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Physical Review A

Enhancement of photon antibunching by passive interferometry

Yujiang Qu, Min Xiao, G. S. Holliday, Surendra Singh, Harry J. Kimble

Published Apr 1, 1992• 10 citations
Publisher

Abstract

Photon antibunching in intracavity second-harmonic generation and intracavity atomic absorption inside a high-Q optical cavity is discussed. A linearized description of quantum dynamics in the weak-field limit is used because the system size, as characterized by the number of photons ${\mathit{n}}_{0}$ needed to probe the nonlinearity of the system, is often quite large for realistic parameters. In both cases standard results are recalled that demonstrate that antibunching is a small effect given by ${\mathit{g}}^{(2)}$(0)-1\ensuremath{\approxeq}-1/${\mathit{n}}_{0}$ for large values of ${\mathit{n}}_{0}$. We show that when higher-order terms that are usually ignored in linearized treatments are retained, ${\mathit{g}}^{(2)}$(0) satisfies the lower bound ${\mathit{g}}^{(2)}$(0)\ensuremath{\ge}0 even for small values of ${\mathit{n}}_{0}$. It is further shown that by employing a high-Q cavity to suppress the coherent part of the spectrum of field fluctuations, perfect antibunching can be achieved even for large systems. Conditions under which this is possible are derived and curves are presented to illustrate the behavior.

DOI
10.1103/physreva.45.4932

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Photon antibunching in intracavity second-harmonic generation and intracavity atomic absorption inside a high-Q optical cavity is discussed. A linearized description of quantum dynamics in the weak-field limit is used because the system size, as characterized by the number of photons n0{\mathit{n}}_{0}n0​ needed to probe the nonlinearity of the system, is often quite large for realistic parameters. In both cases standard results are recalled that demonstrate that antibunching is a small effect given by g(2){\mathit{g}}^{(2)}g(2)(0)-1\ensuremath{\approxeq}-1/n0{\mathit{n}}_{0}n0​ for large values of n0{\mathit{n}}_{0}n0​. We show that when higher-order terms that are usually ignored in linearized treatments are retained, g(2){\mathit{g}}^{(2)}g(2)(0) satisfies the lower bound g(2){\mathit{g}}^{(2)}g(2)(0)\ensuremath{\ge}0 even for small values of n0{\mathit{n}}_{0}n0​. It is further shown that by employing a high-Q cavity to suppress the coherent part of the spectrum of field fluctuations, perfect antibunching can be achieved even for large systems. Conditions under which this is possible are derived and curves are presented to illustrate the behavior.
While the problem of photon antibunching in optical bistability has been the subject of numerous theoretical investigations, there appears to be no general result in the literature that includes a complete specification of the dependence of antibunching on the system parameters. Motivated by the importance of such a result to experimental observation of this effect, we present a treatment that includes the parametric dependences on cavity and atomic detunings, cooperativity parameter, nonradiative (collisional) damping, and the ratio of cavity and atomic damping rates. We also attempt to analyze the contribution of fourth-order correlations of the fluctuating fields, which have been neglected in previous treatments. Although the antibunching initially increases with decreasing system size due to the approximate scaling of quantum fluctuations as the inverse of the saturation photon number ns, higher-order fluctuations begin playing an increasingly important role at values of ns ⪝ 1. We show that the linearized theory itself does not necessarily break down for arbitrarily small values of ns (as previously suggested), but that photon antibunching is lost in this limit, thus placing restrictions on the design of an experiment.
Photon antibunching has been predicted at weak intensities along the lower branch in optical bistability. Existing theories assume large atomic numbers to justify their linearized analysis. From such a theory photon antibunching in absorptive bistability is given for weak intensities by where C is the bistability parameter, μ is the ratio of atomic and cavity decay times, and N is the number of atoms. Clearly this result becomes invalid as the system size is reduced to the limit of a single atom; then g(2) (0) is negative for moderate values of C. I calculate g(2) (0) for the transmitted light from an optical cavity containing a single atom, where the injected field, the atom, and the cavity are all resonant.
By employing the input-output theory of damped quantum systems developed by Gardiner and Collett,1 we discuss the propagation of nonclassical fields through optical systems containing frequency selective elements such as Fabry-Perot interferometers. Our results are of general applicability and are expressed in terms of the linearized drift and diffusion coefficients of the generalized Fokker-Planck equation describing the intracavity field of the nonlinear source. The two nonclassical effects of photon antibunching and squeezing are treated in detail with reference to the examples of intracavity harmonic conversion and optical bistability. Not surprisingly photon antibunching can be enhanced by the suppression of the coherent part of the spectrum of intensity fluctuations with a narrow bandwidth cavity. However the enhancement is ultimately limited and the antibunching lost altogether as the amplitude of the coherent carrier is reduced to a level comparable to that of the field fluctuations (which are set by the system size). Following the suggestion of Levenson et al., 2 we investigate the use of auxiliary cavities for the control of phase and amplitude in the propagation and detection of squeezed states of light. While for a small degree of squeezing such filter cavities operate in a straightforward fashion, a mixing of field quadratures can occur as the degree of squeezing increases leading to a loss of nonclassical behavior.
A review is given of recent theoretical studies devoted to the problem of generating radiation fields that exhibit the opposite of the well-known bunching of photons observed in light from thermal sources, the so-called antibunching effect. It is made clear that this phenomenon reflects the corpuscular nature of light and, hence, cannot be interpreted in terms of classical electrodynamics, needing, instead, the quantum-mechanical formalism for its description. It is shown in some detail that nonlinear interaction mechanisms like multiphoton absorption and parametric three-wave interaction are suited to change the photon statistical properties of incident (in most cases coherent) light such that the output field will be endowed with antibunching properties. Special emphasis is given to the problem of correctly specifying the dimensions of the mode volume occurring in the usual single-mode treatment of the field, which is, in fact, of great practical interest, since the magnitude of the antibunching effect is determined by the inverse average number of photons contained in that volume. In a later section it is pointed out that destructive interference with a coherent reference beam provides a means of (a) effectively enhancing photon antibunching that is already present in a high-intensity field, through reduction of the intensity, and (b) transforming phase fluctuations produced in a Kerr medium into antibunching-type intensity fluctuations. On the other hand, there exists a way of directly generating light with antibunching properties, the physical mechanism being resonance fluorescence from a single atom. The main features of this technique, both theoretical and experimental, are outlined, including a discussion of the first experimental results obtained a few years ago.
The radiative properties of atoms inside an optical cavity can be dramatically changed with respect to those in free space. In the strong-coupling limit, the reversible dipole interaction between an atom and the cavity field dominates the irreversible decay resulting from spontaneous emission and cavity damping. In this limit the atom and field can no longer be regarded as separate quantities but instead form a composite dynamic system. To enhance the dipole coupling constant and increase the photon storage time, our experiments are performed with a small cavity 1 mm long, with a finesse of 8 × 104. On average, 0.4 photons are sufficient to saturate the resonance transition at 852 nm for the cesium atoms used, while the cooperativity parameter for a single atom is 2. Optical bistability is studied in this system over the range 3 < N < 65 atoms inside the cavity, with the semiclassical theory predicting bistability for N > 5. We report observations of manifestly quantum effects in this regime, including photon antibunching and sub-Poissonian photon statistics, with the magnitude of these nonclassical effects observed to be largely independent of the number of intracavity atoms.
A deterministic and scalable array of single photon nonlinearities in the solid state holds great potential for both fundamental physics and technological applications, but its realization has proved extremely challenging. Despite significant advances, leading candidates such as quantum dots and group III-V quantum wells have yet to overcome their respective bottlenecks in random positioning and weak nonlinearity. Here we consider a hybrid light-matter platform, marrying an atomically thin two-dimensional material to a photonic crystal cavity, and analyze its second-order coherence function. We identify several mechanisms for photon antibunching under different system parameters, including one characterized by large dissipation and weak nonlinearity. Finally, we show that by patterning the two-dimensional material into different sizes, we can drive our system dynamics from a coherent state into a regime of strong antibunching with second-order coherence function ${g}^{(2)}(0)\ensuremath{\sim}{10}^{\ensuremath{-}3}$, opening a possible route to scalable, on-chip quantum simulations with correlated photons.