LG Picture

Laser Beams with Orbital Angular Momentum and their Interactions with Ultracold Atoms

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(2014) Electromagnetically induced transparency with Laguerre-Gaussian modes in ultracold rubidium, T. G. Akin, S. P. Krzyzewski, Alberto M. Marino, and E. R. I. Abraham (accepted for publication in Optics Communications).

(2014) Confinement of ultracold atoms in a Laguerre-Gaussian laser beam created with diffractive optics, Sharon A. Kennedy, G. W. Biedermann, J. T. Farrar, T. G. Akin, S. P. Krzyzewski, E. R. I. Abraham, Optics Communications, 321, 110-115.

(2012) Bose-Einstein condensation transition studies for atoms confined in Laguerre-Gaussian laser modes, T. G. Akin, Sharon Kennedy, Ben Dribus, Jeremy L. Marzoula, Lise Johnson, Jason Alexander, and E. R. I. Abraham, Optics Communications, 285, 84-89.

(2002) Creation of Laguerre-Gaussian laser modes using diffractive optics, Sharon A. Kennedy, Matthew J. Szabo, Hilary Teslow, James Z. Porterfield, and E. R. I. Abraham, Physical Review A 66, 043801(1-5).

(2001) Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap, J. Tempere, J. T. Devreese, and E. R. I. Abraham, Physical Review A 64, 023603 (1-8).


Laser beams propagating in Laguerre-Gaussian modes have a characteristic phase singularity, orbital angular momentum, and multiply connected topology. Laguerre-Gaussian beams LG(pl) describe a set of propagation modes where the equation for the radial electric field is proportional to the product of a Gaussian and an associated Laguerre polynomial L(pl). When l is greater than zero, the electric field has an azimuthal phase change of 2pl which results in a phase singularity in the field and a node in the intensity at the center of the beam.

LG Beam Picture

These beams are used as optical tweezers for macroscopic particles, used to write optical waveguides in atomic vapors, and the vortex nature of these beams is exploited in the study of optical solitons for optical communications. They are also used in quantum optics experiments utilizing Electromagnetically-Induced Transparency (EIT) for purposes of optical computing.

These types of laser modes also produce atom traps: magneto-optical traps (MOT) and optical dipole traps. In a dipole trap, a laser tuned to a frequency lower than an atomic resonance transition frequency (red detuned) attracts atoms to the region of maximum light intensity, while a laser tuned above resonance (blue detuned) attracts atoms to minimum intensity regions. Confining atoms in the intensity nodes minimizes effects such as photon absorption and ac Stark shifts, which is important for precision measurements. Multiply-connected traps for Bose-Einstein condensates can fix the cores of vortex states. Confinement of multiple condensates in the concentric, multiply connected traps formed by high-order LG modes allows observation of vortices by matter-wave interference.

Making LG beams with Diffractive Optics

Our group pioneered the construction of LG beams using diffractive optics. In collaboration with the Digital Optics Corporation, we take to substrates and etch wavelength-sized patters on each surface. The wavefront diffracts from each point on the surface, each becoming a new source of outgoing waves. The different outgoing waves interfere (Huygens's Principle) to make a new pattern.

Diffractive Optics

We measured the mode quality of the LG beams created using this method. Even for high order LG beams, we found the mode quality (at the ideal fixed focal plane of the diffractive optics) was consistent with 100% of the laser intensity being in the desired LG mode. While this was only true at the specific plane for which the structures on the diffractive optics are optimized. We also find that the modes maintain their general features over several meters. This is due, no doubt, to their soliton quality.

LG Beam Analysis

Trapping Ultracold Atoms in LG beams

We confined atoms in two dimensions using LG beams created by diffractive optics. We first cooled the atoms in a standard MOT. We then directed an LG beam vertically to confine the atoms radially. They were not confined against gravity. Using a blue-detuned LG(10) laser, we confined the atoms to the central intensity minimum. Detuning the laser to the red, we then trapped the atoms (radially) at the annular intensity maximum.

Trapped Atoms

We found that the density distribution of atoms confined in the LG beam had a sin(3j) variation that matched the intensity imperfections of the beam. Thus, absorption imaging of the density distribution can provide an in situ measurement of the beam quality.

Bose-Einstein Condensates in LG beams

We calculated BEC transition characteristics of atoms trapped in LG beams. We calculated the critical temperature as a function of laser characteristics, the condensate fraction, and the heat capacity. All previous models of LG beams used a simple harmonic approximation for the confining potential formed by the LG beam. We analyzed the characteristics using both the SHO model and the full potential to find the ranges of parameter space where the SHO approximation was appropriate. (T. G. Akin, Sharon Kennedy, Ben Dribus, Jeremy L. Marzoula, Lise Johnson, Jason Alexander, and E. R. I. Abraham, Optics Communications, 285, 84-89.)

We also considered the situation where two condensates were contained in an LG beam. The first in the inner node and the second in the first annular ring. If the annular condensate was promoted into a vortex state and both condensates were released, the resulting matter-wave interference pattern is an Archimedes spiral.

Vortex Matter-Wave Interference

Electromagnetically Induced Transparency with LG beams

We demonstrated electromagnetically induced transparency (EIT) with the control laser in an LG(10) mode. We observed the transmission spectrum in an ultracold atoms prepared in a MOT. We measure linewidths of the EIT feature with the control in the LG(10) mode and compare this to the spectrum with the control in the Gaussian mode. The Rabi frequency of the control laser in the Gaussian mode is approximated as a constant, Ω0. The Rabi frequency of the control laser in the LG(10) mode is defined as: Ω0(r √2)/(w0) Exp(-r2/w02).


We model the experiment using the density matrix formalism. We consider a six level atom composed of two hyperfine levels in the 2S1/2 state, and the remaining four levels belong to the hyperfine levels in the 2P3/2 state in rubidium. We found that the model is in good agreement with the data. Further, the EIT linewidth is narrower for the same value of Ω0 when a control beam is in an LG(10) mode as compared to the control laser in a Gaussian mode. Decoherences due to transit effects are negligible in an ultracold gas. Therefore, we conclude that the narrowing of the EIT feature is due to spatial variation of the Rabi frequency of a control laser in the LG(10) mode. This result is consistent with previous observations in gases at room temperature.

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