We develop and exploit an out-of-equilibrium theory, valid in arbitrary dimensions, which does not require initial thermalization. It is perturbative with respect to a weak time-dependent (TD) Hamiltonian term, but is non-perturbative with respect to strong coupling to an electromagnetic environment, or to Coulomb or superconducting correlations. We derive unifying relations between the current generated by coherent radiation or statistical mixture of radiations, superimposed on a dc voltage $V_{dc}$, and the out-of-equilibrium dc current which encodes the effects of interactions. Thus we extend fully the lateral band-transmission picture, thus quantum superposition, to coherent many-body correlated states. This provides methods for a determination of the carrier's charge q free from unknown parameters through the robustness of the Josephson-like frequency. Similar relations we have derived for noise have allowed, recently, to determine the fractional charge in the Fractional Quantum Hall Effect (FQHE) within the Jain series (M. Kapfer et al, Science 2018). The present theory allows for breakdown of inversion symmetry and for asymmetric rates for emission and absorption of radiations. This generates a photo-ratchet effect we exploit to propose a novel method to measure the charge $q$, as well as spectroscopical analysis of the out-of-equilibrium dc current and the third cumulant of non-gaussian statistical radiations. We apply the theory to the Tomonaga-Luttinger Liquid (TLL), showing a counterintuitive feature: a lorentzian pulse superimposed on $V_{dc}$ can reduce the current compared to its dc value, at the same $V_{dc}$, questioning the terminology photo-assisted. Beyond a charge current, the theory applies to operators such as spin current in the spin Hall effect, or voltage drop across a phase-slip Josephson junction.
We develop and exploit an out-of-equilibrium theory, valid in arbitrary dimensions, which does not require initial thermalization. It is perturbative with respect to a weak time-dependent (TD) Hamiltonian term, but is non-perturbative with respect to strong coupling to an electromagnetic environment, or to Coulomb or superconducting correlations. We derive unifying relations between the current generated by coherent radiation or statistical mixture of radiations, superimposed on a dc voltage Vdc, and the out-of-equilibrium dc current which encodes the effects of interactions. Thus we extend fully the lateral band-transmission picture, thus quantum superposition, to coherent many-body correlated states. This provides methods for a determination of the carrier's charge q free from unknown parameters through the robustness of the Josephson-like frequency. Similar relations we have derived for noise have allowed, recently, to determine the fractional charge in the Fractional Quantum Hall Effect (FQHE) within the Jain series (M. Kapfer et al, Science 2018). The present theory allows for breakdown of inversion symmetry and for asymmetric rates for emission and absorption of radiations. This generates a photo-ratchet effect we exploit to propose a novel method to measure the charge q, as well as spectroscopical analysis of the out-of-equilibrium dc current and the third cumulant of non-gaussian statistical radiations. We apply the theory to the Tomonaga-Luttinger Liquid (TLL), showing a counterintuitive feature: a lorentzian pulse superimposed on Vdc can reduce the current compared to its dc value, at the same Vdc, questioning the terminology photo-assisted. Beyond a charge current, the theory applies to operators such as spin current in the spin Hall effect, or voltage drop across a phase-slip Josephson junction.
We develop and exploit an out-of-equilibrium theory, valid in arbitrary dimensions, which does not require initial thermalization. It is perturbative with respect to a weak time-dependent (TD) Hamiltonian term, but is nonperturbative with respect to strong coupling to an electromagnetic environment or to Coulomb or superconducting correlations. We derive unifying relations between the current generated by coherent radiation or statistical mixture of radiations, superimposed on a dc voltage Vdc, and the out-of-equilibrium dc current which encodes the effects of interactions. We extend fully the lateral band-transmission picture, thus quantum superposition, to coherent many-body correlated states. This provides methods for a determination of the carrier's charge q free from unknown parameters through the robustness of the Josephson-like frequency. We have derived similar relations for noise (I. Safi, arXiv:1401.5950) which have been exploited, recently, to determine the fractional charge in the fractional quantum Hall effect (FQHE) within the Jain series [M. Kapfer et al., Science (to be published)]. The present theory allows for breakdown of inversion symmetry and for asymmetric rates for emission and absorption of radiations. This generates rectification exploited here to propose methods to measure the charge q, as well as spectroscopical analysis of the out-of-equilibrium dc current and the third cumulant of non-Gaussian source of noise. We also apply the theory to the Tomonaga-Luttinger liquid (TLL), showing a counterintuitive feature: A Lorentzian pulse superimposed on Vdc can reduce the current compared to its dc value, at the same Vdc, questioning the terminology ``photoassisted.'' Beyond a charge current, the theory applies to operators such as spin current in the spin Hall effect or voltage drop across a phase-slip Josephson junction.
We consider strongly correlated quantum circuits where a dc drive is added on top of an initial out-of-equilibrium (OE) stationary state. Within a perturbative approach, we derive unifying OE fluctuation relations for high-frequency current noise, shown to be completely determined by zero-frequency noise and dc current. We apply them to the fractional quantum Hall effect at arbitrary incompressible filling factors, driven by OE sources, without knowledge of the underlying model. We show that such OE relations provide robust methods for an unambiguous determination of the fractional charge or of key interaction parameters entering in the exploration of anyonic statistics within an anyon collider.
Collective quantum phenomena are fascinating, as they repeatedly challenge our comprehension of nature and its underlying mechanisms. The qualification ``quantum'' can be attributed to a generic many-body system whenever the interference effects related to the underlying wave nature of its elementary constituents can not be neglected anymore, and a naive classical description in terms of interacting billiard balls fails to catch its most essential features. This interference phenomenon called ``quantum degeneracy'' which occurs at weak temperatures, leads to spectacular collective behaviours such as the celebrated Bose-Einstein Condensation (BEC) phase transition, where a macroscopic fraction of a bosonic system of particles collapses below a critical temperature T_c on a single-particle state. Quantum coherence, when combined with inter-particle interactions, gives rise to highly non-classical frictionless hydrodynamic behaviours such as superfluidity (SF) and superconductivity (SC). \nEven more exotic quantum phases emerge in presence of important interactions as matter reaches a ``strongly correlated regime'' dominated by quantum fluctuations, where each particle is able to affect significantly the surrounding fluid: characteristic examples are the so-called Mott-Insulator (MI) quantum phase where particles are localized on a lattice due to a strong interaction-induced blockade, along with the Tonks-Girardeau (TG) gas where impenetrable bosons in one-dimension acquire effective fermionic statistics up to a unitary transformation, and the Fractional Quantum Hall (FQH) effect which occurs in presence of a gauge field, and features a special type of elementary excitation possessing a fractional charge and obeying to fractional statistics called `anyon'. \nThese quantum many-body effects were explored in a first place in systems well isolated from the external environment such as ultra-cold atomic gases or electrons in solid-state systems, within a physical context well described by ``equilibrium statistical mechanics''. Yet, over the last two decades a broad community has started investigating the possibility of stabilizing interacting quantum phases in novel nonlinear quantum optics architectures, where interacting photons have replaced their atomic and electronic counterpart. Thanks to their high level of controllability and flexibility, and the possibility of reaching the quantum degeneracy regime at exceptionally high temperatures, these platforms appear as extremely promising candidates for the ``quantum simulation'' of the most exotic many-body quantum problems: while the precursors experiments in semiconductor exciton-polariton already allow to reach the Bose-Einstein Condensation and superfluid regimes, novel platforms such as superconducting circuits, coupled cavity arrays or photons coupled to Rydberg EIT (Electromagnetically induced Transparency) atoms have entered the so-called `photon blockade' where photons behave as impenetrable particles, and open a encouraging pathway toward the future generation of strongly correlated phases with light. \nA specificity of quantum optics devices is their intrinsic ``non-equilibrium'' nature: the interplay between the practically unavoidable radiative and non-radiative losses and the external drive needed to replenish the photon gas leads the many-body system toward a steady-state presenting important non-thermal features. One one hand, an overwhelmingly large quantity of novel quantum phenomena is expected in the non-equilibrium framework, as breaking the thermal equilibrium condition releases severe constraints on the state of a quantum system and on the nature of its surrounding environment. On the other hand, we do not benefit yet of an understanding of non-equilibrium statistical mechanics comparable with its well-established equilibrium counterpart, which relies on strong historical foundations. Understanding how to tame (and possibly exploit) non-equilibrium effects in order to stabilize interesting quantum phases in a controlled manner often reveals a hard challenge. \nIn that prospect, an important conceptual issue in the non-equilibrium physics of strongly interacting photons regards the possibility of stabilizing ``incompressible quantum phases'' such as the Mott-Insulator or Fractional Quantum Hall states, and more generally to stabilize the ground-state of a given particle-number conserving Hamiltonian, in a physical context where dissipative losses can not be neglected. While being able to quantum simulate those emblematic strongly correlated quantum phases in this novel experimental context would strongly benefit to the quantum optics community, gaining such a kind of flexibility would also contribute to fill an important bridge between the equilibrium and the non-equilibrium statistical physics of open quantum systems, allowing to access in a controlled manner a whole new phenomenology at the interface between the two theories. \nIn this thesis I address those questions, which I reformulate in the following manner: \n \n-What are the conditions for the emergence of analogue equilibrium properties in open quantum systems in contact with a non-thermal environment ? \n \n-In particular, is it possible to stabilize strongly correlated quantum phases with a perfectly defined particle number in driven-dissipative photonic platforms, in spite of environment-induced losses and heating effects ? \n \nThe structure of the thesis is the following. \n \n \n[Chapter 1.] We give an overview of the physics of many-body photonic systems. As a first step we address the weakly interacting regime in the physical context of exciton-polaritons: after describing the microscopic aspects of typical experiments, we move to the discussion of non-equilibrium Bose-Einstein Condensation and the various mechanisms related to the emergence of thermal signatures at steady-state. The second part of this Chapter is dedicated to strongly interacting fluids. After drawing a quick overview of several experimental platforms presenting a good potential for the study of such physics in a near future, we discuss the relative performance of several schemes proposed in order to replenish the photonic population \n \n[Chapter 2.] We investigate the potential of a non-Markovian pump scheme with a narrow bandpass (Lorentzian shaped) emission spectrum for the generation of strongly correlated states of light in a Bose-Hubbard lattice. Our proposal can be implemented by mean of embedded inverted two-level emitters with a strong incoherent pumping toward the excited state. Our study confirms in a single cavity the possibility of stabilizing photonic Fock states in a single configuration, and strongly localized n=1 Mott-Insulator states in a lattice with n=1 density. We show that a relatively moderate hopping is responsible for a depletion of the Mott-state, which then moves toward a delocalized state reminiscent of the superfluid regime. Finally, we proceed to a mean-field analysis of the phase diagram, and unveil a Mott-to-Superfluid transition characterized by a spontaneous breaking of the U(1) symmetry and incommensurate density. The results of this Chapter are based on the following publications: \n- J. Lebreuilly, M. Wouters and I. Carusotto, ``Towards strongly correlated photons in arrays of dissipative nonlinear cavities under a frequency-dependent incoherent pumping'', C. R. Phys., 17(8), 836, 2016. \n- A. Biella, F. Storme, J. Lebreuilly, D. Rossini, R. Fazio, I. Carusotto and C. Ciuti, ``Phase diagram of incoherently driven strongly correlated photonic lattice'', Phys. Rev. A, 96, 023839, 2017. \n \n[Chapter 3.] In view of improving the performance of the scheme introduced in last chapter, and reproducing in particular the equilibrium zero temperature phenomenology in driven-dissipative photonic lattices, we develop a fully novel scheme based on the use of non-Markovian reservoirs with tailored broadband spectra which allows to mimick the effect of tunable chemical potential. Our proposal can be implemented by mean of a small number of emitters and absorbers and is accessible to current technologies. \n \nWe first analyse the case of a frequency-dependent emission with a square spectrum and confirm the possibility of stabilizing Mott insulator states with arbitrary integer density. Unlike the previous proposal the Mott state is robust against both losses and tunneling. A sharp transition toward a delocalized superfluid-like state can be induced by strong values of the tunneling or a change in the effective chemical potential. While an overall good agreement is found with the T=0 predictions, our analysis highlights small deviations from the equilibrium case in some parts of the parameters space, which are characterized by a non-vanishing entropy and the kinetic generation of doublon excitations. We finally consider an improved scheme involving additional frequency-dependent losses, and show in that case that the Hamiltonian ground-state is fully recovered for any choice of parameters. Our proposal, whose functionality relies on generic energy relaxation mechanisms and is not restricted to the Bose-Hubbard model, appears as a promising quantum simulator of zero temperature physics in photonic devices. The results of this Chapter are based on the following publication: \n- J. Lebreuilly, A. Biella, F. Storme, D. Rossini, R. Fazio, C. Ciuti and I. Carusotto, ``Stabilizing strongly correlated photon fluids with non-Markovian reservoirs'', Phys. Rev. A 96, 033828 (2017). \n \n[Chapter 4.] We adopt a broader perspective, and analyse the conditions for the emergence of analogous thermal properties in driven-dissipative quantum systems. We show that the impact of an equilibrated environment can be mimicked by several non-Markovian and non-equilibrated reservoirs. Chapter 2 already f
Correlations are a central ingredient of modern condensed matter physics. With the advent of mesoscopic physics, it became possible to study correlated systems in non-equilibrium situations, which can be reached by e.g. driving a constant current through a quantum dot. A basic question is how correlations on the one hand and a non-equilibrium current on the other hand influence each other. Here this interplay is studied for the model system of a quantum dot in the Kondo regime using the real time renormalization group (RTRG) method. This method is a functional renormalization group (RG) method allowing a non-perturbative description of correlated systems in non-equilibrium. For the Kondo quantum dot the method is generalized to the case of double vertices. The RTRG method not only provides equations for the calculation of the renormalized coupling between the quantum dot spin and the reservoir electrons, but also equations for the calculation of the non-equilibrium decoherence rate and the non-equilibrium current.The RG equations are derived to second order. This approximation is expected to be valid as long as the quantum dot does not enter the strong coupling regime, i.e. the effective coupling strength between the quantum dot spin and the electrons does not become too large. It is found that this is the case if the bias voltage applied to the dot or the temperature is much larger than the Kondo temperature.It is shown that the RG equations lead to coupling functions depending on the energy of the incident and the scattered electron. This dependence is simplified to the dependence on the average energy of the incident and the scattered electron in the weak coupling regime.A closer inspection of the RG equations for the couplings shows that they not only contain terms leading to a logarithmic increase of the coupling strength but also subleading terms which are unimportant in the weak coupling regime. The RG equations are solved analytically for the case where the subleading terms are neglected. It is found that the coupling functions develop resonances at energies associated with the chemical potentials of the reservoirs. The height of these resonances is determined by the decoherence rate. However, for bias voltages much larger than the Kondo temperature these resonances do not affect the conductance for a two terminal setup, so the conductance does not provide a measure for the decoherence rate in this case. It is found that the conductance for the two terminal setup is a universal function of voltage/Kondo temperature and temperature/Kondo temperature in the weak coupling regime. This function is calculated analytically in the limits of vanishing voltage or temperature. Furthermore, it is found that for zero temperature the decoherence rate is proportional to the non-equilibrium current flowing through the system. This supports the physical picture that a non-equilibrium current is associated with a decoherence rate, which cuts the logarithmic scaling of the coupling strength.Finally, the RG equations are solved numerically for zero temperature including the subleading corrections found before. As expected, the subleading corrections have no impact on the decoherence rate and the conductance in the weak coupling regime. On the other hand, it is found that they lead to strong deviations from the results of the analytic leading logarithmic approximation if the bias voltage approaches the Kondo temperature. Generally, it is found that the subleading corrections lead to a saturation of the decoherence rate and the conductance to some finite value. However, for the numerical solution a numerical regularization parameter has to be introduced. It turns out that the saturation value found depends on its value, so no statements on the precise value of the decoherence rate and the current can be made in this regime.
Periodically driven quantum systems provide a versatile platform for engineering and exploring non-equilibrium states of matter that have no equilibrium counterparts– a field commonly re- ferred to as Floquet engineering. The research presented in this thesis addresses the microscopic interpretation of experimental spectroscopic signatures, the stability of these driven states in the presence of strong many-body interactions, and the emergence of novel forms of non-equilibrium criticality encoded in quantum entanglement. The first part of the thesis focuses on the interpretation of time- and angle-resolved photo- emission spectroscopy (tr-ARPES), the primary experimental tool for detecting Floquet–Bloch sidebands (FBs). The measured signal reflects interference between processes occurring both inside the material and in the vacuum. In particular, Floquet-dressed initial states coexist and interfere with Volkov-dressed final states arising from the laser-assisted photoelectric effect (LAPE). Their experimental identification requires careful comparison with theoretical predic- tions. Using graphene as a model Dirac material, we perform a systematic comparison between two theoretical frameworks: the first-order perturbative Born approximation (PB1) and time- dependent nonequilibrium Green’s functions (tdNEGF), and compare them with experimental results. We disentangle intrinsic Floquet states, LAPE, and their interference, and quantify how polarization, incidence angle, and near-surface screening shape the observed spectra. Our findings show that, once matrix elements are included, both methods capture qualitative trends, but tdNEGF is necessary to describe the full energy–momentum-resolved features, including hybridization gaps. While non-interacting systems exhibit well-defined FBs, interacting systems absorb energy and can evolve toward an infinite-temperature state. To study this competition between coherent driving and many-body heating, in the second part we consider a one-dimensional chain of interacting spinless fermions using exact diagonalization (ED) and matrix product state (MPS) methods. We compute time-dependent spectral functions and correlation measures, and compare the spectral width of the many-body excitation continuum with the driving frequency to define low- and high-frequency regimes. In our parameter regime, low-frequency driving leads to strong overlap between Floquet sectors, resulting in rapid heating and loss of coherence. For weakly populated continua, we find a transient timescale for the suppression of FBs. When the driving frequency exceeds the continuum width, FBs are well separated and long-lived. Thefinalpartofthethesisinvestigatesnon-equilibriumphenomenafromaninformation-theoretic perspective. Wereportanewclassofdynamicalphasetransitions,termedtemporalentanglement transitions (TET) characterized by non-analytic reorganizations of the entanglement spectrum, in a periodically driven transverse-field Ising chain. These transitions occur in the spectrum of the entanglement Hamiltonian and are signaled by dynamical spontaneous symmetry breaking, marked by the closure of the Schmidt gap and parity flips. These transitions remain invisible to conventional local observables. Finite-size scaling reveals that TET belong to a universality class with a correlation-length exponent ν = 1, mirroring equilibrium Ising universality despite their purely dynamical origin.
This thesis describes a series of theoretical proposals of novel circuits that embed ultrathin superconducting nanowires with coherent quantum phase-slips (QPS). The motivation for our proposals is twofold: firstly, to facilitate unambiguous experimental verification of coherent phase-slips. Secondly, to suggest superconducting devices with new features and functionalities. The first circuit is a driven LC oscillator with the superconducting inductance subject to QPS. We have studied the effect of QPS in two limits: for small and for large phase-slip amplitudes. We expect that weakQPS (whereweakmeans that the QPS amplitude is small compared to the resonance frequency) have ameasurable effect when the oscillator is resonantly driven. The charge induced by the gate affects the quantum interference of QPS with opposite shifts and thus the effect of QPS is periodic in gate voltage. The experimental observation of such dependence would unambiguously identify the quantum coherence of phase-slips. The other crucial effect of QPS is that they produce uncommon non-linearities in the proposed device. The distinctive feature of these non-linearities is the oscillatory dependence on number of photons n with a local period of the order of pn. We analyzed the regime where the QPS correction becomes large by employing a semiclassical approximation as well as by solving the full quantum mechanical equations. At semiclassical level, the QPS-induced non-linearities persist until very high photon number and they result in amultitude ofmetastable states. This was illustrated in the responses of the oscillator: the QPS-induced non-linearities cause deviations fromthe otherwise Lorentzian curve that represents the number of photons N versus detuning. At sufficiently large phase-slip amplitudes this results in an impressive characteristic, a "corkscrew" shape. At any given detuning one finds a multitude of states that differ in the number of photons. About half of these states are stable. At quantum level, we have demonstrated that there is indeed a single quantum state corresponding to the semiclassical metastable states. We have found that these states are robust, their switching time is exponentially long, although they encompass only a few photons. The QPS oscillator is highly tunable: small changes of the driving force, detuning, or charge induced change the number of stable states, thereby enabling easy manipulation of the number of photons. All these features of the phase-slip oscillator make it useful for a wide range of applications, such as ultra-sensitive measurements, quantum manipula- tion and naturally, an unambiguous experimental verification of coherent QPS. In Chapter 3 we propose a series of devices that illustrate the emergence of Coulomb blockade from coherent QPS in thin superconducting wires. The basic ideas is that QPS create an isolation in a wire which is similar to the isolation required by Coulomb blockade. We exploit this idea and suggest setups that are derived from Cooper-pair box and Cooper-pair transistor, so we refer to them as QPS-box and QPS-transistor, respectively. Our main goal was to demonstrate that the devices exhibit sensitivity to a charge induced by a gate electrode, this being the main signature of Coulomb blockade. We analyze the emergence of discrete charging in the limit of strong phaseslips. We investigated six distinct regimes that are realized depending on the relation between the three characteristic energy scales: inductive and charging energy, and QPS amplitude. In both cases the charge sensitivity appears already for small QPS amplitudes as a perturbative correction to the ground-state energy. In both cases, the charge-sensitive part of the perturbative correction is exponentially suppressed in the limit of low impedance. In contrast to the QPS-box, the QPStransistor exhibits both flux and charge sensitivity that makes it potentially useful for measurements. However, if the QPS amplitude becomes of the order of either charging energy (large impedance regime) or inductive energy (small impedance regime), both devices showdiscrete charge states that followthe commonCoulomb blockade pattern of "crossing parabolas". The crossover to Coulomb blockade occurs differently in the limits of large and small impedance. For QPS-transistor, we have analyzed the flux sensitivity (superconducting current) as well as combined flux-charge sensitivity. For a symmetric QPS-transistor we have found a variable separation at specific values of induced charge that leads to double degeneracy of the states at q/e = 1 and half-integer external flux. We have calculated the superconducting current through QPS-transistor to show the non-triviality of the device. Experimental realization of these devices (achievable with the state-or-theart technology), will unambiguously prove the Coulomb blockade as an effect of coherent phase-slip processes. For completeness, we discuss the Josephson-based devices that are dual to QPS-box and QPS-transistor. In Chapter 4 we propose a way to realize quantum synchronization of Josephson and Bloch oscillations in a superconducting device. Essentially, this implies the synchronization of quantumconjugated variables: phase and charge. A circuit comprising of a QPS junction, series resistor and biased by a d.c. voltage exhibits Bloch physics of the charge variable. To ensure well-defined classical oscillations, the resistor needs to be large compared to the resistance quantum. We couple this Bloch subcircuit with a Josephson subcircuit in which the phase variable performs thewell-known Josephson oscillations. Themain effect of the coupling is the transfer of oscillating voltage/current from Josephson/Bloch to Bloch/Josephson part, whereby the voltage/current is multiplied with an amplification coefficient. This amplification coefficient is required to be high for stable synchronization. This is achieved by using an LC-resonator with high quality factorQ. The synchronization takes place in a rather broad interval of frequencies near the LC oscillator’s resonant value. Owing to this synchronization, the transresistance of our device exhibits a typical devil’s staircase curve, very similar to (fractional) Quantum Hall samples. In principle, fluctuations of phase and charge could could destroy the synchronization. Using the quantum description in the framework of Keldysh action formalism, we have investigated the effect of fluctuations on our circuit. The minimum synchronization error rate is shown to be exponential in Q. There is also significant practical interest in the field on metrology. The suggested device can be used to close the famous "metrological triangle" for threemetrological standards: those of resistance, voltage and current—within a single device.