From f64f95d0fda22c30f1025c0ae67f5ec5458d22db Mon Sep 17 00:00:00 2001 From: Wojciech Kozlowski Date: Thu, 9 Jun 2016 17:29:43 +0100 Subject: [PATCH] Started writing --- .gitignore | 1 + Chapter2/chapter2.tex | 50 ++++++++++++++++++++++++++++++++++++++ References/references.bib | 38 +++++++++++++++++++++++++++++ thesis.pdf | Bin 368106 -> 0 bytes thesis.tex | 6 ++--- 5 files changed, 92 insertions(+), 3 deletions(-) create mode 100644 Chapter2/chapter2.tex delete mode 100644 thesis.pdf diff --git a/.gitignore b/.gitignore index 8514c63..3af37ca 100644 --- a/.gitignore +++ b/.gitignore @@ -36,3 +36,4 @@ thesis.run.xml* *run.xml* *.latexmkrc* *_latexmk* +*.pdf* \ No newline at end of file diff --git a/Chapter2/chapter2.tex b/Chapter2/chapter2.tex new file mode 100644 index 0000000..e5b45a4 --- /dev/null +++ b/Chapter2/chapter2.tex @@ -0,0 +1,50 @@ +%******************************************************************************* +%*********************************** Second Chapter **************************** +%******************************************************************************* + +%Title of the Second Chapter +\chapter{Quantum Optics of Quantum Gases} + +\ifpdf + \graphicspath{{Chapter2/Figs/Raster/}{Chapter2/Figs/PDF/}{Chapter2/Figs/}} +\else + \graphicspath{{Chapter2/Figs/Vector/}{Chapter2/Figs/}} +\fi + + +%********************************** % First Section **************************** + +\section{Ultracold Atoms in Optical Lattices} + +%********************************** % Second Section *************************** + +\section{Quantum Optics of Quantum Gases} + +Having introduced and described the behaviour of ultracold bosons +trapped and manipulated using classical light, it is time to extend +the discussion to quantized optical fields. We will first derive a +general Hamiltonian that describes the coupling of atoms with +far-detuned optical beams \cite{mekhov2012}. This will serve as the +basis from which we explore the system in different parameter regimes, +such as nondestructive measurement in free space or quantum +measurement backaction in a cavity. + +We consider $N$ two-level atoms in an optical lattice with $M$ +sites. For simplicity we will restrict our attention to spinless +bosons, although it is straightforward to generalise to fermions, +which yields its own set of interesting quantum phenomena +\cite{atoms2015, mazzucchi2016, mazzucchi2016af}, and other spin +particles. The theory can be also be generalised to continuous +systems, but the restriction to optical lattices is convenient for a +variety of reasons. Firstly, it allows us to precisely describe a +many-body atomic state over a broad range of parameter values due to +the inherent tunability of such lattices. Furthermore, this model is +capable of describing a range of different experimental setups ranging +from a small number of sites with a large filling factor (e.g.~BECs +trapped in a double-well potential) to a an extended multi-site +lattice with a low filling factor (e.g.~a system with one atom per +site will exhibit the Mott insulator to superfluid quantum phase +transition). \mynote{extra fermion citations, Piazza?} + + + diff --git a/References/references.bib b/References/references.bib index e69de29..5cee380 100644 --- a/References/references.bib +++ b/References/references.bib @@ -0,0 +1,38 @@ +@article{mekhov2012, + title={Quantum optics with ultracold quantum gases: towards the full quantum regime of the light--matter interaction}, + author={Mekhov, Igor B and Ritsch, Helmut}, + journal={Journal of Physics B: Atomic, Molecular and Optical Physics}, + volume={45}, + number={10}, + pages={102001}, + year={2012}, + publisher={IOP Publishing} +} +@article{mazzucchi2016, + title = {Quantum measurement-induced dynamics of many-body ultracold bosonic and fermionic systems in optical lattices}, + author = {Mazzucchi, Gabriel and Kozlowski, Wojciech and Caballero-Benitez, Santiago F. and Elliott, Thomas J. and Mekhov, Igor B.}, + journal = {Physical Review A}, + volume = {93}, + issue = {2}, + pages = {023632}, + numpages = {12}, + year = {2016}, + month = {Feb}, + publisher = {American Physical Society} +} +@article{atoms2015, + title={Probing and Manipulating Fermionic and Bosonic Quantum Gases with Quantum Light}, + author={Elliott, Thomas J and Mazzucchi, Gabriel and Kozlowski, Wojciech and Caballero-Benitez, Santiago F and Mekhov, Igor B}, + journal={Atoms}, + volume={3}, + number={3}, + pages={392--406}, + year={2015}, + publisher={Multidisciplinary Digital Publishing Institute} +} +@article{mazzucchi2016af, + title={Quantum measurement-induced antiferromagnetic order and density modulations in ultracold Fermi gases in optical lattices}, + author={Mazzucchi, Gabriel and Caballero-Benitez, Santiago F and Mekhov, Igor B}, + journal={arXiv preprint arXiv:1510.04883}, + year={2015} +} \ No newline at end of file diff --git a/thesis.pdf b/thesis.pdf deleted file mode 100644 index e164511f1d5b5792fae022f8176c78ae5430ed76..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 368106 zcmeEP349IL7oOTB)ZW+=g3zcSh^>OycS5P9mWX}dmx{GT|7vN`s=bt|Ql<8Nui9%V zMJ=VO1gWM3;eWq(-%aLCX6DVzn|V)~>-UR0bLTGSo^!tMo_lBBOwnew>bzB^RC%wW zr_LU{;8nJgUunPoU3&Rdt?CujD6(JoAwB%cmoMu_|9J(~>DgyU-1!&Z?-vf}^VyfFay3xBtrc+l-48!6w%|z4 zT=`}Pe=_)kAx-M9DF5d9Ka0IL^wyz(&l~3bz4YbanmJ0&YZ3ER?_X|JD>-=X`)~c0 zuHK$mpJbU?_4t$J?hMyIh)sJ9(twNwARBT z??z92ck|!6{1@*$3s-+jC4uO)Xo?CX4M>A;Ms!=C#7`}KjW z6K79p`SHjj8Na&tXX_IybANlR@5Q)w&ug`S@}?eWevbso(u(z5#PakCfX9e(B4 z@%zW@>)L1AZ%^YR#%0+ZvbJ4lVD*T?OJ+Q*`A`0nUv3&Bw7s+|WMNR2Z1aXc-QK^- z-T3_3zV<1$tHPO9!Rsy!JM{ckg=*8=2X#2@*X!p)-CDQ5)%}Nw{+q^^yK??n_o<`) 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unsorted references %\bibliographystyle{plainnat} % use this to have URLs listed in References \cleardoublepage \bibliography{References/references} % Path to your References.bib file