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Journal of Applied Physics

Intensity Fluctuations of the Radiation from a Dispersive Blackbody

R. K. Osborn, A. Ziya Akcasu

Published Dec 1, 1967• 2 citations
Publisher

Abstract

Statistical properties of the output fluctuations of a photon detector measuring the intensity of radiation at a given frequency emitted by a dispersive blackbody are investigated using Langevin's technique. The variance-to-mean ratio of the accumulated counts, and the power spectral density of the count rate are obtained in terms of properties of the emitting medium. The possibility and limitations of obtaining information about the emitter by measuring these quantities are discussed. It is found in particular that the temperature of the emitting medium can be determined in principle by observing the intensity fluctuations of the radiation at a single frequency. The photon fluctuations in a microwave cavity are also discussed in the framework of the present formalism and compared to previous work.

DOI
10.1063/1.1709295

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Statistical properties of the output fluctuations of a photon detector measuring the intensity of radiation at a given frequency emitted by a dispersive blackbody are investigated using Langevin's technique. The variance-to-mean ratio of the accumulated counts, and the power spectral density of the count rate are obtained in terms of properties of the emitting medium. The possibility and limitations of obtaining information about the emitter by measuring these quantities are discussed. It is found in particular that the temperature of the emitting medium can be determined in principle by observing the intensity fluctuations of the radiation at a single frequency. The photon fluctuations in a microwave cavity are also discussed in the framework of the present formalism and compared to previous work.
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Abstract Microwave photons are essential carriers of quantum information in several promising platforms for quantum computing. However, measurement of the quantum statistical properties of microwave photons is demanding owing to their low energy relative to thermal fluctuations of any room-temperature detector, and phase-insensitive voltage amplification necessarily adds noise. Here, we overcome this trade-off with a nanobolometer that directly measures the photon statistics at millikelvin. Using a cryogenic temperature-controlled blackbody radiator, we demonstrate the detection of the mean photon number ⟨n^⟩\langle \hat{n}\rangle⟨n^⟩ ⟨ n ̂ ⟩ and reveal the expected photon number variance (Δn)2=⟨n^⟩(⟨n^⟩+1){(\Delta n)}^{2}=\langle \hat{n}\rangle \left(\langle \hat{n}\rangle+1\right)(Δn)2=⟨n^⟩(⟨n^⟩+1) ( Δ n ) 2 = ⟨ n ̂ ⟩ ⟨ n ̂ ⟩ + 1 , following the Bose–Einstein distribution. By engineering the coherent and incoherent proportions of the input field, we observe a transition between super-Poissonian and Poissonian statistics from the bolometric second-order correlation measurements. This technique is poised to serve in fundamental tests of quantum mechanics and function as a scalable readout solution for a quantum information processor.
We study the general properties of the photon statistics of fluorescence radiation, emitted by a two-level atom in a strong laser field and a perturber bath. We investigate the deviation of the factorial moments from a Poisson distribution, and we show that for long counting times the lowest-order correction can be expressed entirely by the quantity Q, which represents the deviation of the variance from the average. We introduce and evaluate the quantities gn(t), which serve as a measure for the deviation of the higher-order statistics from Poissonian statistics. Subsequently we obtain explicit expressions for the average waiting time for the appearance of the n th photon, after an arbitrary initialization of the counting process. It turns out that the average time delay is again determined by Q. Hence this parameter can be measured in a photon-counting experiment, which involves only the observation of a single photon, rather than an (in principle) infinite number of photons.
The amplification of noise in a laser amplifier is treated theoretically. The model for the active medium and its description using density-matrix techniques, are taken from the theory of laser operation. The fundamental concern of this investigation is the spectral behavior of the radiation in the nonlinear regime; hence, the formalism is written from the onset in the frequency domain. The statistics of the light are gradually modified by the nonlinear amplification process, and expressions are derived for the rate of change of fluctuations in intensity as a measure of statistical changes. These expressions should be easily susceptible to detailed experimental observations. In addition, the range of validity of Litvak's Gaussian-statistics approximation is discussed with some detail. In the homogeneous-broadening case, the evolution of initially broadband Gaussian radiation toward quasimonochromatic oscillations with laserlike statistics is extensively explored in several numerical examples. The connections of this study with the time-domain work of Risken and Nummedal, on self-pulsing in a ring-laser configuration, are clearly established. Finally, spectral-narrowing and -rebroadening effects in Doppler-broadened media are discussed both analytically and with numerical examples. These examples show the distinct contribution of pulsations in the population ("Raman-type terms"), and saturation phenomena. The predicted narrowing-rebroadening rate is compared with expressions found in previous literature.
The probability distribution p(n)p(n)p(n) for the detection of nnn photons emitted by a single-mode dye laser in a short time at various excitations is measured, together with the distribution of time intervals between pairs of detected photons. The first measurement yields the probability density p(I)\mathcal{p}(I)p(I) and the moments of the light intensity III, and the second one the two-time intensity-correlation function. Measurements are also performed at three different wavelengths. p(I)\mathcal{p}(I)p(I) is found to have a two-component structure, and the relative intensity fluctuations $\frac{〈{(\ensuremath{\Delta}I)}^{2}〉}{{〈I〉}^{2}}$ grow, apparently without limit, as the excitation tends to zero, so that no thermal state is reached. A possible explanation in terms of pumping fluctuations is discussed. The correlation function has the form of a sum of three exponential functions, and the amplitudes and decay constants of the three components are derived. The effective decay-time constant exhibits a thirteenth-power-law dependence on frequency of the laser light.
We apply the laser quantum Langevin equations derived in part I of this paper to the description of the laser intensity fluctuations when the external field entering the input - output port is in a squeezed vacuum state with finite bandwidth. We focus on the two opposite limits in which the detection time is much longer, or much shorter, than the inverse of the cavity linewidth. When there is detuning between the squeezed input and the laser frequency, the variance of the intensity fluctuations displays regular oscillations with frequency equal to the detuning. In the limit of small detection times there is the possibility of substantial reduction of the photon-number fluctuations using a squeezed input.