Exponential precision by reaching a quantum critical point

Quantum metrology shows that by exploiting nonclassical resources it is possible to overcome the fundamental limit of precision found for classical parameter-estimation protocols. The scaling of the quantum Fisher information -- which provides an upper bound to the achievable precision -- with respect to the protocol duration is then of primarily importance to assess its performances. In classical protocols the quantum Fisher information scales linearly with time, while typical quantum-enhanced strategies achieve a quadratic (Heisenberg) or even higher-order polynomial scalings. Here we report a protocol that is capable of surpassing the polynomial scaling, and yields an exponential advantage. Such exponential advantage is achieved by approaching, but without crossing, the critical point of a quantum phase transition of a fully-connected model in the thermodynamic limit. The exponential advantage stems from the breakdown of the adiabatic condition close to a critical point. As we demonstrate, this exponential scaling is well captured by the new bound derived in arXiv:2110.04144, which in turn allows us to obtain approximate analytical expressions for the quantum Fisher information that agree with exact numerical simulations. In addition, we discuss the limitations to the exponential scaling when considering a finite-size system as well as its robustness against decoherence effects. Hence, our findings unveil a novel quantum metrological protocol whose precision scaling goes beyond the paradigmatic Heisenberg limit with respect to the protocol duration.Comment: 12 pages, 4 figures; comments welcome

The bosonic skin effect: boundary condensation in asymmetric transport

We study the incoherent transport of bosonic particles through a one dimensional lattice with different left and right hopping rates, as modelled by the asymmetric simple inclusion process (ASIP). Specifically, we show that as the current passing through this system increases, a transition occurs, which is signified by the appearance of a characteristic zigzag pattern in the stationary density profile near the boundary. In this highly unusual transport phase, the local particle distribution alternates on every site between a thermal distribution and a Bose-condensed state with broken U(1)-symmetry. Furthermore, we show that the onset of this phase is closely related to the so-called non-Hermitian skin effect and coincides with an exceptional point in the spectrum of density fluctuations. Therefore, this effect establishes a direct connection between quantum transport, non-equilibrium condensation phenomena and non-Hermitian topology, which can be probed in cold-atom experiments or in systems with long-lived photonic, polaritonic and plasmonic excitations

Metrological advantage at finite temperature for Gaussian phase estimation

In the context of phase estimation with Gaussian states, we introduce a quantifiable definition of metrological advantage that takes into account thermal noise in the preparation procedure. For a broad set of states, \textit{isotropic non-pure Gaussian states}, we show that squeezing is not only necessary, but sufficient, to achieve metrological advantage. We interpret our results in the framework of resource theory, and discuss possible sources of advantage other than squeezing. Our work is a step towards using phase estimation with pure and mixed state to define and quantify nonclassicality. This work is complementary with studies that defines nonclassicality using quadrature displacement estimation.Comment: Changes to wording, figures replace

Transitions de phase dans des systèmes lumière-matière pour la métrologie quantique

When light and matter are weakly coupled, they can be described as two distinctive systems exchanging quanta of energy. By contrast, when their coupling strength becomes very large, the systems hybridize and form compounds that cannot be described in terms of light or matter only. In this Thesis, we will study some exotic properties which arise in this regime. In particular, we will be interested in the possibility to engineer quantum phase transitions in these systems. One direction we explore is the study of two-photon coupling, a mechanism in which photons are created or emitted in pairs. This mechanism creates a rich phase diagram containing both phase transitions and instabilities. Another point of interest is the possibility to use these transitions for sensing applications. Indeed, near the critical point, the system becomes extremely sensitive to external perturbations. We will present a protocol in which a single qubit coupled to a bosonic field. Despite its simplicity, this system displays a phase transition. Near the critical point, both the frequency of the qubit and the field can be measured with improved accuracy. Hence, finite-size transitions could be used to develop small-scale sensors. As last topic, we study how the ability of a system to perform certain metrological tasks could be used to characterize and quantify nonclassicality, by using the formalism of resource theories.Lorsque lumière et matière sont faiblement couplées, elles peuvent être traitées comme des systèmes distincts, échangeant des quanta d’énergie. En revanche, lorsque le taux de couplage devient très élevé, les deux systèmes se mêlent pour former des excitations hybrides, qui ne peuvent être décrites isolément en termes de lumière ou de matière. Au long de cette dissertation, nous étudierons quelques-unes des propriétés exotiques qui surviennent dans ce régime. Nous accorderons notamment une grande attention à l’émergence de transitions de phase quantiques dans ces systèmes. L’un des axes de recherche développés ici est l’étude d’un mécanisme de couplage à deux photons, par lequel des photons sont créés ou absorbés par paires. Ce mécanisme crée un diagramme de phase très riche, présentant à la fois une transition de phase et des instabilités. Une autre étude porte sur l’utilisation de ces transitions de phase pour le développement de capteurs. En effet, à proximité du point critique, le système devient extrêmement sensible à des perturbations extérieures. Nous présenterons un protocole exploitant un unique système à deux niveaux, couplé à un champ bosonique. En dépit de sa simplicité, un tel système peut générer des transitions de phase. Près du point critique, la fréquence du champ et celle du système à deux niveaux peuvent toutes deux être mesurées avec une précision accrue. Ainsi, des transitions de phase dans des systèmes de taille finie pourraient être utilisées pour développer des capteurs de petite taille. Enfin, en utilisant le formalisme des théories de ressources, nous étudierons comment la capacité d’un système physique à effectuer des tâches métrologiques pourrait être utilisée pour caractériser et quantifier la «non-classicalité» d’un tel système

Critical quantum metrology with fully-connected models: from Heisenberg to Kibble–Zurek scaling

Phase transitions represent a compelling tool for classical and quantum sensing applications. It has been demonstrated that quantum sensors can in principle saturate the Heisenberg scaling, the ultimate precision bound allowed by quantum mechanics, in the limit of large probe number and long measurement time. Due to the critical slowing down, the protocol duration time is of utmost relevance in critical quantum metrology. However, how the long-time limit is reached remains in general an open question. So far, only two dichotomic approaches have been considered, based on either static or dynamical properties of critical quantum systems. Here, we provide a comprehensive analysis of the scaling of the quantum Fisher information for different families of protocols that create a continuous connection between static and dynamical approaches. In particular, we consider fully-connected models, a broad class of quantum critical systems of high experimental relevance. Our analysis unveils the existence of universal precision-scaling regimes. These regimes remain valid even for finite-time protocols and finite-size systems. We also frame these results in a general theoretical perspective, by deriving a precision bound for arbitrary time-dependent quadratic Hamiltonians.Comment: 24 pages, 8 figures. Comments welcome

The bosonic skin effect: boundary condensation in asymmetric transport

We study the incoherent transport of bosonic particles through a one dimensional lattice with different left and right hopping rates, as modelled by the asymmetric simple inclusion process (ASIP). Specically, we show that as the current passing through this system increases, a transition occurs, which is signied by the appearance of a characteristic zigzag pattern in the stationary density profile near the boundary. In this highly unusual transport phase, the local particle distribution alternates on every site between a thermal state and a bose-condensed distribution with broken U (1)-symmetry. We further show that the onset of this phase is closely related to the so-called non-Hermitian skin effect and coincides with an exceptional point in the spectrum of density fluctuations. Therefore, this effect establishes an interesting connection between quantum transport, non-equilibrium condensation phenomena and non-Hermitian topology, which can be probed in cold-atom experiments or in systems with long-lived photonic, polaritonic or plasmonic excitations