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arXiv:quant-ph/0012002 · Journal of Physics B Atomic Molecular and Optical Physics

Perturbative corrections to photon coincidence spectroscopy

Levente Horvath, Barry C. Sanders

Published Aug 24, 2001• 0 citations
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Abstract

Photon coincidence spectroscopy is a promising technique for probing the nonlinear regime of cavity quantum electrodynamics in the optical domain, however its accuracy is mitigated by two factors: higher-order photon correlations, which contribute to an enhanced pair count rate, and non-simultaneity of emitted photon pairs from the optical cavity. We show that the technique of photon coincidence spectroscopy is effective in the presence of these effects if the quantitative predictions are adjusted to include non-simultaneity and higher-order correlations.

DOI
10.1088/0953-4075/34/17/319

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Photon coincidence spectroscopy is a promising technique for probing the nonlinear regime of cavity quantum electrodynamics in the optical domain, however its accuracy is mitigated by two factors: higher-order photon correlations, which contribute to an enhanced pair count rate, and non-simultaneity of emitted photon pairs from the optical cavity. We show that the technique of photon coincidence spectroscopy is effective in the presence of these effects if the quantitative predictions are adjusted to include non-simultaneity and higher-order correlations.
Photon coincidence spectroscopy relies on detecting multiphoton emissions from the combined atom-cavity system in atomic beam cavity quantum electrodynamics experiments. These multiphoton emissions from the cavity are nearly simultaneous approximately on the cavity lifetime scale. We determine the optimal time for the detection window of photon pairs in two-photon coincidence spectroscopy. If the window time is too short, some photon pairs will not be detected; if the window time is too long, too many nearly coincident independent single photons will be falsely interpreted as being a photon pair. The paper has been submitted to The European Physical Journal D.
We show that photon coincidence spectroscopy can provide an unambiguous signature of two atoms simultaneously interacting with a quantized cavity field mode. We also show that the single-atom Jaynes—Cummings model can be probed effectively via photon coincidence spectroscopy, even with deleterious contributions to the signal from two-atom events. In addition, we have explicitly solved the eigenvectors and eigenvalues of two two-level atoms coupled to a quantized cavity mode for differing coupling strengths.
Summary form only given.The Jaynes-Cummings model (JCM) of a two-level atom interacting with a single mode of a high-finesse cavity in the strong-coupling regime forms the basis of studies in strong-coupling cavity quantum electrodynamics. Jaynes and Cummings demonstrated that the semiclassical model of radiation could account for the observed properties of the coupled atom-cavity system, and it has remained a challenge to observe the nonclassical features of the JCM, specifically those that reveal quantum entanglement between the atomic internal degrees of freedom and the single-mode cavity field. The key to observing nonclassical effects is to access the nonlinear regimen of the spectrum (beyond the first couplet of the JCM ladder). This has been accomplished in the microwave domain, but the optical domain presents difficulties that are not significant in the microwave experiments. Recently, the method of photon coincidence (or correlation) spectroscopy (PCS) has been proposed to overcome these difficulties and provide an experimental signature of the nonlinear regimen of the JCM spectrum. The atom is excited directly by a bichromatic laser field, and two-photon coincidence detection is performed on the cavity output field. Here we consider the complication that arises because the two-photon de-excitation is not instantaneous: the temporal separation between the two photons in the pair is random and of the order of the cavity lifetime. We also determine the optimal window time T for detecting photon pairs in order to maximize the number of genuine pairs while minimizing the number of false pairs. Our simulations, using a Bloch function expansion for solving the master equation, yield optimal values of T.
This thesis intends to familiarize the reader with the concepts of photon statistics and correlations in quantum optics. Developing light sources that emit quantum states is central for the realization of quantum technologies. One important step in characterizing these sources is the measurement of field fluctuations and correlations, by coincidence measurements. The expectation value of a coincidence measurement, a simultaneous measurement of two intensities (or, more general, four fields), is represented by the fourth-order correlation function. The value of the correlation function, at zero delay between the detection of two photons, reveals important properties of the state to which they belonged, for example the fluctuations of the photon number. Since predictability is important for many applications, light sources emitting single photons are also characterized by the indistinguishability of consecutively emitted photons, or of two photons from separate emitters. In paper I we investigate blinking behaviour in quantum emitters, and its effect on the interference pattern and photon statistics with photons from two separate emitters. Blinking refers to an emitters transition into a non-emitting state, and subsequent transition back to an emitting state. We show that blinking can not be treated as linear loss, when measuring the fourth-order correlation function for two emitters in a Hong-Ou-Mandel setup. In general, a measurement of the fourth-order correlation function is robust to loss, which makes it a very practical tool. However, the relation between recorded coincidence counts and the correlation function is only direct in the limit of zero detection efficiency, and depends on the detection system. In paper II, we show that by adding a variable attenuation in the beam path, we can trace back to the ''true'' value of the correlation function at zero quantum efficiency. This method improves accuracy in correlation measurements by decreasing a systematic error at the expense of an increased statistical error, which is easier to handle, extending the use of coincidence methods to classical and non-classical multi-photon states.
Summary form only given. In any optical system, quantum and classical theory yield identical predictions for the mean intensity. The quantum mechanical predictions diverge from the classical theory only for higher order correlations. For this reason, typical quantum-interference experiments are performed by measuring coincidence rates between two or more detectors. The usual approximation, following Glauber, is that a single-photon counter fires at a rate proportional to the intensity, or number of incident photons per unit time. This approximation is so good and so entrenched that one routinely assumes that all singles-detection rates are insensitive to quantum effects. However, if one of these detectors fires, it cannot fire again for a characteristic time, called the dead-time. This characteristic of the detectors makes them highly nonlinear over times shorter than the dead-time, and thus sensitive to the higher order intensity correlations. In other words the detector has a different response for two photons arriving at different times, than for two photons arriving at the same time. We use the process of spontaneous parametric-downconversion (SPDC) to create correlated photon-pairs and send them through a polarization-based Hong-Ou-Mander interferometer. This quantum interferometer allows us to change the photon statistics without changing the intensity of the beams.
We study theoretically a photon-coincidence counting technique aimed at measuring the entanglement between two optical cavities connected by an optical waveguide. Delocalized doubly excited polariton states can be selectively probed by two-photon absorption of an entangled photon pair generated by spontaneous parametric down-conversion with a narrowband pump. Deviations from unity of the second-order correlation function g (2) (τ) of photons emitted from remote cavities reveal intercavity correlations. The coincidence counting signal in the frequency domain reveals the transition frequencies between single-polariton states and between single polaritons and tripolaritons. High-frequency spectral features arise from the counter-rotating terms in the cavity–molecule coupling, rendering them a direct signature for the ultrastrong coupling regime in cavity quantum electrodynamics.