Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials

Quasiperiodic systems offer an appealing intermediate between long-range ordered and genuine disordered systems, with unusual critical properties. One-dimensional models that break the so-called self-dual symmetry usually display a mobility edge, similarly as truly disordered systems in dimension strictly higher than two. Here, we determine the critical localization properties of single particles in shallow, one-dimensional, quasiperiodic models and relate them to the fractal character of the energy spectrum. On the one hand, we determine the mobility edge and show that it separates the localized and extended phases, with no intermediate phase. On the other hand, we determine the critical potential amplitude and find the universal critical exponent $\nu \simeq 1/3$. We also study the spectral Hausdorff dimension and show that it is nonuniversal but always smaller than unity, hence showing that the spectrum is nowhere dense. Finally, applications to ongoing studies of Anderson localization, Bose-glass physics, and many-body localization in ultracold atoms are discussed

A two-qubit engine fueled by entangling operations and local measurements

We introduce a two-qubit engine that is powered by entangling operations and projective local quantum measurements. Energy is extracted from the detuned qubits coherently exchanging a single excitation. This engine, which uses the information and back-action of the measurement, is generalized to an N-qubit chain. We show that by gradually increasing the energy splitting along the chain, the initial low energy of the first qubit can be up-converted deterministically to an arbitrarily high energy at the last qubit by successive neighbor swap operations and local measurements. Modeling the local measurement as the entanglement of a qubit with a meter, we identify the measurement fuel as the energetic cost to erase correlations between the qubits.Comment: 5 pages, 4 figure

Quantum energetics of a non-commuting measurement

When a measurement observable does not commute with a quantum system's Hamiltonian, the energy of the measured system is typically not conserved during the measurement. Instead, energy can be transferred between the measured system and the meter. In this work, we experimentally investigate the energetics of non-commuting measurements in a circuit quantum electrodynamics system containing a transmon qubit embedded in a 3D microwave cavity. We show through spectral analysis of the cavity photons that a frequency shift is imparted on the probe, in balance with the associated energy changes of the qubit. Our experiment provides new insights into foundations of quantum measurement, as well as a better understanding of the key mechanisms at play in quantum energetics.Comment: 9 pages, 4 figure

Stability of long-sustained oscillations induced by electron tunneling

Self-oscillations are the result of an efficient mechanism generating periodic motion from a constant power source. In quantum devices, these oscillations may arise due to the interaction between single electron dynamics and mechanical motion. Due to the complexity of this mechanism, these self-oscillations may irrupt, vanish, or exhibit a bistable behavior causing hysteresis cycles. We observe these hysteresis cycles and characterize the stability of different regimes in single and double quantum dot configurations. In particular cases, we find these oscillations stable for over 20 seconds, many orders of magnitude above electronic and mechanical characteristic timescales, revealing the robustness of the mechanism at play. The experimental results are reproduced by our theoretical model that provides a complete understanding of bistability in nanoelectromechanical devices.Comment: 11 pages, 10 figures, includes the complete paper and the Supplemental Materia

Énergétique de la mesure quantique

Quantum measurements are known to affect the state of the measured system. Such a measurement backaction is due to the interaction of the quantum system with the measuring device. When the measured observable and the system's Hamiltonian do not commute, the backaction can lead to a mean energy change of the system. This energy change has been dubbed "quantum heat" and, in association with feedback processes and/or the interaction with thermal bath(s), proves to be a genuinely quantum resource to fuel new kinds quantum engines. We propose such a measurement powered engine exploiting the non-commutativity of local and non-local operations on a bipartite quantum system.We then investigate the origin of the quantum heat. Even if one cannot model the full dynamics of a measurement due to the collapse of the wavefunction, the energetic aspects can still be investigated by modeling the so-called pre-measurement. During this step, the system interacts and gets correlated with a quantum system which can be viewed as a small part of the measuring apparatus and called the quantum meter. Ideally, at the end of this process, the system's reduced state will be fully decohered in the measurement basis, thus corresponding to the averaged collapsed output states given by the measurement postulate. We find that the quantum heat received by the measured system corresponds to the energy necessary to turn off the coupling between the meter and the system. Using generalized definitions of heat and work, we moreover characterize the work and heat nature of these energy exchanges.Tracing the source of this energy one step further, we propose an autonomous description of a measurement. This is done by considering a flying qubit measured by the quantum field of the cavity it crosses. The interaction being position dependent, the kinetic degree of freedom is providing the required energy to switch on and off the interaction between the qubit and the meter field. A full quantum treatment allows us to evaluate the impact of the finite spatial and momentum extension of the qubit wavepacket. Since the kinetic degree of freedom can be affected by the interaction, it does not simply generate a time dependent Hamiltonian for the other degrees of freedom. We find the correction to this ideal dynamic and analyse its consequences on the nature of the energy fluxes. %spread/extension/broadnessTaking the opposite point of view, we compare the measurement cost of a qubit by a field propagating in a waveguide, depending on the initial state of the field. In the context of a circuit quantum electrodynamics setup, we find that thermal and coherent fields induce the same backaction on the qubit given the same energy constraints.The results presented and discussed in this thesis contribute to unravel the mysterious effects and mechanisms due to quantum measurements. Notably, they give an outlook to further analyse quantum measurement-based engines and to understand the energetic resource that measurements cost and constitute at the same time.En mesurant l’état d’un objet quantique, il est possible de modifier son état. Cet effet est dû à son interaction avec l’appareil de mesure. Lorsque l’observable mesuré et l’Hamiltonien du système ne commutent pas, l’énergie moyenne du système mesuré peut être modifiée. Ce changement d’énergie parfois appelé « chaleur quantique » peut être utilisé comme ressource pour alimenter de nouveaux types de machines quantiques : les moteurs quantiques à mesure. Nous proposons un tel moteur en exploitant la non-commutativité de certaines mesures locales et globales dans un système à deux parties.Ce type de plateforme est idéal pour comprendre l’origine de la chaleur quantique. Bien que l’évolution temporelle de l’état d’un système mesuré ne soit pas aujourd’hui connue à cause du phénomène de réduction du paquet d’onde, les aspects énergétiques restent accessibles en modélisant la pré-mesure. Durant cette étape, des corrélations sont créées entre système et appareil de mesure. Idéalement, à la fin de ce processus, l’état réduit du système correspondra à la moyenne des états projetés prévus par le postulat de la mesure. Je montre alors que l’énergie reçue par le système correspond à celle nécessaire pour allumer et éteindre l’interaction entre le système et l’appareil de mesure. En utilisant une définition généralisée du travail et de la chaleur, cet échange est interprété comme une conversion de travail en chaleur.En remontant encore la source de cette énergie, nous proposons une version autonome de ce mécanisme. Pour cela, le système choisi est un qubit se déplaçant à travers une cavité dont le champ constitue l’appareil de mesure. L’interaction entre eux étant dépendante de leur position relative, l’énergie cinétique apporte l’énergie nécessaire à faire interagir ces deux systèmes. En modélisant cette évolution de manière purement quantique, nous caractérisons l’impact de l’extension spatiale finie du paquet d’onde sur la nature de ces échanges d’énergie.Du point de vue opposé, nous comparons le cout énergétique de la mesure d’un qubit en fonction de l’état initial du champ utilisé pour le mesurer. Dans le cas d’un circuit d’électrodynamique quantique, nous trouvons que les états cohérents et thermiques permettent une même qualité de mesure à énergie fixée.Les résultats présentés et décrits dans cette thèse contribuent à améliorer notre compréhension profonde des effets et mécanismes surprenants induits par la mesure quantique. En particulier, ils permettent de mieux comprendre le fonctionnement des moteurs quantiques à mesure et d’identifier précisément la ressource et le coût que constitue la mesure en physique quantique

Énergétique de la mesure quantique

Quantum measurements are known to affect the state of the measured system. Such a measurement backaction is due to the interaction of the quantum system with the measuring device. When the measured observable and the system's Hamiltonian do not commute, the backaction can lead to a mean energy change of the system. This energy change has been dubbed "quantum heat" and, in association with feedback processes and/or the interaction with thermal bath(s), proves to be a genuinely quantum resource to fuel new kinds quantum engines. We propose such a measurement powered engine exploiting the non-commutativity of local and non-local operations on a bipartite quantum system.We then investigate the origin of the quantum heat. Even if one cannot model the full dynamics of a measurement due to the collapse of the wavefunction, the energetic aspects can still be investigated by modeling the so-called pre-measurement. During this step, the system interacts and gets correlated with a quantum system which can be viewed as a small part of the measuring apparatus and called the quantum meter. Ideally, at the end of this process, the system's reduced state will be fully decohered in the measurement basis, thus corresponding to the averaged collapsed output states given by the measurement postulate. We find that the quantum heat received by the measured system corresponds to the energy necessary to turn off the coupling between the meter and the system. Using generalized definitions of heat and work, we moreover characterize the work and heat nature of these energy exchanges.Tracing the source of this energy one step further, we propose an autonomous description of a measurement. This is done by considering a flying qubit measured by the quantum field of the cavity it crosses. The interaction being position dependent, the kinetic degree of freedom is providing the required energy to switch on and off the interaction between the qubit and the meter field. A full quantum treatment allows us to evaluate the impact of the finite spatial and momentum extension of the qubit wavepacket. Since the kinetic degree of freedom can be affected by the interaction, it does not simply generate a time dependent Hamiltonian for the other degrees of freedom. We find the correction to this ideal dynamic and analyse its consequences on the nature of the energy fluxes. %spread/extension/broadnessTaking the opposite point of view, we compare the measurement cost of a qubit by a field propagating in a waveguide, depending on the initial state of the field. In the context of a circuit quantum electrodynamics setup, we find that thermal and coherent fields induce the same backaction on the qubit given the same energy constraints.The results presented and discussed in this thesis contribute to unravel the mysterious effects and mechanisms due to quantum measurements. Notably, they give an outlook to further analyse quantum measurement-based engines and to understand the energetic resource that measurements cost and constitute at the same time.En mesurant l’état d’un objet quantique, il est possible de modifier son état. Cet effet est dû à son interaction avec l’appareil de mesure. Lorsque l’observable mesuré et l’Hamiltonien du système ne commutent pas, l’énergie moyenne du système mesuré peut être modifiée. Ce changement d’énergie parfois appelé « chaleur quantique » peut être utilisé comme ressource pour alimenter de nouveaux types de machines quantiques : les moteurs quantiques à mesure. Nous proposons un tel moteur en exploitant la non-commutativité de certaines mesures locales et globales dans un système à deux parties.Ce type de plateforme est idéal pour comprendre l’origine de la chaleur quantique. Bien que l’évolution temporelle de l’état d’un système mesuré ne soit pas aujourd’hui connue à cause du phénomène de réduction du paquet d’onde, les aspects énergétiques restent accessibles en modélisant la pré-mesure. Durant cette étape, des corrélations sont créées entre système et appareil de mesure. Idéalement, à la fin de ce processus, l’état réduit du système correspondra à la moyenne des états projetés prévus par le postulat de la mesure. Je montre alors que l’énergie reçue par le système correspond à celle nécessaire pour allumer et éteindre l’interaction entre le système et l’appareil de mesure. En utilisant une définition généralisée du travail et de la chaleur, cet échange est interprété comme une conversion de travail en chaleur.En remontant encore la source de cette énergie, nous proposons une version autonome de ce mécanisme. Pour cela, le système choisi est un qubit se déplaçant à travers une cavité dont le champ constitue l’appareil de mesure. L’interaction entre eux étant dépendante de leur position relative, l’énergie cinétique apporte l’énergie nécessaire à faire interagir ces deux systèmes. En modélisant cette évolution de manière purement quantique, nous caractérisons l’impact de l’extension spatiale finie du paquet d’onde sur la nature de ces échanges d’énergie.Du point de vue opposé, nous comparons le cout énergétique de la mesure d’un qubit en fonction de l’état initial du champ utilisé pour le mesurer. Dans le cas d’un circuit d’électrodynamique quantique, nous trouvons que les états cohérents et thermiques permettent une même qualité de mesure à énergie fixée.Les résultats présentés et décrits dans cette thèse contribuent à améliorer notre compréhension profonde des effets et mécanismes surprenants induits par la mesure quantique. En particulier, ils permettent de mieux comprendre le fonctionnement des moteurs quantiques à mesure et d’identifier précisément la ressource et le coût que constitue la mesure en physique quantique

Experimental demonstration of a quantum engine driven by entanglement and local measurements

International audienceUnderstanding entanglement and quantum measurements from a thermodynamics point of view is a fundamental and challenging task. Recently, a two-qubit engine was put forward as an appropriate platform to tackle these challenges. Here we achieve an experimental simulation and provide the direct experimental proof of these findings using single photons and linear optics. Encoding the qubits by polarization and transverse spatial modes of single photons, entanglement is created through the interaction between them. We show that, upon local measurement, classical mutual information can be extracted in order to fuel a quantum measurement engine. By measuring the energy changes, we identify that the energy gain comes from the measurement channel and corresponds to the cost of erasing the quantum correlations between qubits. The scheme is further generalized to an N-qubit chain for energy upconversion. Our experimental results provide a thorough understanding of this quantum engine with entanglement and local measurements as a new kind of fuel, as well as a general platform for exploration of quantum engines

Many-body quantum vacuum fluctuation engines

We propose a many-body quantum engine powered by the energy difference between the entangled ground state of the interacting system and local separable states. Performing local energy measurements on an interacting many-body system can produce excited states from which work can be extracted via local feedback operations. These measurements reveal the quantum vacuum fluctuations of the global ground state in the local basis and provide the energy required to run the engine. The reset part of the engine cycle is particularly simple: The interacting many-body system is coupled to a cold bath and allowed to relax to its entangled ground state. We illustrate our proposal on two types of many-body systems: a chain of coupled qubits and coupled harmonic oscillator networks. These models faithfully represent fermionic and bosonic excitations, respectively. In both cases, analytical results for the work output and efficiency of the engine can be obtained. Generically, the work output scales as the number of quantum systems involved, while the efficiency limits to a constant. We prove the efficiency is controlled by the ``local entanglement gap''-- the energy difference between the global ground state and the lowest energy eigenstate of the local Hamiltonian. In the qubit chain case, we highlight the impact of a quantum phase transition on the engine's performance as work and efficiency sharply increase at the critical point. In the case of a one-dimensional oscillator chain, we show the efficiency approaches unity as the number of coupled oscillators increases, even at finite work output

Reservoir-free decoherence in flying qubits

International audienceAn effective time-dependent Hamiltonian can be implemented by making a quantum system fly through an inhomogeneous potential, realizing, for example, a quantum gate on its internal degrees of freedom. However, flying systems have a spatial spread that will generically entangle the internal and spatial degrees of freedom, leading to decoherence in the internal state dynamics, even in the absence of any external reservoir. We provide formulas valid at all times for the dynamics, fidelity, and change of entropy for small spatial spreads, quantified by $\Delta x$. This decoherence is non-Markovian and its effect can be significant for ballistic qubits (scaling as $\Delta x^2$) but not for qubits carried by a moving potential well (scaling as $\Delta x^6$). We also discuss a method to completely counteract this decoherence for a ballistic qubit later measured