There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The Theory of Stochastic Processes. By D. R. Cox and H. D. Miller. Pp. x, 398. 70s. (Methuen)

http://fafnir.phyast.pitt.edu/py3765/walkingTCReview.pdf

Strong dynamics and electroweak symmetry breaking

Quantum-mechanical effects at the macroscopic level were first explored in Josephson-junction-based superconducting circuits in the 1980s. In recent decades, the emergence of quantum information science has intensified research toward using these circuits as qubits in quantum information processors. The realization that superconducting qubits can be made to strongly and controllably interact with microwave photons, the quantized electromagnetic fields stored in superconducting circuits, led to the creation of the field of circuit quantum electrodynamics (QED), the topic of this review. While atomic cavity QED inspired many of the early developments of circuit QED, the latter has now become an independent and thriving field of research in its own right. Circuit QED allows the study and control of light-matter interaction at the quantum level in unprecedented detail. It also plays an essential role in all current approaches to gate-based digital quantum information processing with superconducting circuits. In addition, circuit QED provides a framework for the study of hybrid quantum systems, such as quantum dots, magnons, Rydberg atoms, surface acoustic waves, and mechanical systems interacting with microwave photons. Here the coherent coupling of superconducting qubits to microwave photons in high-quality oscillators focusing on the physics of the Jaynes-Cummings model, its dispersive limit, and the different regimes of light-matter interaction in this system are reviewed. Also discussed is coupling of superconducting circuits to their environment, which is necessary for coherent control and measurements in circuit QED, but which also invariably leads to decoherence. Dispersive qubit readout, a central ingredient in almost all circuit QED experiments, is also described. Following an introduction to these fundamental concepts that are at the heart of circuit QED, important use cases of these ideas in quantum information processing and in quantum optics are discussed. Circuit QED realizes a broad set of concepts that open up new possibilities for the study of quantum physics at the macro scale with superconducting circuits and applications to quantum information science in the widest sense.

/pdf/circuit-quantum-electrodynamics-bcs9sxffu0.pdf

Circuit quantum electrodynamics

Advances in mathematics

A feedhorn driving method and apparatus allows the establishment of multiple phase centers using only a single multimode feedhorn. At least two higher-order modes are extracted from the feedhorn and weighted in amplitude and phase. The phase center separation is established in accordance with an assigned weights. The feedhorn has application in i.a. moving target indication systems.

Multiple phase center feedhorn for reflector antenna

We propose a protocol for quantum illumination: a quantum-enhanced noise radar. A two-mode squeezed state, which exhibits continuous-variable entanglement between so-called signal and idler beams, is used as input to the radar system. Compared to existing proposals for quantum illumination, our protocol does not require joint measurement of the signal and idler beams. This greatly enhances the practicality of the system by, for instance, eliminating the need for a quantum memory to store the idler. We perform a proof-of-principle experiment in the microwave regime, directly comparing the performance of a two-mode squeezed source to an ideal classical noise source that saturates the classical bound for correlation. We find that, even in the presence of significant added noise and loss, the quantum source outperforms the classical source by as much as an order of magnitude.

Quantum-enhanced noise radar

We investigate the use of correlated photon pair sources for the improved quantum-level detection of a target in the presence of a noise background. Photon pairs are generated by spontaneous four-wave mixing, one photon from each pair (the herald) is measured locally while the other (the signal) is sent to illuminate the target. Following diffuse reflection from the target, the signal photons are detected by a receiver and nonclassical timing correlations between the signal and herald are measured in the presence of a configurable background noise source. Quantum correlations from the photon pair source can be used to provide an enhanced signal-to-noise ratio when compared to a classical light source of the same intensity.

Quantum-enhanced standoff detection using correlated photon pairs

We built and evaluated a prototype quantum radar, which we call a quantum two-mode squeezing (QTMS) radar, in the laboratory. It operates solely at microwave frequencies; there is no downconversion from optical frequencies. Because the signal generation process relies on quantum mechanical principles, the system is considered to contain a quantum-enhanced radar transmitter. This transmitter generates a pair of entangled microwave signals and transmits one of them through free space, where the signal is measured using a simple and rudimentary receiver. At the heart of the transmitter is a device called a Josephson parametric amplifier, which generates a pair of entangled signals called two-mode squeezed vacuums at 6.1445 and 7.5376 GHz. These are then sent through a chain of amplifiers. The 7.5376 GHz beam passes through 0.5 m of free space; the 6.1445 GHz signal is measured directly after amplification. The two measurement results are correlated in order to distinguish signal from noise. We compare our QTMS radar to a classical radar setup using conventional components, which we call a two-mode noise (TMN) radar, and find that there is significant gain when both systems broadcast signals at $-$82 dBm. This is shown via a comparison of receiver operating characteristic curves. In particular, we find that the quantum radar requires eight times fewer integrated samples compared to the TMN radar to achieve the same performance.

/pdf/receiver-operating-characteristics-for-a-prototype-quantum-34dhxgs96f.pdf

Receiver Operating Characteristics for a Prototype Quantum Two-Mode Squeezing Radar

DRDC has been involved in the development of airborne SAR systems since the 1980s The current system, designated
XWEAR (X-band Wideband Experimental Airborne Radar), is an instrument for the collection of SAR, GMTI and
maritime surveillance data at long ranges
VideoSAR is a land imaging mode in which the radar is operated in the spotlight mode for an extended period of time
Radar data is collected persistently on a target of interest while the aircraft is either flying by or circling it The time
span for a single circular data collection can be on the order of 30 minutes The spotlight data is processed using
synthetic apertures of up to 60 seconds in duration, where consecutive apertures can be contiguous or overlapped The
imagery is formed using a back-projection algorithm to a common Cartesian grid The DRDC VideoSAR mode noncoherently
sums the images, either cumulatively, or via a sliding window of, for example, 5 images, to generate an
imagery stream presenting the target reflectivity as a function of viewing angle The image summation results in
significant speckle reduction which provides for increased image contrast The contrast increases rapidly over the first
few summed images and continues to increase, but at a lesser rate, as more images are summed In the case of
cumulative summation of the imagery, the shadows quickly become filled in In the case of a sliding window, the
summation introduces a form of persistence into the VideoSAR output analogous to the persistence of analog displays
from early radars

Bhashyam Balaji

Papers

Multiple phase center feedhorn for reflector antenna

Quantum-enhanced noise radar

Quantum-enhanced standoff detection using correlated photon pairs

Receiver Operating Characteristics for a Prototype Quantum Two-Mode Squeezing Radar

A videoSAR mode for the x-band wideband experimental airborne radar