DISPERSION ENGINEERING OF BOSE-EINSTEIN CONDENSATES By MOHAMMAD AMIN

209 Pages·2016·27.45 MB·English

DISPERSION ENGINEERING OF BOSE-EINSTEIN CONDENSATES
By
MOHAMMAD AMIN KHAMEHCHI
A dissertation submitted in partial fulfillment of
the requirements for the degree of
DOCTOR OF PHILOSOPHY
WASHINGTON STATE UNIVERSITY
Department of Physics and Astronomy
MAY 2017
©Copyright by MOHAMMAD AMIN KHAMEHCHI, 2017
All Rights Reserved
©Copyright by MOHAMMAD AMIN KHAMEHCHI, 2017
All Rights Reserved
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To the Faculty of Washington State University:
The members of the Committee appointed to examine the dissertation of MOHAMMAD
AMIN KHAMEHCHI find it satisfactory and recommend that it be accepted.
————————————————————
Peter Engels, Ph.D., Chair
————————————————————
Doerte Blume, Ph.D.
————————————————————
Mark Kuzyk, Ph.D.
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ACKNOWLEDGEMENTS
I would like to thank my adviser, Prof. Peter Engels for helping me succeeding in my Ph.D.
Peter has patiently helped me understand many scientific concepts as well as practicing many
different lab skills varying from mechanics and electronics to optics. His step by step approach to
solving complex problems has been my major takeaway from Peter’s lab. This has been a unique
opportunity for me and what I have learned will continue enlightening my life. I would also like to
thank Chris Hamner, who worked as a post-doc in our lab when I joined the group, for answering
my questions tirelessly despite the long hours of work in the lab.
This work would not have been possible without the help, support, and the hard work of our
theorist collaborators: Michael Forbes, Khalid Hossain, Chunlei Qu, Chuanwei Zhang, Yongping
Zhang, Thomas Busch, Panos Kevrekidis, and Kuei Sun. I would also like to thank Doerte Blume
for accepting to be on my committee, her support, and fruitful discussions. She made our journal
club meetings much more educational with her discussions and asking the right questions to help
us understand difficult subjects. I would also like to thank Mark Kuzyk for his support throughout
my Ph.D. and for being on my committee.
I would like to thank our administrative staff at the physics department for their support and
making lengthy administrative processes short especially Robin Stratton, Mary Guenther, and
Laura Krueger. I would like to extend my gratitude to Sabreen Dadson and Kris Boreen for being
there for us as international graduate students and making us feel like home.
I would like to express my appreciation to my colleagues in the lab Vandna Gokhroo, Maren
Mossman, Chunde Huang, and Thomas Bersano for their encouragement and friendship. I am
thankful to my friends at WSU and home.
I, hereby, convey my heartfelt thanks to my mom and dad for their unconditional support
throughout many years of my education. This would not have been possible without their sacrifice
and kindness. Vast physical boundaries between us do not make me forget about what they have
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done for me. I would like to thank my wife Yasmin for bringing happiness to my life, her constant
support, patience, and kindness.
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DISPERSION ENGINEERING OF BOSE-EINSTEIN CONDENSATES
Abstract
by Mohammad Amin Khamehchi, Ph.D.
Washington State University
May 2017
Chair: Peter Engels
The subject of this dissertation is engineering the dispersion relation for dilute Bose-Einstein con-
densates (BECs). When a BEC is immersed into suitably tailored laser fields its dispersion can be
strongly modified. Prominent examples for such laser fields include optical lattice geometries and
Raman dressing fields. The ability to engineer the dispersion of a BEC allows for the investigation
of a range of phenomena related to quantum hydrodynamics and condensed matter.
In the first context, this dissertation studies the excitation spectrum of a spin-orbit coupled
(SOC) BEC. The spin-orbit coupling is generated by “dressing” the atoms with two Raman laser
fields. The excitation spectrum has a Roton-like feature that can be altered by tuning the Raman
laser parameters. It is demonstrated that the Roton mode can be softened, but it does not reach
the ground state energy for the experimental conditions we had. Furthermore, the expansion
of SOC BECs in 1D is studied by relaxing the trap allowing the BEC to expand in the SOC
direction. Contrary to the findings for optical lattices, it is observed that the condensate partially
occupies quasimomentum states with negative effective mass, and therefore an abrupt deceleration
is observed although the mean field force is along the direction of expansion.
In condensed-matter systems, a periodic lattice structure often plays an important role. In this
context,analternativetotheRamandressingschemecanberealizedbycouplingthes-andp-bands
ofastaticopticallatticeviaaweakmovinglattice. Thebandscanbetreatedaspseudo-spinstates.
It is shown that similar to the dispersion relation of a Raman dressed SOC, the quasimomentum
of the ground state is different from zero. Coherent coupling of the SOC dispersion minima can
lead to the realization of the stripe phase even though it is not the thermodynamic ground state of
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the system. Along the lines of studying the hydrodynamics of BECs, three novel multicomponent
solitonic states are realized. It is shown that the solitons are structurally stable and the oscillation
of vector dark-anti-dark solitons is studied in a weak harmonic trap.
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TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
DEDICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .x.xviii
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 OVERVIEW OF THE BEC MACHINE . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 An introduction to BEC generation . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 BEC MACHINE COMPONENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Vacuum chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Control system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.3 Magneto-Optical Trap (MOT) . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.4 Track system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.5 Magnetic trap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Magnetic field configuration in the magnetic trap . . . . . . . . . . . . . . . . 15
2.2.6 Chiller system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.7 Laser setups. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1064 nm laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
viii
Ti-Sapphire laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1540 nm laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.8 Crossed dipole trap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.9 Imaging system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
PI (Princeton Instruments) camera imaging system . . . . . . . . . . . . . . . 26
PixelFly camera imaging system . . . . . . . . . . . . . . . . . . . . . . . . . 27
Imaging procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.10 Atom number calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Imaging magnification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Trapping frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Thomas-Fermi approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Imaging calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 DUAL MANIFOLD SPIN-ORBIT COUPLING FOR 87Rb . . . . . . . . . . . . . . 33
2.3.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4 BILAYER SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4.1 Alternative design for phaseplate . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.5 COMBINED LATTICES WITH THE SAME PERIODICITY . . . . . . . . . . . . . 40
2.6 TEMPERATURESTABILIZINGTHEDIPOLEBEAMINTENSITYCONTROLLER 42
2.7 DIRECT DIGITAL SYNTHESIZERS FOR LATTICES AND RAMAN DRESSING 44
2.8 DEVELOPMENT OF A SIMPLE MATLAB TOOL FOR SIMULATING ARBI-
TRARY BEAM DIFFRACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3 RAMAN DRESSING AND SPIN-ORBIT COUPLING OF BOSE-EINSTEIN
CONDENSTATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2 EXCITATIONSPECTRUMOFSPIN-ORBIT-COUPLEDBOSEEINSTEINCON-
DENSATES AND EMERGENCE OF ROTON-LIKE FEATURES . . . . . . . . . . 54
3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
ix
3.2.2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2.3 Experimental implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Bragg Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3 1D EXPANSION OF SPIN-ORBIT COUPLED BOSE-EINSTEIN CONDENSATE. 64
3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3.2 Methods and results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.3.3 Experimental considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Magnetic field gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Adiabatically loading the BEC into the SOC states . . . . . . . . . . . . . . . 74
Centering the laser beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Magic wavelength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Finding the Raman zero detuning . . . . . . . . . . . . . . . . . . . . . . . . 76
Expansion anomalies for lower detunings. . . . . . . . . . . . . . . . . . . . . 76
Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.3.4 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Single Band Model and Spin-Quasimomentum Map . . . . . . . . . . . . . . 83
Hydrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Self-Trapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Dynamical Instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.4 MAGNETIZATIONOFLATTICEDRIVENSPIN-ORBITCOUPLEDBOSE-EINSTEIN
CONDENSATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.4.2 Experimental implementation and results . . . . . . . . . . . . . . . . . . . . 94
3.4.3 Theoretical notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.5 OBSERVATION OF THE FESHBACH RESONANCE BETWEEN 1,+1 AND
| (cid:105)
2, 1 STATES OF 87Rb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
| − (cid:105)
3.6 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111