This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

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Many-Body Physics with Ultracold Gases

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

As they travel through space, some light beams rotate. Such light beams have angular momentum. There are two particularly important ways in which a light beam can rotate: if every polarization vector rotates, the light has spin; if the phase structure rotates, the light has orbital angular momentum (OAM), which can be many times greater than the spin. Only in the past 20 years has it been realized that beams carrying OAM, which have an optical vortex along the axis, can be easily made in the laboratory. These light beams are able to spin microscopic objects, give rise to rotational frequency shifts, create new forms of imaging systems, and behave within nonlinear material to give new insights into quantum optics.

/pdf/orbital-angular-momentum-origins-behavior-and-applications-1sv8qfuhrs.pdf

Orbital angular momentum: origins, behavior and applications

Hybrid plasmonic waveguides are described that employ a high-gain semiconductor nanostructure functioning as a gain medium that is separated from a metal substrate surface by a nanoscale thickness thick low-index gap. The waveguides are capable of efficient generation of sub-wavelength high intensity light and have the potential for large modulation bandwidth >1 THz.

/pdf/plasmon-lasers-at-deep-subwavelength-scale-luevvk8jie.pdf

Plasmon lasers at deep subwavelength scale

(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

We investigate the separation of the total angular momentum J of the electromagnetic field into a ‘spin’ part S and an ‘orbital’ part L. We show that both ‘spin’ and ‘orbital’ angular momentum are ...

Commutation Rules and Eigenvalues of Spin and Orbital Angular Momentum of Radiation Fields

We consider the separation of the total angular momentum of the electromagnetic field into a "spin" and an "orbital" part. Though this separation is normally considered to be unphysical and not observable, we argue that both members in the separation are separately measurable quantities. However, the commutation relations for the associated quantum operators reveal that neither of them is an angular-momentum operator.

https://iopscience.iop.org/article/10.1209/0295-5075/25/7/004/pdf

Spin and Orbital Angular Momentum of Photons

Eigenfunction description of laser beams and orbital angular momentum of light

The operator algebra of the quantum harmonic oscillator is applied to the description of Gaussian modes of a laser beam. Higher-order modes of the Hermite-Gaussian or the Laguerre-Gaussian form are generated from the fundamental mode by ladder operators. This approach allows the description of both free propagation and refraction by ideal astigmatic lenses. The paraxial optics analog of a coherent state is shown to be a light beam with a displaced beam axis which is refracted by lenses according to geometric optics. The expectation value of the orbital angular momentum of a paraxial beam of light is found to be expressible in terms of a contribution analogous to the angular momentum of the oscillator plus contributions which arise from the ellipticity of the wave fronts and of the light spot. This clarifies the process by which a transfer of orbital angular momentum between a light beam and astigmatic lenses or diaphragms occurs.

Paraxial wave optics and harmonic oscillators

We calculate the reflection coefficient for a light beam incident on the interface between a dielectric and a resonant atomic vapor to first order in the dipole polarization in the vapor. The angle of incidence and the polarization direction are chosen arbitrarily, and saturation is fully accounted for. The atoms are supposed to get deexcited at collisions with the surface. The resulting transient behavior of atoms leaving the surface is responsible for a nonlocal response. This spatial dispersion near the surface is known to produce a natural-linewidth-limited resonance in the vapor reflection coefficient at normal incidence. Our analysis shows that this sub-Doppler structure is broadened by the residual Doppler effect for non-normal incidence. This structure disappears at the critical angle for total internal reflection, where one predicts a conventional Voigt-type dispersion response, based on the complex-refractive-index approach. We also calculate the saturation broadening of the atomic response for large intensities. Beyond the critical angle, the spectral response suddenly shifts from dispersion to absorption line shapes. In the case of total internal reflection, the spatial dispersion leads to an additional Lorentzian broadening, which results from an effective imaginary Doppler shift at passage through the evanescent wave (transit-time broadening).

Gerard Nienhuis

Papers

Commutation Rules and Eigenvalues of Spin and Orbital Angular Momentum of Radiation Fields

Spin and Orbital Angular Momentum of Photons

Eigenfunction description of laser beams and orbital angular momentum of light

Paraxial wave optics and harmonic oscillators

Nonlinear selective reflection from an atomic vapor at arbitrary incidence angle