arXiv subjects

Fabrizio Minganti

Publications and source records attributed to Fabrizio Minganti.

49 records · Page 3Linked to original sources

arXiv2020

Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories

Exceptional points (EPs) are degeneracies of classical and quantum open systems, which are studied in many areas of physics including optics, optoelectronics, plasmonics, and condensed matter physics. In the semiclassical regime, open systems can be described by phenomenological effective non-Hermitian Hamiltonians (NHHs) capturing the effects of gain and loss in terms of imaginary fields. The EPs that characterize the spectra of such Hamiltonians (HEPs) describe the time evolution of a system without quantum jumps. It is well known that a full quantum treatment describing more generic dynamics must crucially take into account such quantum jumps. In a recent paper [F. Minganti $et$ $al.$, Phys. Rev. A $\mathbf{100}$, $062131$ ($2019$)], we generalized the notion of EPs to the spectra of Liouvillian superoperators governing open system dynamics described by Lindblad master equations. Intriguingly, we found that in situations where a classical-to-quantum correspondence exists, the two types of dynamics can yield different EPs. In a recent experimental work [M. Naghiloo $et$ $al.$, Nat. Phys. $\mathbf{15}$, $1232$ ($2019$)], it was shown that one can engineer a non-Hermitian Hamiltonian in the quantum limit by postselecting on certain quantum jump trajectories. This raises an interesting question concerning the relation between Hamiltonian and Lindbladian EPs, and quantum trajectories. We discuss these connections by introducing a hybrid-Liouvillian superoperator, capable of describing the passage from an NHH (when one postselects only those trajectories without quantum jumps) to a true Liouvillian including quantum jumps (without postselection). Beyond its fundamental interest, our approach allows to intuitively relate the effects of postselection and finite-efficiency detectors.

quant-ph↗

arXiv2020

Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps

Exceptional points (EPs) correspond to degeneracies of open systems. These are attracting much interest in optics, optoelectronics, plasmonics, and condensed matter physics. In the classical and semiclassical approaches, Hamiltonian EPs (HEPs) are usually defined as degeneracies of non-Hermitian Hamiltonians such that at least two eigenfrequencies are identical and the corresponding eigenstates coalesce. HEPs result from continuous, mostly slow, nonunitary evolution without quantum jumps. Clearly, quantum jumps should be included in a fully quantum approach to make it equivalent to, e.g., the Lindblad master-equation approach. Thus, we suggest to define EPs via degeneracies of a Liouvillian superoperator (including the full Lindbladian term, LEPs), and we clarify the relations between HEPs and LEPs. We prove two main theorems: Theorem 1 proves that, in the quantum limit, LEPs and HEPs must have essentially different properties. Theorem 2 dictates a condition under which, in the ``semiclassical'' limit, LEPs and HEPs recover the same properties. In particular, we show the validity of Theorem 1 studying systems which have (1) an LEP but no HEPs, and (2) both LEPs and HEPs but for shifted parameters. As for Theorem 2, (3) we show that these two types of EPs become essentially equivalent in the semiclassical limit. We introduce a series of mathematical techniques to unveil analogies and differences between the HEPs and LEPs. We analytically compare LEPs and HEPs for some quantum and semiclassical prototype models with loss and gain.

quant-ph↗

arXiv2020

Quantum and semiclassical exceptional points of a linear system of coupled cavities with losses and gain within the Scully-Lamb laser theory

In the past few decades, many works have been devoted to the study of exceptional points (EPs), i.e., exotic degeneracies of non-Hermitian systems. The usual approach in those studies involves the introduction of a phenomenological effective non-Hermitian Hamiltonian (NHH), where the gain and losses are incorporated as the imaginary frequencies of fields and from which the Hamiltonian EPs (HEPs) are derived. Although this approach can provide valid equations of motion for the fields in the classical limit, its application in the derivation of EPs in the quantum regime is questionable. Recently, a framework [Minganti {\it et al.}, \href{https://doi.org/10.1103/PhysRevA.100.062131}{Phys. Rev. A {\bf 100}, 062131 (2019)}], which allows one to determine quantum EPs from a Liouvillian EP (LEP), rather than from an NHH, has been proposed. Compared to the NHHs, a Liouvillian naturally includes quantum noise effects via quantum-jump terms, thus allowing one to consistently determine its EPs purely in the quantum regime. In this work we study a non-Hermitian system consisting of coupled cavities with unbalanced gain and losses, where the gain is far from saturation, i.e, the system is assumed to be linear. We apply both formalisms, based on an NHH and a Liouvillian within the Scully-Lamb laser theory, to determine and compare the corresponding HEPs and LEPs in the semiclassical and quantum regimes. {Our results indicate that, although the overall spectral properties of the NHH and the corresponding Liouvillian for a given system can differ substantially, their LEPs and HEPs occur for the same combination of system parameters.}

quant-ph↗

arXiv2019

Mean-field validity in a dissipative critical system: Liouvillian gap, $\mathbb{PT}$-symmetric antigap, and permutational symmetry in the $XYZ$ model

We study the all-to-all connected $XYZ$ (anisotropic-Heisenberg) spin model with local and collective dissipations, comparing the results of mean field theory with the solution of the Lindblad quantum evolution. Leveraging the permutational symmetry of the model [N. Shammah et al., Phys Rev. A 98, 063815 (2018)], we find exactly (up to numerical precision) the steady state up to $N=95$ spins. We characterize criticality, studying, as a function of the number of spins $N$, the spin structure factor, the magnetization, the Liouvillian gap and the Von Neumann entropy of the steady state. Exploiting the weak $\mathcal{PT}$-symmetry of the model, we efficiently calculate the Liouvillian gap, introducing the idea of an antigap. For small anisotropy, we find a paramagnetic-to-ferromagnetic phase transition in agreement with the mean-field theory. For large anisotropy, instead, we find a significant discrepancy from the scaling of the low-anisotropy ferromagnetic phase. We also study other more experimentally-accessible witnesses of the transition, which can be used for finite-size studies, namely the bimodality coefficient and the angular averaged susceptibility. In contrast to the bimodality coefficient, the angular averaged susceptibility fails to capture the onset of the transition, in striking difference with respect to lower-dimensional studies. We also analyze the competition between local dissipative processes (which disentangle the spin system) and collective dissipative ones (generating entanglement). The nature of the phase transition is almost unaffected by the presence of these terms. Our results mark a stark difference with the common intuition that an all-to-all connected system should fall onto the mean-field solution also for intermediate number of spins.

quant-ph↗

arXiv2019

Dissipation-induced bistability in the two-photon Dicke model

The Dicke model is a paradigmatic quantum-optical model describing the interaction of a collection of two-level systems with a single bosonic mode. Effective implementations of this model made it possible to observe the emergence of superradiance, i.e., cooperative phenomena arising from the collective nature of light-matter interactions. Via reservoir engineering and analogue quantum simulation techniques, current experimental platforms allow us not only to implement the Dicke model, but also to design more exotic interactions, such as the two-photon Dicke model. In the Hamiltonian case, this model presents an interesting phase diagram characterized by two quantum criticalities: a superradiant phase transition and a spectral collapse, that is, the coalescence of discrete energy levels into a continuous band. Here, we investigate the effects of both qubit and photon dissipation on the phase transition and on the instability induced by the spectral collapse. Using a mean-field decoupling approximation, we analytically obtain the steady-state expectation values of the observables signaling a symmetry breaking, identifying a first-order phase transition from the normal to the superradiant phase. Our stability analysis unveils a very rich phase diagram, which features stable, bistable, and unstable phases depending on dissipation rate.

quant-ph↗

arXiv2019

Dynamical properties of dissipative XYZ Heisenberg lattices

We study dynamical properties of dissipative XYZ Heisenberg lattices where anisotropic spin-spin coupling competes with local incoherent spin flip processes. In particular, we explore a region of the parameter space where dissipative magnetic phase transitions for the steady state have been recently predicted by mean-field theories and exact numerical methods. We investigate the asymptotic decay rate towards the steady state both in 1D (up to the thermodynamical limit) and in finite-size 2D lattices, showing that critical dynamics does not occur in 1D, but it can emerge in 2D. We also analyze the behavior of individual homodyne quantum trajectories, which well reveal the nature of the transition.

quant-ph↗

arXiv2019

Quantum critical regime in a quadratically-driven nonlinear photonic lattice

We study an array of coupled optical cavities in presence of two-photon driving and dissipation. The system displays a critical behavior similar to that of a quantum Ising model at finite temperature. Using the corner-space renormalization method, we compute the steady-state properties of finite lattices of varying size, both in one- and two-dimensions. From a finite-size scaling of the average of the photon number parity, we highlight the emergence of a critical point in regimes of small dissipations, belonging to the quantum Ising universality class. For increasing photon loss rates, a departure from this universal behavior signals the onset of a quantum critical regime, where classical fluctuations induced by losses compete with long-range quantum correlations.

quant-ph↗

arXiv2019

Optimal stochastic unraveling of disordered open quantum systems: application to driven-dissipative photonic lattices

We propose an efficient numerical method to compute configuration averages of observables in disordered open quantum systems whose dynamics can be unraveled via stochastic trajectories. We prove that the optimal sampling of trajectories and disorder configurations is simply achieved by considering one random disorder configuration for each individual trajectory. As a first application, we exploit the present method to the study the role of disorder on the physics of the driven-dissipative Bose-Hubbard model in two different regimes: (i) for strong interactions, we explore the dissipative physics of fermionized bosons in disordered one-dimensional chains; (ii) for weak interactions, we investigate the role of on-site inhomogeneities on a first-order dissipative phase transition in a two-dimensional square lattice.

quant-ph↗

arXiv2018

Spectral theory of Liouvillians for dissipative phase transitions

A state of an open quantum system is described by a density matrix, whose dynamics is governed by a Liouvillian superoperator. Within a general framework, we explore fundamental properties of both first-order dissipative phase transitions and second-order dissipative phase transitions associated with a symmetry breaking. In the critical region, we determine the general form of the steady-state density matrix and of the Liouvillian eigenmatrix whose eigenvalue defines the Liouvillian spectral gap. We illustrate our exact results by studying some paradigmatic quantum optical models exhibiting critical behavior.

quant-ph↗

arXiv2018

Critical slowing down in driven-dissipative Bose-Hubbard lattices

We theoretically explore the dynamical properties of a first-order dissipative phase transition in coherently driven Bose-Hubbard systems, describing, e.g., lattices of coupled nonlinear optical cavities. Via stochastic trajectory calculations based on the truncated Wigner approximation, we investigate the dynamical behavior as a function of system size for 1D and 2D square lattices in the regime where mean-field theory predicts nonlinear bistability. We show that a critical slowing down emerges for increasing number of sites in 2D square lattices, while it is absent in 1D arrays. We characterize the peculiar properties of the collective phases in the critical region.

quant-ph↗

arXiv2017

Homodyne versus photon-counting quantum trajectories for dissipative Kerr resonators with two-photon driving

We investigate two different kinds of quantum trajectories for a nonlinear photon resonator subject to two-photon pumping, a configuration recently studied for the generation of photonic Schroedinger cat states. In the absence of feedback control and in the strong-driving limit, the steady-state density matrix is a statistical mixture of two states with equal weight. While along a single photon-counting trajectory the systems intermittently switches between an odd and an even cat state, we show that upon homodyne detection the situation is different. Indeed, homodyne quantum trajectories reveal switches between coherent states of opposite phase.

quant-ph↗

arXiv2016

Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions

We present exact results for the steady-state density matrix of a general class of driven-dissipative systems consisting of a nonlinear Kerr resonator in the presence of both coherent (one-photon) and parametric (two-photon) driving and dissipation. Thanks to the analytical solution, obtained via the complex P-representation formalism, we are able to explore any regime, including photon blockade, multiphoton resonant effects, and a mesoscopic regime with large photon density and quantum correlations. We show how the interplay between one- and two-photon driving provides a way to control the multimodality of the Wigner function in regimes where the semiclassical theory exhibits multistability. We also study the emergence of dissipative phase transitions in the thermodynamic limit of large photon numbers.

quant-ph↗

arXiv2015

Momentum-dependent pseudo-spin dimers of coherently coupled bosons in optical lattices

We study the two-body bound and scattering states of two particles in a one dimensional optical lattice in the presence of a coherent coupling between two internal atomic levels. Due to the interplay between periodic potential, interactions and coherent coupling, the internal structure of the bound states depends on their center of mass momentum. This phenomenon corresponds to an effective momentum-dependent magnetic field for the dimer pseudo-spin, which could be observed in a chirping of the precession frequency during Bloch oscillations. The essence of this effect can be easily interpreted in terms of an effective bound state Hamiltonian. Moreover for indistinguishable bosons, the two-body eigenstates can present simultaneously attractive and repulsive bound-state nature or even bound and scattering properties.

cond-mat.quant-gas↗