arXiv subjects

Luca Ferialdi

Publications and source records attributed to Luca Ferialdi.

At least 19 recordsLinked to original sources

arXiv2024

Multimode-cavity picture of non-Markovian waveguide QED

We introduce a picture to describe and intrepret waveguide-QED problems in the non-Markovian regime of long photonic retardation times resulting in delayed coherent feedback. The framework is based on an intuitive spatial decomposition of the waveguide into blocks. Among these, the block directly coupled to the atoms embodies an effective lossy multimode cavity leaking into the rest of the waveguide, in turn embodying an effective white-noise bath. The dynamics can be approximated by retaining only a finite number of cavity modes which grows with the time delay. This description captures the atomic as well as the field's dynamics, even with many excitations, in both emission and scattering processes. As an application, we show that the recently identified non-Markovian steady states can be understood by retaining very few or even only one cavity modes.

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arXiv2023

Collapse dynamics are diffusive

Non-interferometric experiments have been successfully employed to constrain models of spontaneous wave function collapse, which predict a violation of the quantum superposition principle for large systems. These experiments are grounded on the fact that, according to these models, the dynamics is driven by a noise that, besides collapsing the wave function in space, generates a diffusive motion with characteristic signatures, which, though small, can be tested. The non-interferometric approach might seem applicable only to those models which implement the collapse through a noisy dynamics, not to any model, which collapses the wave function in space. Here we show that this is not the case: under reasonable assumptions, any collapse dynamics (in space) is diffusive. Specifically, we prove that any space-translation invariant dynamics which complies with the no-signaling constraint, if collapsing the wave function in space, must change the average momentum of the system, and/or its spread.

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arXiv2023

General ordering theorem

The problem of ordering operators has afflicted quantum mechanics since its foundation. Several orderings have been devised, but a systematic procedure to move from one ordering to another is still missing. The importance of establishing relations among different orderings is demonstrated by Wick's theorem (which relates time ordering to normal ordering), which played a crucial role in the development of quantum field theory. We prove the General Ordering Theorem (GOT), which establishes a relation among any pair of orderings, that act on operators satisfying generic (i.e. operatorial) commutation relations. We expose the working principles of the GOT by simple examples, and we demonstrate its potential by recovering two famous algebraic theorems as special instances: the Magnus expansion and the Baker-Campbell-Hausdorff formula. Remarkably, the GOT establishes a formal relation between these two theorems, and it provides compact expressions for them, unlike the notoriously complicated ones currently known.

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arXiv2022

Present status and future challenges of non-interferometric tests of collapse models

The superposition principle is the cornerstone of quantum mechanics, leading to a variety of genuinely quantum effects. Whether the principle applies also to macroscopic systems or, instead, there is a progressive breakdown when moving to larger scales, is a fundamental and still open question. Spontaneous wavefunction collapse models predict the latter option, thus questioning the universality of quantum mechanics. Technological advances allow to challenge collapse models and the quantum superposition principle more and more with a variety of different experiments. Among them, non-interferometric experiments proved to be the most effective in testing these models. We provide an overview of such experiments, including cold atoms, optomechanical systems, X-rays detection, bulk heating as well as comparisons with cosmological observations. We also discuss avenues for future dedicated experiments, which aim at further testing collapse models and the validity of quantum mechanics.

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arXiv2022

Fundamental limits of superconducting quantum computers

The Continuous Spontaneous Localization (CSL) model is an alternative formulation of quantum mechanics which introduces a noise coupled non linearly to the wave function to account for its collapse. We consider CSL effects on quantum computers made of superconducting transmon qubits. As a direct effect CSL reduces quantum superpositions of the computational basis states of the qubits: we show the reduction rate to be negligibly small. However, an indirect effect of CSL, dissipation induced by the noise, also leads transmon qubits to decohere, by generating additional quasiparticles. Since the decoherence rate of transmon qubits depends on the quasiparticle density, by computing their generation rate induced by CSL, we can estimate the corresponding quasiparticle density and thus the limit set by CSL on the performances of transmon quantum computers. We show that CSL could spoil the quantum computation of practical algorithms on large devices. We further explore the possibility of testing CSL effects on superconducting devices.

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arXiv2020

CSL reduction rate for rigid bodies

In the context of spontaneous wave function collapse models, we investigate the properties of the Continuous Spontaneous Localization (CSL) collapse rate for rigid bodies. By exploiting the Euler-Maclaurin formula, we show that for standard matter the rate for a continuous mass distribution accurately reproduces the exact rate (i.e. the one for a point-like distribution). We compare the exact rate with previous estimates in the literature and we asses their validity. We find that the reduction rate displays a peculiar mass difference effect, which we investigate and describe in detail. We show that the recently proposed layering effect is a consequence of the mass difference effect.

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arXiv2020

Minimum measurement time: lower bound on the frequency cutoff for collapse models

The CSL model predicts a progressive breakdown of the quantum superposition principle, with a noise randomly driving the state of the system towards a localized one, thus accounting for the emergence of a classical world within a quantum framework. In the original model the noise is supposed to be white, but since white noises do not exist in nature, it becomes relevant to identify some of its spectral properties. Experimental data set an upper bound on its frequencies, while in this paper we bound it from below. We do so in two ways: by considering a 'minimal' measurement setup, requiring that the collapse is completed within the measurement time; and in a measurement modeling-independent way, by requiring that the fluctuations average to zero before the measurement time.

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arXiv2019

Optimal control for feedback cooling in cavityless levitated optomechanics

We consider feedback cooling in a cavityless levitated optomechanics setup, and we investigate the possibility to improve the feedback implementation. We apply optimal control theory to derive the optimal feedback signal both for quadratic (parametric) and linear (electric) feedback. We numerically compare optimal feedback against the typical feedback implementation used for experiments. In order to do so, we implement a tracking scheme that takes into account the modulation of the laser intensity. We show that such a tracking implementation allows us to increase the feedback strength, leading to faster cooling rates and lower center-of-mass temperatures.

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arXiv2019

Qubit Entanglement generation by Gaussian non-Markovian dynamics

We consider two qubits interacting with a common bosonic bath, but not directly between themselves. We derive the (bipartite) entanglement generation conditions for Gaussian non-Markovian dynamical maps and show that they are similar as in the Markovian regime; however, they depend on different physical coefficients and hold on different time scales. Indeed, for small times, in the non-Markovian regime entanglement is possibly generated on a shorter time scale ($\propto t^2$) than in the Markovian one ($\propto t$). Moreover, although the singular coupling limit of non-Markovian dynamics yields Markovian ones, we show that the same limit does not lead from non-Markovian entanglement generation conditions to Markovian ones. Also, the entanglement generation conditions do not depend on the initial time for non-Markovian open dynamics resulting from couplings to bosonic Gaussian baths, while they may depend on time for open dynamics originated by couplings to classical, stochastic Gaussian environments.

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arXiv2018

Stochastic unravellings of non-Markovian completely positive and trace preserving maps

We consider open quantum systems with factorized initial states, providing the structure of the reduced system dynamics, in terms of environment cumulants. We show that such completely positive (CP) and trace preserving (TP) maps can be unraveled by linear stochastic Schrödinger equations (SSEs) characterized by sets of colored stochastic processes (with n-th order cumulants). We obtain both the conditions such that the SSEs provide CPTP dynamics, and those for unraveling an open system dynamics. We then focus on Gaussian non-Markovian unravellings, whose known structure displays a functional derivative. We provide a novel description that replaces the functional derivative with a recursive operatorial structure. Moreover, for the family of quadratic bosonic Hamiltonians, we are able to provide an explicit operatorial dependence for the unravelling.

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arXiv2018

Colored collapse models from the non-interferometric perspective

Models of spontaneous wave function collapse describe the quantum-to-classical transition by assuming a progressive breakdown of the superposition principle when the mass of the system increases, providing a well-defined phenomenology in terms of a non-linearly and stochastically modified Schrodinger equation, which can be tested experimentally. The most popular of such models is the Continuous Spontaneous Localization (CSL) model: in its original version, the collapse is driven by a white noise, and more recently, generalizations in terms of colored noises, which are more realistic, have been formulated. We will analyze how current non-interferometric tests bound the model, depending on the spectrum of the noise. We will find that low frequency purely mechanical experiments provide the most stable and strongest bounds.

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arXiv2018

Recursive approach for non-Markovian time-convolutionless master equations

We consider a general open system dynamics and we provide a recursive method to derive the associated non-Markovian master equation in a perturbative series. The approach relies on a momenta expansion of the open system evolution. Unlike previous perturbative approaches of this kind, the method presented in this paper provides a recursive definition of each perturbative term. Furthermore, we give an intuitive diagrammatic description of each term of the series, which pro- vides an useful analytical tool to build them and to derive their structure in terms of commutators and anticommutators. We eventually apply our formalism to the evolution of the observables of the reduced system, by showing how the method can be applied to the adjoint master equation, and by developing a diagrammatic description of the associated series.

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arXiv2017

Momentum coupling in non-Markovian Quantum Brownian motion

We consider a model of non-Markovian Quantum Brownian motion that consists of an harmonic oscillator bilinearly coupled to a thermal bath, both via its position and momentum operators. We derive the master equation for such a model and we solve the equations of motion for a generic Gaussian system state. We then investigate the resulting evolution of the first and second moments for both an Ohmic and a super-Ohmic spectral density. In particular, we show that, irrespective of the specific form of the spectral density, the coupling with the momentum enhances the dissipation experienced by the system, accelerating its relaxation to the equilibrium, as well as modifying the asymptotic state of the dynamics. Eventually, we characterize explicitly the non-Markovianity of the evolution, using a general criterion which relies on the positivity of the master equation coefficients.

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arXiv2014

General Non-Markovian structure of Gaussian Master and Stochastic Schrödinger Equations

General open quantum systems display memory features, their master equations are non-Markovian. We show that the subclass of Gaussian non-Markovian open system dynamics is tractable in a depth similar to the Markovian class. The structure of master equations exhibits a transparent generalization of the Lindblad structure. We find and parametrize the class of stochastic Schrödinger equations that unravel a given master equation, such class was before known for Markovian systems only. We show that particular non-Markovian unravellings known in the literature are special cases of our class.

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arXiv2012

Exact solution for a non-Markovian dissipative quantum dynamics

We provide the exact analytic solution of the stochastic Schrödinger equation describing an harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models, for infinite dimensional systems. We compute the Green's function; in the case of a free particle, and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.

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arXiv2011

Dissipative collapse models with non-white noises

We study the generalization of the QMUPL model which accounts both for memory and dissipative effects. This is the first model where both features are combined. After having derived the non-local Action describing the system, we solve the equation for a quantum harmonic oscillator via the path integral formalism. We give the explicit expression for the Green's function of the process. We focus on the case of an exponential correlation function and we analyze in detail the behavior Gaussian wave functions. We eventually study the collapse process, comparing the results with those of previous models.

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arXiv2011

Functional Lagrange formalism for time-non-local Lagrangians

We develop a time-non-local (TNL) formalism based on variational calculus, which allows for the analysis of TNL Lagrangians. We derive the generalized Euler-Lagrange equations starting from the Hamilton's principle and, by defining a generalized momentum, we introduce the corresponding Hamiltonian formalism. We apply the formalism to second order TNL Lagrangians and we show that it reproduces standard results in the time-local limit. An example will show how the formalism works, and will provide an interesting insight on the non-standard features of TNL equations.

math-ph↗

arXiv2010

Breaking quantum linearity: constraints from human perception and cosmological implications

Resolving the tension between quantum superpositions and the uniqueness of the classical world is a major open problem. One possibility, which is extensively explored both theoretically and experimentally, is that quantum linearity breaks above a given scale. Theoretically, this possibility is predicted by collapse models. They provide quantitative information on where violations of the superposition principle become manifest. Here we show that the lower bound on the collapse parameter lambda, coming from the analysis of the human visual process, is ~ 7 +/- 2 orders of magnitude stronger than the original bound, in agreement with more recent analysis. This implies that the collapse becomes effective with systems containing ~ 10^4 - 10^5 nucleons, and thus falls within the range of testability with present-day technology. We also compare the spectrum of the collapsing field with those of known cosmological fields, showing that a typical cosmological random field can yield an efficient wave function collapse.

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