arXiv subjects

Philipp Uhrich

Publications and source records attributed to Philipp Uhrich.

11 recordsLinked to original sources

arXiv2023

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.

cond-mat.str-el↗

arXiv2023

Absence of operator growth for average equal-time observables in charge-conserved sectors of the Sachdev-Ye-Kitaev model

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.

quant-ph↗

arXiv2023

A cavity quantum electrodynamics implementation of the Sachdev--Ye--Kitaev model

The search for a quantum theory of gravity has led to the discovery of quantum many-body systems that are dual to gravitational models with quantum properties. The perhaps most famous of these systems is the Sachdev-Ye-Kitaev (SYK) model. It features maximal scrambling of quantum information, and opens a potential inroad to experimentally investigating aspects of quantum gravity. A scalable laboratory realisation of this model, however, remains outstanding. Here, we propose a feasible implementation of the SYK model in cavity quantum electrodynamics platforms. Through detailed analytical and numerical demonstrations, we show how driving a cloud of fermionic atoms trapped in a multi-mode optical cavity, and subjecting it to a spatially disordered AC-Stark shift retrieves the physics of the SYK model, with random all-to-all interactions and fast scrambling. Our work provides a blueprint for realising the SYK model in a scalable system, with the prospect of studying holographic quantum matter in the laboratory.

quant-ph↗

arXiv2022

Detecting quantum phase transitions in the quasi-stationary regime of Ising chains

Recently, single-site observables have been shown to be useful for the detection of dynamical criticality due to an emergence of a universal critically-prethermal temporal regime in the magnetization [arXiv:2105.05986]. Here, we explore the potential of single-site observables as probes of quantum phase transitions in integrable and nonintegrable transverse-field Ising chains (TFIC). We analytically prove the requirement of zero modes for a quasi-stationary temporal regime to emerge at a bulk probe site, and show how this regime gives rise to a non-analytic behavior in the dynamical order profiles. Our $t$-DMRG calculations verify the results of the quench mean-field theory for near-integrable TFIC both with finite-size and finite-time scaling analyses. We find that both finite-size and finite-time analyses suggest a dynamical critical point for a strongly nonintegrable and locally connected TFIC. We finally demonstrate the presence of a quasi-stationary regime in the power-law interacting TFIC, and extract local dynamical order profiles for TFIC in the long-range Ising universality class with algebraic light cones.

cond-mat.quant-gas↗

arXiv2022

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.

cond-mat.quant-gas↗

arXiv2022

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.

cond-mat.quant-gas↗

arXiv2020

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.

quant-ph↗

arXiv2020

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 [Fläschner \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.

cond-mat.stat-mech↗

arXiv2018

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-$1/2$ 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.

quant-ph↗

arXiv2018

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.

quant-ph↗

arXiv2017

Noninvasive Measurement of Dynamic Correlation Functions

The measurement of dynamic correlation functions of quantum systems is complicated by measurement backaction. To facilitate such measurements we introduce a protocol, based on weak ancilla--system couplings, that is applicable to arbitrary (pseudo)spin systems and arbitrary equilibrium or nonequilibrium initial states. Different choices of the coupling operator give access to the real and imaginary parts of the dynamic correlation function. This protocol reduces disturbances due to the early time measurements to a minimum, and we quantify the deviation of the measured correlation functions from the theoretical, unitarily-evolved ones. Implementations of the protocol in trapped ions and other experimental platforms are discussed. For spin-$1/2$ models and single-site observables we prove that measurement backaction can be avoided altogether, allowing for the use of ancilla-free protocols.

quant-ph↗