Anomalous time delays and quantum weak measurements in optical micro-resonators

Abstract

Quantum weak measurements, wavepacket shifts and optical vortices are universal wave phenomena, which originate from fine interference of multiple plane waves. These effects have attracted considerable attention in both classical and quantum wave systems. Here we report on a phenomenon that brings together all the above topics in a simple one-dimensional scalar wave system. We consider inelastic scattering of Gaussian wave packets with parameters close to a zero of the complex scattering coefficient. We demonstrate that the scattered wave packets experience anomalously large time and frequency shifts in such near-zero scattering. These shifts reveal close analogies with the Goos–Hänchen beam shifts and quantum weak measurements of the momentum in a vortex wavefunction. We verify our general theory by an optical experiment using the near-zero transmission (near-critical coupling) of Gaussian pulses propagating through a nano-fibre with a side-coupled toroidal micro-resonator. Measurements demonstrate the amplification of the time delays from the typical inverse-resonator-linewidth scale to the pulse-duration scale.

Lorentz-boost eigenmodes

“…For example, the wavefunction can be chosen to vanish for z > t and to be non-zero for z < t . In contrast, even localized (square-integrable) superpositions of plane waves or vortex modes spread over all spacetime, and it this feature that results in the counterintuitive "superluminal" propagation of Gaussian wave packets [22][23][24]. Therefore, the boost eigenmodes can play an important role in problems involving causality and signal propagation [19][20][21].…”

“…Such modes are well suited for problems involving causal signal propagation [19][20][21]. Indeed, even localized (i.e., square-integrable but spatially unbounded) wave packets made of plane waves bring about paradoxes with the superluminal propagation [22][23][24]. In contrast, boost eigenmodes immediately provide step-like singularities (signals) propagating exactly with the speed of light and never violating causality.…”

Experimental probe of weak-value amplification and geometric phase through the complex zeros of the response function

“…G(y) may thus be treated as the spatial response function. Note that this space dependent response function for momentum domain Spin Hall shift is in precise analogy with the frequency response of the system corresponding to time delay or frequency shifts of Gaussian temporal pulse [33,34]. The complex root of the response function can be obtained as…”

Faster light with competing absorption and gain

“…In general it is desirable to achieve tunable pulse delays or advancements upwards of the pulse width τ or more, while at the same time minimizing pulse distortion and reductions in the signal-to-noise ratio. Dispersive effects in optical media with narrow-band resonances, such as gain lines [11][12][13][14], absorption lines [3,15], transparency features [16][17][18] and optical cavities [19,20], have been studied extensively for this purpose. As an example, it has been shown in an ultracold atomic gas that light can be delayed by more than 5τ, corresponding to a group velocity of only v g = 17 m/s [16].…”

“…On the other hand, experiments on superluminal pulse propagation (with v g > c or v g < 0) have seen less progress in comparison. While advancements on the order of τ have been reported using anomalous dispersion in absorbing media [15] and high-Q optical cavities [20], these approaches are limited by the fact that the optimal advancement occurs at the point of minimum transmission, and as a result the advanced pulses are less than 1% of the original pulse intensity. One notable exception is a four-wave mixing (4WM) experiment which achieved advancements of 0.63 τ in the amplifying regime [14].…”