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.
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.
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.
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.
In radar, the amount of returns that an object sends back to the receiver after
being struck by an electromagnetic wave is characterized by what is known as the
radar cross section, denoted by � typically. There are many mechanisms that affect
how much radiation is reflected back in the receiver direction, such as reflectivity,
physical contours and dimensions, attenuation properties of the materials, projected
cross sectional area and so on. All of these characteristics are lumped together in a
single value of �, which has units of m2. Stealth aircrafts for example are designed
to minimize its radar cross section and return the smallest amount of radiation
possible in the receiver direction.
A new concept has been introduced called quantum radar, that uses correlated
quantum states of photons as well as the unique properties of quantum mechanics
to ascertain information on a target at a distance. At the time of writing this
dissertation, quantum radar is very much in its infancy. There still exist fundamental
questions about the feasibility of its implementation, especially in the microwave
spectrum. However, what has been theoretically determined, is that quantum radar
has a fundamental advantage over classical radar in terms of resolution and returns
in certain regimes.
Analogous to the classical radar cross section (CRCS), the concept of the
quantum radar cross section (QRCS) has been introduced. This quantity measures
how “large” an object looks to a quantum radar be describing how a single photon, or
small cluster of photons scatter off of a macroscopic target. Preliminary simulations
of the basic quantum radar cross section equation have yielded promising results
showing an advantage in sidelobe response in comparison to the classical RCS. This
document expands upon this idea by providing insight as to where this advantage expanding upon the theory.
The expanded theory presented in this document includes re-deriving the QRCS
formula to be a general bistatic formula, as the current equation is only valid for
monostatic radar geometries. This re-derivation process also leads to the addition of
terms that capture the effect of photon polarization, something that is not properly
taken into account in the current literature. Most importantly, a new formulation
of the QRCS formula will be derived that includes writing the equation in terms
of Fourier transforms. This has a profound impact on the analysis of the theory
of the QRCS as it allows for the derivation of closed form solutions of certain
geometries, something that has never been possible due to the form of the current
QRCS equation. All together, this document will provide a complete and general
theory of the QRCS.
After deriving the necessary equations, there will be extensive work in the
utilization of these equations in deriving geometry dependent responses and comparing
the closed form solutions to the classical solutions as well as comparing the
solutions to the numerical simulations.
The current literature relies exclusively on numerical simulations…
This work presents a study on quantum remote sensing applied to national defense using RADAR (Radio Detection and Ranging) and LIDAR (Light Detection and Ranging) technologies, which can be adopted in metrology and remote sensing processes, capable of detecting and intercepting targets in a given coverage area. In this context, the work presents a bibliographic research addressing concepts, principles of quantum mechanics, basic configurations, methods of photon entanglement, projects, experiments, and potential applications of RADAR and LIDAR systems, highlighting advantages and aspects, such as speed, greater precision, lower cost, greater security guarantee, higher sensitivity, and resolution of quantum remote sensing operation, as well as associated challenges: photon loss, technical difficulties, the phenomenon of decoherence, sensitivity to noise, and the need for integration of quantum remote sensing systems with quantum error correction modules.
Since the wavefunction of a photon only describes the probability of photon detection in time and space, it is impossible to derive uniquely defined trajectories describing the path taken by the photon between emission and detection. However, it is possible to test whether a particular set of trajectories is consistent with the statistics observed at different times for photons in the same initial state. Recently, I have shown that quantum interference effects between position and momentum can result in a violation of inequalities associated with motion along straight lines. Here, I present a more detailed analysis on the origin of the effect and its relation with other experimentally observable aspects of quantum statistics such as weak measurements and quantum tomography. It is shown that the interference pattern between a quantum state component of well-defined position and a quantum state component of well-defined momentum describes a modified causality relation between the positions detected at different times. The phase of the interference pattern is identified with the classical action of particle motion and the relation between uncertainty and causality is considered. The specific case of single photon wavefunctions is used to explain the possibilities and limitations of control at the ultimate quantum limit.
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.