new functionalities such as broadband slow light.…”