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3
papers/Report/flake.nix
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@ -15,7 +15,8 @@
pgfplots microtype fancyvrb csquotes setspace newunicodechar hyperref
cleveref multirow bbold unicode-math biblatex-phys xpatch beamerposter
type1cm changepage lualatex-math footmisc wrapfig2 curve2e pict2e wrapfig
appendixnumberbeamer sidecap appendix orcidlink ncctools bigfoot crop xcolor;
appendixnumberbeamer sidecap appendix orcidlink ncctools bigfoot crop xcolor
acro translations;
};
in
rec {

5
papers/Report/hiromacros.sty
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@ -122,6 +122,11 @@
\newcommand{\qrelent}[2]{\ensuremath{S\qty(#1\,\middle|\middle|\,#2)}}
\newcommand{\cyc}{\ensuremath{\mathrm{cyc}}}
% time evolution operator
\newcommand{\tevop}[2][t]{\ensuremath{\mathcal{U}_{#1}\bqty{#2}}}
% effective hamiltonian
\newcommand{\heff}[2][t]{\ensuremath{H_{\eff}\bqty{#2}(#1)}}
\makeatletter
\newsavebox\myboxA
\newsavebox\myboxB

2
papers/Report/hirostyle.sty
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@ -48,6 +48,8 @@ linkcolor=blue,
\usepackage{wrapfig2}
\usepackage{xpatch}
\usepackage{acro}
\usepackage{lualatex-math}
\usepackage{manyfoot}
\usepackage[bottom]{footmisc}

279
papers/Report/index.tex
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@ -5,9 +5,18 @@ headinclude=true,footinclude=false,BCOR=0mm]{scrartcl}
\pdfvariable suppressoptionalinfo 512\relax
\synctex=1
\usepackage{hirostyle}
\usepackage{hiromacros}
\addbibresource{references.bib}
\acsetup{
make-links = true ,
format = \emph ,
list / display = all ,
pages / display = all
}
\DeclareAcronym{mlong}{short=LTAD, long=long-time time-averaged mean displacement}
\DeclareAcronym{rwa}{short=RWA, long=Rotating-Wave Approximation}
\title{Report on the Reservoir Engineering Efforts}
\date{2023}
@ -146,7 +155,8 @@ we should recover \(\dot{b}_{m}=0\), which implies
\begin{equation}
\label{eq:8}
ω_{m}^{2}=\pqty{\frac{mc}{Rn_{0}}}^{2} \implies ω_{m} = \pm
\abs{\frac{mc}{Rn_{0}}},
\abs{\frac{mc}{Rn_{0}}}= \pm
\abs{m Ω},
\end{equation}
which defines the \(ω_{m}\) in this case. However, to correctly
determine the \(ω_{m}\), a slightly more delicate argument has to be
@ -263,6 +273,8 @@ makes \(κ_{lm}\) hermitian and reproduces the result of
\frac{n_{1}(t)}{n_{0}}\sinc\pqty{(m-l)\frac{ϕ_{W}}{2}}\sgn(l).
\end{aligned}
\end{equation}
However, this normalization does not yield the correct creation and
annihilation operators.
As we are interested in the case where \(m,l\gg 1\) and
\(m=M+δm\), \(l=M+δl\) with \(δm,δl\ll M\), the pre-factor of \(κ_{lm}\)
@ -364,14 +376,14 @@ The goal is now to choose the geometry and the modulation so that
the time evolution operator
\begin{equation}
\label{eq:23}
\mathcal{U}_{t}[H] = \mathcal{T}\,\exp(-\iu ∫_{0}^{t}H(t))
\tevop{H} = \mathcal{T}\,\exp(-\iu ∫_{0}^{t}H(t))
\end{equation}
for the Hamiltonian \(H\) of \cref{eq:20} matches the time evolution
operator for some reference Hamiltonian \(H_{\target}\)
\begin{equation}
\label{eq:24}
\norm{\mathcal{U}_{t}[U H U^\dag]-\mathcal{U}_{t}[H_{\target}]} < ε
\iff \norm{\bqty{U_{t}[U H U^†]-U_{t}[H_{\target}]}\ket{ψ}} \leq ε.
\norm{\tevop{U H U^\dag}-\tevop{H_{\target}}} < ε
\iff \norm{\qty{\tevop{U H U^†}-\tevop{H_{\target}}}\ket{ψ}} \leq ε.
\end{equation}
for \(0\leq t\leq T\), where \(\norm{\cdot}\) on the left side is the
operator norm restricted \(\hilb_{\mathrm{phys}}\), \(U\) is some
@ -382,7 +394,7 @@ equivalence with the same unitary for all times. As
perfect equivalence using a time dependent unitary
\begin{equation}
\label{eq:25}
U(t)=\mathcal{U}_{t}[H_{\target}] \mathcal{U}_{t}[H_{\target}]^†.
U(t)=\tevop{H_{\target}}\tevop{H_{\target}}^†.
\end{equation}
As transformations into rotating frames are necessary we have to
@ -409,13 +421,13 @@ defeat the point.
It is useful to express the above in terms of an effective Hamiltonian
\begin{equation}
\label{eq:26}
H_{\eff}[H](t)\equiv \frac{1}{-\iu t} \log[\mathcal{U}_{t}[H]].
\heff{H}\equiv \frac{1}{-\iu t} \log[\tevop{H}].
\end{equation}
This Hamiltonian, similar to the Floquet Hamiltonian, has a spectrum
limited by the branch cut of the complex logarithm, which however has
no influence on the dynamics it generates. By continuity of the
operator exponential the closeness
\(\norm{H_{\eff}[H](t) -H_{\eff}[H_{\target}](t)} \leq ε/t\) of the
\(\norm{\heff{H} -\heff{H_{\target}}} \leq ε/t\) of the
effective Hamiltonians implies the condition \cref{eq:24}. This
representation lends itself particularly well to visualizations and
numerical studies.
@ -442,16 +454,267 @@ There we employ periodic boundary conditions to simplify the
calculations, so that \(\ket{m+N} = \ket{m}\) and
\(t_{m,n}=\min_{l\in \ZZ}{\abs{m-n + l N}}\). Here, we choose
\(N=2M +1\) for some \(M\in\NN\) and \(m_{0}\) so, that the relevant
subspace \(\hilb_{phys}\) is contained in it so that states within
subspace \(\hilb_{\mathrm{phys}}\) is contained in it so that states within
this subspace don't ``see'' the boundary at the relevant time scales.
After transforming into a rotating frame with respect to the uncoupled
modes of the ring, we obtain from \cref{eq:9} in the language of
\cref{sec:notat-prel}
\begin{equation}
\label{eq:28}
\begin{aligned}
H(t) &= \tilde{V}(t) & \pqty{\tilde{V}(t)}_{mn} =
Δ_{{m_{0}+m},{m_{0}+n}} \,f(t) \eu^{-i(ω_{m_{0}+n}-ω_{m_{0}+m})t}.
\end{aligned}
\end{equation}
Neglecting dispersion and other constraints on the number of
equidistant modes physically present in the fiber loop, we can assume
that \cref{eq:28} represents our system, restricted to
\(\hilb_{\mathrm{phys}}\) faithfully. We can then continue to note
that \(ω_{m} = m Ω\) where \(Ω={{c}/{Rn_{0}}}\) is the free spectral
range of the fiber loop. Further, as \(H_{mn}(t) = H_{m-n}(t)\) for
\(m,n\) unrestricted\footnote{This is a choice of boundary condition
as explained in \cref{sec:notat-prel}. We assume that the states of
interest never venture outside of \(\hilb_{\mathrm{phys}}\).}
implies that the Hamiltonian can be diagonalized by Fourier states
\begin{equation}
\label{eq:30}
\ket{k} = \frac{1}{\sqrt{2π}}∑_{m} \eu^{\iu km}\ket{m},
\end{equation}
where \(k\in [-π,π]\).
This Eigenbasis is independent in time making the Hamiltonian commute
with itself at unequal times \(\comm{H(t)}{H(s)} = 0\, \forall t,s\),
leading to a particularly simple form of the time evolution operator
\begin{equation}
\label{eq:31}
\pqty{\tevop{H}}_{m,n} = \exp(-\iu Δ_{{m_{0}+m},{m_{0}+n}} ∫_{0}^{t}
\,f(t) \eu^{-i(m-n)Ω t}\dd{t}).
\end{equation}
Assuming that \(f(t) = f(t+2π/Ω) = f(t+T)\) the corresponding Floquet
Hamiltonian is
\begin{equation}
\label{eq:29}
H_{F,mn} = \bqty{\heff[T]{H}}_{mn} = \frac{1}{T} Δ_{{m_{0}+m},{m_{0}+n}} ∫_{0}^{T}
\,f(t) \eu^{-i(m-n)Ω t}\dd{t} = Δ_{{m_{0}+m},{m_{0}+n}} c_{m-n},
\end{equation}
where \(c_{m-n}\) is the \((m-n)\)th (complex) Fourier coefficient of
the drive
\begin{equation}
\label{eq:33}
f(t) = ∑_{l\in \ZZ}\eu^{\iu l Ω t} c_{l}.
\end{equation}
This is a feature that may have been overlooked in
\cite{Dutt2019}, as they only give a Floquet Hamiltonian in the \ac{rwa}.
The Floquet theorem implies that \cref{eq:24} is valid once a period.
To quantify the deviations from the Floquet dynamics \(\eu^{-\iu H_{F}
t}\) within each period \(T\), we consider the ``Kick Operator'' \cite{Viebahn}
\begin{equation}
\label{eq:32}
\eu^{-i K(t)} = \tevop{H}\eu^{\iu H_{F} t},
\end{equation}
so that \(\ket{ψ(t)} = \eu^{-i K(t)}\eu^{-\iu H_{F} t}\ket{ψ(0)}\)
with the property \(K(t+T)=K(t)\) and \(K(0)=K(nT)=0\).
In the present we have
\begin{equation}
\label{eq:34}
K_{mn}
\end{equation}
If we additionally demand that \(Ω\gg Δ_{m,n}f(t)\) we find that
the kick operator
\section{Measuring the State Amplitudes}
\label{sec:meas-state-ampl}
TBD
\section{The non-Markovian Quantum Walk for Finite Baths}
\label{sec:non-mark-quant}
We will discuss how the behavior of the model introduced in
\refcite{Ricottone2020} for the limit of weak coupling and an infinite
bath may be reproduced with both finite coupling strength and a finite
number of bath levels.
The model Hamiltonian is that of an SSH-Chain~\cite{Su1979} with a
number of bath states coupled to each unit cell \(H=H_{A}+H_{\bar{A}}+V\)
\begin{align}
\label{eq:36}
H_{A} &= ∑_{m}ω_{A} \ketbra{A,m} \\
H_{\bar{A}} &= Σ_{m}(ω_{A} + ω)\ketbra{B,m}+
∑_{j}\bqty{ω_{j}\ketbra{j, k} + g_{j}
\pqty{\ketbra{j,m}{B,m} + \hc}}\\
V&=∑_{m} v\pqty{\ketbra{A,m}{B,m} + u\ketbra{A,m}{B,m+1} + \hc}
\end{align}
In momentum space, the model Hamiltonian takes the form \(H=H_{A}(k) +
H_{\bar{A}}(k) + V(k)\) with
\begin{align}
\label{eq:35}
H_{A}(k) &= ω_{A} \ketbra{A,k} \\
H_{\bar{A}}(k) &= (ω_{A} + ω)\ketbra{B,k}+
∑_{j}\bqty{ω_{j}\ketbra{j, k} + g_{j}
\pqty{\ketbra{j,k}{B,k} + \hc}}\\
V(k)&=\abs{v(k)}\pqty{\eu^{\iu ϕ(k)}\ketbra{A,k}{B,k} + \hc}
\end{align}
with \(v(k) = \abs{v (1+u\eu^{\iu k})}\).
Upon eliminating the \(B\) site from the above through a
Schrieffer-Wolff transformation for \(ω\gg v(k)\), we end up with
\begin{equation}
\label{eq:37}
H(k) = \tilde{ω}_{A} \ketbra{j,k} + ∑_{j} \bqty{\tilde{ω}_{j} \ketbra{j, k}
+ \pqty{\tilde{η}_{j}\ketbra{A,k}{j,k} + \hc}},
\end{equation}
where the \(\tilde{η}_{j}(k) \sim \tilde{η}_{j}(0) v(k)\). The tildas
signify quantities renormalized due to the Schrieffer-Wolff transform
and will be dropped in the following.
The \emph{mean displacement} is defined as
\begin{equation}
\label{eq:38}
\ev{m(t)} \equiv ∑_{m}m \pqty{1-ρ_{A,m}} = ∑_{m}m \pqty{1-\abs{\braket{A,m}{ψ(t)}}^{2}}
\end{equation}
where we consider the initial condition \(\ket{ψ(0)}=\ket{A,0}\) and
define \(ρ_{A}(t)=\abs{\braket{A,m}{ψ(t)}}^{2}\) for convenience.
As the quantity \(\ev{m(t)}\) can fluctuate in time and we will be
interested in long-time beahavior, we additionally define
\begin{equation}
\label{eq:39}
\ev{m} \equiv \lim_{T\to ∞} \frac{1}{T}∫_{0}^{T}\ev{m(t)} \dd{t}
\end{equation}
which we will refer to as \ac{mlong}.
In momentum space this becomes
\begin{equation}
\label{eq:40}
\ev{m} = ∫_{0}^{2π}(1-ρ_{A})\pdv{ϕ(k)}{k} \frac{\dd{k}}{2π}
\end{equation}
with
\begin{equation}
\label{eq:41}
ρ_{A}(k) = \lim_{T\to ∞}\frac{1}{T} ∫_{0}^{T}ρ_{A}(t, k)\dd{t} = \lim_{T\to
∞}\frac{1}{T} ∫_{0}^{T}\abs{\braket{A,k}{ψ(t)}}^{2}\dd{t}.
\end{equation}
\subsection{Born Approximation}
\label{sec:born-approximation}
In the limit of very weak coupling we can solve for \(ρ_{A}\) in terms
of a non-Markovian master equation by employing perturbation theory to
second order\footnote{Which is the first nontrivial order} in the
coupling \(V\).
\begin{equation}
\label{eq:42}
\dot{ρ}_{A}(k,t) = ∫_{0}^{t}Σ(k, t-t\prime) ρ_{A}(k, t\prime)
\end{equation}
with the self-energy
\begin{equation}
\label{eq:43}
Σ(k,t)=-2 ∑_{j}\abs{η_{j}(k)}^{2}\cos(ω_{k}t)
\end{equation}
with \(j=\overline{1,N}\).
We are interested in the long time average of \(ρ\) which can be
expressed as
\begin{equation}
\label{eq:44}
{ρ}_{A}(k)=\lim_{T\to
∞}\frac{1}{T}∫_{0}^{∞}\eu^{-\frac{t}{T}}ρ_{A}(k,t)\dd{t} =
\lim_{s\to 0} s \tilde{ρ}_{A}(k, s) = \eval{\bqty{\dv{s} \frac{1}{\tilde{ρ}_{A}(k,s)}}^{-1}}_{s=0}
\end{equation}
where \(\tilde{ρ}_{A}({k, s})\) is the Laplace transform of \(ρ_{A}(k,
t)\).
The equation of motion \cref{eq:42} gives direct access to
\(\tilde{ρ}_{A}\)
\begin{equation}
\label{eq:45}
\tilde{ρ}_{A}({k, s}) = \frac{ρ_{A}(k,0)}{s - \tilde{Σ}(k, s)} = \frac{1}{s - \tilde{Σ}(k, s)},
\end{equation}
with
\begin{equation}
\label{eq:46}
\tilde{Σ}(k, s) = -2 ∑_{j}\abs{η_{j}}^{2} \frac{s}{s^{2}+ω_{j}^{2}} =
-∑_{j}\abs{η_{j}}^{2} \bqty{\frac{1}{s+\iu ω_{j}} + \frac{1}{s-\iu
ω_{j}}}.
\end{equation}
Using \cref{eq:44}, this yields
\begin{equation}
\label{eq:47}
ρ_{A}(k) = \frac{1}{1 + 2∑_{j}\frac{\abs{η_{j}}^{2}}{ω_{j}^{2}}} =
\frac{1}{1+2 U_{A}}.
\end{equation}
We now assume that the \(η_{j}\) are chosen so that in the continuum
limit \(N\to ∞\)
\begin{equation}
\label{eq:48}
∫_{0}^{∞}f(ω)∑_{j}\abs{η_{j}}^{2} δ(ω-ω_{j})^{2}\dd{ω} =
∫_{0}^{∞}J(ω) f(ω)
\end{equation}
for arbitrary (smooth) functions \(f\), where \(J\) is called the
spectral density. We make the model assumption
of an ohmic-type spectral density
\begin{equation}
\label{eq:49}
J(ω) =g_{0}^{2}\frac{α+1}{ω_{c}^{α+1}}
\begin{dcases}
ω^{α} & \mathrm{if}\, ω \leq ω_{c},\\
0 & \mathrm{otherwise}.
\end{dcases}
\end{equation}
For \(α<(>)1\) this we call \(J\) a sub(super)-Ohmic spectral density,
whereas for \(α=1\) we have an Ohmic spectral density.
The \(ω_{j}\) and \(η_{j}\) may be chosen according to
\cref{sec:discretization-bath}.
In the continuum limit \(U_{A}\to ∞\) for \(α<=1\) and remains finite
for \(α>1\), which leads to the \ac{mlong} \(\ev{m}\) having a sharp
transition from \(0\) to \(1\) for \(α\leq 1\) which becomes washed
out for \(α>1\).
We wish to study how this limit is approached with a finite bath and
in finite times. The born approximation requires that \(η\to 0\)
sufficiently fast for \(N\to ∞\) so that the resulting long timescale is
unlikely to be resolved experimentally.
\section{Exact Solution}
\label{sec:exact-solution}
Numerics at finite coupling strengths suggest, that
\newpage
\subsection{Discretization of the Bath}
\label{sec:discretization-bath}
TBD
\section{Ideas for Future Work}
\label{sec:ideas-future-work}
\begin{itemize}
\item Using the Floquet picture to justify the RWA more
rigorously. (Magnus Expansion etc.)
\end{itemize}
\printbibliography{}
\printacronyms{}
\end{document}

489
papers/Report/references.bib
View file

@ -63,6 +63,7 @@
urldate = {2023-01-27},
abstract = {This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological band insulators in one and two dimensions. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. We use noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the model is introduced first and then its properties are discussed and subsequently generalized. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.},
keywords = {Condensed Matter - Mesoscale and Nanoscale Physics,Condensed Matter - Other Condensed Matter},
annotation = {offset: 8},
note = {Comment: Submitted to Lect. Notes Phys},
file = {/home/hiro/Zotero/storage/JJ38FC7U/Asbóth et al. - 2016 - A Short Course on Topological Insulators Band-str.pdf;/home/hiro/Zotero/storage/W9DCLXEH/978-3-319-25607-8.pdf;/home/hiro/Zotero/storage/7TBW55ZY/1509.html}
}
@ -85,9 +86,9 @@
title = {Programmable Photonic System for Quantum Simulation in Arbitrary Topologies},
author = {Bartlett, Ben and Long, Olivia Y. and Dutt, Avik and Fan, Shanhui},
date = {2022-11-17},
number = {arXiv:2211.09805},
eprint = {arXiv:2211.09805},
eprint = {2211.09805},
eprinttype = {arxiv},
eprintclass = {physics, physics:quant-ph},
doi = {10.48550/arXiv.2211.09805},
url = {http://arxiv.org/abs/2211.09805},
urldate = {2023-03-09},
@ -154,6 +155,20 @@
file = {/home/hiro/Zotero/storage/ULPSNGEL/Bera et al. - 2021 - Quantum Heat Engines with Carnot Efficiency at Max.pdf}
}
@book{Bernevig2013,
title = {Topological {{Insulators}} and {{Topological Superconductors}}},
author = {Bernevig, B. Andrei and Hughes, Taylor L.},
date = {2013-04-07},
publisher = {{Princeton University Press}},
doi = {10.1515/9781400846733},
url = {https://www.degruyter.com/document/doi/10.1515/9781400846733/html},
urldate = {2023-04-12},
isbn = {978-1-4008-4673-3},
langid = {english},
annotation = {offset: 13},
file = {/home/hiro/Zotero/storage/64Y4VM2J/Bernevig and Hughes - 2013 - Topological Insulators and Topological Superconduc.pdf}
}
@article{Bilitewski2015,
title = {Scattering Theory for {{Floquet-Bloch}} States},
author = {Bilitewski, Thomas and Cooper, Nigel R.},
@ -224,6 +239,24 @@
file = {/home/hiro/Zotero/storage/42FYDQJP/Boisvert - ENGINEERING A SSH MODEL WITH RESERVOIR.pdf}
}
@article{Boyers2020,
title = {Exploring {{2D Synthetic Quantum Hall Physics}} with a {{Quasiperiodically Driven Qubit}}},
author = {Boyers, Eric and Crowley, Philip J. D. and Chandran, Anushya and Sushkov, Alexander O.},
date = {2020-10-16},
journaltitle = {Physical Review Letters},
shortjournal = {Phys. Rev. Lett.},
volume = {125},
number = {16},
pages = {160505},
publisher = {{American Physical Society}},
doi = {10.1103/PhysRevLett.125.160505},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.125.160505},
urldate = {2023-03-14},
abstract = {Quasiperiodically driven quantum systems are predicted to exhibit quantized topological properties, in analogy with the quantized transport properties of topological insulators. We use a single nitrogen-vacancy center in diamond to experimentally study a synthetic quantum Hall effect with a two-tone drive. We measure the evolution of trajectories of two quantum states, initially prepared at nearby points in synthetic phase space. We detect the synthetic Hall effect through the predicted overlap oscillations at a quantized fundamental frequency proportional to the Chern number, which characterizes the topological phases of the system. We further observe half-quantization of the Chern number at the transition between the synthetic Hall regime and the trivial regime, and the associated concentration of local Berry curvature in synthetic phase space. Our Letter opens up the possibility of using driven qubits to design and study higher-dimensional topological insulators and semimetals in synthetic dimensions.},
annotation = {offset: 1},
file = {/home/hiro/Zotero/storage/6WAGU7ZF/Boyers et al. - 2020 - Exploring 2D Synthetic Quantum Hall Physics with a.pdf}
}
@book{Bratteli1987,
title = {Operator Algebras and Quantum Statistical Mechanics 1 {{C}}*- and {{W}}*-Algebras, Symmetry Groups, Decomposition of States},
author = {Bratteli, Ola and Robinson, Derek W.},
@ -305,6 +338,23 @@
file = {/home/hiro/Zotero/storage/SAECW24Y/Buffoni and Campisi - 2022 - Spontaneous Fluctuation-Symmetry Breaking and the .pdf}
}
@article{Buser2021,
title = {Probing the {{Hall Voltage}} in {{Synthetic Quantum Systems}}},
author = {Buser, Maximilian and Greschner, Sebastian and Schollwöck, Ulrich and Giamarchi, Thierry},
date = {2021-01-19},
journaltitle = {Physical Review Letters},
shortjournal = {Phys. Rev. Lett.},
volume = {126},
number = {3},
pages = {030501},
publisher = {{American Physical Society}},
doi = {10.1103/PhysRevLett.126.030501},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.126.030501},
urldate = {2023-03-14},
abstract = {In the context of experimental advances in the realization of artificial magnetic fields in quantum gases, we discuss feasible schemes to extend measurements of the Hall polarization to a study of the Hall voltage, allowing for direct comparison with solid state systems. Specifically, for the paradigmatic example of interacting flux ladders, we report on characteristic zero crossings and a remarkable robustness of the Hall voltage with respect to interaction strengths, particle fillings, and ladder geometries, which is unobservable in the Hall polarization. Moreover, we investigate the site-resolved Hall response in spatially inhomogeneous quantum phases.},
file = {/home/hiro/Zotero/storage/ZLLWX29N/Buser et al. - 2021 - Probing the Hall Voltage in Synthetic Quantum Syst.pdf;/home/hiro/Zotero/storage/Q7JJMCC3/PhysRevLett.126.html}
}
@article{Caldeira1981,
title = {Influence of {{Dissipation}} on {{Quantum Tunneling}} in {{Macroscopic Systems}}},
author = {Caldeira, A. O. and Leggett, A. J.},
@ -348,13 +398,35 @@
isbn = {978-0-521-11375-5}
}
@article{Cardano2017,
title = {Detection of {{Zak}} Phases and Topological Invariants in a Chiral Quantum Walk of Twisted Photons},
author = {Cardano, Filippo and D’Errico, Alessio and Dauphin, Alexandre and Maffei, Maria and Piccirillo, Bruno and de Lisio, Corrado and De Filippis, Giulio and Cataudella, Vittorio and Santamato, Enrico and Marrucci, Lorenzo and Lewenstein, Maciej and Massignan, Pietro},
options = {useprefix=true},
date = {2017-06-01},
journaltitle = {Nature Communications},
shortjournal = {Nat Commun},
volume = {8},
number = {1},
pages = {15516},
publisher = {{Nature Publishing Group}},
issn = {2041-1723},
doi = {10.1038/ncomms15516},
url = {https://www.nature.com/articles/ncomms15516},
urldate = {2023-03-15},
abstract = {Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, an observable that rapidly approaches a value proportional to the Zak phase during the free evolution of the system. Then we measure the Zak phase in a photonic quantum walk of twisted photons, by observing the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general and readily applicable to all present one-dimensional platforms simulating static or Floquet chiral systems.},
issue = {1},
langid = {english},
keywords = {Quantum optics,Quantum simulation,Topological matter},
file = {/home/hiro/Zotero/storage/5G3CF852/Cardano et al. - 2017 - Detection of Zak phases and topological invariants.pdf}
}
@online{Cardin2022,
title = {Photon-Number Moments and Cumulants of {{Gaussian}} States},
author = {Cardin, Yanic and Quesada, Nicolás},
date = {2022-12-12},
number = {arXiv:2212.06067},
eprint = {arXiv:2212.06067},
eprint = {2212.06067},
eprinttype = {arxiv},
eprintclass = {quant-ph},
doi = {10.48550/arXiv.2212.06067},
url = {http://arxiv.org/abs/2212.06067},
urldate = {2023-01-20},
@ -393,6 +465,23 @@
file = {/home/hiro/Zotero/storage/8NNPCY2Y/Chen et al. - 2010 - Fast Optimal Frictionless Atom Cooling in Harmonic.pdf}
}
@article{Chen2018,
title = {Observation of {{Topologically Protected Edge States}} in a {{Photonic Two-Dimensional Quantum Walk}}},
author = {Chen, Chao and Ding, Xing and Qin, Jian and He, Yu and Luo, Yi-Han and Chen, Ming-Cheng and Liu, Chang and Wang, Xi-Lin and Zhang, Wei-Jun and Li, Hao and You, Li-Xing and Wang, Zhen and Wang, Da-Wei and Sanders, Barry C. and Lu, Chao-Yang and Pan, Jian-Wei},
date = {2018-09-06},
journaltitle = {Physical Review Letters},
shortjournal = {Phys. Rev. Lett.},
volume = {121},
number = {10},
pages = {100502},
publisher = {{American Physical Society}},
doi = {10.1103/PhysRevLett.121.100502},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.121.100502},
urldate = {2023-03-15},
abstract = {Periodically driven systems have displayed a variety of fascinating phenomena without analogies in static systems, which enrich the classification of quantum phases of matter and stimulate a wide range of research interests. Here, we employ discrete-time quantum walks to investigate a nontrivial topological effect unique to a two-dimensional periodically driven system: chiral edge states can exist at the interface of Floquet insulators whose Chern numbers vanish. Thanks to a resource-saving and flexible fiber-loop architecture, we realize inhomogeneous two-dimensional quantum walks up to 25 steps, over an effective 51×51 lattice with tunable local parameters. Spin-polarized chiral edge states are observed at the boundary of two distinct quantum walk domains. Our results contribute to establishing a well-controlled platform for exploring nontrivial topological phases.},
file = {/home/hiro/Zotero/storage/LKTA6ZHC/Chen et al. - 2018 - Observation of Topologically Protected Edge States.pdf;/home/hiro/Zotero/storage/DBP7DVBS/PhysRevLett.121.html}
}
@article{Cheng2005,
title = {Markovian {{Approximation}} in the {{Relaxation}} of {{Open Quantum Systems}}},
author = {Cheng, Y. C. and Silbey, R. J.},
@ -422,6 +511,23 @@
file = {/home/hiro/Zotero/storage/2WG9TXBT/Cheng et al. - 2023 - Artificial Non-Abelian Lattice Gauge Fields for Ph.pdf;/home/hiro/Zotero/storage/RP7ZITJP/PhysRevLett.130.html}
}
@article{Chiu2016,
title = {Classification of Topological Quantum Matter with Symmetries},
author = {Chiu, Ching-Kai and Teo, Jeffrey C. Y. and Schnyder, Andreas P. and Ryu, Shinsei},
date = {2016-08-31},
journaltitle = {Reviews of Modern Physics},
shortjournal = {Rev. Mod. Phys.},
volume = {88},
number = {3},
pages = {035005},
publisher = {{American Physical Society}},
doi = {10.1103/RevModPhys.88.035005},
url = {https://link.aps.org/doi/10.1103/RevModPhys.88.035005},
urldate = {2023-04-15},
abstract = {Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks of topological materials is the existence of protected gapless surface states, which arise due to a nontrivial topology of the bulk wave functions. This review provides a pedagogical introduction into the field of topological quantum matter with an emphasis on classification schemes. Both fully gapped and gapless topological materials and their classification in terms of nonspatial symmetries, such as time reversal, as well as spatial symmetries, such as reflection, are considered. Furthermore, the classification of gapless modes localized on topological defects is surveyed. The classification of these systems is discussed by use of homotopy groups, Clifford algebras, K theory, and nonlinear sigma models describing the Anderson (de)localization at the surface or inside a defect of the material. Theoretical model systems and their topological invariants are reviewed together with recent experimental results in order to provide a unified and comprehensive perspective of the field. While the bulk of this article is concerned with the topological properties of noninteracting or mean-field Hamiltonians, a brief overview of recent results and open questions concerning the topological classifications of interacting systems is also provided.},
file = {/home/hiro/Zotero/storage/D66F3HQT/Chiu et al. - 2016 - Classification of topological quantum matter with .pdf;/home/hiro/Zotero/storage/AGD4AJTT/RevModPhys.88.html}
}
@book{Chruscinski2004,
title = {Geometric {{Phases}} in {{Classical}} and {{Quantum Mechanics}}},
author = {Chruściński, Dariusz and Jamiołkowski, Andrzej},
@ -664,6 +770,8 @@
urldate = {2023-01-06},
isbn = {978-3-8274-3035-9 978-3-8274-3036-6},
langid = {ngerman},
annotation = {offset: 7},
note = {3},
file = {/home/hiro/Zotero/storage/4JDJHWBD/Fließbach - 2012 - Elektrodynamik.pdf}
}
@ -746,6 +854,23 @@
file = {/home/hiro/Zotero/storage/N3MWPTX8/Gisin and Percival - 1992 - The quantum-state diffusion model applied to open .pdf}
}
@book{Godinho2014,
title = {An {{Introduction}} to {{Riemannian Geometry}}: {{With Applications}} to {{Mechanics}} and {{Relativity}}},
shorttitle = {An {{Introduction}} to {{Riemannian Geometry}}},
author = {Godinho, Leonor and Natário, José},
date = {2014},
series = {Universitext},
publisher = {{Springer International Publishing}},
location = {{Cham}},
doi = {10.1007/978-3-319-08666-8},
url = {https://link.springer.com/10.1007/978-3-319-08666-8},
urldate = {2023-04-11},
isbn = {978-3-319-08665-1 978-3-319-08666-8},
langid = {english},
annotation = {offset: 11},
file = {/home/hiro/Zotero/storage/WS9JFB53/Godinho and Natário - 2014 - An Introduction to Riemannian Geometry With Appli.pdf}
}
@article{Grabert1988,
title = {Quantum {{Brownian}} Motion: {{The}} Functional Integral Approach},
author = {Grabert, Hermann and Schramm, Peter and Ingold, Gert-Ludwig},
@ -789,6 +914,24 @@
abstract = {We describe a method for the solution of initial-value problems for random processes arising through adiabatic approximations from Markov processes of higher dimension. In applications to overdamped Brownian motion and to the single-mode laser we calculate correlation functions and discuss initial slips.}
}
@article{Haldane1988,
title = {Model for a {{Quantum Hall Effect}} without {{Landau Levels}}: {{Condensed-Matter Realization}} of the "{{Parity Anomaly}}"},
shorttitle = {Model for a {{Quantum Hall Effect}} without {{Landau Levels}}},
author = {Haldane, F. D. M.},
date = {1988-10-31},
journaltitle = {Physical Review Letters},
shortjournal = {Phys. Rev. Lett.},
volume = {61},
number = {18},
pages = {2015--2018},
publisher = {{American Physical Society}},
doi = {10.1103/PhysRevLett.61.2015},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.61.2015},
urldate = {2023-04-12},
abstract = {A two-dimensional condensed-matter lattice model is presented which exhibits a nonzero quantization of the Hall conductance σxy in the absence of an external magnetic field. Massless fermions without spectral doubling occur at critical values of the model parameters, and exhibit the so-called "parity anomaly" of (2+1)-dimensional field theories.},
file = {/home/hiro/Zotero/storage/FTHRXMKI/Haldane - 1988 - Model for a Quantum Hall Effect without Landau Lev.pdf;/home/hiro/Zotero/storage/BYN97P69/PhysRevLett.61.html}
}
@article{Harris2020,
title = {Array Programming with {{NumPy}}},
author = {Harris, Charles R. and Millman, K. Jarrod and van der Walt, Stéfan J. and Gommers, Ralf and Virtanen, Pauli and Cournapeau, David and Wieser, Eric and Taylor, Julian and Berg, Sebastian and Smith, Nathaniel J. and Kern, Robert and Picus, Matti and Hoyer, Stephan and van Kerkwijk, Marten H. and Brett, Matthew and Haldane, Allan and del Río, Jaime Fernández and Wiebe, Mark and Peterson, Pearu and Gérard-Marchant, Pierre and Sheppard, Kevin and Reddy, Tyler and Weckesser, Warren and Abbasi, Hameer and Gohlke, Christoph and Oliphant, Travis E.},
@ -817,6 +960,24 @@
file = {/home/hiro/Zotero/storage/9ZTPC4R8/Hartmann and Strunz - 2017 - Exact Open Quantum System Dynamics Using the Hiera.pdf;/home/hiro/Zotero/storage/VVVZXRZE/hartmann2017.pdf.pdf}
}
@article{Hartmann2019,
title = {Exact Open Quantum System Dynamics: {{Optimal}} Frequency vs Time Representation of Bath Correlations},
shorttitle = {Exact Open Quantum System Dynamics},
author = {Hartmann, Richard and Werther, Michael and Grossmann, Frank and Strunz, Walter T.},
date = {2019-06-17},
journaltitle = {The Journal of Chemical Physics},
shortjournal = {The Journal of Chemical Physics},
volume = {150},
number = {23},
pages = {234105},
issn = {0021-9606},
doi = {10.1063/1.5097158},
url = {https://doi.org/10.1063/1.5097158},
urldate = {2023-04-19},
abstract = {Two different numerically exact methods for open quantum system dynamics, the hierarchy of pure states (HOPS) method, and the multi-Davydov-Ansatz are discussed. We focus on the suitability of the underlying representations of bath correlations. While in the HOPS case the correct description of the bath correlation function (BCF) in the time domain is decisive, it turns out that a windowed Fourier transform of the BCF is an appropriate indicator of the quality of the discretization in the multi-Davydov-Ansatz. For the spin-boson model with sub-Ohmic spectral density considered here, a discretization of the spectral density based on an exponential distribution, used previously, turns out to be most favorable.},
file = {/home/hiro/Zotero/storage/PEP8E9DB/10.1063@1.5097158.pdf.pdf;/home/hiro/Zotero/storage/TZUUZ3C9/Hartmann et al. - 2019 - Exact open quantum system dynamics Optimal freque.pdf;/home/hiro/Zotero/storage/UP5PQIRP/Exact-open-quantum-system-dynamics-Optimal.html}
}
@thesis{Hartmann2021,
type = {phdthesis},
title = {Exact {{Open Quantum System Dynamics}} – {{Investigating Environmentally Induced Entanglement}}},
@ -856,6 +1017,21 @@
file = {/home/hiro/Zotero/storage/M95ZTBRT/Haus - 1984 - Waves and Fields in Optoelectronics.pdf}
}
@book{Hennig2022,
title = {Probabilistic {{Numerics}}},
author = {Hennig, Philipp and Osborne, Michael A. and Kersting, Hans P.},
date = {2022-06-30},
eprint = {TNduEAAAQBAJ},
eprinttype = {googlebooks},
publisher = {{Cambridge University Press}},
abstract = {Probabilistic numerical computation formalises the connection between machine learning and applied mathematics. Numerical algorithms approximate intractable quantities from computable ones. They estimate integrals from evaluations of the integrand, or the path of a dynamical system described by differential equations from evaluations of the vector field. In other words, they infer a latent quantity from data. This book shows that it is thus formally possible to think of computational routines as learning machines, and to use the notion of Bayesian inference to build more flexible, efficient, or customised algorithms for computation. The text caters for Masters' and PhD students, as well as postgraduate researchers in artificial intelligence, computer science, statistics, and applied mathematics. Extensive background material is provided along with a wealth of figures, worked examples, and exercises (with solutions) to develop intuition.},
isbn = {978-1-107-16344-7},
langid = {english},
pagetotal = {411},
keywords = {Computers / Artificial Intelligence / General,Computers / General,Computers / Programming / Algorithms,Mathematics / Discrete Mathematics,Mathematics / Numerical Analysis,Mathematics / Probability & Statistics / General},
file = {/home/hiro/Zotero/storage/CVGW82QF/Hennig et al. - 2022 - Probabilistic Numerics.pdf}
}
@article{Hita-Pifmmodeacuteeelseefirez2021,
title = {Three-{{Josephson}} Junctions Flux Qubit Couplings},
author = {Hita-Pıfmmode\textbackslash acutee\textbackslash elseé\textbackslash firez, Marıfmmode\textbackslash acuteımath\textbackslash elseí\textbackslash fia and Jaumıfmmode\textbackslash gravea\textbackslash elseà\textbackslash fi, Gabriel and Pino, Manuel and Garcıfmmode\textbackslash acuteımath\textbackslash elseí\textbackslash fia-Ripoll, Juan Josıfmmode\textbackslash acutee\textbackslash elseé\textbackslash fi},
@ -915,6 +1091,23 @@
file = {/home/hiro/Zotero/storage/2T439YPV/Johansson - 2017 - Arb efficient arbitrary-precision midpoint-radius.pdf;/home/hiro/Zotero/storage/TI7XWRCG/johansson2017.pdf.pdf}
}
@incollection{Kane2013,
title = {Topological {{Band Theory}} and the {{ℤ2 Invariant}}},
booktitle = {Contemporary {{Concepts}} of {{Condensed Matter Science}}},
author = {Kane, C.L.},
date = {2013},
volume = {6},
pages = {3--34},
publisher = {{Elsevier}},
doi = {10.1016/B978-0-444-63314-9.00001-9},
url = {https://linkinghub.elsevier.com/retrieve/pii/B9780444633149000019},
urldate = {2023-04-11},
isbn = {978-0-444-63314-9},
langid = {english},
annotation = {offset: -2},
file = {/home/hiro/Zotero/storage/T722ZHCX/Kane - 2013 - Topological Band Theory and the ℤ2 Invariant.pdf}
}
@article{Karimi2016,
title = {Otto Refrigerator Based on a Superconducting Qubit: {{Classical}} and Quantum Performance},
author = {Karimi, B. and Pekola, J. P.},
@ -957,6 +1150,39 @@
file = {/home/hiro/Zotero/storage/FR3BD4N4/Kato and Tanimura - 2016 - Quantum heat current under non-perturbative and no.pdf}
}
@article{Kitaev2009,
title = {Periodic Table for Topological Insulators and Superconductors},
author = {Kitaev, Alexei},
date = {2009-05-14},
journaltitle = {AIP Conference Proceedings},
volume = {1134},
number = {1},
pages = {22--30},
publisher = {{American Institute of Physics}},
issn = {0094-243X},
doi = {10.1063/1.3149495},
url = {https://aip.scitation.org/doi/abs/10.1063/1.3149495},
urldate = {2023-04-14},
file = {/home/hiro/Zotero/storage/AQA3PISV/Kitaev - 2009 - Periodic table for topological insulators and supe.pdf}
}
@article{Kitagawa2010,
title = {Exploring Topological Phases with Quantum Walks},
author = {Kitagawa, Takuya and Rudner, Mark S. and Berg, Erez and Demler, Eugene},
date = {2010-09-24},
journaltitle = {Physical Review A},
shortjournal = {Phys. Rev. A},
volume = {82},
number = {3},
pages = {033429},
publisher = {{American Physical Society}},
doi = {10.1103/PhysRevA.82.033429},
url = {https://link.aps.org/doi/10.1103/PhysRevA.82.033429},
urldate = {2023-03-20},
abstract = {The quantum walk was originally proposed as a quantum-mechanical analog of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete-time quantum walks provide a versatile platform for studying topological phases, which are currently the subject of intense theoretical and experimental investigations. In particular, we demonstrate that recent experimental realizations of quantum walks with cold atoms, photons, and ions simulate a nontrivial one-dimensional topological phase. With simple modifications, the quantum walk can be engineered to realize all of the topological phases, which have been classified in one and two dimensions. We further discuss the existence of robust edge modes at phase boundaries, which provide experimental signatures for the nontrivial topological character of the system.},
file = {/home/hiro/Zotero/storage/HR8JLATF/Kitagawa et al. - 2010 - Exploring topological phases with quantum walks.pdf;/home/hiro/Zotero/storage/WNBPELVA/PhysRevA.82.html}
}
@article{Klatzow2019,
title = {Experimental {{Demonstration}} of {{Quantum Effects}} in the {{Operation}} of {{Microscopic Heat Engines}}},
author = {Klatzow, James and Becker, Jonas N. and Ledingham, Patrick M. and Weinzetl, Christian and Kaczmarek, Krzysztof T. and Saunders, Dylan J. and Nunn, Joshua and Walmsley, Ian A. and Uzdin, Raam and Poem, Eilon},
@ -1040,6 +1266,23 @@
file = {/home/hiro/Zotero/storage/7PG7ZIYE/Kurizki and Kofman - 2021 - Thermodynamics and Control of Open Quantum Systems.pdf}
}
@article{Laughlin1981,
title = {Quantized {{Hall}} Conductivity in Two Dimensions},
author = {Laughlin, R. B.},
date = {1981-05-15},
journaltitle = {Physical Review B},
shortjournal = {Phys. Rev. B},
volume = {23},
number = {10},
pages = {5632--5633},
publisher = {{American Physical Society}},
doi = {10.1103/PhysRevB.23.5632},
url = {https://link.aps.org/doi/10.1103/PhysRevB.23.5632},
urldate = {2023-04-12},
abstract = {It is shown that the quantization of the Hall conductivity of two-dimensional metals which has been observed recently by Klitzing, Dorda, and Pepper and by Tsui and Gossard is a consequence of gauge invariance and the existence of a mobility gap. Edge effects are shown to have no influence on the accuracy of quantization. An estimate of the error based on thermal activation of carriers to the mobility edge is suggested., This article appears in the following collection:},
file = {/home/hiro/Zotero/storage/CNFP5BNF/Laughlin - 1981 - Quantized Hall conductivity in two dimensions.pdf}
}
@article{Lenard1978,
title = {Thermodynamical Proof of the {{Gibbs}} Formula for Elementary Quantum Systems},
author = {Lenard, A.},
@ -1054,6 +1297,23 @@
file = {/home/hiro/Zotero/storage/IV52P9V7/Lenard - 1978 - Thermodynamical proof of the Gibbs formula for ele.pdf}
}
@article{Levine2019,
title = {Quantum {{Entanglement}} in {{Deep Learning Architectures}}},
author = {Levine, Yoav and Sharir, Or and Cohen, Nadav and Shashua, Amnon},
date = {2019-02-12},
journaltitle = {Physical Review Letters},
shortjournal = {Phys. Rev. Lett.},
volume = {122},
number = {6},
pages = {065301},
publisher = {{American Physical Society}},
doi = {10.1103/PhysRevLett.122.065301},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.065301},
urldate = {2023-03-14},
abstract = {Modern deep learning has enabled unprecedented achievements in various domains. Nonetheless, employment of machine learning for wave function representations is focused on more traditional architectures such as restricted Boltzmann machines (RBMs) and fully connected neural networks. In this Letter, we establish that contemporary deep learning architectures, in the form of deep convolutional and recurrent networks, can efficiently represent highly entangled quantum systems. By constructing tensor network equivalents of these architectures, we identify an inherent reuse of information in the network operation as a key trait which distinguishes them from standard tensor network-based representations, and which enhances their entanglement capacity. Our results show that such architectures can support volume-law entanglement scaling, polynomially more efficiently than presently employed RBMs. Thus, beyond a quantification of the entanglement capacity of leading deep learning architectures, our analysis formally motivates a shift of trending neural-network-based wave function representations closer to the state-of-the-art in machine learning.},
file = {/home/hiro/Zotero/storage/VXYVI95B/Levine et al. - 2019 - Quantum Entanglement in Deep Learning Architecture.pdf}
}
@article{Link2022,
title = {Non-{{Markovian Quantum Dynamics}} in a {{Squeezed Reservoir}}},
author = {Link, Valentin and Strunz, Walter T. and Luoma, Kimmo},
@ -1093,6 +1353,26 @@
file = {/home/hiro/Zotero/storage/2CLDGP85/Lobejko - 2021 - The tight Second Law inequality for coherent quant.pdf}
}
@article{Lustig2019,
title = {Photonic Topological Insulator in Synthetic Dimensions},
author = {Lustig, Eran and Weimann, Steffen and Plotnik, Yonatan and Lumer, Yaakov and Bandres, Miguel A. and Szameit, Alexander and Segev, Mordechai},
date = {2019-03},
journaltitle = {Nature},
volume = {567},
number = {7748},
pages = {356--360},
publisher = {{Nature Publishing Group}},
issn = {1476-4687},
doi = {10.1038/s41586-019-0943-7},
url = {https://www.nature.com/articles/s41586-019-0943-7},
urldate = {2023-03-15},
abstract = {Topological phases enable protected transport along the edges of materials, offering immunity against scattering from disorder and imperfections. These phases have been demonstrated for electronic systems, electromagnetic waves1–5, cold atoms6,7, acoustics8 and even mechanics9, and their potential applications include spintronics, quantum computing and highly efficient lasers10–12. Typically, the model describing topological insulators is a spatial lattice in two or three dimensions. However, topological edge states have~also been observed in a lattice with one spatial dimension and one synthetic dimension (corresponding to the spin modes of an ultracold atom13–15), and atomic modes have been used as synthetic dimensions to demonstrate lattice models and physical phenomena that are not accessible to experiments in spatial lattices13,16,17. In photonics, topological lattices with synthetic dimensions have been proposed for the study of physical phenomena in high dimensions and interacting photons18–22, but so far photonic topological insulators in synthetic dimensions have not been observed. Here we demonstrate experimentally a photonic topological insulator in synthetic dimensions. We fabricate a photonic lattice in which photons are subjected to an effective magnetic field in a space with one spatial dimension and one synthetic modal dimension. Our scheme supports topological edge states in this spatial-modal lattice, resulting in a robust topological state that extends over the bulk of a two-dimensional real-space lattice. Our system can be used to increase the dimensionality of a photonic lattice and induce long-range coupling by design, leading to lattice models that can be used to study unexplored physical phenomena.},
issue = {7748},
langid = {english},
keywords = {Optical physics,Photonic crystals},
file = {/home/hiro/Zotero/storage/HCBPS6FK/Lustig et al. - 2019 - Photonic topological insulator in synthetic dimens.pdf;/home/hiro/Zotero/storage/Q7NECFTK/10.1038@s41586-019-0943-7.pdf.pdf}
}
@article{MacQuarrie2020,
title = {Progress toward a Capacitively Mediated {{CNOT}} between Two Charge Qubits in {{Si}}/{{SiGe}} - Npj {{Quantum Information}}},
author = {MacQuarrie, E. R. and Neyens, Samuel F. and Dodson, J. P. and Corrigan, J. and Thorgrimsson, Brandur and Holman, Nathan and Palma, M. and Edge, L. F. and Friesen, Mark and Coppersmith, S. N. and Eriksson, M. A.},
@ -1107,6 +1387,25 @@
file = {/home/hiro/Zotero/storage/8WPBZG5G/MacQuarrie et al. - 2020 - Progress toward a capacitively mediated CNOT betwe.pdf}
}
@article{Maffei2018,
title = {Topological Characterization of Chiral Models through Their Long Time Dynamics},
author = {Maffei, Maria and Dauphin, Alexandre and Cardano, Filippo and Lewenstein, Maciej and Massignan, Pietro},
date = {2018-01},
journaltitle = {New Journal of Physics},
shortjournal = {New J. Phys.},
volume = {20},
number = {1},
pages = {013023},
publisher = {{IOP Publishing}},
issn = {1367-2630},
doi = {10.1088/1367-2630/aa9d4c},
url = {https://dx.doi.org/10.1088/1367-2630/aa9d4c},
urldate = {2023-04-13},
abstract = {We study chiral models in one spatial dimension, both static and periodically driven. We demonstrate that their topological properties may be read out through the long time limit of a bulk observable, the mean chiral displacement. The derivation of this result is done in terms of spectral projectors, allowing for a detailed understanding of the physics. We show that the proposed detection converges rapidly and it can be implemented in a wide class of chiral systems. Furthermore, it can measure arbitrary winding numbers and topological boundaries, it applies to all non-interacting systems, independently of their quantum statistics, and it requires no additional elements, such as external fields, nor filled bands.},
langid = {english},
file = {/home/hiro/Zotero/storage/K3PB5IVM/Maffei et al. - 2018 - Topological characterization of chiral models thro.pdf}
}
@article{Magazzifmmodegraveuelseufi2018,
title = {Probing the Strongly Driven Spin-Boson Model in a Superconducting Quantum Circuit},
author = {Magazzıfmmode\textbackslash graveu\textbackslash elseù\textbackslash fi, L. and Forn-Dıfmmode\textbackslash acuteımath\textbackslash elseí\textbackslash fiaz, P. and Belyansky, R. and Orgiazzi, J.-L. and Yurtalan, M. A. and Otto, M. R. and Lupascu, A. and Wilson, C. M. and Grifoni, M.},
@ -1276,6 +1575,27 @@
file = {/home/hiro/Zotero/storage/7CER4GYZ/Olver et al. - 2010 - The NIST handbook of mathematical functions.pdf}
}
@article{Orus2019,
title = {Tensor Networks for Complex Quantum Systems},
author = {Orús, Román},
date = {2019-09},
journaltitle = {Nature Reviews Physics},
shortjournal = {Nat Rev Phys},
volume = {1},
number = {9},
pages = {538--550},
publisher = {{Nature Publishing Group}},
issn = {2522-5820},
doi = {10.1038/s42254-019-0086-7},
url = {https://www.nature.com/articles/s42254-019-0086-7},
urldate = {2023-03-14},
abstract = {Originally developed in the context of condensed-matter physics and based on renormalization group ideas, tensor networks have been revived thanks to quantum information theory and the progress in understanding the role of entanglement in quantum many-body systems. Moreover, tensor network states have turned out to play a key role in other scientific disciplines. In this context, here I provide an overview of the basic concepts and key developments in the field. I briefly discuss the most important tensor network structures and algorithms, together with an outline of advances related to global and gauge symmetries, fermions, topological order, classification of phases, entanglement Hamiltonians, holografic duality, artificial intelligence, the 2D Hubbard model, 2D quantum antiferromagnets, conformal field theory, quantum chemistry, disordered systems and many-body localization.},
issue = {9},
langid = {english},
keywords = {Condensed-matter physics,Quantum information,Theoretical physics},
file = {/home/hiro/Zotero/storage/NYG9W5IH/Orús - 2019 - Tensor networks for complex quantum systems.pdf}
}
@article{Ozawa2018,
title = {Extracting the Quantum Metric Tensor through Periodic Driving},
author = {Ozawa, Tomoki and Goldman, Nathan},
@ -1351,6 +1671,21 @@
file = {/home/hiro/Zotero/storage/IM7J4VXT/Pusz and Woronowicz - 1978 - Passive states and KMS states for general quantum .pdf}
}
@book{Quigg2013,
title = {Gauge Theories of the Strong, Weak, and Electromagnetic Interactions},
author = {Quigg, Chris},
date = {2013},
edition = {Second edition},
publisher = {{Princeton University Press}},
location = {{Princeton, New Jersey}},
abstract = {"This completely revised and updated graduate-level textbook is an ideal introduction to gauge theories and their applications to high-energy particle physics, and takes an in-depth look at two new laws of nature--quantum chromodynamics and the electroweak theory. From quantum electrodynamics through unified theories of the interactions among leptons and quarks, Chris Quigg examines the logic and structure behind gauge theories and the experimental underpinnings of today's theories. Quigg emphasizes how we know what we know, and in the era of the Large Hadron Collider, his insightful survey of the standard model and the next great questions for particle physics makes for compelling reading.The brand-new edition shows how the electroweak theory developed in conversation with experiment. Featuring a wide-ranging treatment of electroweak symmetry breaking, the physics of the Higgs boson, and the importance of the 1-TeV scale, the book moves beyond established knowledge and investigates the path toward unified theories of strong, weak, and electromagnetic interactions. Explicit calculations and diverse exercises allow readers to derive the consequences of these theories. Extensive annotated bibliographies accompany each chapter, amplify points of conceptual or technical interest, introduce further applications, and lead readers to the research literature. Students and seasoned practitioners will profit from the text's current insights, and specialists wishing to understand gauge theories will find the book an ideal reference for self-study. Brand-new edition of a landmark text introducing gauge theories Consistent attention to how we know what we know Explicit calculations develop concepts and engage with experiment Interesting and diverse problems sharpen skills and ideas Extensive annotated bibliographies "--},
isbn = {978-0-691-13548-9},
langid = {english},
pagetotal = {482},
keywords = {Gauge fields (Physics),Nuclear reactions,SCIENCE / Electromagnetism,SCIENCE / Quantum Theory,Strong interactions (Nuclear physics)},
file = {/home/hiro/Zotero/storage/Y93DCTHK/Quigg - 2013 - Gauge theories of the strong, weak, and electromag.pdf}
}
@article{Raja2021,
title = {Finite-Time Quantum {{Stirling}} Heat Engine},
author = {Raja, S. Hamedani and Maniscalco, S. and Paraoanu, G. S. and Pekola, J. P. and Gullo, N. Lo},
@ -1476,6 +1811,24 @@
keywords = {Condensed matter,Textbooks}
}
@article{Salerno2019,
title = {Quantized {{Hall Conductance}} of a {{Single Atomic Wire}}: {{A Proposal Based}} on {{Synthetic Dimensions}}},
shorttitle = {Quantized {{Hall Conductance}} of a {{Single Atomic Wire}}},
author = {Salerno, G. and Price, H. M. and Lebrat, M. and Häusler, S. and Esslinger, T. and Corman, L. and Brantut, J.-P. and Goldman, N.},
date = {2019-10-01},
journaltitle = {Physical Review X},
shortjournal = {Phys. Rev. X},
volume = {9},
number = {4},
pages = {041001},
publisher = {{American Physical Society}},
doi = {10.1103/PhysRevX.9.041001},
url = {https://link.aps.org/doi/10.1103/PhysRevX.9.041001},
urldate = {2023-03-14},
abstract = {We propose a method by which the quantization of the Hall conductance can be directly measured in the transport of a one-dimensional atomic gas. Our approach builds on two main ingredients: (1) a constriction optical potential, which generates a mesoscopic channel connected to two reservoirs, and (2) a time-periodic modulation of the channel specifically designed to generate motion along an additional synthetic dimension. This fictitious dimension is spanned by the harmonic oscillator modes associated with the tightly confined channel, and hence, the corresponding “lattice sites” are intimately related to the energy of the system. We analyze the quantum-transport properties of this hybrid two-dimensional system, highlighting the appealing features offered by the synthetic dimension. In particular, we demonstrate how the energetic nature of the synthetic dimension combined with the quasienergy spectrum of the periodically driven channel allows for the direct and unambiguous observation of the quantized Hall effect in a two-reservoir geometry. Our work illustrates how topological properties of matter can be accessed in a minimal one-dimensional setup, with direct and practical experimental consequences.},
file = {/home/hiro/Zotero/storage/BFAIIUPB/Salerno et al. - 2019 - Quantized Hall Conductance of a Single Atomic Wire.pdf;/home/hiro/Zotero/storage/97YTTFRM/PhysRevX.9.html}
}
@misc{Santoro2022,
title = {Introduction to {{Floquet}}},
author = {Santoro, Giuseppe E.},
@ -1769,6 +2122,23 @@
institution = {{Fachbereich Physik der Universität Essen}}
}
@article{Su1979,
title = {Solitons in {{Polyacetylene}}},
author = {Su, W. P. and Schrieffer, J. R. and Heeger, A. J.},
date = {1979-06-18},
journaltitle = {Physical Review Letters},
shortjournal = {Phys. Rev. Lett.},
volume = {42},
number = {25},
pages = {1698--1701},
publisher = {{American Physical Society}},
doi = {10.1103/PhysRevLett.42.1698},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.42.1698},
urldate = {2023-04-15},
abstract = {We present a theoretical study of soliton formation in long-chain polyenes, including the energy of formation, length, mass, and activation energy for motion. The results provide an explanation of the mobile neutral defect observed in undoped (CH)x. Since the soliton formation energy is less than that needed to create band excitation, solitons play a fundamental role in the charge-transfer doping mechanism.},
file = {/home/hiro/Zotero/storage/5YVFP4PK/Su et al. - 1979 - Solitons in Polyacetylene.pdf;/home/hiro/Zotero/storage/ANNZW5F4/su1979.pdf.pdf;/home/hiro/Zotero/storage/6TZ6G6YH/PhysRevLett.42.html}
}
@article{Suarez1992,
title = {Memory {{Effects}} in the {{Relaxation}} of {{Quantum Open Systems}}},
author = {Suárez, Alberto and Silbey, Robert and Oppenheim, Irwin},
@ -1895,6 +2265,38 @@
file = {/home/hiro/Zotero/storage/2FLNWVVD/tanimura1990.pdf.pdf;/home/hiro/Zotero/storage/8QAMYSPF/Tanimura - 1990 - Nonperturbative expansion method for a quantum sys.pdf}
}
@article{Thouless1982,
title = {Quantized Hall Conductance in a Two-{{Dimensional}} Periodic Potential},
author = {Thouless, D.J. and Kohmoto, M. and Nightingale, M.P. and Den Nijs, M.},
date = {1982},
journaltitle = {Physical Review Letters},
volume = {49},
number = {6},
pages = {405--408},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.49.405},
abstract = {The Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field and a periodic substrate potential U. The Kubo formula is written in a form that makes apparent the quantization when the Fermi energy lies in a gap. Explicit expressions have been obtained for the Hall conductance for both large and small Uc. © 1982 The American Physical Society.},
langid = {english},
note = {Cited By :4356},
file = {/home/hiro/Zotero/storage/A8CRH9G8/Thouless et al. - 1982 - Quantized hall conductance in a two-Dimensional pe.pdf;/home/hiro/Zotero/storage/IR9Z7D6Y/thouless1982.pdf.pdf;/home/hiro/Zotero/storage/F4BEVG5Q/display.html}
}
@article{Thouless1983,
title = {Quantization of Particle Transport},
author = {Thouless, D.J.},
date = {1983},
journaltitle = {Physical Review B},
volume = {27},
number = {10},
pages = {6083--6087},
issn = {0163-1829},
doi = {10.1103/PhysRevB.27.6083},
abstract = {The integrated particle current produced by a slow periodic variation of the potential of a Schrödinger equation is evaluated. It is shown that in a finite torus the integral of the current over a period can vary continuously, but in an infinite periodic system with full bands it must have an integer value. This quantization of particle transport is used to classify the energy gaps in a one-dimensional system with competing or incommensurate periods. It is also used to rederive Prange's results for the fractional charge of a soliton. © 1983 The American Physical Society.},
langid = {english},
note = {Cited By :1146},
file = {/home/hiro/Zotero/storage/UW8FSNL6/Thouless - 1983 - Quantization of particle transport.pdf;/home/hiro/Zotero/storage/CSL38FQ6/display.html}
}
@article{Uzdin2015,
title = {Equivalence of {{Quantum Heat Machines}}, and {{Quantum-Thermodynamic Signatures}}},
author = {Uzdin, Raam and Levy, Amikam and Kosloff, Ronnie},
@ -1923,6 +2325,25 @@
file = {/home/hiro/Zotero/storage/Y7ZPKMS5/Vaccaro and Barnett - 2011 - Information erasure without an energy cost.pdf}
}
@article{Verdeny2016,
title = {Quasi-{{Periodically Driven Quantum Systems}}},
author = {Verdeny, Albert and Puig, Joaquim and Mintert, Florian},
date = {2016-10-01},
journaltitle = {Zeitschrift für Naturforschung A},
volume = {71},
number = {10},
pages = {897--907},
publisher = {{De Gruyter}},
issn = {1865-7109},
doi = {10.1515/zna-2016-0079},
url = {https://www.degruyter.com/document/doi/10.1515/zna-2016-0079/html},
urldate = {2023-03-16},
abstract = {Floquet theory provides rigorous foundations for the theory of periodically driven quantum systems. In the case of non-periodic driving, however, the situation is not so well understood. Here, we provide a critical review of the theoretical framework developed for quasi-periodically driven quantum systems. Although the theoretical footing is still under development, we argue that quasi-periodically driven quantum systems can be treated with generalisations of Floquet theory in suitable parameter regimes. Moreover, we provide a generalisation of the Floquet-Magnus expansion and argue that quasi-periodic driving offers a promising route for quantum simulations.},
langid = {english},
keywords = {Driven Quantum Systems,Floquet Theory,Quasi-Periodicity,Reducibility},
file = {/home/hiro/Zotero/storage/UUU9JYRC/Verdeny et al. - 2016 - Quasi-Periodically Driven Quantum Systems.pdf}
}
@article{Viebahn,
title = {Introduction to {{Floquet}} Theory},
author = {Viebahn, Konrad},
@ -1956,6 +2377,24 @@
file = {/home/hiro/Zotero/storage/74LUQ73M/Virtanen et al. - 2020 - SciPy 1.0 Fundamental Algorithms for Scientific C.pdf}
}
@article{vonKlitzing1986,
title = {The Quantized {{Hall}} Effect},
author = {von Klitzing, Klaus},
options = {useprefix=true},
date = {1986-07-01},
journaltitle = {Reviews of Modern Physics},
shortjournal = {Rev. Mod. Phys.},
volume = {58},
number = {3},
pages = {519--531},
publisher = {{American Physical Society}},
doi = {10.1103/RevModPhys.58.519},
url = {https://link.aps.org/doi/10.1103/RevModPhys.58.519},
urldate = {2023-04-15},
abstract = {DOI:https://doi.org/10.1103/RevModPhys.58.519},
file = {/home/hiro/Zotero/storage/GDVZNE6R/von Klitzing - 1986 - The quantized Hall effect.pdf;/home/hiro/Zotero/storage/X27UUGJX/RevModPhys.58.html}
}
@article{Wan2021,
title = {Fault-Tolerant Qubit from a Constant Number of Components},
author = {Wan, Kianna and Choi, Soonwon and Kim, Isaac H. and Shutty, Noah and Hayden, Patrick},
@ -2198,6 +2637,41 @@
file = {/home/hiro/Zotero/storage/XHGETQ2F/Yuan et al. - 2019 - Photonic Gauge Potential in One Cavity with Synthe.pdf;/home/hiro/Zotero/storage/SHLF87TQ/PhysRevLett.122.html}
}
@article{Zak1964,
title = {Magnetic {{Translation Group}}},
author = {Zak, J.},
date = {1964-06-15},
journaltitle = {Physical Review},
shortjournal = {Phys. Rev.},
volume = {134},
pages = {A1602-A1606},
publisher = {{American Physical Society}},
doi = {10.1103/PhysRev.134.A1602},
url = {https://link.aps.org/doi/10.1103/PhysRev.134.A1602},
urldate = {2023-04-13},
abstract = {In this paper a group-theoretical approach to the problem of a Bloch electron in a magnetic field is given. A magnetic translation group is defined and its properties, in particular its connection with the usual translation group, are established.},
issue = {6A},
file = {/home/hiro/Zotero/storage/7F6HYC9E/Zak - 1964 - Magnetic Translation Group.pdf;/home/hiro/Zotero/storage/GPXSKECL/PhysRev.134.html}
}
@article{Zhang2010,
title = {Quantum Phase Transition in the Sub-{{Ohmic}} Spin-Boson Model: {{An}} Extended Coherent-State Approach},
shorttitle = {Quantum Phase Transition in the Sub-{{Ohmic}} Spin-Boson Model},
author = {Zhang, Yu-Yu and Chen, Qing-Hu and Wang, Ke-Lin},
date = {2010-03-26},
journaltitle = {Physical Review B},
shortjournal = {Phys. Rev. B},
volume = {81},
number = {12},
pages = {121105},
publisher = {{American Physical Society}},
doi = {10.1103/PhysRevB.81.121105},
url = {https://link.aps.org/doi/10.1103/PhysRevB.81.121105},
urldate = {2023-04-19},
abstract = {We propose a general extended coherent state approach to the qubit (or fermion) and multimode boson coupling systems. The application to the spin-boson model with the discretization of a bosonic bath with arbitrary continuous spectral density is described in detail, and very accurate solutions can be obtained. The quantum phase transition in the nontrivial sub-Ohmic case can be located by the fidelity and the order-parameter critical exponents for the bath exponents s{$<$}1/2 can be correctly given by the fidelity susceptibility, demonstrating the strength of the approach.},
file = {/home/hiro/Zotero/storage/GE99JLTP/zhang2010.pdf.pdf;/home/hiro/Zotero/storage/Y5C6DPHN/Zhang et al. - 2010 - Quantum phase transition in the sub-Ohmic spin-bos.pdf;/home/hiro/Zotero/storage/RCXPS7SF/PhysRevB.81.html}
}
@article{Zhang2018,
title = {Flexible Scheme to Truncate the Hierarchy of Pure States},
author = {Zhang, P.-P. and Bentley, C. D. B. and Eisfeld, A.},
@ -2283,3 +2757,10 @@
urldate = {2023-02-15},
file = {/home/hiro/Zotero/storage/DUB3BE69/collect_payment_data.html}
}
@online{zotero-415,
title = {Phys. {{Rev}}. {{Lett}}. 121, 100502 (2018) - {{Observation}} of {{Topologically Protected Edge States}} in a {{Photonic Two-Dimensional Quantum Walk}}},
url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.100502},
urldate = {2023-03-15},
file = {/home/hiro/Zotero/storage/4VPFH74L/PhysRevLett.121.html}
}