arXiv subjects

José Lebreuilly

Publications and source records attributed to José Lebreuilly.

9 recordsLinked to original sources

arXiv2022

Stabilizing the Laughlin state of light: dynamics of hole fractionalization

Particle loss is the ultimate challenge for preparation of strongly correlated many-body states of photons. An established way to overcome the loss is to employ a stabilization setup that autonomously injects new photons in place of the lost ones. However, as we show, the effectiveness of such a stabilization setup is compromised for fractional quantum Hall states. There, a hole formed by a lost photon can separate into several remote quasiholes none of which can be refilled by injecting a photon locally. By deriving an exact expression for the steady-state density matrix, we demonstrate that isolated quasiholes proliferate in the steady state which damages the quality of the state preparation. The motion of quasiholes leading to their separation is allowed by a repeated process in which a photon is first lost and then quickly refilled in the vicinity of the quasihole. We develop the theory of this dissipative quasihole dynamics and show that it has diffusive character. Our results demonstrate that fractionalization might present an obstacle for both creation and stabilization of strongly-correlated states with photons.

cond-mat.mes-hall↗

arXiv2021

Photon-Number-Dependent Hamiltonian Engineering for Cavities

Cavity resonators are promising resources for quantum technology, while native nonlinear interactions for cavities are typically too weak to provide the level of quantum control required to deliver complex targeted operations. Here we investigate a scheme to engineer a target Hamiltonian for photonic cavities using ancilla qubits. By off-resonantly driving dispersively coupled ancilla qubits, we develop an optimized approach to engineering an arbitrary photon-number-dependent (PND) Hamiltonian for the cavities while minimizing the operation errors. The engineered Hamiltonian admits various applications including canceling unwanted cavity self-Kerr interactions, creating higher-order nonlinearities for quantum simulations, and designing quantum gates resilient to noise. Our scheme can be implemented with coupled microwave cavities and transmon qubits in superconducting circuit systems.

quant-ph↗

arXiv2021

Autonomous quantum error correction and quantum computation

In this work, we present a general theoretical framework for the study of autonomously corrected quantum devices. First, we identify a necessary and sufficient revised version of the Knill-Laflamme conditions for the existence of an engineered Lindbladian providing protection against at most $c$ consecutive errors of natural dissipation, giving rise to an effective logical decoherence rate suppressed to order $c$. Moreover, we demonstrate that such engineered dissipation can be combined with generalized realizations of error-transparent Hamiltonians (ETH) in order to perform a quantum computation in the logical space while maintaining the same degree of suppression of decoherence. Finally, we introduce a formalism predicting with precision the emergent dynamics in the logical code space resulting from the interplay of natural, engineered dissipations sources and the generalized ETH.

quant-ph↗

arXiv2019

Stabilizing arrays of photonic cat states via spontaneous symmetry breaking

The controlled generation and the protection of entanglement is key to quantum simulation and quantum computation. At the single-mode level, protocols based on photonic cat states hold strong promise as they present unprecedentedly long-lived coherence and may be combined with powerful error correction schemes. Here, we demonstrate that robust ensembles of "many-body photonic cat states" can be generated in a Bose-Hubbard model with pair hopping via a spontaneous U(1) symmetry breaking mechanism. We identify a parameter region where the ground state is a massively degenerate manifold consisting of local cat states which are factorized throughout the lattice and whose conserved individual parities can be used to make a register of qubits. This phenomenology occurs for arbitrary system sizes or geometries, as soon as long-range order is established, and it extends to driven-dissipative conditions. In the thermodynamic limit, it is related to a Mott insulator to pair-superfluid phase transition.

quant-ph↗

arXiv2018

Quantum simulation of zero temperature quantum phases and incompressible states of light via non-Markovian reservoir engineering techniques

We review recent theoretical developments on the stabilization of strongly correlated quantum fluids of light in driven-dissipative photonic devices through novel non-Markovian reservoir engineering techniques. This approach allows to compensate losses and refill selectively the photonic population so to sustain a desired steady-state. It relies in particular on the use of a frequency-dependent incoherent pump which can be implemented, e.g., via embedded two-level systems maintained at a strong inversion of population. As specific applications of these methods, we discuss the generation of Mott Insulator (MI) and Fractional Quantum Hall (FQH) states of light. As a first step, we present the case of a narrowband emission spectrum and show how this allows for the stabilization of MI and FQH states under the condition that the photonic states are relatively flat in energy. As soon as the photonic bandbwidth becomes comparable to the emission linewidth, important non-equilibrium signatures and entropy generation appear. As a second step, we review a more advanced configuration based on reservoirs with a broadband frequency distribution, and we highlight the potential of this configuration for the quantum simulation of equilibrium quantum phases at zero temperature with tunable chemical potential. As a proof of principle we establish the applicability of our scheme to the Bose-Hubbard model by confirming the presence of a perfect agreement with the ground-state predictions both in the Mott Insulating and superfluid regions, and more generally in all parts of the parameter space. Future prospects towards the quantum simulation of more complex configurations are finally outlined, along with a discussion of our scheme as a concrete realization of quantum annealing.

cond-mat.quant-gas↗

arXiv2017

Pseudo-thermalization in driven-dissipative non-Markovian open quantum systems

We investigate a `pseudo thermalization' effect, where an open quantum system coupled to several non-Markovian reservoirs presents an emergent thermal behaviour in spite of its coupling to a non-equilibrated environment. The thermal behaviour is visible at both static and dynamical levels and the system satisfies the fluctuation-dissipation theorem. Our analysis is focused on the exactly solvable model of a weakly interacting driven-dissipative Bose gas in presence of frequency-dependent particle pumping and losses, and is based on a quantum Langevin theory, which we derive starting from a microscopical quantum optics model. For generic non-Markovian reservoirs, we demonstrate that the emergence of thermal properties occurs in the range of frequencies corresponding to low-energy excitations. For the specific case of non-Markovian baths verifying the Kennard-Stepanov relation, we show that pseudo-thermalization can instead occur at all energy scales. The possible implications regarding the interpretation of thermal laws in exciton-polariton low temperature experiments are discussed. We finally show that the presence of either a saturable pumping or a dispersive environment leads to a breakdown of the pseudo-thermalization effect.

cond-mat.quant-gas↗

arXiv2017

Phase diagram of incoherently driven strongly correlated photonic lattices

We explore theoretically the nonequilibrium photonic phases of an array of coupled cavities in presence of incoherent driving and dissipation. In particular, we consider a Hubbard model system where each site is a Kerr nonlinear resonator coupled to a two-level emitter, which is pumped incoherently. Within a Gutzwiller mean-field approach, we determine the steady-state phase diagram of such a system. We find that, at a critical value of the inter-cavity photon hopping rate, a second-order nonequilibrium phase transition associated with the spontaneous breaking of the $U(1)$ symmetry occurs. The transition from an incompressible Mott-like photon fluid to a coherent delocalized phase is driven by commensurability effects and not by the competition between photon hopping and optical nonlinearity. The essence of the mean-field predictions is corroborated by finite-size simulations obtained with matrix product operators and corner-space renormalization methods.

cond-mat.other↗

arXiv2017

Stabilizing strongly correlated photon fluids with non-Markovian reservoirs

We introduce a novel frequency-dependent incoherent pump scheme with a square-shaped spectrum as a way to study strongly correlated photons in arrays of coupled nonlinear resonators. This scheme can be implemented via a reservoir of population-inverted two-level emitters with a broad distribution of transition frequencies. Our proposal is predicted to stabilize a non-equilibrium steady state sharing important features with a zero-temperature equilibrium state with a tunable chemical potential. We confirm the efficiency of our proposal for the Bose-Hubbard model by computing numerically the steady state for finite system sizes: first, we predict the occurrence of a sequence of incompressible Mott-Insulator-like states with arbitrary integer densities presenting strong robustness against tunneling and losses. Secondly, for stronger tunneling amplitudes or non-integer densities, the system enters a coherent regime analogous to the superfluid state. In addition to an overall agreement with the zero-temperature equilibrium state, exotic non-equilibrium processes leading to a finite entropy generation are pointed out in specific regions of parameter space. The equilibrium ground state is shown to be recovered by adding frequency-dependent losses. The promise of this improved scheme in view of quantum simulation of the zero temperature many-body physics is highlighted.

quant-ph↗

arXiv2016

Towards strongly correlated photons in arrays of dissipative nonlinear cavities under a frequency-dependent incoherent pumping

We report a theoretical study of a quantum optical model consisting of an array of strongly nonlinear cavities incoherently pumped by an ensemble of population-inverted two-level atoms. Projective methods are used to eliminate the atomic dynamics and write a generalized master equation for the photonic degrees of freedom only, where the frequency-dependence of gain introduces non-Markovian features. In the simplest single cavity configuration, this pumping scheme gives novel optical bistability effects and allows for the selective generation of Fock states with a well-defined photon number. For many cavities in a weakly non-Markovian limit, the non-equilibrium steady state recovers a Grand-Canonical statistical ensemble at a temperature determined by the effective atomic linewidth. For a two-cavity system in the strongly nonlinear regime, signatures of a Mott state with one photon per cavity are found.

cond-mat.quant-gas↗