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\documentclass[11pt]{article}

\usepackage{hrms}  %% Page settings, style ... for the HRMS abstract book.

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\title{IMPLEMENTATION OF A PHASE-TRACING INTERFEROMETER FOR THE ALIGNEMENT OF ANTIPARALLEL LASER BEAMS}

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\author{\underline{\FirstName K. \LastName GAMLIN},
  \FirstName G. \LastName CLAUSEN,
  \FirstName H. \LastName SCHMUTZ,
  \FirstName F. \LastName MERKT}
\address{\\Institute for Molecular Physical Science, ETH Z\"urich, Vladimir-Prelog-Weg 2, 8093 Z\"urich, Switzerland}

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%  \underline{\FirstName L. \LastName MM NN PPPPPP}}
%\address{Address of the institution for the second author(s)}

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\usepackage{fancyhdr}
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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
\fancyfoot[C]{}
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\category {15,2}
\begin{document}

\maketitle  %% This will also build the list of author(s) and addresse(s).

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\index{Interferometry}
\index{Doppler effect}
\index{High-precision spectroscopy}

%% Place the body of your abstract below.
High-resolution laser spectroscopy of electronic transitions in atomic-beam experiments 
%in experimental set-ups using atomic beams 
often suffers from the Doppler effect.
Next to the broadening of spectral lines resulting from the velocity spread of atoms moving in the direction of the laser beam, the 1st-order Doppler shift provides an obstacle in the determination of Doppler-free transition frequencies. 
%Contrary to the Doppler broadening, the 1st-order Doppler shift impinges the determination of Doppler-compensated transition frequencies.
Experimental methods have been designed for the compensation of the 1st-order Doppler shift,\footnote{\href{https://doi.org/10.1103/PhysRevA.97.012501}{doi:10.1103/PhysRevA.97.012501} Maximilian Beyer et al., \textbf{Physical Review A 97 no. 1},  (January 3, 2018): 012501.} which rely on recording two Doppler components resulting from the absorption induced by %Exciting the atoms with two anti-parallel laser beams results in two Doppler components.
%The two Doppler components result from the excitations of the atomic beam from 
two antiparallel laser beams of the same frequency, which intersect the atomic beam at near-right angles. 
Their respective Doppler shifts are equal in magnitude but of opposite sign. %Usually the laser beams intersect the atomic beam at near-right angles.
%enabling the experimentalist to determine the Doppler-compensated transition frequency.
The Doppler-free frequency lies in the center of the two peaks in the spectrum. The deviation from an exact antiparallel overlapping arrangement of the two beams, typically achieved by retroreflection,
%The antiparallelism and overlap of the two beams 
is the main limiting factor of the precision of this technique.
Different methods have been developed to minimize the tilt angle between the propagation axes of the initial and retro-reflected beams.\footnote{\href{ https://doi.org/10.1364/OE.417455}{doi:10.1364/OE.417455} Vitaly Wirthl et al., \textbf{Optics Express 29, no. 5} (March 1, 2021): 7024.}$^{,}$\footnote{\href{https://doi.org/10.1364/OL.30.003323}{doi:10.1364/OL.30.003323} Holger M\"uller et al., \textbf{Optics Letters 30, no. 24} (December 15, 2005): 3323.} We present the implementation of a phase-tracing Michelson interferometer to measure and minimize the tilt angle between the incoming and reflected beams. This angle is encoded in the interference pattern of both beams. 
A spatial gradient of the phase is introduced by modulating the phase of the initial beam.
%A phase modulation of the initial beam causes a spatial gradient of the phase in the interference pattern.
The resulting phase gradient is read out using a quadrant photodiode enabling correction of the alignment along two axes using a feedback loop. The tilt angle is proportional to the phase and can therefore be calculated. The poster will demonstrate the sensitivity of this method.
%Currently, this method reaches a sensitivity of up to $\sim10\,\upmu$rad.
%tilt angle between the initial beam and its back-reflection. 
%\footnote{\href{https://doi.org/10.1103/PhysRevLett.127.093001}{doi:10.1103/PhysRevLett.127.093001} Gloria Clausen et al., \textbf{Physical Review Letters 127, no. 9}  (August 27, 2021): 093001.}

%The laser beam from its source is split using a beam splitter into a ``reference'' arm and an ``experimental arm'' going to the spectroscopy chamber. The reference arm of the interferometer acts as the initial beam via reflection through a corner cube, and interferes with the back reflection from the experimental arm. The tilt angle causes an asymmetric spatial intensity interference pattern. A modulation of the phase in the reference arm, via physical displacement using a piezo motor, induces a modulation of the intensity profile. Using a quadrant photodiode, we record the ensuing intensity modulation with pairs of quadrants , which measure the integrated intensity over their respective surface, along two spatial axis. The tilt angle along $x/y$-axis is proportional to the phase shift between the quadrants along the $x/y$-axis. Via the determination of the phase between the signals one can conclude the tilt angle and correct the experimental set-up. 
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