Motivated by the experimental search for "GHz nonclassical light," we identify the conditions under which current fluctuations in a narrow constriction generate sub-Poissonian radiation. Antibunched electrons generically produce bunched photons, because the same photon mode can be populated by electrons decaying independently from a range of initial energies. Photon antibunching becomes possible at frequencies close to the applied voltage V x e/variant Planck's over 2pi, when the initial energy range of a decaying electron is restricted. The condition for photon antibunching in a narrow frequency interval below eV/variant Planck's over 2pi reads [SigmanTn(1-Tn)]2<2Sigman[Tn(1-Tn)]2, with Tn an eigenvalue of the transmission matrix. This condition is satisfied in a quantum point contact, where only a single Tn differs from 0 or 1. The photon statistics is then a superposition of binomial distributions.
Shot noise of electrons that are transmitted with probability
T through a quantum point contact (biased at a voltage
V0) leads to a fluctuating current that in turn emits radiation in the microwave regime. By calculating the Fano factor
F for the case where only a single channel contributes to the transport, it has been shown that the radiation produced at finite frequency ${\ensuremath{\omega}}_{0}$ close to $e{V}_{0}/\ensuremath{\hbar}$ and at low temperatures is nonclassical with sub-Poissonian statistics (
F<1). The origin of this effect is the fermionic nature of the electrons producing the radiation, which reduces the probability of simultaneous emission of two or more photons. However, the Fano factor, being a time-averaged quantity, offers only limited information about the system. Here, we calculate the second-order coherence ${g}^{(2)}(\ensuremath{\tau})$ for this source of radiation. We show that due to the interference of two contributions, two photon processes (leading to bunching) are completely absent at zero temperature for
T=50. At low temperatures, we find a competition of the contribution due to Gaussian current-current fluctuations (leading to bunching) with the one due to non-Gaussian fluctuations (leading to antibunching). At slightly elevated temperatures, the non-Gaussian contribution becomes suppressed, whereas the Gaussian contributions remain largely independent of temperature. We show that the competition of the two contributions leads to a nonmonotonic behavior of the second-order coherence as a function of time. As a result, ${g}^{(2)}(\ensuremath{\tau})$ obtains a minimal value for times ${\ensuremath{\tau}}^{*}\ensuremath{\simeq}{\ensuremath{\omega}}_{0}^{\ensuremath{-}1}$. Close to this time, the second-order coherence remains below 1 at temperatures where the Fano factor is already above 1. We identify realistic experimental parameters that can be used to test the sub-Poissonian nature of the radiation.
Nonclassical effects such as squeezing, antibunching, and sub-Poissonian statistics of photons have been attracting attention in quantum optics over the last decade. Up to now most theoretical and experimental investigations have been carried out exclusively in the time domain while neglecting the spatial aspects by considering only one spatial mode of the electromagnetic field. In many situations such an approximation is well justified. There are, however, problems that do not allow in principle a single-mode consideration. This is the case when one wants to investigate the quantum fluctuations of light at different spatial points in the plane perpendicular to the direction of propagation of the light beam. Such an investigation requires a complete description of quantum fluctuations of light in both time and space and cannot be done within a single-mode theory. This space-time description brings about a natural generalization into the spatial domain of such notions as the standard quantum limit, squeezing, antibunching, etc. It predicts, for example, the possibility of generating a light beam with sub-Poissonian statistics of photons not only in time but also in the beam's transverse plane. Of particular relevance to the applications is a situation in which the cross section of the light beam contains several nonoverlapping areas with sub-Poissonian statistics of photons in each. Photodetection of such a beam produces several sub-shot-noise photocurrents depending on the number of independent areas with sub-Poissonian statistics. This is in marked contrast to the case of a single-mode sub-Poissonian light beam in which any attempt to collect light from only a part of the beam deteriorates the degree of shot-noise reduction. This property of multimode squeezed light opens a range of interesting new applications in optical imaging, optical parallel processing of information, parallel computing, and many other areas in which it is desirable to have a light beam with regular photon statistics across its transverse area. The aim of this review is to describe the recent development in this branch of quantum optics.
The statistical fluctuations of light can, under certain circumstances, exhibit a number of interesting nonclassical features. These include photon antibunching, sub-Poissonian statistics, and squeezing, all of which exist only in a quantum field. The three effects are distinct, and do not necessarily go together, although the first two are sometimes mistakenly treated as interchangeable. Both photon antibunching and sub-Poissonian statistics have been observed in experiments on resonance fluorescence from single atoms, which is described. Squeezing has not yet been seen experimentally, although many nonlinear processes are expected to give rise to it. The squeezed state can be recognized in heterodyne or homodyne experiments, where the squeezing becomes manifest as sub-Poissonian photon fluctuations.
A great deal of effort has been devoted during the last decade to the theory of nonclassical states of the radiation field. From a practical point of view some of the most interesting predictions of these theories concern the generation of light with sub-Poissonian photon counting statistics for which Such light is evidently less noisy than laser radiation with obvious implications for the improved performance of optical systems. When the temporal autocorrelation function of the photon counts increases as the delay time increases from zero the light is also said to be antibunched.