Quantum Noise Theory of Exceptional Point Amplifying Sensors.

Open quantum systems can have exceptional points (EPs), degeneracies where both eigenvalues and eigenvectors coalesce. Recently, it has been proposed and demonstrated that EPs can enhance the performance of sensors in terms of amplification of a detected signal. However, typically amplification of signals also increases the system noise, and it has not yet been shown that an EP sensor can have improved signal-to-noise performance. We develop a quantum noise theory to calculate the signal-to-noise performance of an EP sensor. We use the quantum Fisher information to extract a lower bound for the signal-to-noise ratio (SNR) and show that parametrically improved SNR is possible. Finally, we construct a specific experimental protocol for sensing using an EP amplifier near its lasing threshold and heterodyne signal detection that achieves the optimal scaling predicted by the Fisher bound. Our results can be generalized to higher order EPs for any bosonic non-Hermitian system with linear interactions.

Coherent control of total transmission of light through disordered media.

We demonstrate order of magnitude coherent control of total transmission of light through random media by shaping the wave front of the input light. To understand how the finite illumination area on a wide slab affects the maximum values of total transmission, we develop a model based on random matrix theory that reveals the role of long-range correlations. Its predictions are confirmed by numerical simulations and provide physical insight into the experimental results.

Filtering random matrices: the effect of incomplete channel control in multiple scattering.

We present an analytic random matrix theory for the effect of incomplete channel control on the measured statistical properties of the scattering matrix of a disordered multiple-scattering medium. When the fraction of the controlled input channels, m1, and output channels, m2, is decreased from unity, the density of the transmission eigenvalues is shown to evolve from the bimodal distribution describing coherent diffusion, to the distribution characteristic of uncorrelated Gaussian random matrices, with a rapid loss of access to the open eigenchannels. The loss of correlation is also reflected in an increase in the information capacity per channel of the medium. Our results have strong implications for optical and microwave experiments on diffusive scattering media.

Pump-induced exceptional points in lasers.

We demonstrate that the above-threshold behavior of a laser can be strongly affected by exceptional points which are induced by pumping the laser nonuniformly. At these singularities, the eigenstates of the non-Hermitian operator which describes the lasing modes coalesce. In their vicinity, the laser may turn off even when the overall pump power deposited in the system is increased. Such signatures of a pump-induced exceptional point can be experimentally probed with coupled ridge or microdisk lasers.

Hidden black: coherent enhancement of absorption in strongly scattering media.

We show that a weakly absorbing, strongly scattering (white) medium can be made very strongly absorbing at any frequency within its strong-scattering bandwidth by optimizing the input electromagnetic field. For uniform absorption, results from random matrix theory imply that the reflectivity of the medium can be suppressed by a factor ∼(ℓ(a)/ℓ)N(-2), where N is the number of incident channels and ℓ, ℓ(a) are the elastic and absorption mean free paths, respectively. It is thus possible to increase absorption from a few percent to >99%. For a localized weak absorber buried in a nonabsorbing scattering medium, we find a large but bounded enhancement.

Directional laser emission from a wavelength-scale chaotic microcavity.

We demonstrate directional output from a deformed disk laser of dimensions comparable to the emission wavelength. Unlike larger deformed cavity lasers, which exhibit universal output directionality determined by chaotic ray dynamics, the far-field patterns differ between lasing modes. The directional emission results from weak coupling of isotropic high-quality modes to anisotropic low-quality modes, combined with chiral symmetry breaking of clockwise and counterclockwise propagating waves. This mechanism makes it possible to control the output properties of wavelength-scale lasers.

Coherent perfect absorbers: time-reversed lasers.

We show that an arbitrary body or aggregate can be made perfectly absorbing at discrete frequencies if a precise amount of dissipation is added under specific conditions of coherent monochromatic illumination. This effect arises from the interaction of optical absorption and wave interference and corresponds to moving a zero of the elastic S matrix onto the real wave vector axis. It is thus the time-reversed process of lasing at threshold. The effect is demonstrated in a simple Si slab geometry illuminated in the 500-900 nm range. Coherent perfect absorbers act as linear, absorptive interferometers, which may be useful as detectors, transducers, and switches.

Quantitative verification of ab initio self-consistent laser theory.

We generalize and test the recent "ab initio" self-consistent (AISC) time-independent semiclassical laser theory. This self-consistent formalism generates all the stationary lasing properties in the multimode regime (frequencies, thresholds, internal and external fields, output power and emission pattern) from simple inputs: the dielectric function of the passive cavity, the atomic transition frequency, and the transverse relaxation time of the lasing transition.We find that the theory gives excellent quantitative agreement with full time-dependent simulations of the Maxwell-Bloch equations after it has been generalized to drop the slowly-varying envelope approximation. The theory is infinite order in the non-linear hole-burning interaction; the widely used third order approximation is shown to fail badly.

Resonant cooper-pair tunneling: quantum noise and measurement characteristics.

We study the quantum charge noise and measurement properties of the double Cooper-pair resonance point in a superconducting single-electron transistor (SSET) coupled to a Josephson charge qubit. Using a density-matrix approach for the coupled system, we obtain a full description of the measurement backaction; for weak coupling, this is used to extract the quantum charge noise. Unlike the case of a nonsuperconducting SET, the backaction here can induce population inversion in the qubit. We find that the Cooper-pair resonance process allows for a much better measurement than a similar nonsuperconducting SET, and can approach the quantum limit of efficiency.

Directional emission from asymmetric resonant cavities.

Asymmetric resonant cavities with highly noncircular but convex cross sections are predicted theoretically to have high-Q whispering gallery modes with highly anisotropic emission. We develop a ray dynamics model for the emission pattern and present numerical and experimental confirmation of the theory.

Q spoiling and directionality in deformed ring cavities.

A ray-optics model is developed to describe the spoiling of the high-Q (whispering gallery) modes of ring-shaped cavities as they are deformed from perfect circularity. A sharp threshold is found for the onset of Q spoiling as predicted by the Kolmogorov-Arnol'd-Moser (KAM) theorem of nonlinear dynamics. Beyond the critical deformation b(c), Q ~ (b - b(c))(-alpha), alpha asymptotically equal to 2.4-2.6. The escaping light emerges in certain specific directions, which may be predicted.