2D OPTICAL TRAPPING POTENTIAL FOR THE CONFINEMENT OF HETERONUCLEAR MOLECULES RAYMOND SANTOSO A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF SCIENCE

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1 2D OPTICAL TRAPPING POTENTIAL FOR THE CONFINEMENT OF HETERONUCLEAR MOLECULES RAYMOND SANTOSO B.SC. (HONS), NUS A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF SCIENCE DEPARTMENT OF PHYSICS NATIONAL UNIVERSITY OF SINGAPORE 2014

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3 DECLARATION I hereby declare that the thesis is my original work and it has been done by me in its entirety. I have dully acknowledged all the sources of information which have been used in this thesis. This thesis has also not been submitted for any degree in any university previously. Raymond Santoso 31 st of July, 2014

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5 Acknowledgment Firstly, I would like to thank God for His blessing and strength for me that allows me to finish this project to the best of my abilities. I am blessed with such a colorful journey during the one year of the completion of this project. I would like to thank my supervisor, Prof. Kai Dieckmann, for the wonderful opportunity he has given me with this project. I am indebted for his guidance, insightful discussions and his constant evaluation which allows me to always improve. In the same way, thank you for the members of the Fermi Mixture group which has helped me a lot during the working of this project. Thank you to Sambit and Markus for their assistance and consultations, Mark and especially Johannes which has been a great support during difficult times. I also would like to thank the members of the Fermi Lattice group for allowing me to use the space and facilities from their lab for this project. My gratitude for Jimmy Li Ke, and Saptarishi for their technical advices, Jaren for his companionship and last but not least, Christian with whom I had an extensive interaction during this project. Thank you as well for the research supports and administrative supports from the Centre for Quantum Technologies which hosted the laboratory in which this project took place. Lastly, I would like to thank my families and friends for their material and moral supports without which the completion of this project would have been impossible. A special thanks to Prof. Valerio, Prof. Christian Kurtsiefer and Prof. Bjorn Hessmo which have kindly offered me their advices both technical and non technical for the benefit of this project. iii

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7 Summary Ground state polar ultracold molecules such as the mixture of two species of alkali-metal dimers are interesting systems to study due to the presence of the long range dipole-dipole interaction. Such molecules have been produced from cold-atom clouds of the two atomic species by a Feshbach resonance and then brought to the ground state by a Stimulated Raman Transfer Passage (STIRAP). The ground state molecules are held by an optical trap formed by a high power laser. This trapping method, however, leads to a high peak molecule density and hence suffers from a short lifetime due to the enhanced density-dependent chemical reaction. In this thesis, we show that a reduced loss rate with sufficiently strong confinement can be attained by choosing a particular trap geometry which combines a optical lattice along one axis and a flat-top (uniform intensity) beam shape in the transverse direction. Several schemes are studied in this work to realize a flat-top intensity beam from the Gaussian beam found in commercial lasers. Taking into account the available spatial light modulators (SLM) devices which can be used to shape the beam, we review three beam shaping schemes and we perform numerical simulations for each scheme in order to determine their feasibility for an experimental realization of the optical trap. In particular, we choose to implement a scheme which combines a binary amplitude modulation SLM and a spatial filtering to achieve the aforementioned shaping. The numerical simulation of such scheme is found to produce a flat-top beam with an average error of 0.5% and a peak error of 2%. An experimental trial of the shaping scheme is done with a Mephisto MOPA laser and DLP3000 SLM from Texas Instruments. Modeling the input beam profile as an ideal Gaussian beam, the binary reflection pattern of the SLM created by the design algorithm produces a flat-top beam with an average error of 7% and a maximum error of 27%. Subsequently, a new correction algorithm that adapts the SLM pattern based on the observed beam profile is created and implemented. The correction algorithm is able to optimize the SLM pattern in less than 20 iterations, bringing down the average error to 3.5% and maximum error to 16%. ii

8 Contents List of Figures iv 1 Introduction Ultracold Molecules in an Optical Trap Scope of This Thesis Optical Dipole Trap Design for LiK Molecules Optical Potential of a Red-Detuned Light Controlling the Reaction Loss in LiK Molecules The Geometry of the Optical Trap Comparison with Other Trap Geometries Beam Shaping with a Phase-Modulation SLM Examples of Commercially Available Phase-Modulation SLM Beam Shaping with the Iterative Fourier Transform Algorithm Beam Shaping with an Amplitude-Modulation SLM Examples of Commercially Available Amplitude-Modulation SLM Beam Shaping with the Holography Method Beam Shaping with the Error Diffusion Algorithm First Experimental Results of the Flat-Top Shaping Method The Laser System Beam Profile Measurement Before the SLM Optical Setup Preparation Beam Shaping Result Iterative Correction Algorithms First Correction Algorithm Second Correction Algorithm Conclusion and Outlook A Fourier Optics 79 A.1 Beam Propagation Equation A.2 The Effect of a Thin Spherical Lens A.3 Special Optical Configurations B Gaussian Beam Properties 83 B.1 Gaussian Beam Propagation B.2 Focusing through a Lens Bibliography 87 iii

9 List of Figures 1.1 Polar molecules in a lattice configuration The dipole-dipole interaction of polarized ground state LiK molecules Trapped alkali dimer molecules in the optical lattice configuration, with the polarizing static electric field The setup and trapping geometry of an optical lattice configuration Chemical reaction loss rate coefficient of several alkali dimers in the optical lattice trap, in function of the induced electric dipole moment Trap depth and molecule lifetime in function of beam power and waist for a Gaussianbeam trap The required waist to achieve a 50 µk deep trap, and the trap lifetime at this state in function of beam power for a Gaussian-beam trap Trap confinement profile for a Gaussian-beam trap and a flat-top-beam trap The required radius to achieve a 50 µk deep trap, and the trap lifetime at this state in function of beam power for a flat-top-beam trap Schematic of a typical LCoS type SLM Schematic of the piston-type MEMS SLM The schematic of the optical setup used in the Fourier Transform-based beam shaping algorithm Flowchart diagram illustrating the IFTA Algorithm Comparison between the Gaussian and higher order Super-Lorentz functions Intensity profile of the output beam in the Fourier plane after 200 iterations for the 400 µm target profile Evolution of the RMS Error and the Diffraction Efficiency over the 200 iterations of the MRAF algorithm Initial and final SLM phase guess with 200 iterations for the 400 µm target profile Intensity profile of the output beam in the Fourier plane after 200 iteration steps for the 200 µm target profile Evolution of the RMS Error and the Diffraction Efficiency over the 200 iterations of the MRAF algorithm for the 200 µm target profile Intensity profile of the output beam in the Fourier plane after 200 iteration steps for the 120 µm target profile Evolution of the RMS Error and the Diffraction Efficiency over the 200 iteration steps of the MRAF algorithm for the 120 µm target profile The RMS Error and the Diffraction Efficiency in function of the mixing parameter m after 100 iteration steps The measurement setup for the beam intensity profile at the SLM plane The intensity profile comparison of the diffraction pattern with a discretized phase modulation The intensity profile of the output beam in the Fourier plane with the modified MRAF algorithm after 200 iteration steps iv

10 3.17 The phase profile of the output beam at the Fourier plane with the modified MRAF algorithm after 200 iteration steps The cross section view of the DMD device The schematic diagram of the Fourier-Transform Holography scheme Numerical Simulation result of the Fourier-Transform Holography scheme Comparison between the object beam intensity profile in the Fourier plane with the ideal and binary hologram Beam shaping from a gaussian intensity pattern to a flat-top intensity pattern with a space-varying reflectivity pattern The schematic of the optical setup used in the error diffusion beam shaping algorithm Plot of the convolution kernel function of the telescope with a spatial filter The diagrammatic illustration of the error diffusion algorithm The pixel structure of the DLP3000 [Texas Instruments, ] The representation of the DLP3000 pixel geometry for the simulation Beam shaping efficiency for various values of flat-top maximum intensity and width Beam shaping efficiency for various values of flat-top maximum intensity and width Input, output and reflectivity pattern in the numerical simulation of the Error Diffusion Algorithm Output profile of the beam shaped with the error diffusion algorithm Cut across X axis of the output profiles from the error diffusion algorithm with various pinhole opening diameter RMS error of the beam shaped with the error diffusion algorithm in function of pinhole diameter Output profiles of the beam shaped with the error diffusion algorithm Output profiles of the beam shaped with the error diffusion algorithm Optical setup of a relay telescope Optical setup of a single-lens demagnification telescope Mounted optical isolator, with safety tubes to house the high power beam Schematic diagram of a Faraday isolator The transmission and isolation of the optical isolator in function of the power incident to the isolator Experimental setup for the beam profile measurement The principle behind the operation of the Beam Master device Vertical axis intensity profile for some selected beam power Horizontal axis intensity profile of the laser output beam for some selected distances Vertical axis intensity profile of the laser output beam for some selected distances Laser output beam spot size in function of position from the collimating lens Horizontal axis intensity profile of the collimated beam for some selected distances Experimental setup for the placement of the iris Comparison of the horizontal axis intensity profile with and without the iris Horizontal axis intensity profile of the collimated, filtered beam for some selected distances Vertical axis intensity profile of the collimated, filtered beam for some selected distances Collimated, filtered beam spot size in function of position from the laser output port The proposed optical setup as discussed in chapter 4 and the actual setup assembled for our testing purposes The DLP Lightcrafter module and the extracted DLP3000 with the electronic control board housed in the Al box Schematic setup of the reflection off the DLP3000 chip for each of the three tilt states. 58 v

11 5.19 The 2f-2f configuration used in the measurement of the angle-dependence of the DLP3000 chip reflection factor Measurement result of the angle-dependence of the DLP3000 chip reflection factor Relay telescope setup in front of the SLM Setup for centering the beam at the DLP chip and the Beam Master at the output plane of the telescope Vertical axis intensity profile of the collimated beam diffracted by the hole pattern and magnified by the relay telescope, in function of the detector position from the telescope The setup of the iris placed between the telescope lenses and the camera Camera image of the beam reflected by the central pixel of the SLM Camera image of the beam reflected by the entire SLM chip Camera image of the flat-top beam shaped with the binary pattern produced by the Error Diffusion algorithm Flat-top profile taken at different iris opening Best-fitted beam order value of the flat-top profile taken at various iris opening RMS error values of the flat-top profile shaped with different input waist values Maximum error values of the flat-top profile shaped with different input waist values dimensional plot of the beam error of the flat-top profile shaped with different input waist values Maximum error and RMS error of the optimized flat-top profiles, taken with 1 second time lapse Illustration of the first correction algorithm Evolution of the output profile RMS and maximum error in function of the number of iterations with the first algorithm The RMS and maximum error in of the output profile optimized by algorithm 1, taken with 1 second time lapse Profile of the output beam optimized by algorithm Definition of I out and I ft in equation Evolution of the output profile RMS and maximum error in function of the number of iterations with the second algorithm The RMS and maximum error in of the output profile optimized by algorithm 2, taken with 1 second time lapse Profile of the output beam optimized by algorithm Profile of the flat-top beam, cut along the X axis for various camera positions along the Z axis Profile of the flat-top beam, cut along the Y axis for various camera positions along the Z axis RMS and maximum error, cut along the Y axis for various camera positions Summary of RMS and maximum error figures obtained from numerical simulations and experimental results Calibration of the response time of the photodiode using a square wave signal from an infrared LED Intensity fluctuation measurement with a photodiode in the spectral range of 200 khz Intensity fluctuation measurement with a photodiode in the spectral range of 200 Hz Input Gaussian beam stability at the SLM plane Intensity captured by the camera without any incident light A.1 Huygens principle of diffraction A.2 The geometry of a spherical lens A.3 Optical setup for a relay telescope and a single-lens Fourier imaging B.1 Parameters in the propagation of a Gaussian beam. Figure is taken from [Siegman, 1986] 83 vi

12 B.2 Linear expansion of an uncollimated beam vii

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