Electromagnetic Noise and Quantum Optical Measurements

M.E. Marhic

Introduction In previous chapters we studied wave propagation in fiber OPAs from a classical standpoint, i.e. starting from Maxwell's equations. That approach provides only a partial view of the rich nature of the electromagnetic field, namely its wave nature. However, a complete description of the electromagnetic field requires quantum mechanics. This quantum description of the electromagnetic field (called quantum electrodynamics, or QED) predicts fluctuations in measurable quantities due to the Heisenberg uncertainty principle and sets ultimate limits on the performance of devices such as optical amplifiers. A remarkable result of this theory is that the statistics and thus the noise performance of a system are affected by the quantum statistics of the source and by the physical measurement that is made. Thus a different analysis is needed depending on whether homodyne, heterodyne, or direct detection (where the field simply impinges on a photodiode) is used. Direct detection reveals the particle nature of the electromagnetic field. More specifically, energy arrives in discrete units, called photons, each of which may create an electron–hole pair in a semiconductor photodetector. In particular, the number of photons in an optical pulse can be thought of as a random variable having a mean and a variance. By deriving the mean and variance of the photocurrent that would be present if one performed direct detection of ideal laser light at the input of an optical amplifier and then a similar measurement at its exit, one can quantify the degradation of the signal-to-noise ratio (SNR) caused by the amplifier.

Harry J. Kimble

P. L. Knight

Víctor M. Acosta, Kasper Jensen, Charles Santori +2 more

We use electromagnetically induced transparency (EIT) to probe the narrow electron-spin resonance of nitrogen-vacancy centers in diamond. Working with a multipass diamond chip at temperatures 6--30 K, the zero-phonon absorption line (637 nm) exhibits an optical depth of 6 and inhomogeneous linewidth of $\ensuremath{\sim}30\text{ }\text{ }\mathrm{GHz}$ FWHM. Simultaneous optical excitation at two frequencies separated by the ground-state zero-field splitting (2.88 GHz) reveals EIT resonances with a contrast exceeding 6% and FWHM down to 0.4 MHz. The resonances provide an all-optical probe of external electric and magnetic fields with a projected photon-shot-noise-limited sensitivity of $0.2\text{ }\text{ }\mathrm{V}/\mathrm{cm}/\sqrt{\mathrm{Hz}}$ and $0.1\text{ }\text{ }\mathrm{nT}/\sqrt{\mathrm{Hz}}$, respectively. Operation of a prototype diamond-EIT magnetometer measures a noise floor of $\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{nT}/\sqrt{\mathrm{Hz}}$ for frequencies above 10 Hz and Allan deviation of $1.3\ifmmode\pm\else\textpm\fi{}1.1\text{ }\text{ }\mathrm{nT}$ for 100 s intervals. The results demonstrate the potential of diamond-EIT devices for applications ranging from quantum-optical memory to precision measurement and tests of fundamental physics.

Wayne H. Richardson, Susumu Machida, Y. Yamamoto

Number states of the electromagnetic field are ideal for optical communication and for a variety of high precision measurements. It has been shown theoretically that the light from a semiconductor laser can opproach a number state1. In previous experiments2,3 the observed amplitude noise reduction, below the standard quantum limit, was at most 1.5 db. In this experiment we have been able to reduce the effects of optical feedback, increase the collection efficiency and consequently further elucidate the basic device physics necessary for improvement in the noise reduction. We have observed that the measured squeezing is not limited by the laser overall quantum efficiency but only by the optical output coupling efficiency. An explanation is advanced based on the premise that current division does not introduce Poissonian noise but thermal noise.

P. L. Knight