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

Multiparameter Estimation Perspective on Non-Hermitian Singularity-Enhanced Sensing

Describing the evolution of quantum systems by means of non-Hermitian generators opens a new avenue to explore the dynamical properties naturally emerging in such a picture, e.g. operation at the so-called exceptional points, preservation of parity-time symmetry, or capitalizing on the singular behavior of the dynamics. In this Letter, we focus on the possibility of achieving unbounded sensitivity when using the system to sense linear perturbations away from a singular point. By combining multiparameter estimation theory of Gaussian quantum systems with the one of singular-matrix perturbations, we introduce the necessary tools to study the ultimate limits on the precision attained by such singularity-tuned sensors. We identify under what conditions and at what rate can the resulting sensitivity indeed diverge, in order to show that nuisance parameters should be generally included in the analysis, as their presence may alter the scaling of the error with the estimated parameter.

Free-space optical delay line using space-time wave packets

An optical buffer featuring a large delay-bandwidth-product-a critical component for future all-optical communications networks-remains elusive. Central to its realization is a controllable inline optical delay line, previously accomplished via engineered dispersion in optical materials or photonic structures constrained by a low delay-bandwidth product. Here we show that space-time wave packets whose group velocity is continuously tunable in free space provide a versatile platform for constructing inline optical delay lines. By spatio-temporal spectral-phase-modulation, wave packets in the same or in different spectral windows that initially overlap in space and time subsequently separate by multiple pulse widths upon free propagation by virtue of their different group velocities. Delay-bandwidth products of  ~100 for pulses of width  ~1 ps are observed, with no fundamental limit on the system bandwidth.

Arbitrarily high time bandwidth performance in a nonreciprocal optical resonator with broken time invariance

Most present-day resonant systems, throughout physics and engineering, are characterized by a strict time-reversal symmetry between the rates of energy coupled in and out of the system, which leads to a trade-off between how long a wave can be stored in the system and the system's bandwidth. Any attempt to reduce the losses of the resonant system, and hence store a (mechanical, acoustic, electronic, optical, or of any other nature) wave for more time, will inevitably also reduce the bandwidth of the system. Until recently, this time-bandwidth limit has been considered fundamental, arising from basic Fourier reciprocity. In this work, using a simple macroscopic, fiber-optic resonator where the nonreciprocity is induced by breaking its time-invariance, we report, in full agreement with accompanying numerical simulations, a time-bandwidth product (TBP) exceeding the 'fundamental' limit of ordinary resonant systems by a factor of 30. We show that, although in practice experimental constraints limit our scheme, the TBP can be arbitrarily large, simply dictated by the finesse of the cavity. Our results open the path for designing resonant systems, ubiquitous in physics and engineering, that can simultaneously be broadband and possessing long storage times, thereby offering a potential for new functionalities in wave-matter interactions.

Absence of unidirectionally propagating surface plasmon-polaritons at nonreciprocal metal-dielectric interfaces

In the presence of an external magnetic field, the surface plasmon polariton that exists at the metal-dielectric interface is believed to support a unidirectional frequency range near the surface plasmon frequency, where the surface plasmon polariton propagates along one but not the opposite direction. Recent works have pointed to some of the paradoxical consequences of such a unidirectional range, including in particular the violation of the time-bandwidth product constraint that should otherwise apply in general in static systems. Here we show that such a unidirectional frequency range is nonphysical using both a general thermodynamic argument and a detailed calculation based on a nonlocal hydrodynamic Drude model for the metal permittivity. Our calculation reveals that the surface plasmon-polariton at metal-dielectric interfaces remains bidirectional for all frequencies.

The local Drude model predicts that, under certain conditions, surface plasmon polaritons at a metal-dielectric surface have a frequency range where only unidirectional propagation is supported. Here, the authors show that in more realistic non-local models surface plasmon polaritons exhibit bidirectional propagation for all frequencies.