Eduardo Mascarenhas

Matrix-product-operator approach to the nonequilibrium steady state of driven-dissipative quantum arrays

We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null eigenvalue of the Liouvillian superoperator by sweeping along the system while carrying out a partial diagonalization of the single-site stationary problem. It bears full analogy to the density-matrix renormalization-group approach to the ground state of isolated systems, and its numerical complexity scales as a power law with the bond dimension. The method brings considerable advantage when compared to the integration of the time-dependent problem via Trotter decomposition, as it can address arbitrarily long-ranged couplings. Additionally, it ensures numerical stability in the case of weakly dissipative systems thanks to a slow tuning of the dissipation rates along the sweeps. We have tested the method on a driven-dissipative spin chain, under various assumptions for the Hamiltonian, drive, and dissipation parameters, and compared the results to those obtained both by Trotter dynamics and Monte Carlo wave function methods. Accurate and numerically stable convergence was always achieved when applying the method to systems with a gapped Liouvillian and a nondegenerate steady state.

A quantum optical valve in a nonlinear-linear resonators junction

Electronic diodes, which enable the rectification of an electrical energy flux, have played a crucial role in the development of current microelectronics after the invention of semiconductor p-n junctions. Analogously, signal rectification at specific target wavelengths has recently become a key goal in optical communication and signal processing. Here we propose a genuinely quantum device with the essential rectifying features being demonstrated in a general model of a nonlinear-linear junction of coupled resonators. It is shown that such a surprisingly simple structure is a versatile valve and may be alternatively tuned to behave as: a photonic diode, a single- or two-photon rectified source turning a classical input into a quantum output depending on the input frequency, or a quantum photonic splitter. Given the relevance of non-reciprocal operations in integrated circuits, the nonlinear-linear junction realizes a crucial building component in prospective quantum photonic applications.

Protection of quantum information and optimal singlet conversion through higher-dimensional quantum systems and environment monitoring

We study how to protect quantum information in quantum systems subjected to local dissipation. We show that combining the use of three-level systems, environment monitoring, and local feedback can fully and deterministically protect any available quantum information, including entanglement initially shared by different parties. These results can represent a gain in resources and/or distances in quantum communication protocols such as quantum repeaters and teleportation as well as time for quantum memories. Finally, we show that monitoring local environments physically implements the optimum singlet conversion protocol, which is essential for classical entanglement percolation.

Cooperativity of a few quantum emitters in a single-mode cavity

We theoretically investigate the emission properties of a single-mode cavity coupled to a mesoscopic number of incoherently pumped quantum emitters. We propose an operational measure for the medium cooperativity, valid both in the bad- and in the good-cavity regimes. We show that the opposite regimes of subradiance and super-radiance correspond to negative and positive cooperativity, respectively. The lasing regime is shown to be characterized by non-negative cooperativity. In the bad-cavity regime we show that the cooperativity defines the transitions from subradiance to super-radiance. In the good-cavity regime it helps to define the lasing threshold, also providing distinguishable signatures indicating the lasing regime. Increasing the quality factor of the cavity mode induces a crossover from the solely super-radiant to the lasing regime. Furthermore, we verify that lasing is manifested in a wide range of positive cooperative behavior, showing that stimulated emission and super-radiance can coexist. The robustness of the cooperativity is studied with respect to experimental imperfections, such as inhomogeneous broadening and pure dephasing.

Emergent transport in a many-body open system driven by interacting quantum baths

We analyze an open many-body system that is strongly coupled at its boundaries to interacting quantum baths. We show that the two-body interactions inside the baths induce emergent phenomena in the spin transport. The system and baths are modeled as independent spin chains resulting in a global nonhomogeneous XXZ model. The evolution of the system-bath state is simulated using matrix-product-states methods. We present two phase transitions induced by bath interactions. For weak bath interactions we observe ballistic and insulating phases. However, for strong bath interactions a diffusive phase emerges with a distinct power-law decay of the time-dependent spin current Q alpha t(-alpha). Furthermore, we investigate long-lasting current oscillations arising from the non-Markovian dynamics in the homogeneous case and find a sharp change in their frequency scaling coinciding with the triple point of the phase diagram.

Quantum rectifier in a one-dimensional photonic channel

By using a fully quantum approach based on an input-output formulation of the stochastic Schrodinger equation, we show rectification of radiation fields in a one-dimensional waveguide doped with a pair of ideal two-level systems for three topical cases: classical driving, under the action of noise, and single-photon pulsed excitation. We show that even under the constant action of unwanted noise the device still operates effectively as an optical isolator, which is of critical importance for noise resistance. Finally, harnessing stimulated emission allows for nonreciprocal behavior for single-photon inputs, thus showing purely quantum rectification at the single-photon level. The latter is a considerable step towards the ultimate goal of devising an unconditional quantum rectifier for arbitrary quantum states.

Equilibrium and disorder-induced behavior in quantum light–matter systems

We analyze equilibrium properties of coupled-doped cavities described by the Jaynes–Cummings–Hubbard Hamiltonian. In particular, we characterize the entanglement of the system in relation to the insulating–superfluid phase transition. We point out the existence of a crossover inside the superfluid phase of the system when the excitations change from polaritonic to purely photonic. Using an ensemble statistical approach for small systems and stochastic mean-field theory for large systems, we analyze static disorder of the characteristic parameters of the system and explore the ground state-induced statistics. We report on a variety of glassy phases deriving from the hybrid statistics of the system. On-site strong disorder induces insulating behavior through two different mechanisms. For disorder in the light–matter detuning, low-energy cavities dominate the statistics, allowing the excitations to localize and bunch in such cavities. In the case of disorder in the light–matter coupling, sites with strong coupling between light and matter become very significant, which enhances the Mott-like insulating behavior. Inter-site (hopping) disorder induces fluidity and the dominant sites are strongly coupled to each other.

Quantum critical probing and simulation of colored quantum noise

We propose a protocol to simulate the evolution of a non-Markovian open quantum system by considering a collisional process with a many-body system, which plays the role of an environment. As a result of our protocol, the environment spatial correlations are mapped into the time correlations of a noise that drives the dynamics of the open system. Considering the weak coupling limit, the open system can also be considered as a probe of the environment properties. In this regard, when preparing the environment in its ground state, a measurement of the dynamics of the open system allows to determine the length of the environment spatial correlations and therefore its critical properties. To illustrate our proposal we simulate the full system dynamics with matrix-product-states and compare this to the reduced dynamics obtained with an approximated variational master equation.

Nonequilibrium photonic transport and phase transition in an array of optical cavities

We characterize photonic transport in a boundary driven array of nonlinear optical cavities. We find that the output field suddenly drops when the chain length is increased beyond a threshold. After this threshold a highly chaotic and unstable regime emerges, which marks the onset of a super-diffusive photonic transport. We show the scaling of the threshold with pump intensity and nonlinearity. Finally, we address the competition of disorder and nonlinearity presenting a diffusive-insulator phase transition.

Nonuniversality of entanglement convertibility

Recently, it has been suggested that operational properties connected to quantum computation can be alternative indicators of quantum phase transitions. In this work we systematically study these operational properties in 1D systems that present phase transitions of different orders. For this purpose, we evaluate the local convertibility between bipartite ground states. Our results suggest that the operational properties, related to non-analyticities of the entanglement spectrum, are good detectors of explicit symmetries of the model, but not necessarily of phase transitions. We also show that thermodynamically equivalent phases, such as Luttinger liquids, may display different convertibility properties depending on the underlying microscopic model.