(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

Have you ever felt that the very title, Progress in Optics, conjured an image in your mind? Don’t you see a row of handsomely printed books, bearing the editorial stamp of one of the most brilliant members of the optics community, and chronicling the field of optics since the invention of the laser? If so, you are certain to move the bookend to make room for Volume 16, the latest of this series. It contains seven chapters on widely diverging topics, written by well-known authorities in their fields. These are: 1) Laser Selective Photophysics and Photochemistry by V. S. Letokhov, 2) Recent Advances in Phase Profiles (sic) Generation by J. J. Clair and C. I. Abitbol, 3 ) Computer-Generated Holograms: Techniques and Applications by W.-H. Lee, 4) Speckle Interferometry by A. E. Ennos, 5 ) Deformation  Invariant, Space-Variant Optical  Pattern Recognition by D. Casasent and D. Psaltis, 6) Light Emission from High-Current Surface-Spark Discharges by R. E. Beverly, and 7) Semiclassical Radiation  Theory within a  QuantumMechanical Framework by I. R. Senitzkt. The  breadth of topic  matter  spanned  by  these  chapters makes it impossible, for this reviewer at least, to pass judgement on the comprehensiveness, relevance, and completeness of every chapter. With an editorial board as prominent as that of Progress in Optics, however, it seems hardly likely that such comments should be necessary. It should certainly be possible to take the authority of each author as credible. The only remaining judgment to be  made on these chapters is their readability. In short, what are they like to read? The first sentence of the first chapter greets the eye with an obvious typographical error: “The creation of coherent laser light source, that have tunable radiation, opened the . . . .” Two pages later we find: “When two types of atoms or molecules of different isotopic composition ( A and B ) have even one spectral line that does not overlap with others, it is pos-

Progress in optics

The Wigner function was formulated in 1932 by Eugene Paul Wigner, at a time when quantum mechanics was in its infancy. In doing so, he brought phase space representations into quantum mechanics. However, its unique nature also made it very interesting for classical approaches and for identifying the deviations from classical behavior and the entanglement that can occur in quantum systems. What stands out, though, is the feature to experimentally reconstruct the Wigner function, which provides far more information on the system than can be obtained by any other quantum approach. This feature is particularly important for the field of quantum information processing and quantum physics. However, the Wigner function finds wide-ranging use cases in other dominant and highly active fields as well, such as in quantum electronics—to model the electron transport, in quantum chemistry—to calculate the static and dynamical properties of many-body quantum systems, and in signal processing—to investigate waves passing through certain media. What is peculiar in recent years is a strong increase in applying it: Although originally formulated 86 years ago, only today the full potential of the Wigner function—both in ability and diversity—begins to surface. This review, as well as a growing, dedicated Wigner community, is a testament to this development and gives a broad and concise overview of recent advancements in different fields.

Recent advances in Wigner function approaches

https://www.prl.res.in/~library/Banerji_J_2013_abst.pdf

Measuring the topological charge of an optical vortex by using a tilted convex lens

A tomographic measurement is a ubiquitous tool for estimating the properties of quantum states, and its application is known as quantum state tomography (QST). The process involves manipulating single photons in a sequence of projective measurements, often to construct a density matrix from which other information can be inferred, and is as laborious as it is complex. Here we unravel the steps of a QST and outline how it may be demonstrated in a fast and simple manner with intense (classical) light. We use scalar beams in a time reversal approach to simulate the outcome of a QST and exploit non-separability in classical vector beams as a means to treat the latter as a “classically entangled” state for illustrating QSTs directly. We provide a complete do-it-yourself resource for the practical implementation of this approach, complete with tutorial video, which we hope will facilitate the introduction of this core quantum tool into teaching and research laboratories alike. Our work highlights the value of using intense classical light as a means to study quantum systems and in the process provides a tutorial on the fundamentals of QSTs.

/pdf/concepts-in-quantum-state-tomography-and-classical-3alooq5e8b.pdf

Concepts in quantum state tomography and classical implementation with intense light: a tutorial

We are describing a novel way to find the Mueller matrix of an arbitrary optical element, by taking advantage of projection of resulting polarization states on four known input polarization states by using Simon-Mukunda gadget.

http://ieeexplore.ieee.org/iel7/6524692/6545200/06545212.pdf

Determination of Mueller matrix of an optical element with Simon-Mukunda gadget

Quantum technologies, i.e., technologies benefiting from the features of
quantum physics such as objective randomness, superposition, and entanglement,
have enabled an entirely different way of distributing and processing
information. The enormous progress over the last decades has also led to an
urgent need for young professionals and new educational programs. However, the
lack of intuitive analogies and the necessity of complex mathematical
frameworks often hinder teaching and learning efforts. Thus, novel education
methods, such as those involving gamification, are promising supplements to
traditional teaching methods. Here, we present a strategic card game in which
the building blocks of a quantum computer can be experienced. While playing,
participants start with the lowest quantum state, play cards to "program" a
quantum computer, and aim to achieve the highest possible quantum state. By
extending the game to high-dimensional quantum systems, i.e., systems that can
take more than two possible values, and by developing different multi-player
modes, the game can be used as an introduction to quantum computational tasks
for students. As such, it can also be used in a classroom environment to
increase the conceptual understanding, interest, and motivation of a student.
Therefore, the presented game contributes to the ongoing efforts on gamifying
quantum physics education with a particular focus on the counter-intuitive
features which quantum computing is based on.

Endless Fun in high dimensions -- A Quantum Card Game

We generate two dimensional Airy beams using a cubic phase mask and study its propagation through photorefractive
material experimentally. The diffraction free nature as well as the acceleration of Airy beams is observed. Using beam
propagation method (BPM), we confirm the experimental results. We also study the effect of an applied electric field on
the propagation of Airy beams through photorefractive materials numerically. It is observed that the applied field leads to
interaction between the lobes of Airy beams.

2D Airy beams propagation through photorefractive materials

Optical vortex beams are profiled as helical wavefronts with a phase singularity carrying an orbital angular momentum (OAM) associated with their spatial distribution. The transverse intensity distribution of a conventional optical vortex has a strong dependence on the carried topological charge. However, perfect optical vortex (POV) beams have their transverse intensity distribution independent of their charge. Such `size-invariant' POV beams have found exciting applications in optical manipulation, imaging and communication. In this article, we investigate the use of POV modes in the efficient generation of high dimensional quantum states of light. We generate heralded single photons carrying OAM using spontaneous parametric down-conversion (SPDC) of POV beams. We show that the heralding efficiency of the SPDC single photons generated with POV pump is greater than that with normal optical vortex beams. The dimensionality of the two-photon OAM states is increased with POV modes in the pump and projective measurements using Bessel-Gaussian vortex modes that give POV, instead of the Laguerre-Gaussian modes.

Size invariant twisted optical modes for efficient generation of higher dimensional quantum states

An eavesdropper may gain information by exploiting device imperfections while implementing quantum key distribution protocols. We find information leakage due to coupling mismatch at receiver’s detectors in terms of mutual information between eaves-dropper and receiver.

Shashi Prabhakar

Papers

Determination of Mueller matrix of an optical element with Simon-Mukunda gadget

Endless Fun in high dimensions -- A Quantum Card Game

2D Airy beams propagation through photorefractive materials

Size invariant twisted optical modes for efficient generation of higher dimensional quantum states

Information Leakage due to Detection Coupling Mismatch