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IEEE Aerospace and Electronic Systems Magazine

Equivalence of Classical and Quantum Electromagnetic Scattering in the Far-Field Regime

Matthew J. Brandsema, Marco O. Lanzagorta, Ram M. Narayanan

Published Apr 1, 2020• 17 citations
Publisher

Abstract

Quantum remote sensing, also known as quantum detection and ranging (QUDAR), is the use of entangled photon states to detect targets at a stand-off distance. It inherently relies on sending many single photons through free space, bouncing off of a target and returning to the sensor. It is therefore necessary to understand how single photons interact and scatter from targets of macroscopic size. This article relates quantum and classical scattering in the far-field regime. Specifically, we show that due to the photon's position uncertainty, the path over which the photon traverses is not well defined, and this causes quantum interference. The result of this interference exactly replicates classical scattering behavior of electromagnetic waves. We will show that one can exactly derive the classical electric field scattering integral using a purely quantum construction. Although this article focuses on the context of QUDAR, it is very general to any application involving far-field electromagnetic scattering. Finally, we delve into the QUDAR multiphoton quantum scattering advantage shown in previous literature and further develop the theory. Specifically, we provide explanations as to why this advantage has not been observed in the classical regime, as well as provide insight as to the experimental requirements necessary to achieve this cross-section enhancement.

DOI
10.1109/maes.2020.2970264

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Quantum remote sensing, also known as quantum detection and ranging (QUDAR), is the use of entangled photon states to detect targets at a stand-off distance. It inherently relies on sending many single photons through free space, bouncing off of a target and returning to the sensor. It is therefore necessary to understand how single photons interact and scatter from targets of macroscopic size. This article relates quantum and classical scattering in the far-field regime. Specifically, we show that due to the photon's position uncertainty, the path over which the photon traverses is not well defined, and this causes quantum interference. The result of this interference exactly replicates classical scattering behavior of electromagnetic waves. We will show that one can exactly derive the classical electric field scattering integral using a purely quantum construction. Although this article focuses on the context of QUDAR, it is very general to any application involving far-field electromagnetic scattering. Finally, we delve into the QUDAR multiphoton quantum scattering advantage shown in previous literature and further develop the theory. Specifically, we provide explanations as to why this advantage has not been observed in the classical regime, as well as provide insight as to the experimental requirements necessary to achieve this cross-section enhancement.
Quantum remote sensing, also known as Quantum Detection and Ranging (QUDAR), is the use of entangled photon states to detect targets at a stand-off distance. It inherently relies on sending many single photons through free space, bouncing off of a target and returning to the sensor. It is therefore necessary to understand how single photons interact and scatter from targets of macroscopic size. This paper relates quantum and classical scattering in the far field regime. Specifically, we show that due to the photon's position uncertainty, the path over which the photon traverses is not well defined, and this causes quantum interference. The result of this interference exactly replicates classical scattering behavior of electromagnetic waves. We will show that one can exactly derive the classical electric field scattering integral using a purely quantum construction. Although this paper focuses on the context of QUDAR, it is very general to any application involving far-field electromagnetic scattering.
In this paper, we derive the electric field covariance matrix of the signal and idler beams from an entangled source for applications involving quantum radar. We also derive the corresponding covariance matrix for a classical matched filtering remote sensing system and compare to the quantum result. We use this comparison to derive an expression for the quantum enhancement factor as a function of the mean photon number per mode, Ns. This result is significant because it allows one to exactly calculate the predicted quantum enhancement as a function of transmit power, rather than only having an upper bound. Additionally, we look into previous analog correlation techniques using an optical parametric amplifier (OPA) and show that immediately detecting the idler produces the same cross correlation terms. However, the actual measurements needed to harness these correlations is enhanced when one immediately detects the idler because it minimizes the added noise caused by the additional length of the idler path in the conventional method. Finally, our results also show that one does not need to count photons to harness these correlations, but rather, perform electric field measurements.
Recently, much of the quantum radar/lidar research is focused on correlating single photon detection events with no delay line on the idler path. In other words, measuring the idler immediately, and correlating these events with later received photon events from the returning signal. This research approach has raised some questions due to the fact that all measurements done are classical, yet researchers are still observing sensor improvement in comparison to classical techniques. This therefore implies that the benefits from quantum radar/lidar using these techniques should be able to be explained entirely classically. This paper explores this concept by asserting that the correlation between the signals used in quantum remote sensing is largely due to the fact that the signal and idler photons are created simultaneously (which is only possible from an entangled source). We show, using very simple computer simulations, that having a single photon correlated (binary) waveform leads to correlation SNR advantages only in the low photon level regime, agreeing with previous literature.
The wave aspect of light is observed experimentally through interference phenomena, and in a certain sense such observations always require a division of the given (initial) light field into two or more space-time parts. The division can only be done by introducing matter (massive particles) in the field region, and the light-matter interaction inevitably changes the initial state of the field. Not least when one is dealing with single and few-photon interference, it is good to remember again a central point of Niels Bohr, namely that no elementary phenomenon is a phenomenon until it is a registered (observed) phenomenon. It turns out that it is possible to observe interference with a quantized electromagnetic field which contains only one photon. Since the irreversible final detection destroys the photon, it is in practice necessary to repeat the experiment starting from the same initial (given) conditions. Below we shall discuss the basics of single-photon interference in the simplest terms.
This thesis concerns the theoretical investigation of interference phenomena related to elastic and inelastic scattering of quantized light. The presented work is naturally divided into two parts, the first is concerning elastic scattering while the second explores inelastic scattering. In the first part we use a scattering-matrix formalism combined with results from random-matrix theory to investigate the interference of quantum optical states on a multiple scattering medium. We investigate a single realization of a scattering medium thereby showing that it is possible to create entangled states by interference of squeezed beams. Mixing photon states on the single realization also shows that quantum interference naturally arises by interfering quantum states. We further investigate the ensemble averaged transmission properties of the quantized light and see that the induced quantum interference survives even after disorder averaging. The quantum interference manifests itself through increased photon correlations. Furthermore, the theoretical description of a measurement procedure is presented. In this work we relate the noise power spectrum of the total transmitted or reflected light to the photon correlations after ensemble averaging. This analysis enables us to describe an experimental observation of the quantum nature of light that survives the averaging over disorder. In the second part we investigate inelastic scattering. This we do by first treating the scattering of light on dipoles embedded in an arbitrary dielectric environment. By considering the two different models for dipole interaction known as the minimal-coupling and electric-dipole interaction Hamiltonians, we find exact relations between the electric field and the dipole operators in the Heisenberg picture, while keeping the model of the dipoles arbitrary. Due to the exact treatment of the electric-field operators, we obtain kernels known from classical scattering theory to describe the propagation of the field from the dipoles. Using the found electric field operators we derive the Heisenberg equations of motion for the dipoles while treating them as quantum two-level systems and using the Born–Markov and rotating-wave approximations. Postponing the rotating-wave approximation to the very end of the formal calculations allows us to identify the different physical parameters of the dipole evolution in terms of physical quantities known from optics. Finally, we use our Heisenberg picture formalism to treat a dilute cloud of two-level atoms, by simplifying the equations of motion using a single-scattering approximation for the interaction between the atoms. This enables us to derive expressions for the steady-state population and fluorescence spectrum, where we find cooperative effects in both the elastic and the inelastic spectra.
Quantum radar is an emerging technique, currently at the experimental stage, that promises to disrupt the well-established field of conventional radar. Recent progress shows that it is possible to generate and use entangled pairs of microwave photons for detection purposes and to obtain an advantage over a classical radar. In this work, we study the currently experimentally feasible type of quantum correlation radar. To this end, we compare different radar architectures, quantum and classical, by analyzing their detection performances by means of the receiver operating characteristic (ROC), the minimum error probability as well as the Chernoff bound. The underlying system models are based on quantum mechanical formulations as well as conventional signal theory. Where it is appropriate and necessary to facilitate our analysis, we apply the central limit theorem to establish the Gaussianity of the observable quantities. A conceptual analogy between the quantum and classic points-of-view is drawn and supported by results showing the asymptotic behavior of the ROC curves of both physical descriptions depending on the power levels of signal and noise. We come to exact and comprehensible conclusions on the current state of quantum radar in comparison to classic radar with a detailed mapping of the radar operating regime (measurement time, signal-to-noise ratio, environmental noise level, target object size and distance) in which a quantum advantage is attainable.