init commit
This commit is contained in:
commit
6407a78fab
GPG Key ID:
64BF53A3369104E7
1
.gitattributes
vendored
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1
.gitattributes
vendored
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* text=auto
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17
.gitignore
vendored
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17
.gitignore
vendored
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.idea
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dist
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*.aux
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*.fdb_latexmk
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||||
*.fls
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||||
*.tdo
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*.toc
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||||
*.log
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||||
*.pdf
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||||
*.bbl
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*.bcf
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*.blg
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||||
*.run.xml
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||||
*.out
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||||
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||||
*.nb
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||||
56
Makefile
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56
Makefile
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@ -0,0 +1,56 @@
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### Build tools
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#
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LATEXMK := latexmk -pdflatex="luahblatex %O %S" -pdf -dvi- -ps- -quiet -logfilewarninglist
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WS := wolframscript -f
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||||
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### Directory variables
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#
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PDF_DIR := pdfs
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FIG_DIR := figures
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||||
CALC_DIR := calc
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||||
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### Here we go
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#
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OUT_PDF:= $(PDF_DIR)/notes.pdf
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||||
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.PHONY: all
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||||
all: $(OUT_PDF)
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||||
|
||||
### How we do that
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#
|
||||
|
||||
## setup main pdf deps as variable that subdirs can add to
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||||
MAIN_PDF_DEPS := bibliography.bib
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||||
## Defining common directory recipes
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||||
$(PDF_DIR):
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mkdir $(PDF_DIR)
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$(FIG_DIR):
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mkdir -p $(FIG_DIR)
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$(CALC_DIR):
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mkdir -p $(CALC_DIR)
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## Figures
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#
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||||
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FIGURES :=
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## Making main.pdf and other pdfs
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#
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$(PDF_DIR)/notes.pdf: notes.tex $(MAIN_PDF_DEPS) | $(PDF_DIR) $(FIGURES)
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$(LATEXMK) $(<F)
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cp $(@F) $@
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||||
|
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### Convenience scripts for tidying tex
|
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.PHONY: declutter
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||||
declutter:
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||||
@rm -f *.tdo
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@rm -f *.run.xml
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@rm -f *.bbl
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.PHONY: tidy
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tidy: declutter
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@latexmk -c
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.PHONY: clean
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clean: declutter
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rm -rf $(PDF_DIR)
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@latexmk -C
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258
bibliography.bib
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258
bibliography.bib
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@ -0,0 +1,258 @@
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@article{Nam1967,
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doi = {10.1103/physrev.156.470},
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||||
url = {https://doi.org/10.1103/physrev.156.470},
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||||
year = {1967},
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||||
month = apr,
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publisher = {American Physical Society ({APS})},
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volume = {156},
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number = {2},
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pages = {470--486},
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author = {Sang Boo Nam},
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title = {Theory of Electromagnetic Properties of Superconducting and Normal Systems. {I}},
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journal = {Physical Review}
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}
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@book{SolyomV3,
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doi = {10.1007/978-3-642-04518-9},
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||||
url = {https://doi.org/10.1007/978-3-642-04518-9},
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||||
year = {2010},
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||||
publisher = {Springer Berlin Heidelberg},
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||||
author = {Jen{\H{o}} S{\'{o}}lyom},
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||||
title = {Fundamentals of the Physics of Solids},
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subtitle = {Normal, Broken-Symmetry, and Correlated Systems},
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volume = {3},
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}
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@article{Henkel1999,
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||||
doi = {10.1007/s003400050823},
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url = {https://doi.org/10.1007/s003400050823},
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||||
year = {1999},
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||||
month = dec,
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||||
publisher = {Springer Science and Business Media {LLC}},
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||||
volume = {69},
|
||||
number = {5-6},
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||||
pages = {379--387},
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||||
author = {C. Henkel and S. P\"{o}tting and M. Wilkens},
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||||
title = {Loss and heating of particles in small and noisy traps},
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||||
journal = {Applied Physics B}
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}
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@article{Henkel2006,
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doi = {10.1007/s00340-006-2219-9},
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||||
url = {https://doi.org/10.1007/s00340-006-2219-9},
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||||
year = {2006},
|
||||
month = apr,
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||||
publisher = {Springer Science and Business Media {LLC}},
|
||||
volume = {84},
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||||
number = {1-2},
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||||
pages = {61--68},
|
||||
author = {C. Henkel and K. Joulain},
|
||||
title = {Electromagnetic field correlations near a surface with a nonlocal optical response},
|
||||
journal = {Applied Physics B}
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||||
}
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@article{QubitRelax,
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||||
doi = {10.1103/physreva.86.010301},
|
||||
url = {https://doi.org/10.1103/physreva.86.010301},
|
||||
year = {2012},
|
||||
month = jul,
|
||||
publisher = {American Physical Society ({APS})},
|
||||
volume = {86},
|
||||
number = {1},
|
||||
author = {Luke S. Langsjoen and Amrit Poudel and Maxim G. Vavilov and Robert Joynt},
|
||||
title = {Qubit relaxation from evanescent-wave Johnson noise},
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||||
journal = {Physical Review A}
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}
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@incollection{Pippard,
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doi = {10.1016/s0065-2539(08)60130-4},
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||||
url = {https://doi.org/10.1016/s0065-2539(08)60130-4},
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||||
year = {1954},
|
||||
publisher = {Elsevier},
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||||
pages = {1--45},
|
||||
author = {A.B. Pippard},
|
||||
title = {Metallic Conduction at High Frequencies and Low Temperatures},
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||||
booktitle = {Advances in Electronics and Electron Physics Volume 6}
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||||
}
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||||
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||||
@article{Churchill2016,
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doi = {10.1103/physrevb.94.235422},
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url = {https://doi.org/10.1103/physrevb.94.235422},
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||||
year = {2016},
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month = dec,
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||||
publisher = {American Physical Society ({APS})},
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||||
volume = {94},
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||||
number = {23},
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||||
author = {R. J. Churchill and T. G. Philbin},
|
||||
title = {Electromagnetic reflection, transmission, and energy density at boundaries of nonlocal media},
|
||||
journal = {Physical Review B}
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||||
}
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||||
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||||
@book{AGD,
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||||
author = {Abrikosov, A A and Dzyaloshinskii, I and Gorkov, L P and Silverman, Richard A},
|
||||
title = {Methods of quantum field theory in statistical physics},
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||||
publisher = {Dover},
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||||
address = {New York, NY},
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||||
year = {1975},
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||||
}
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@article{Zimmermann1991,
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||||
doi = {10.1016/0921-4534(91)90771-p},
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||||
url = {https://doi.org/10.1016/0921-4534(91)90771-p},
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||||
year = {1991},
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||||
month = nov,
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||||
publisher = {Elsevier {BV}},
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||||
volume = {183},
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||||
number = {1-3},
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||||
pages = {99--104},
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||||
author = {W. Zimmermann and E.H. Brandt and M. Bauer and E. Seider and L. Genzel},
|
||||
title = {Optical conductivity of {BCS} superconductors with arbitrary purity},
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||||
journal = {Physica C: Superconductivity}
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||||
}
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||||
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||||
@article{Ford1984,
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||||
doi = {10.1016/0370-1573(84)90098-x},
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||||
url = {https://doi.org/10.1016/0370-1573(84)90098-x},
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||||
year = {1984},
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||||
month = nov,
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||||
publisher = {Elsevier {BV}},
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||||
volume = {113},
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||||
number = {4},
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||||
pages = {195--287},
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||||
author = {G.W. Ford and W.H. Weber},
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title = {Electromagnetic interactions of molecules with metal surfaces},
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journal = {Physics Reports}
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}
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@article{Agarwal1975,
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doi = {10.1103/physreva.11.230},
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||||
url = {https://doi.org/10.1103/physreva.11.230},
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year = {1975},
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month = jan,
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publisher = {American Physical Society ({APS})},
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volume = {11},
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||||
number = {1},
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||||
pages = {230--242},
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||||
author = {G. S. Agarwal},
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title = {Quantum electrodynamics in the presence of dielectrics and conductors. I. Electromagnetic-field response functions and black-body fluctuations in finite geometries},
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journal = {Physical Review A}
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}
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@article{Nam1967_Part2,
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doi = {10.1103/physrev.156.487},
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url = {https://doi.org/10.1103/physrev.156.487},
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year = {1967},
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month = apr,
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publisher = {American Physical Society ({APS})},
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volume = {156},
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number = {2},
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pages = {487--493},
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author = {Sang Boo Nam},
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title = {Theory of Electromagnetic Properties of Strong-Coupling and Impure Superconductors. {II}},
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journal = {Physical Review}
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}
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@article{Tenberg2019,
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doi = {10.1103/physrevb.99.205306},
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url = {https://doi.org/10.1103/physrevb.99.205306},
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||||
year = {2019},
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||||
month = may,
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publisher = {American Physical Society ({APS})},
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volume = {99},
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||||
number = {20},
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||||
author = {Stefanie B. Tenberg and Serwan Asaad and Mateusz T. M{\k{a}}dzik and Mark A. I. Johnson and Benjamin Joecker and Arne Laucht and Fay E. Hudson and Kohei M. Itoh and A. Malwin Jakob and Brett C. Johnson and David N. Jamieson and Jeffrey C. McCallum and Andrew S. Dzurak and Robert Joynt and Andrea Morello},
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||||
title = {Electron spin relaxation of single phosphorus donors in metal-oxide-semiconductor nanoscale devices},
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||||
journal = {Physical Review B}
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||||
}
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||||
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||||
@article{Kolkowitz2015,
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||||
doi = {10.1126/science.aaa4298},
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||||
url = {https://doi.org/10.1126/science.aaa4298},
|
||||
year = {2015},
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||||
month = jan,
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||||
publisher = {American Association for the Advancement of Science ({AAAS})},
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||||
volume = {347},
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||||
number = {6226},
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||||
pages = {1129--1132},
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||||
author = {S. Kolkowitz and A. Safira and A. A. High and R. C. Devlin and S. Choi and Q. P. Unterreithmeier and D. Patterson and A. S. Zibrov and V. E. Manucharyan and H. Park and M. D. Lukin},
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||||
title = {Probing Johnson noise and ballistic transport in normal metals with a single-spin qubit},
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||||
journal = {Science}
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||||
}
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||||
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@book{llv9,
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||||
place={Oxford},
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||||
title={Statistical Physics. Part 2},
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||||
volume={9},
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||||
publisher={Pergamon Press},
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||||
author={Lifshitz, Evgenii Mikhailovich. and Pitaevskii, Lev Petrovich.},
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||||
year={1980}
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||||
}
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||||
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||||
@book{Tinkham,
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||||
title={Introduction to Superconductivity},
|
||||
author={Michael Tinkham},
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||||
edition = 2,
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||||
isbn={9780486435039},
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||||
lccn={95022378},
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||||
series={Dover Books on Physics},
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||||
year={2004},
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||||
publisher={Dover Publications},
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||||
location={Mineola, N.Y.},
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||||
}
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@article{Mattis,
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||||
doi = {10.1103/physrev.111.412},
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url = {https://doi.org/10.1103/physrev.111.412},
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||||
year = {1958},
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||||
month = jul,
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publisher = {American Physical Society ({APS})},
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volume = {111},
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number = {2},
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||||
pages = {412--417},
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||||
author = {D. C. Mattis and J. Bardeen},
|
||||
title = {Theory of the Anomalous Skin Effect in Normal and Superconducting Metals},
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||||
journal = {Physical Review}
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||||
}
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||||
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||||
@book{FetterWalecka,
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||||
address = {Boston},
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||||
author = {Fetter, A. L. and Walecka, J. D.},
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||||
publisher = {McGraw-Hill},
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||||
title = {Quantum Theory of Many-Particle Systems},
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||||
year = 1971
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||||
}
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||||
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@article{Lindhard,
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title = {ON THE PROPERTIES OF A GAS OF CHARGED PARTICLES},
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||||
author = {Lindhard, J},
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||||
abstractNote = {},
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||||
doi = {},
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||||
journal = {Kgl. Danske Videnskab. Selskab Mat.-fys. Medd.},
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||||
number = 8,
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||||
volume = 28,
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||||
year = {1954},
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||||
month = {1}
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||||
}
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@book{LandauLifshitzElectrodynamics,
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||||
author = "Landau, Lev Davidovich and Lifshitz, Evgenii Mikhailovich and Pitaevskii, Lev Petrovich",
|
||||
title = "{Electrodynamics of continuous media; 2nd ed.}",
|
||||
publisher = "Butterworth",
|
||||
address = "Oxford",
|
||||
series = "Course of theoretical physics",
|
||||
year = "1984",
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||||
url = "https://cds.cern.ch/record/712712",
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||||
}
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@article{Lakhmanskiy2019,
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||||
doi = {10.1103/physreva.99.023405},
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||||
url = {https://doi.org/10.1103/physreva.99.023405},
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||||
year = {2019},
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||||
month = feb,
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publisher = {American Physical Society ({APS})},
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volume = {99},
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||||
number = {2},
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author = {K. Lakhmanskiy and P. C. Holz and D. Sch\"{a}rtl and B. Ames and R. Assouly and T. Monz and Y. Colombe and R. Blatt},
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||||
title = {Observation of superconductivity and surface noise using a single trapped ion as a field probe},
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||||
journal = {Physical Review A}
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||||
}
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18
do.sh
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18
do.sh
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#!/usr/bin/env sh
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||||
# Do - The Simplest Build Tool on Earth.
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||||
# Documentation and examples see https://github.com/8gears/do
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||||
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||||
set -Eeuo pipefail # -e "Automatic exit from bash shell script on error" -u "Treat unset variables and parameters as errors"
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build() {
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echo "I am ${FUNCNAME[0]}ing"
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make pdfs/notes.pdf
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}
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all() {
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build
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}
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"$@" # <- execute the task
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[ "$#" -gt 0 ] || printf "Usage:\n\t./do.sh %s\n" "($(compgen -A function | grep '^[^_]' | paste -sd '|' -))"
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59
notes.tex
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59
notes.tex
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\documentclass{article}
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%other packages
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||||
\usepackage{amsmath}
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\usepackage{amssymb}
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\usepackage{physics}
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\usepackage[
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||||
style=phys, articletitle=false, biblabel=brackets, chaptertitle=false, pageranges=false, url=true
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]{biblatex}
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||||
\usepackage{graphicx}
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||||
\usepackage{todonotes}
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||||
\usepackage{siunitx}
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||||
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||||
\usepackage{cleveref}
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||||
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||||
\title{Lakhmanskiy paper and SC EWJN}
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\addbibresource{./bibliography.bib}
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||||
\graphicspath{{./figures/}}
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||||
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||||
\newcommand{\vf}{v_{\mathrm{F}}}
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||||
\newcommand{\qf}{q_{\mathrm{F}}}
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||||
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||||
\begin{document}
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||||
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||||
\maketitle
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||||
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Let's look at the Lakhmanskiy et. al paper\cite{Lakhmanskiy2019}.
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||||
We care about the following parameters for the calculation, two of which are easy enough to pull from the paper:
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||||
\begin{gather}
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||||
\omega \sim 2 \pi \times \SI{1}{\mega\Hz} \\
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||||
\vf \\
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||||
\omega_p \\
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||||
\tau \\
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||||
d \\
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||||
T_c \sim \SI{85}{\kelvin} \sim \SI{e13}{\Hz}
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\end{gather}
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||||
For the dipole moment we're looking at, I \emph{think} it works to approximate the calcium ion as a dipole of charge $e$ and radius on the order of $\SI{0.1}{\nm}$.
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As it will turn out we don't need to worry too much about a few orders of magnitude.
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||||
For the Fermi velocity and plasma frequency of the YBCO they used, a few quick searches suggested rough average values around $\vf \sim \SI{2.5e5}{\m\per\s}$ and $\omega_p \sim \SI{2e16}{\Hz}$.
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These seem like reasonable enough values.
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Lastly it's hard to estimate the purity of their sample, but a collision time of around $\tau \sim \SI{2e-14}{\s}$ seemed to be a reasonable value for clean YBCO samples.
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The big issue here is clearly that the frequency is incredibly small compared to $T_c$, so we should really not expect that SC EWJN is an issue anywhere except right at the superconducting transition.
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||||
To make matters slightly harder, the distance between the ion and the trap electrodes (which would be the closest electrodes to the ion, and thus the dominant source of EWJN) is massive, at $\SI{225}{\micro\m}$, which means that EWJN from the trap electrodes will drop off very quickly, (and I think faster than any of the other noise results they are looking at from the meander resistors etc., need to double check that specific fact).
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The code actually has an issue with $\omega$ so small, as it has trouble doing some of the integrals.
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Increasing $\omega$ by a factor of $10^3$ to be on the order of gigahertz, at the distance of $z = \SI{225}{\micro\m}$, we get $T_1 \approx \SI{e5}{\s}$, which is massive.
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If I'm understanding how the phonon per second rate works, each phonon measured would correspond to one qubit transition, so the $\Gamma$ measured in Lakhmanskiy should correspond to $\flatfrac{1}{T_1}$, so we're looking at rates around $\SI{e-5}{\per\s}$ for $T = 0.99 T_c$.
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This is tiny compared to their noise, on the order of $\SI{1}{\per\s}$.
|
||||
|
||||
\printbibliography
|
||||
|
||||
\end{document}
|
||||
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