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Poor man's Majorana Bound States (MBS) arise in minimal Kitaev chains when the parameters are fine-tuned to a sweet spot. We consider an interacting two-site Kitaev chain coupled to a single-mode cavity and show that the sweet spot condition can be controlled with the cavity frequency and the hopping between sites. Furthermore, we demonstrate that photon-mediated effective interactions can be used to screen intrinsic interactions, improving the original quality of the MBS. We describe experimental signatures in the cavity transmission to detect their presence and quality. Our work proposes a new way to tune poor man's MBS in a quantum dot array coupled to a cavity., Comment: 5 pages, 4 figures and supplementary material

We develop a linear response theory for materials collectively coupled to a cavity that is valid in all regimes of light-matter coupling, including symmetry-broken phases. We present and compare two different approaches. First, using a coherent path integral formulation for the partition function to obtain thermal Green functions. This approach relies on a saddle point expansion for the action, that can be truncated in the thermodynamic limit. Second, by formulating the equations of motion for the retarded Green functions and solving them. We use a mean-field decoupling of high-order Green functions in order to obtain a closed, solvable system of equations. Both approaches yield identical results in the calculation of response functions for the cavity and material. These are obtained in terms of the bare cavity and material responses. In combination, the two techniques clarify the validity of a mean-field decoupling in correlated light-matter systems and provide complementary means to compute finite-size corrections to the thermodynamic limit. The theory is formulated for a general model that encompasses most of the systems typically considered in the field of cavity QED materials, within a long-wavelength approximation. Finally, we provide a detailed application of the theory to the Quantum Hall effect and to a collection of magnetic models. We validate our predictions against analytical and finite-size exact-diagonalization results., Comment: No significant changes in second version, just a cross reference with another preprint

We present a rigorous framework for linear response theory in cavity QED materials. Our approach leverages the collective coupling between light and matter, drawing parallels with large-N theories in quantum field theory. We derive closed formulas for various responses of both the cavity and the matter. Our theory is validated by recovering established results for the Dicke model and the Quantum Hall Effect. Additionally, we discover novel excitations in quantum magnets, where the cavity binds magnon pairs into localized states., Comment: No significant changes in second version, just a cross reference with another preprint

Anomalous Floquet topological phases are a hallmark, without a static analog, of periodically driven systems. Recently, Quantum Floquet Engineering has emerged as an interesting approach to cavity-QED materials, which recovers the physics of Floquet engineering in its semi-classical limit. However, the mapping between these two widely different scenarios remains mysterious in many aspects. We discuss the emergence of anomalous topological phases in cavity-QED materials, and link topological phase transitions in the many-body spectrum with those in the $0$- and $\pi$-gaps of Floquet quasienergies. Our results allow to establish the microscopic origin of an emergent discrete time-translation symmetry in the matter sector, and link the physics of isolated many-body systems with that of periodically driven ones. Finally, the relation between many-body and Floquet topological invariants is discussed, as well as the bulk-edge correspondence., Comment: 5 pages, 2 figures and Appendix

Floquet topological phases emerge when systems are periodically driven out-of-equilibrium. They gained attention due to their external control, which allows to simulate a wide variety of static systems by just tuning the external field in the high frequency regime. However, it was soon clear that their relevance goes beyond that, as for lower frequencies, anomalous phases without a static counterpart are present and the bulk-to-boundary correspondence can fail. In this work we discuss the important role of resonances in Floquet phases. For that, we present a method to find analytical solutions when the frequency of the drive matches the band gap, extending the well-known high frequency analysis of Floquet systems. With this formalism, we show that the topology of Floquet phases with resonances can be accurately captured in analytical terms. We also find a bulk-to-boundary correspondence between the number of edge states in finite systems and a set of topological invariants in different frames of reference, which crucially do not explicitly involve the micromotion. To illustrate our results, we periodically drive a SSH chain and a $\pi$-flux lattice, showing that our findings remain valid in various two-band systems and in different dimensions. In addition, we notice that the competition between rotating and counter-rotating terms must be carefully treated when the undriven system is a semi-metal. To conclude, we discuss the implications to experimental setups, including the direct detection of anomalous topological phases and the measurement of their invariants., Comment: 20 pages, 12 figures and Appendix

Anomalous topological phases, where edge states coexist with topologically trivial Chern bands, can only appear in periodically driven lattices. When the driving is smooth and continuous, the bulk-edge correspondence is guaranteed by the existence of a bulk invariant known as the winding number. However, in lattices subject to periodic discrete-step walks the existence of edge states does not only depend on bulk invariants but also on the boundary. This is a consequence of the absence of an intrinsic time-dependence or micromotion in discrete-step walks. We report the observation of edge states and a simultaneous measurement of the bulk invariants in anomalous topological phases in a two-dimensional synthetic photonic lattice subject to discrete-step walks. The lattice is implemented using time multiplexing of light pulses in two coupled fibre rings, in which one of the dimensions displays real space dynamics and the other one is parametric. The presence of edge states is inherent to the periodic driving and depends on the properties of the boundary in the implemented two-band model with zero Chern number. We provide a suitable expression for the topological invariants whose calculation does not rely on micromotion dynamics., Comment: 12 pages main text plus 7 pages of apppendix (19 pages total). Published version

The implementation of a universal quantum processor still poses fundamental issues related to error mitigation and correction, which demand to investigate also platforms and computing schemes alternative to the main stream. A possibility is offered by employing multi-level logical units (qudits), naturally provided by molecular spins. Here we present the blueprint of a Molecular Spin Quantum Processor consisting of single Molecular Nanomagnets, acting as qudits, placed within superconducting resonators adapted to the size and interactions of these molecules to achieve a strong single spin to photon coupling. We show how to implement a universal set of gates in such a platform and to readout the final qudit state. Single-qudit unitaries (potentially embedding multiple qubits) are implemented by fast classical drives, while a novel scheme is introduced to obtain two-qubit gates via resonant photon exchange. The latter is compared to the dispersive approach, finding in general a significant improvement. The performance of the platform is assessed by realistic numerical simulations of gate sequences, such as Deutsch-Josza and quantum simulation algorithms. The very good results demonstrate the feasibility of the molecular route towards a universal quantum processor., Comment: 16 pages, 11 figures. Accepted in Physical Review Applied

Quantum Floquet engineering (QFE) seeks to generalize the control of quantum systems with classical external fields, widely known as Semi-Classical Floquet engineering (SCFE), to quantum fields. However, to faithfully capture the physics at arbitrary coupling, a gauge-invariant description of light-matter interaction in cavity-QED materials is required, which makes the Hamiltonian highly non-linear in photonic operators. We provide a non-perturbative truncation scheme of the Hamiltonian, which is valid or arbitrary coupling strength, and use it to investigate the role of light-matter correlations, which are absent in SCFE. We find that even in the high-frequency regime, light-matter correlations can be crucial, in particular for the topological properties of a system. As an example, we show that for a SSH chain coupled to a cavity, light-matter correlations break the original chiral symmetry of the chain, strongly affecting the robustness of its edge states. In addition, we show how light-matter correlations are imprinted in the photonic spectral function and discuss their relation with the topology of the bands., Comment: 29 pages, 13 figures

Low-noise microwave amplifiers are crucial for detecting weak signals in quantum technologies and radio astronomy. Building an ideal device is challenging as it must amplify a broad range of frequencies while adding minimal noise. The amplification must also be directional so that it favors the observer's direction while protecting the source from its environment. Here, we introduce a fundamentally new type of superconducting Josephson traveling-wave parametric amplifier that fulfills all these requirements by exploiting non-Hermitian topological effects and time-reversal symmetry breaking via the phase of the four-wave-mixing pump. In the topological amplification phase, the device acquires an unprecedented performance such as a gain growing exponentially with system size and largely surpassing 20 dB, exponential suppression of back-wards noise below -30 dB, a bandwidth of GHz, and topological protection against disorder. This opens the door for integrating near-ideal and compact pre-amplifiers on the same chip as quantum processors., Comment: Comments welcome. 8 + 8 pages and 4 + 4 figures. Figure 1 has been expanded to emphasize the importance of the non-local pump acting on the JJ array. SM has been integrated as Appendix

We study the phenomena of topological amplification in arrays of parametric oscillators. We find two phases of topological amplification, both with directional transport and exponential gain with the number of sites, and one of them featuring squeezing. We also find a topologically trivial phase with zero-energy modes which produces amplification but lacks the robust topological protection of the others. We characterize the resilience to disorder of the different phases and their stability, gain, and noise-to-signal ratio. Finally, we discuss their experimental implementation with state-of-the-art techniques., Comment: 23 pages and 19 labeled figures. Also An Appendix with the detailed calculations at the end

The unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics, which can be radically different from closed-system scenarios. Such open quantum system dynamics is generally described by Lindblad master equations, whose dynamical and steady-state properties are challenging to obtain, especially in the many-particle regime. Here, we introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function with a real-space decimation technique. Compared to other methods, such technique enables obtaining compact analytical expressions for the dynamics and steady-state properties, such as asymptotic decays or correlation lengths. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity, including the Hatano-Nelson model. The latter is especially illustrative because its surface and bulk dissipative behavior are linked due to its non-trivial topology, which manifests in directional amplification., Comment: 12 pages, 11 figures and Appendix

We study photon-mediated interactions between molecular spin qudits in the dispersive regime of operation. We derive from a microscopic model the effective interaction between molecular spins, including their crystal field anisotropy (i.e., the presence of non-linear spin terms) and their multi-level structure. Finally, we calculate the long time dynamics for a pair of interacting molecular spins using the method of multiple scales analysis. This allows to find the set of 2-qudit gates that can be realized for a specific choice of molecular spins and to determine the time required for their implementation. Our results are relevant for the implementation of logical gates in general systems of qudits with unequally spaced levels or to determine an adequate computational subspace to encode and process the information., Comment: 9 pages, 7 figures and Appendix. To be published in PRA

We study the physics of a magnetic molecule described by a "giant" spin with multiple ($d > 2$) spin states interacting with the quantized cavity field produced by a superconducting resonator. By means of the input-output formalism, we derive an expression for the output modes in the dispersive regime of operation. It includes the effect of magnetic anisotropy, which makes different spin transitions addressable. We find that the measurement of the cavity transmission allows to uniquely determine the spin state of the qudits. We discuss, from an effective Hamiltonian perspective, the conditions under which the qudit read-out is a non-demolition measurement and consider possible experimental protocols to perform it. Finally, we illustrate our results with simulations performed for realistic models of existing magnetic molecules., Comment: 11 pages, 9 figures and Appendix. Accepted in Physical Review Applied

We relate topological properties of non-Hermitian systems and observables of quantum open systems by using the Keldysh path-integral method. We express Keldysh Green's functions in terms of effective non-Hermitian Hamiltonians that contain all the relevant topological information. We arrive at a frequency dependent topological index that is linked to the response of the system to perturbations at a given frequency. We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases, Comment: 5 pages, 3 figures and Appendix

We explore the physics of topological lattice models in c-QED architectures for arbitrary coupling strength, and the use of the cavity transmission as a topological marker. For this, we develop an approach combining the input-output formalism with an expansion in quantum fluctuations which allows to go beyond the small-coupling regime. We apply our formalism to a fermionic Su-Schrieffer-Heeger (SSH) chain coupled to a single-mode cavity, and find that the cavity can indeed act as a quantum sensor for topological phases, where the initial state preparation plays a crutial role. Additionally, we discuss the persistence of topological features as the coupling strength increases, in terms of an effective Hamiltonian, and calculate the entanglement entropy., Comment: 13 pages, 7 figures

Artificial magnetic molecules can contribute to progressing towards large scale quantum computation by: a) integrating multiple quantum resources and b) reducing the computational costs of some applications. Chemical design, guided by theoretical proposals, allows embedding nontrivial quantum functionalities in each molecular unit, which then acts as a microscopic quantum processor able to encode error protected logical qubits or to implement quantum simulations. Scaling up even further requires 'wiring-up' multiple molecules. We discuss how to achieve this goal by the coupling to on-chip superconducting resonators. The potential advantages of this hybrid approach and the challenges that still lay ahead are critically reviewed., Comment: 9 pages, 4 figures

We investigate the quantum dynamics of a two-level system driven by a bichromatic field, using a non-perturbative analysis. We make special emphasis in the case of two large frequencies, where the Magnus expansion can fail, and in the case of a large and a small frequency, where resonances can dominate. In the first case, we show that two large frequencies can be combined to produce an effective adiabatic evolution. In the second case, we show that high frequency terms (which naturally arise as corrections to the adiabatic evolution obtained in the first case) can be used to produce a highly tunable adiabatic evolution over the whole Bloch sphere, controlled by multi-photon resonances., Comment: 5 pages, 8 figures and Appendix. To be published in Physical Review Research

We propose a driving protocol which allows to use quantum dot arrays as quantum simulators for 1D topological phases. We show that by driving the system out of equilibrium, one can imprint bond-order in the lattice (producing structures such as dimers, trimers, etc) and selectively modify the hopping amplitudes at will. Our driving protocol also allows for the simultaneous suppression of all the undesired hopping processes and the enhancement of the necessary ones, enforcing certain key symmetries which provide topological protection. In addition, we have discussed its implementation in a 12-QD array with two interacting electrons and found correlation effects in their dynamics, when configurations with different number of edge states are considered., Comment: 9 pages, 4 figures

Abstract We discuss the quantum dynamics of the central spin model in a regime where the central spin and bath are slaved to each other. The exact solution is found when the bath is static, and is compared with the effect of an external field, finding that they are inequivalent due to the quantum nature of the environment. When the bath has dynamics, we analyze the differences between the numerical simulation using time-dependent perturbation theory and the equation of motion technique, which shows better accuracy. We demonstrate that the use of dynamical Renormalization Group (dRG), simultaneously with the equation of motion technique, provides a suitable analytical tool to understand the physics, to capture the main physical processes, and a powerful method to eliminate secular terms. In addition, this approach allows to separate classical non-linear behavior from corrections due to quantum correlations., Comment: Main text and Appendix

We propose to Floquet-engineer Dirac cones at the surface of a three-dimensional topological insulator. We show that a large tunability of the Fermi velocity can be achieved as a function of the polarization, direction and amplitude of the driving field. Using this external control, the Dirac cones in the quasienergy spectrum may become elliptic or massive, in accordance to experimental evidences. These results help us to understand the interplay of surface states and external ac driving fields in topological insulators. In our work we use the full Hamiltonian for the three-dimensional system instead of effective surface Hamiltonians, which are usually considered in the literature. Our findings show that the Dirac cones in the quasienergy spectrum remain robust even in the presence of bulk states and, therefore, they validate the usage of effective surface Hamiltonians to explore the properties of Floquet-driven topological boundaries. Furthermore, our model allows us to introduce new out-of-plane field configurations, which cannot be accounted for by effective surface Hamiltonians.

We analyze the effect of a bath of spins interacting with a spin system in terms of the equation of motion technique. We show that this formalism can be used with general spin systems and baths, and discuss the concrete case of a Quantum Ising model longitudinally coupled to the bath. We show how the uncorrelated solutions change when spin-spin correlations are included, the properties of the quasiparticle excitations and the effect of internal dynamics in the spin bath., Comment: Main text and Appendix

We extend the standard SSH model to include long range hopping and disorder, and study how the electronic and topological properties are affected. We show that long range hopping can change the symmetry class and the topological invariant, while diagonal and off-diagonal disorder lead to Anderson localization. Interestingly we find that the Lyapunov exponent $\gamma(E)$ can be linked in two ways to the topological properties in the presence of disorder: Either due to the different response of mid-gap states to increasing disorder, or due to an extra contribution to $\gamma$ due to the presence of edge modes. Finally we discuss its implications in realistic transport measurements., Comment: 8 pages, 6figures