J. Rogel-Salazar

Bessel–Gauss beam optical resonator

Abstract In a simple picture, a Bessel beam is viewed as a transverse standing wave formed in the interference region between incoming and outgoing conical waves. Based on this interpretation we propose an optical resonator that supports modes that are approximations to Bessel–Gauss beams. The Fox–Li algorithm in two transverse dimensions is applied to confirm the conclusion.

Unstable Bessel beam resonator

Abstract We examine the properties of a Bessel–Gauss resonator design studied previously, and explain the bell-shaped modulation imposed on its lowest-order mode in terms of an equivalent linear cavity. We propose an unstable cavity to eliminate this effect, and obtain modes whose intensities resemble a true Bessel function along the diameter of the defining aperture of the resonator.

The Gross–Pitaevskii equation and Bose–Einstein condensates

The Gross–Pitaevskii equation (GPE) is discussed at the level of an advanced course on statistical physics. In the standard literature the GPE is usually obtained in the framework of the second quantization formalism, which in many cases goes beyond the material covered in many advanced undergraduate courses. In this paper, we motivate the derivation of the GPE in relationship to concepts from statistical physics, highlighting a number of applications from the dynamics of a Bose–Einstein condensate to the excitations of the gas cloud. This paper may be helpful for encouraging the discussion of modern developments in a statistical mechanics course, and can also be of use in other contexts such as mathematical physics and modelling. The paper is suitable for undergraduate and graduate students, as well as for general physicists.

Full characterization of Airy beams under physical principles

The propagation characteristics of Airy beams is investigated and fully described under the traveling-wave approach analogous to that used for nondiffracting Bessel beams. This is possible when noticing that Airy functions are, in fact, Bessel functions of fractional order

Squeezing and entanglement in quasiparticle excitations of trapped Bose-Einstein condensates

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Characterisation of the dynamical quantum state of a zero temperature Bose–Einstein condensate

. We show how physical principles impose restrictions such that the nondiffracting Airy beams cannot be of infinite extent as has been argued and introduce quantitative expressions for the maximum transverse and longitudinal extent of Airy beams. We show that under the appropriate physical conditions it is possible to obtain higher-order Airy beams.

Engineering structured light with optical vortices

We estimate the amount of temperature-dependent squeezing and entanglement in the collective excitations of trapped Bose-Einstein condensates. We also demonstrate an alternative method of temperature measurement for temperatures much less than the critical temperature

Methods of quantum field theory for trapped Bose–Einstein condensates

(T\ensuremath{\ll}{T}_{c}).

An efficient method-of-lines simulation procedure for organic semiconductor devices

Abstract We describe the quantum state of a Bose–Einstein condensate at zero temperature. By evaluating the Q -function we show that the ground state of Bose–Einstein condensate under the Hartree approximation is squeezed. We find that multimode Schrodinger cat states are generated as the condensate evolves in a ballistic expansion.