15 research outputs found
Reducing backaction when measuring temporal correlations in quantum systems
Dynamic correlations of quantum observables are challenging to measure due to
measurement backaction incurred at early times. Recent work [P. Uhrich et al.,
Phys. Rev. A, 96:022127 (2017)] has shown that ancilla-based noninvasive
measurements are able to reduce this backaction, allowing for dynamic
correlations of single-site spin observables to be measured. We generalise this
result to correlations of arbitrary spin observables and extend the measurement
protocol to simultaneous noninvasive measurements which allow for real and
imaginary parts of correlations to be extracted from a single set of
measurements. We use positive operator-valued measures to analyse the dynamics
generated by the ancilla-based measurements. Using this framework we prove that
special observables exist for which measurement backaction is of no concern, so
that dynamic correlations of these can be obtained without making use of
ancillas.Comment: 13 page
Probing unitary two-time correlations in a neutral atom quantum simulator
Measuring unitarily-evolved quantum mechanical two-time correlations is
challenging in general. In a recent paper [P.~Uhrich {\em et al.}, Phys.\
Rev.~A {\bf 96}, 022127 (2017)], a considerable simplification of this task has
been pointed out to occur in spin- lattice models, bringing such
measurements into reach of state-of-the-art or near-future quantum simulators
of such models. Here we discuss the challenges of an experimental
implementation of measurement schemes of two-time correlations in quantum gas
microscopes or microtrap arrays. We propose a modified measurement protocol
that mitigates these challenges, and we rigorously estimate the accuracy of the
protocols by means of Lieb-Robinson bounds. On the basis of these bounds we
identify a parameter regime in which the proposed protocols allow for accurate
measurements of the desired two-time correlations.Comment: 15 pages, 2 figure
Out-of-equilibrium phase diagram of long-range superconductors
Within the ultimate goal of classifying universality in quantum many-body
dynamics, understanding the relation between out-of-equilibrium and equilibrium
criticality is a crucial objective. Models with power-law interactions exhibit
rich well-understood critical behavior in equilibrium, but the
out-of-equilibrium picture has remained incomplete, despite recent experimental
progress. We construct the rich dynamical phase diagram of free-fermionic
chains with power-law hopping and pairing, and provide analytic and numerical
evidence showing a direct connection between nonanalyticities of the return
rate and zero crossings of the string order parameter. Our results may explain
the experimental observation of so-called \textit{accidental} dynamical
vortices, which appear for quenches within the same topological phase of the
Haldane model, as reported in [Fl\"aschner \textit{et al.}, Nature Physics
\textbf{14}, 265 (2018)]. Our work is readily applicable to modern
ultracold-atom experiments, not least because state-of-the-art quantum gas
microscopes can now reliably measure the string order parameter, which, as we
show, can serve as an indicator of dynamical criticality.Comment: 17 pages, 9 figures, accepted versio
Probing dynamical criticality near quantum phase transitions
We reveal a prethermal temporal regime upon suddenly quenching to the
vicinity of a quantum phase transition in the time evolution of 1D spin chains.
The prethermal regime is analytically found to be self-similar, and its
duration is governed by the ground-state energy gap. Based on analytical
insights and numerical evidence, we show that this critically prethermal regime
universally exists independently of the location of the probe site, the
presence of weak interactions, or the initial state. Moreover, the resulting
prethermal dynamics leads to an out-of-equilibrium scaling function of the
order parameter in the vicinity of the transition.Comment: Revised with an analytical theory and improved presentation. Main
text: 4 Pages, 2 Figures; Supplementary: 6 Pages, 5 Figure
Engineering random spin models with atoms in a high-finesse cavity
All-to-all interacting, disordered quantum many-body models have a wide range
of applications across disciplines, from spin glasses in condensed-matter
physics, over holographic duality in high-energy physics, to annealing
algorithms in quantum computing. Typically, these models are abstractions that
do not find unambiguous physical realisations in nature. Here, we realise an
all-to-all interacting, disordered spin system by subjecting an atomic cloud in
a cavity to a controllable light shift. Adjusting the detuning between atom
resonance and cavity mode, we can tune between disordered versions of a
central-mode model and a Lipkin-Meshkov-Glick model. By spectroscopically
probing the low-energy excitations of the system, we explore the competition of
interactions with disorder across a broad parameter range. We show how disorder
in the central-mode model breaks the strong collective coupling, making the
dark state manifold cross over to a random distribution of weakly-mixed
light-matter, "grey", states. In the Lipkin-Meshkov-Glick model the
ferromagnetic finite-size ground state evolves towards a paramagnet as disorder
is increased. In that regime, semi-localised eigenstates emerge, as we observe
by extracting bounds on the participation ratio. These results present
significant steps towards freely programmable cavity-mediated interactions for
the design of arbitrary spin Hamiltonians.Comment: 8 pages, 4 figures, methods, supplementary materia
Cryogenic electro-optic interconnect for superconducting devices
Encoding information onto optical fields is the backbone of modern
telecommunication networks. Optical fibers offer low loss transport and vast
bandwidth compared to electrical cables, and are currently also replacing
coaxial cables for short-range communications. Optical fibers also exhibit
significantly lower thermal conductivity, making optical interconnects
attractive for interfacing with superconducting circuits and devices. Yet
little is known about modulation at cryogenic temperatures. Here we demonstrate
a proof-of-principle experiment, showing that currently employed Ti-doped LiNbO
modulators maintain the Pockels coefficient at 3K---a base temperature for
classical microwave amplifier circuitry. We realize electro-optical read-out of
a superconducting electromechanical circuit to perform both coherent
spectroscopy, measuring optomechanically-induced transparency, and incoherent
thermometry, encoding the thermomechanical sidebands in an optical signal.
Although the achieved noise figures are high, approaches that match the
lower-bandwidth microwave signals, use integrated devices or materials with
higher EO coefficient, should achieve added noise similar to current HEMT
amplifiers, providing a route to parallel readout for emerging quantum or
classical computing platforms.Comment: Experimental details added. The heating experiment update
Noninvasive measurement of dynamic correlations in spin systems
Thesis (MSc)--Stellenbosch University, 2017ENGLISH ABSTRACT : Dynamic correlations hψ| O1(t1)O2(t2)|ψi of quantum observables are useful quantities
for the study of quantum dynamics. Attempts at measuring these correlations
are however complicated, due to the measurement backaction (wave function collapse)
incurred during measurements at the early time t1. We propose a noninvasive
measurement protocol, based on a weak ancilla target coupling, which reduces this
backaction at t1. We show that both real and imaginary parts of the desired correlation
can be extracted through appropriate choices of the initial ancilla state and
of the ancilla target coupling Hamiltonian. The protocol is applicable to arbitrary
(pseudo)spin systems with arbitrary (non)equilibrium initial states. Errors arising
in experimental implementations are analysed, and we show that deviations from
the desired correlation can be minimised through an optimal choice of the ancilla
target coupling time. Implementation in linear ion trap experiments is discussed.
We derive the positive-operator-valued measure which describes the noninvasive
measurement at t1. For dynamic correlations of single-site spin-1/2 observables, this
operator formalism shows that measurement backaction is of no concern. Real parts
can be obtained with projective measurements of the target at t1 and t2. Imaginary
parts are obtained by performing a local rotation of the target at t1, followed
by a projective measurement at t2. These ancilla-free protocols are theoretically
simpler than the noninvasive measurement protocol, but remain experimentally
challenging. Rotations and projections performed at t1 may be subject to noise,
which propagates into the measured correlation. We use Lieb-Robinson theory to
bound the size of the resulting error terms. An analysis of the spatio-temporal
behaviour of these errors provides guidance for experimental implementation of the
ancilla-free measurement protocols.AFRIKAANSE OPSOMMING : Dinamiese korrelasies hψ| O1(t1)O2(t2)|ψi van kwantum waarneembares is nuttig in
die studie van kwantum dinamika. Die meting van hierdie hoeveelhede word egter
gekompliseer deur die meetingsterugreaksie (gol unksie ineenstorting), wat tydens
die meting by die vroeër tyd t1 plaasvind. Ons stel 'n nie-ingrypende metingsprotokol
voor, gebaseer op 'n swak ancilla teikenstelsel koppeling, wat die meetingsterugreaksie
by t1 verminder. Ons toon dat die reële en imaginêre dele van
die korrelasiefunksie deur geskikte keuses van die ancilla begintoestand en van die
ancilla teikenstelsel koppeling bepaal kan word. Die protokol is van toepassing op
(pseudo)spin stelsels met arbitrêre nie-ewewig begintoestande. Foute wat in eksperimentele
implementering ontstaan word geanaliseer. Ons toon dat afwykings van
die gewenste korrelasie geminimeer kan word deur 'n optimale ancilla teikenstelsel
koppelingstyd. Implementering in liniêre ioonputte word bespreek.
Ons herlei die positiewe operator-waardige maat wat die nie-ingrypende meting
by t1 beskryf. Hierdie formalisme toon dat die meetingsterugreaksie van geen belang
is vir dinamiese korrelasies van enkelpunt spin-1/2 waarneembares nie. Die
reële deel kan deur projektiewe meetings by t1 en t2 bepaal word. Die imaginêre
deel word verkry deur 'n lokale rotasie by t1, gevolg deur 'n projektiewe meting
by t2. Hierdie ancilla-vrye protokolle is teoreties eenvoudiger as die nie-ingrypende
metingsprotokol, maar eksperimentele implementering bly uitdagend. Rotasies en
projeksies wat by t1 uitgevoer word kan onder steurings ly, wat dan ook die gemete
korrelasies a ekteer. Ons gebruik Lieb-Robinson teorie om die grootte van die resulterende
foute te begrens. 'n Analise van die foute se tyd en ruimtelike gedrag
bied leiding vir die eksperimentele implementering van die ancilla-vrye metingsprotokoll
Universal equilibration dynamics of the Sachdev-Ye-Kitaev model
Equilibrium quantum many-body systems in the vicinity of phase transitions
generically manifest universality. In contrast, limited knowledge has been
gained on possible universal characteristics in the non-equilibrium evolution
of systems in quantum critical phases. In this context, universality is
generically attributed to the insensitivity of observables to the microscopic
system parameters and initial conditions. Here, we present such a universal
feature in the equilibration dynamics of the Sachdev-Ye-Kitaev (SYK)
Hamiltonian -- a paradigmatic system of disordered, all-to-all interacting
fermions that has been designed as a phenomenological description of quantum
critical regions. We drive the system far away from equilibrium by performing a
global quench, and track how its ensemble average relaxes to a steady state.
Employing state-of-the-art numerical simulations for the exact evolution, we
reveal that the disorder-averaged evolution of few-body observables, including
the quantum Fisher information and low-order moments of local operators,
exhibit within numerical resolution a universal equilibration process. Under a
straightforward rescaling, data that correspond to different initial states
collapse onto a universal curve, which can be well approximated by a Gaussian
throughout large parts of the evolution. To reveal the physics behind this
process, we formulate a general theoretical framework based on the
Novikov--Furutsu theorem. This framework extracts the disorder-averaged
dynamics of a many-body system as an effective dissipative evolution, and can
have applications beyond this work. The exact non-Markovian evolution of the
SYK ensemble is very well captured by Bourret--Markov approximations, which
contrary to common lore become justified thanks to the extreme chaoticity of
the system, and universality is revealed in a spectral analysis of the
corresponding Liouvillian.Comment: 20 pages, 13 figure
Absence of operator growth for average equal-time observables in charge-conserved sectors of the Sachdev-Ye-Kitaev model
Abstract Quantum scrambling plays an important role in understanding thermalization in closed quantum systems. By this effect, quantum information spreads throughout the system and becomes hidden in the form of non-local correlations. Alternatively, it can be described in terms of the increase in complexity and spatial support of operators in the Heisenberg picture, a phenomenon known as operator growth. In this work, we study the disordered fully-connected Sachdev-Ye-Kitaev (SYK) model, and we demonstrate that scrambling is absent for disorder-averaged expectation values of observables. In detail, we adopt a formalism typical of open quantum systems to show that, on average and within charge-conserved sectors, operators evolve in a relatively simple way which is governed by their operator size. This feature only affects single-time correlation functions, and in particular it does not hold for out-of-time-order correlators, which are well-known to show scrambling behavior. Making use of these findings, we develop a cumulant expansion approach to approximate the evolution of equal-time observables. We employ this scheme to obtain analytic results that apply to arbitrary system size, and we benchmark its effectiveness by exact numerics. Our findings shed light on the structure of the dynamics of observables in the SYK model, and provide an approximate numerical description that overcomes the limitation to small systems of standard methods