(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

This article reviews recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems. In the presence of effective photon-photon interactions induced by the optical nonlinearity of the medium, a many-photon system can behave collectively as a quantum fluid with a number of novel features stemming from its intrinsically nonequilibrium nature. A rich variety of recently observed photon hydrodynamical effects is presented, from the superfluid flow around a defect at low speeds, to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles. While the review is mostly focused on a specific class of semiconductor systems that have been extensively studied in recent years (planar semiconductor microcavities in the strong light-matter coupling regime having cavity polaritons as elementary excitations), the very concept of quantum fluids of light applies to a broad spectrum of systems, ranging from bulk nonlinear crystals, to atomic clouds embedded in optical fibers and cavities, to photonic crystal cavities, to superconducting quantum circuits based on Josephson junctions. The conclusive part of the article is devoted to a review of the future perspectives in the direction of strongly correlated photon gases and of artificial gauge fields for photons. In particular, several mechanisms to obtain efficient photon blockade are presented, together with their application to the generation of novel quantum phases.

Quantum fluids of light

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Electronic Transport In Mesoscopic Systems

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.

/pdf/roadmap-on-structured-light-3r840pnxka.pdf

Roadmap on structured light

We present an inversion method called pBasex aimed at reconstructing the original Newton sphere of expanding charged particles from its two-dimensional projection by fitting a set of basis functions with a known inverse Abel integral. The basis functions have been adapted to the polar symmetry of the photoionization process to optimize the energy and angular resolution while minimizing the CPU time and the response to the cartesian noise that could be given by the detection system. The method presented here only applies to systems with a unique axis of symmetry although it can be adapted to overcome this restriction. It has been tested on both simulated and experimental noisy images and compared to the Fourier-Hankel algorithm and the original Cartesian basis set used by [Dribinski et al.Rev. Sci. Instrum. 73, 2634 (2002)], and appears to give a better performance where odd Legendre polynomials are involved, while in the images where only even terms are present the method has been shown to be faster and simpler without compromising its accuracy.

Two-dimensional charged particle image inversion using a polar basis function expansion

We have created a long-lived ($\ensuremath{\approx}40\text{ }\text{ }\mathrm{s}$) persistent current in a toroidal Bose-Einstein condensate held in an all-optical trap. A repulsive optical barrier across one side of the torus creates a tunable weak link in the condensate circuit, which can affect the current around the loop. Superflow stops abruptly at a barrier strength such that the local flow velocity at the barrier exceeds a critical velocity. The measured critical velocity is consistent with dissipation due to the creation of vortex-antivortex pairs. This system is the first realization of an elementary closed-loop atom circuit.

Superflow in a Toroidal Bose-Einstein Condensate: An Atom Circuit with a Tunable Weak Link

A laser beam with phase singularities is an interesting object to study in optics and may have important applications in guiding atoms and molecules. We explore the characteristics of a singularity in a nondiffracting Bessel beam experimentally by use of a programmable spatial light modulator with 64-level phase holograms. The diffraction efficiency with 64-level phase holograms is greatly improved in comparison with that obtained with a binary grating. The experiments show that the size and deflection angle of the beam can be controlled in real time. The observations are in agreement with scalar diffraction theory.

Generation of nondiffracting Bessel beams by use of a spatial light modulator

A 1-mm-diameter all-light atom guide capable of transporting ultracold atoms tens of centimeters with high efficiency is described. We made the atom tunnel, a dark hollow beam that is blue detuned from resonance, by passing a few tens of milliwatts of power from a TEM00 diode laser beam through an optical sequence composed of three axicons and a simple lens. We demonstrate transport of 108 Cs atoms approximately 20 cm with minimal heating. We show that it is possible for one to control the direction and speed of the atoms in the tunnel by varying the detuning of the tunnel beam.

/pdf/long-narrow-all-light-atom-guide-2u689qhgnt.pdf

Long, narrow all-light atom guide.

Time-correlated single-photon counting is used to measure the lifetimes of the 6p $^{2}$${\mathit{P}}_{1/2}$ and 6p $^{2}$${\mathit{P}}_{3/2}$ levels in atomic Cs with accuracies \ensuremath{\approxeq}0.2--0.3 %. A high-repetition-rate, femtosecond, self-mode-locked Ti:sapphire laser is used to excite Cs produced in a well-collimated atomic beam. The time interval between the excitation pulse and the arrival of a fluorescence photon is measured repetitively until the desired statistics are obtained. The lifetime results are 34.75(7) and 30.41(10) ns for the 6p $^{2}$${\mathit{P}}_{1/2}$ and 6p $^{2}$${\mathit{P}}_{3/2}$ levels, respectively. These lifetimes fall between those extracted from ab initio many-body perturbation-theory calculations by Blundell, Johnson, and Sapirstein [Phys. Rev. A 43, 3407 (1991)] and V. A. Dzuba et al. [Phys. Lett. A 142, 373 (1989)] and are in all cases within 0.9% of the calculated values. The measurement errors are dominated by systematic effects, and methods to alleviate these and to approach an accuracy of 0.1% are discussed. The technique is a viable alternative to the fast-beam laser approach for measuring lifetimes with extreme accuracy.

Precision lifetime measurements of Cs 6p 2P1/2 and 6p 2P3/2 levels by single-photon counting.

We experimentally measure transport of superfluid, bosonic atoms in a mesoscopic system: a small channel connecting two large reservoirs. Starting far from equilibrium (superfluid in a single reservoir), we observe first resistive flow transitioning at a critical current into superflow, characterized by oscillations. We reproduce this full evolution with a simple electronic circuit model. We compare our fitted conductance to two different microscopic phenomenological models. We also show that the oscillations are consistent with LC oscillations as estimated by the kinetic inductance and effective capacitance in our system. Our experiment provides an attractive platform to begin to probe the mesoscopic transport properties of a dilute, superfluid, Bose gas.

https://link.aps.org/accepted/10.1103/PhysRevA.93.063619

Wendell T. Hill

Papers

Superflow in a Toroidal Bose-Einstein Condensate: An Atom Circuit with a Tunable Weak Link

Generation of nondiffracting Bessel beams by use of a spatial light modulator

Long, narrow all-light atom guide.

Precision lifetime measurements of Cs 6p 2P1/2 and 6p 2P3/2 levels by single-photon counting.

Contact resistance and phase slips in mesoscopic superfluid-atom transport