arXiv subjects

J. I. Cirac

Publications and source records attributed to J. I. Cirac.

At least 19 recordsLinked to original sources

arXiv2025

Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories

We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced by F. Verstraete et al. in 2005 and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced by Cirac et al. in 2011.

quant-ph↗

arXiv2021

Weakly invasive metrology: quantum advantage and physical implementations

We consider the estimation of a Hamiltonian parameter of a set of highly photosensitive samples, which are damaged after a few photons $N_{\rm abs}$ are absorbed, for a total time $T$. The samples are modelled as a two mode photonic system, where photons simultaneously acquire information on the unknown parameter and are absorbed at a fixed rate. We show that arbitrarily intense coherent states can obtain information at a rate that scales at most linearly with $N_{\rm abs}$ and $T$, whereas quantum states with finite intensity can overcome this bound. We characterise the quantum advantage as a function of $N_{\rm abs}$ and $T$, as well as its robustness to imperfections (non-ideal detectors, finite preparation and measurement rates for quantum photonic states). We discuss an implementation in cavity QED, where Fock states are both prepared and measured by coupling atomic ensembles to the cavities. We show that superradiance, arising due to a collective coupling between the cavities and the atoms, can be exploited for improving the speed and efficiency of the measurement.

quant-ph↗

arXiv2020

Analog quantum chemistry simulation

Computing the electronic structure of molecules with high precision is a central challenge in the field of quantum chemistry. Despite the enormous success of approximate methods, tackling this problem exactly with conventional computers is still a formidable task. This has triggered several theoretical and experimental efforts to use quantum computers to solve chemistry problems, with first proof-of-principle realizations done in a digital manner. An appealing alternative to the digital approach is analog quantum simulation, which does not require a scalable quantum computer, and has already been successfully applied in condensed matter physics problems. However, all available or planned setups cannot be used in quantum chemistry problems, since it is not known how to engineer the required Coulomb interactions with them. Here, we present a new approach to the simulation of quantum chemistry problems in an analog way. Our method relies on the careful combination of two technologies: ultra-cold atoms in optical lattices and cavity QED. In the proposed simulator, fermionic atoms hopping in an optical potential play the role of electrons, additional optical potentials provide the nuclear attraction, and a single spin excitation over a Mott insulator mediates the electronic Coulomb repulsion with the help of a cavity mode. We also provide the operational conditions of the simulator and benchmark it with a simple molecule. Our work opens up the possibility of efficiently computing electronic structures of molecules with analog quantum simulation.

quant-ph↗

arXiv2020

Multimode Fock states with large photon number: effective descriptions and applications in quantum metrology

We develop general tools to characterise and efficiently compute relevant observables of multimode $N$-photon states generated in non-linear decays in one-dimensional waveguides. We then consider optical interferometry in a Mach-Zender interferometer where a $d$-mode photonic state enters in each arm of the interferometer. We derive a simple expression for the Quantum Fisher Information in terms of the average photon number in each mode, and show that it can be saturated by number-resolved photon measurements that do not distinguish between the different $d$ modes.

quant-ph↗

arXiv2020

Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model

Infinite projected entangled pair states (iPEPS) provide a convenient variational description of infinite, translationally-invariant two-dimensional quantum states. However, the simulation of local excitations is not directly possible due to the translationally-invariant ansatz. Furthermore, as iPEPS are either identical or orthogonal, expectation values between different states as required during the evaluation of non-equal-time correlators are ill-defined. Here, we show that by introducing auxiliary states on each site, it becomes possible to simulate both local excitations and evaluate non-equal-time correlators in an iPEPS setting under real-time evolution. We showcase the method by simulating the t-J model after a single hole has been placed in the half-filled antiferromagnetic background and evaluating both return probabilities and spin correlation functions, as accessible in quantum gas microscopes.

cond-mat.str-el↗

arXiv2019

Markovianity of an emitter coupled to a structured spin chain bath

We analyze the dynamics of a spin 1/2 subsystem coupled to a spin chain. We simulate numerically the full quantum many-body system for various sets of parameters and initial states of the chain, and characterize the divisibility of the subsystem dynamics, i.e. whether it is Markovian and can be described by a (time dependent) master equation. We identify regimes in which the subsystem admits such Markovian description, despite the many-body setting, and provide insight about why the same is not possible in other regimes. Interestingly, coupling the subsystem at the edge, instead of the center, of the chain gives rise to qualitatively distinct behavior.

quant-ph↗

arXiv2019

Simulating Lattice Gauge Theories within Quantum Technologies

Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented - a classical simulation approach - applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed.

quant-ph↗

arXiv2019

Cold atoms in twisted bilayer optical potentials

The possibility of creating crystal bilayers twisted with respect to each other has led to the discovery of a wide range of novel electron correlated phenomena whose full understanding is still under debate. Here we propose and analyze a method to simulate twisted bilayers using cold atoms in state-dependent optical lattices. Our proposed setup can be used as an alternative platform to explore twisted bilayers which allows one to control the inter/intra-layer coupling in a more flexible way than in the solid-state realizations. We focus on square geometries but also point how it can be extended to simulate other lattices which show Dirac-like physics. This setup opens a path to observe similar physics, e.g., band narrowing, with larger twist angles, to rule out some of the mechanisms to explain the observed strongly correlated effects, as well as to study other phenomena difficult to realize with crystals. As an example of the latter we explore the quantum optical consequences of letting emitters interact with twisted bilayer reservoirs, and predict the appearance of unconventional radiation patterns and emitter interactions following the emergent Moiré geometry.

quant-ph↗

arXiv2019

Engineering and harnessing giant atoms in high-dimensional baths: a cold atoms' implementation

Emitters coupled simultaneously to distant positions of a photonic bath, the so-called giant atoms, represent a new paradigm in quantum optics. When coupled to one-dimensional baths, as recently implemented with transmission lines or SAW waveguides, they lead to striking effects such as chiral emission or decoherence-free atomic interactions. Here, we show how to create giant atoms in dynamical state-dependent optical lattices, which offers the possibility of coupling them to structured baths in arbitrary dimensions. This opens up new avenues to a variety of phenomena and opportunities for quantum simulation. In particular, we show how to engineer unconventional radiation patterns, like multi-directional chiral emission, as well as collective interactions that can be used to simulate non-equilibrium many-body dynamics with no analogue in other setups. Besides, the recipes we provide to harness giant atoms in high dimensions can be exported to other platforms where such non-local couplings can be engineered.

quant-ph↗

arXiv2019

Quantum metrology with one-dimensional superradiant photonic states

Photonic states with large and fixed photon numbers, such as Fock states, enable quantum-enhanced metrology but remain an experimentally elusive resource. A potentially simple, deterministic and scalable way to generate these states consists of fully exciting $N$ quantum emitters equally coupled to a common photonic reservoir, which leads to a collective decay known as Dicke superradiance. The emitted $N$-photon state turns out to be a highly entangled multimode state, and to characterise its metrological properties in this work we: (i) develop theoretical tools to compute the Quantum Fisher Information of general multimode photonic states; (ii) use it to show that Dicke superradiant photons in 1D waveguides achieve Heisenberg scaling, which can be saturated by a parity measurement; (iii) and study the robustness of these states to experimental limitations in state-of-art atom-waveguide QED setups.

quant-ph↗

arXiv2018

Gaussian states for the variational study of (1+1)-dimensional lattice gauge models

We introduce a variational ansatz based on Gaussian states for (1+1)-dimensional lattice gauge models. To this end we identify a set of unitary transformations which decouple the gauge degrees of freedom from the matter fields. Using our ansatz, we study static aspects as well as real-time dynamics of string breaking in two (1+1)-dimensional theories, namely QED and two-color QCD. We show that our ansatz captures the relevant features and is in excellent agreement with data from numerical calculations with tensor networks.

hep-lat↗

arXiv2018

Variational study of U(1) and SU(2) lattice gauge theories with Gaussian states in 1+1 dimensions

We introduce a method to investigate the static and dynamic properties of both Abelian and non-Abelian lattice gauge models in 1+1 dimensions. Specifically, we identify a set of transformations that disentangle different degrees of freedom, and apply a simple Gaussian variational ansatz to the resulting Hamiltonian. To demonstrate the suitability of the method, we analyze both static and dynamic aspects of string breaking for the U(1) and SU(2) gauge models. We benchmark our results against tensor network simulations and observe excellent agreement, although the number of variational parameters in the Gaussian ansatz is much smaller.

hep-lat↗

arXiv2018

Non-Markovian Quantum Optics with Three-Dimensional State-Dependent Optical Lattices

Quantum emitters coupled to structured photonic reservoirs experience unconventional individual and collective dynamics emerging from the interplay between dimensionality and non-trivial photon energy dispersions. In this work, we systematically study several paradigmatic three dimensional structured baths with qualitative differences in their bath spectral density. We discover non-Markovian individual and collective effects absent in simplified descriptions, such as perfect subradiant states or long-range anisotropic interactions. Furthermore, we show how to implement these models using only cold atoms in state-dependent optical lattices and show how this unconventional dynamics can be observed with these systems.

quant-ph↗

arXiv2018

Effective many-body Hamiltonians of qubit-photon bound states

Quantum emitters (QEs) coupled to structured baths can localize multiple photons around them and form qubit-photon bound states. In the Markovian or weak coupling regime, the interaction of QEs through these single-photon bound states is known to lead to effective many-body QE Hamiltonians with tuneable but yet perturbative interactions. In this work we study the emergence of such models in the non-Markovian or strong coupling regime in different excitation subspaces. The effective models for the non-Markovian regime with up to three excitations are characterized using analytical methods, uncovering the existence of doublons or triplon states. Furthermore, we provide numerical results for systems with multiple excitations and demonstrate the emergence of polariton models with optically tuneable interactions, whose many-body ground state exhibits a superfluid-Mott insulator transition.

quant-ph↗

arXiv2018

Unitary $n$-designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of Rényi entropies

We present a general framework for the generation of random unitaries based on random quenches in atomic Hubbard and spin models, forming approximate unitary $n$-designs, and their application to the measurement of Rényi entropies. We generalize our protocol presented in [Elben2017: arXiv:1709.05060, to appear in Phys. Rev. Lett.] to a broad class of atomic and spin lattice models. We further present an in-depth numerical and analytical study of experimental imperfections, including the effect of decoherence and statistical errors, and discuss connections of our approach with many-body quantum chaos.

quant-ph↗

arXiv2018

Generation of single and two-mode multiphoton states in waveguide QED

Single and two-mode multiphoton states are the cornerstone of many quantum technologies, e.g., metrology. In the optical regime these states are generally obtained combining heralded single-photons with linear optics tools and post-selection, leading to inherent low success probabilities. In a recent paper, we design several protocols that harness the long-range atomic interactions induced in waveguide QED to improve fidelities and protocols of single-mode multiphoton emission. Here, we give full details of these protocols, revisit them to simplify some of their requirements and also extend them to generate two-mode multiphoton states, such as Yurke or NOON states.

quant-ph↗

arXiv2018

Markovian and Non-Markovian Dynamics of Quantum Emitters coupled to Two-dimensional Structured Reservoirs

The interaction of quantum emitters with structured baths modifies both their individual and collective dynamics. In González-Tudela \emph{et al} we show how exotic quantum dynamics emerge when QEs are spectrally tuned around the middle of the band of a two-dimensional structured reservoir, where we predict the failure of perturbative treatments, anisotropic interactions and novel super and subradiant behaviour. In this work, we provide further analysis of that situation, together with a complete analysis for the quantum emitter dynamics in spectral regions different from the center of the band.

quant-ph↗

arXiv2018

Purely Long-Range Coherent Interactions in Two-Dimensional Structured Baths

In this work we study the quantum dynamics emerging when quantum emitters exchange excitations with a two-dimensional bosonic bath with hexagonal symmetry. We show that a single quantum emitter spectrally tuned to the middle of the band relaxes following a logarithmic law in time due to the existence of a singular point with vanishing density of states, i.e., the Dirac point. Moreover, when several emitters are coupled to the bath at that frequency, long-range coherent interactions between them appear which decay inversely proportional to their distance without exponential attenuation. We analyze both the finite and infinite system situation using both perturbative and non-perturbative methods.

quant-ph↗