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IEEE Transactions on Microwave Theory and Techniques

Quantum Fluctuations in Microwave Radiometry

L.P. Bolgiano

Published Jul 1, 1961• 4 citations
Publisher

Abstract

This paper assesses the possible significance of the quantum nature of electromagnetic radiation in limiting the measurement accuracy attainable with a microwave radiometer. Analogies are shown to exist between the form of a formula describing fluctuations in the radiometer output, and both a formula describing the radiometer input signal, and also, a formula describing the output of a photocell detector. Detailed quantum mechanical consideration of the processes of amplification and detection are circumvented by considering how the formula for fluctuations in the radiometer output might be modfied so as to make it consistent with the measurement precision implied by these other formulas. A modified formula is suggested which includes a quantum fluctuation whose magnitude depends on signal power.

DOI
10.1109/tmtt.1961.1125337

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This paper assesses the possible significance of the quantum nature of electromagnetic radiation in limiting the measurement accuracy attainable with a microwave radiometer. Analogies are shown to exist between the form of a formula describing fluctuations in the radiometer output, and both a formula describing the radiometer input signal, and also, a formula describing the output of a photocell detector. Detailed quantum mechanical consideration of the processes of amplification and detection are circumvented by considering how the formula for fluctuations in the radiometer output might be modfied so as to make it consistent with the measurement precision implied by these other formulas. A modified formula is suggested which includes a quantum fluctuation whose magnitude depends on signal power.
The interaction of photons and coherent quantum systems can be employed to detect electromagnetic radiation with remarkable sensitivity. We introduce a quantum radiometer based on the photon-induced dephasing process of a superconducting qubit for sensing microwave radiation at the subunit photon level. Using this radiometer, we demonstrate the radiative cooling of a 1 K microwave resonator and measure its mode temperature with an uncertainty ∼0.01 K. We thus develop a precise tool for studying the thermodynamics of quantum microwave circuits, which provides new solutions for calibrating hybrid quantum systems and detecting candidate particles for dark matter.
We consider a communication system consisting of an information source of electromagnetic radiation. It is assumed that the information source radiates an electromagnetic signal with an average power S, and the signal propagated through the electromagnetic channel is assumed to be perturbed by additive thermal noise at temperature T. For simplicity, we assume that the electromagnetic signal is one-dimensional (i.e., the photon fluctuation is restricted to only one polarized state), in which the propagation occurs in the same direction of the wave vectors. It is emphasized that the corresponding occupation number of the quantum levels can be fully described. Obviously, these occupation quantum levels correspond to the microsignal structure of the information source. It is therefore assumed that these occupation numbers can be uniquely determined for those representing an input signal ensemble. We further assume that an ideal receiver (an ideal photon counter) is used at the output end of the channel. That is, the receiver is able to detect the specified frequencies of the electromagnetic signal. It is also emphasized that in practice the interaction of the electromagnetic signal and the detector are strictly statistical, that is, a certain amount of information loss is expected at the output end of the receiver. The idealized model of the receiver we have proposed mainly simplifies the method by which the quantum effect on the communication channel can be easily calculated.
We present a model of detectors operating with classical random fields and producing probabilities described by the formalism of quantum mechanics. The basic assumption of this measurement theory is that the probability of detection of field (= signal) is proportional to the power of this field. (Therefore we call this approach "power signal-field detection theory" – PFSDT.) Our approach has some similarities with stochastic electrodynamics. However, formalisms describing random fields – "quantum fluctuations" – are different. Moreover, our approach all particles are represented by random fields, e.g., electronic or neutronic field. Thus we have various types of "quantum fluctuations".
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.
In this paper we consider further the quantum-statistical properties of radiation in nondegenerate parametric-type amplifiers. In particular we find moment-generating functions and probability distribution functions for the field variables at the output of an amplifier for various input conditions. We find that a classical description of the input fields and of the amplification process is completely valid provided we take correctly into account the response of the amplifier to the input zero-point noise fields. This result is valid for inputs of arbitrarily small power.