Publications of Carlos Sánchez-Muñoz

We report a driven-dissipative mechanism to generate stationary entangled $W$ states among strongly-interacting quantum emitters placed within a cavity. Driving the ensemble into the highest energy state — whether coherently or incoherently — enables a subsequent cavity-enhanced decay into an entangled steady state consisting of a single de-excitation shared coherently among all emitters, i.e., a $W$ state, well known for its robustness against qubit loss. The non-harmonic energy structure of the interacting ensemble allows this transition to be resonantly selected by the cavity, while quenching subsequent off-resonant decays. Evidence of this purely dissipative mechanism should be observable in state-of-the-art cavity QED systems in the solid-state, enabling new prospects for the scalable stabilization of quantum states in dissipative quantum platforms.

We present an inference method utilizing artificial neural networks for parameter estimation of a quantum probe monitored through a single continuous measurement. Unlike existing approaches focusing on the diffusive signals generated by continuous weak measurements, our method harnesses quantum correlations in discrete photon-counting data characterized by quantum jumps. We benchmark the precision of this method against Bayesian inference, which is optimal in the sense of information retrieval. By using numerical experiments on a two-level quantum system, we demonstrate that our approach can achieve a similar optimal performance as Bayesian inference, while drastically reducing computational costs. Additionally, the method exhibits robustness against the presence of imperfections in both measurement and training data. This approach offers a promising and computationally efficient tool for quantum parameter estimation with photon-counting data, relevant for applications such as quantum sensing or quantum imaging, as well as robust calibration tasks in laboratory-based settings.

Two non-identical quantum emitters, when placed within a cavity and coherently excited at the two-photon resonance, can reach stationary states of nearly maximal entanglement. In Vivas-Via\~na et al., we introduce a frequency-resolved Purcell effect stabilizing entangled $W$ states among strongly interacting quantum emitters embedded in a cavity. Here, we delve deeper into a specific configuration with a particularly rich phenomenology: two interacting quantum emitters under coherent excitation at the two-photon resonance. This scenario yields two resonant cavity frequencies where the combination of two-photon driving and Purcell-enhanced decay stabilizes the system into the sub- and superradiant states, respectively. By considering the case of non-degenerate emitters and exploring the parameter space of the system, we show that this mechanism is merely one among a complex family of phenomena that can generate both stationary and metastable entanglement when driving the emitters at the two-photon resonance. We provide a global perspective of this landscape of mechanisms and contribute analytical characterizations and insights into these phenomena, establishing connections with previous reports in the literature and discussing how some of these effects can be optically detected.

We discuss how two-photon absorption (TPA) of squeezed and coherent states of light can be detected in measurements of the transmitted light fields. Such measurements typically suffer from competing loss mechanisms such as experimental imperfections and linear scattering losses inside the sample itself, which can lead to incorrect assessments of the two-photon absorption cross section. We evaluate the sensitivity with which TPA can be detected and find that TPA sensitivity of squeezed vacua or squeezed coherent states can become independent of linear losses at sufficiently large photon numbers. In particular, this happens for measurements of the photon number or of the anti-squeezed field quadrature, where large fluctuations counteract and exactly cancel the degradation caused by single photon losses.

In this work, we study the driven-dissipative dynamics of a coherently-driven spin ensemble with a squeezed, superradiant decay. This decay consists of a sum of both raising and lowering collective spin operators with a tunable weight. The model presents different critical non-equilibrium phases with a gapless Liouvillian that are associated to particular symmetries and that give rise to distinct kinds of non-ergodic dynamics. In Ref. [1] we focus on the case of a strong-symmetry and use this model to introduce and discuss the effect of dissipative freezing, where, regardless of the system size, stochastic quantum trajectories initialized in a superposition of different symmetry sectors always select a single one of them and remain there for the rest of the evolution. Here, we deepen this analysis and study in more detail the other type of non-ergodic physics present in the model, namely, the emergence of non-stationary dynamics in the thermodynamic limit. We complete our description of squeezed superradiance by analysing its metrological properties in terms of spin squeezing and by analysing the features that each of these critical phases imprint on the light emitted by the system.

Engineering multiphoton states is an outstanding challenge with applications in multiple fields, such as quan- tum metrology, quantum lithography or even biological systems. State-of-the-art methods to obtain them rely on post-selection, multi-level systems or Rydberg atomic ensembles. Recently, it was shown that a strongly driven two-level system interacting with a detuned cavity mode can be engineered to continuously emit n-photon states. In the present work, we show that spectral filtering of its emission relaxes considerably the requirements on the system parameters even to the more accessible bad-cavity situation, opening up the possibility of implementing this protocol in a much wider landscape of different platforms. This improvement is based on a key observation: in the imperfect case where only a certain fraction of emission is composed of n-photon states, these have a well defined energy separated from the rest of the signal, which allows to reveal and purify multiphoton emission just by frequency filtering. We demonstrate these results by obtaining analytical expressions for relevant figures of merit of multiphoton emission, such as the n-photon coupling rate between cavity and emitter, the fraction of light emitted as n-photon states, and n-photon emission rates. This allows us to make a systematic study of such figures of merit as a function of the system parameters and demonstrate the viability of the protocol in several relevant types of cavity QED setups, where we take into account the impact of their respective experimental limitations.

Sum-frequency generation (SFG) allows for coherent upconversion of an electromagnetic signal and has applications in mid-infrared vibrational spectroscopy of molecules. Recent experimental and theoretical studies have shown that plasmonic nanocavities, with their deep sub-wavelength mode volumes, may allow to obtain vibrational SFG signals from a single molecule. In this article, we compute the degree of second order coherence ($g^{(2)}(0)$) of the upconverted mid-infrared field under realistic parameters and accounting for the anharmonic potential that characterizes vibrational modes of individual molecules. On the one hand, we delineate the regime in which the device should operate in order to preserve the second-order coherence of the mid-infrared source, as required in quantum applications. On the other hand, we show that an anharmonic molecular potential can lead to antibunching of the upconverted photons under coherent, Poisson-distributed mid-infrared and visible drives. Our results therefore open a path toward a new kind of bright and tunable source of indistinguishable single photons by leveraging “vibrational blockade” in a resonantly and parametrically driven molecule, without the need for strong light-matter coupling.

Recently gained insights into equilibrium squeezing and entanglement harbored by magnets point towards exciting opportunities for quantum science and technology, while concrete protocols for exploiting these are needed. Here, we theoretically demonstrate that a direct dispersive coupling between a qubit and a noneigenmode magnon enables detecting the magnonic number states’ quantum superposition that forms the ground state of the actual eigenmode – squeezed-magnon – via qubit excitation spectroscopy. Furthermore, this unique coupling is found to enable control over the equilibrium magnon squeezing and a deterministic generation of squeezed even Fock states via the qubit state and its excitation. Our work demonstrates direct dispersive coupling to noneigenmodes, realizable in spin systems, as a general pathway to exploiting the equilibrium squeezing and related quantum properties thereby motivating a search for similar realizations in other platforms.

Multiphoton absorption is of vital importance in many spectroscopic, microscopic or lithographic applications. However, given that it is an inherently weak process, the detection of multiphoton absorption signals typically requires large field intensities, hindering its applicability in many practical situations. In this work, we show that placing a multiphoton absorbent inside an imbalanced nonlinear interferometer can enhance the precision of multiphoton cross-section estimation with respect to strategies based on direct transmission measurements by coherent or even squeezed light. In particular, the power scaling of the sensitivity with photon flux can be increased by an order of magnitude compared to transmission measurements of the sample with coherent light, meaning that a signal could be observed at substantially reduced excitation intensities. Furthermore, we show that this enhanced measurement precision is robust against experimental imperfections leading to photon losses, which usually tend to degrade the detection sensitivity. We trace the origin of this enhancement to an optimal degree of squeezing which has to be generated in a nonlinear SU(1,1)-interferometer.

We show that spontaneous Raman scattering of incident radiation can be observed in cavity-QED systems without external enhancement or coupling to any vibrational degree of freedom. Raman scattering processes can be evidenced as resonances in the emission spectrum, which become clearly visible as the cavity-QED system approaches the ultrastrong coupling regime. We provide a quantum mechanical description of the effect, and show that ultrastrong light-matter coupling is a necessary condition for the observation of Raman scattering. This effect, and its strong sensitivity to the system parameters, opens new avenues for the characterization of cavity QED setups and the generation of quantum states of light.

Virtual states are a central concept in quantum mechanics. By definition, the probability of finding a quantum system in a virtual state should be vanishingly small at all times. In contrast to this notion, we report a phenomenon occurring in open quantum systems by which virtual states can acquire a sizable population in the long time limit, even if they are not directly coupled to any dissipative channel. This means that the situation where the virtual state remains unpopulated can be metastable. We describe this effect by introducing a two-step adiabiatic elimination method, that we termed hierarchical adiabatic elimination, which allows one to obtain analytical expressions of the timescale of metastability in general open quantum systems. We show how these results can be relevant for practical questions such as the generation of stable and metastable entangled states in dissipative systems of interacting qubits.

We introduce the concept of a squeezed laser, in which a squeezed cavity mode develops a macroscopic photonic occupation due to stimulated emission. Above the lasing threshold, the emitted light retains both the spectral purity inherent of a laser and the photon correlations characteristic of a photonic mode with squeezed quadratures. Our proposal, which can be implemented in optical setups, relies on the parametric driving of the cavity and dissipative stabilization by a broadband squeezed vacuum. The squeezed laser can find applications that go beyond those of standard lasers thanks to the squeezed character, such as the direct application in Michelson interferometry beyond the standard quantum limit, or its use in atomic metrology.

We apply deep-neural-network-based techniques to quantum state classification and reconstruction. We demonstrate high classification accuracies and reconstruction fidelities, even in the presence of noise and with little data. Using optical quantum states as examples, we first demonstrate how convolutional neural networks (CNNs) can successfully classify several types of states distorted by, e.g., additive Gaussian noise or photon loss. We further show that a CNN trained on noisy inputs can learn to identify the most important regions in the data, which potentially can reduce the cost of tomography by guiding adaptive data collection. Secondly, we demonstrate reconstruction of quantum-state density matrices using neural networks that incorporate quantum-physics knowledge. The knowledge is implemented as custom neural-network layers that convert outputs from standard feedforward neural networks to valid descriptions of quantum states. Any standard feed-forward neural-network architecture can be adapted for quantum state tomography (QST) with our method. We present further demonstrations of our proposed [arXiv:2008.03240] QST technique with conditional generative adversarial networks (QST-CGAN). We motivate our choice of a learnable loss function within an adversarial framework by demonstrating that the QST-CGAN outperforms, across a range of scenarios, generative networks trained with standard loss functions. For pure states with additive or convolutional Gaussian noise, the QST-CGAN is able to adapt to the noise and reconstruct the underlying state. The QST-CGAN reconstructs states using up to two orders of magnitude fewer iterative steps than a standard iterative maximum likelihood (iMLE) method. Further, the QST-CGAN can reconstruct both pure and mixed states from two orders of magnitude fewer randomly chosen data points than iMLE.

Two-photon absorption (TPA) is of fundamental importance in super-resolution imaging and spectroscopy. Its nonlinear character allows for the prospect of using quantum resources, such as entanglement, to improve measurement precision or to gain new information on, e.g., ultrafast molecular dynamics. Here, we establish the metrological properties of nonclassical squeezed light sources for precision measurements of TPA cross sections. We find that there is no fundamental limit for the precision achievable with squeezed states in the limit of very small cross sections. Considering the most relevant measurement strategies — namely photon counting and quadrature measurements — we determine the quantum advantage provided by squeezed states as compared to coherent states. We find that squeezed states outperform the precision achievable by coherent states when performing quadrature measurements, which provide improved scaling of the Fisher information with respect to the mean photon number $\sim n^4$. Due to the interplay of the incoherent nature and the nonlinearity of the TPA process, unusual scaling can also be obtained with coherent states, which feature a $\sim n^3$ scaling in both quadrature and photon-counting measurements.

We study a system of two interacting, non-indentical quantum emitters driven by a coherent field. We focus on the particular condition of two-photon resonance and obtain analytical expressions for the stationary density matrix of the system and observables of the fluorescent emission. Importantly, our expressions are valid for the general situation of non-identical emitters with different transition energies. Our results allow us to determine the regime of parameters in which coherent two-photon excitation, enabled by the coherent coupling between emitters, is dominant over competing, first-order processes. Using the formalism of quantum parameter estimation, we show that the features imprinted by the two-photon dynamics into the spectrum of resonance fluorescence are particularly sensitive to changes in the distance between emitters, making two-photon excitation the optimal driving regime for the estimation of inter-emitter distance. This can be exploited for applications such as superresolution imaging of point-like sources.

We propose the effective simulation of light-matter ultrastrong-coupling phenomena with strong-coupling systems. Recent theory and experiments have shown that the quantum Rabi Hamiltonian can be simulated by a Jaynes–Cummings system with the addition of two classical drives. This allows to implement nonlinear processes that do not conserve the total number of excitations. However, parity is still a conserved quantity in the quantum Rabi Hamiltonian, which forbids a wide family of processes involving virtual transitions that break this conservation. Here, we show that these parity-non-conserving processes can be simulated, and that this can be done in an even simpler setup: a Jaynes-Cummings type system with the addition of a single classical drive. By shifting the paradigm from simulating a particular model to simulating a particular process, we are able to implement a much wider family of nonlinear coherent protocols than in previous simulation approaches, doing so with fewer resources and constraints. We focus our analysis on three particular examples: a single atom exciting two photons, frequency conversion, and a single photon exciting two atoms.

The development of spectroscopic techniques able to detect and verify quantum coherence is a goal of increasing importance given the rapid progress of new quantum technologies, the advances in the field of quantum thermodynamics, and the emergence of new questions in chemistry and biology regarding the possible relevance of quantum coherence in biochemical processes. Ideally, these tools should be able to detect and verify the presence of quantum coherence in both the transient dynamics and the steady state of driven-dissipative systems, such as light-harvesting complexes driven by thermal photons in natural conditions. This requirement poses a challenge for standard laser spectroscopy methods. Here, we propose photon correlation measurements as a new tool to analyse quantum dynamics in molecular aggregates in driven-dissipative situations. We show that the photon correlation statistics on the light emitted by a molecular dimer model can signal the presence of coherent dynamics. Deviations from the counting statistics of independent emitters constitute a direct fingerprint of quantum coherence in the steady state. Furthermore, the analysis of frequency resolved photon correlations can signal the presence of coherent dynamics even in the absence of steady state coherence, providing direct spectroscopic access to the much sought-after site energies in molecular aggregates.

In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying conditions which, when satisfied, guarantee that the individual constituents of a generic open quantum system will undergo completely synchronous limit cycles which are, to first order, robust to symmetry-breaking perturbations. We then describe how these conditions can be satisfied by the interplay between several elements: interactions, local dephasing and the presence of a strong dynamical symmetry – an operator which guarantees long-time non-stationary dynamics. These elements cause the formation of entanglement and off-diagonal long-range order which drive the synchronised response of the system. To illustrate these ideas we present two central examples: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their non-linear responses elicit long-lived signatures of both phase and frequency-locking.

In driven-dissipative systems, the presence of a strong symmetry guarantees the existence of several steady states belonging to different symmetry sectors. Here we show that, when a system with a strong symmetry is initialized in a quantum superposition involving several of these sectors, each individual stochastic trajectory will randomly select a single one of them and remain there for the rest of the evolution. Since a strong symmetry implies a conservation law for the corresponding symmetry operator on the ensemble level, this selection of a single sector from an initial superposition entails a breakdown of this conservation law at the level of individual realizations. Given that such a superposition is impossible in a classical, stochastic trajectory, this is a a purely quantum effect with no classical analogue. Our results show that a system with a closed Liouvillian gap may exhibit, when monitored over a single run of an experiment, a behaviour completely opposite to the usual notion of dynamical phase coexistence and intermittency, which are typically considered hallmarks of a dissipative phase transition. We discuss our results with a simple, realistic model of squeezed superradiance.

We present a method to implement two-phonon interactions between mechanical resonators and spin qubits in hybrid setups, and show that these systems can be applied for the generation of nonclassical mechanical states even in the presence of dissipation. In particular, we demonstrate that the implementation of a two-phonon Jaynes-Cummings Hamiltonian under coherent driving of the qubit yields a dissipative phase transition with similarities to the one predicted in the model of the degenerate parametric oscillator: beyond a certain threshold in the driving amplitude, the driven-dissipative system sustains a mixed steady state consisting of a `jumping cat’, i.e., a cat state undergoing random jumps between two phases. We consider realistic setups and show that, in samples within reach of current technology, the system features non-classical transient states, characterized by a negative Wigner function, that persist during timescales of fractions of a second.

Recent technological developments have made it increasingly easy to access the non-perturbative regimes of cavity quantum electrodynamics known as ultra or deep strong coupling, where the light-matter coupling becomes comparable to the bare modal frequencies. In this work, we address the adequacy of the broadly used single-mode cavity approximation to describe such regimes. We demonstrate that, in the non-perturbative light-matter coupling regimes, the single-mode models become unphysical, allowing for superluminal signalling. Moreover, considering the specific example of the quantum Rabi model, we show that the multi-mode description of the electromagnetic field, necessary to account for light propagation at finite speed, yields physical observables that differ radically from their single-mode counterparts already for moderate values of the coupling. Our multi-mode analysis also reveals phenomena of fundamental interest on the dynamics of the intracavity electric field, where a free photonic wavefront and a bound state of virtual photons are shown to coexist.

The development, characterization and control of $N$-photon sources are instrumental for quantum technological applications. This work constitutes a step forward in this direction, where we propose a cavity quantum electrodynamics setup designed for the generation of photon pairs. We analyze it both via the scattering and master equation formalisms. From the connection between these two frameworks it naturally arises a physical criterion characterizing when weakly-driven systems behave as continuous antibunched two-photon sources. We find the optimal parameters for which our setup works as an efficient photon-pair source, showing also that it becomes a deterministic down-converter of single photons. We provide a specific implementation based on state-of-the-art superconducting circuits, showing how our proposal is within the reach of current technologies.

Radiative two-photon cascades from biexcitons in semiconductor quantum dots under resonant two-photon excitation are promising candidates for the generation of photon pairs. In this work, we propose a scheme to obtain two-photon emission that allows to operate under very intense driving fields. This approach relies on the Purcell enhancement of two-photon virtual transitions between states of the biexciton dressed by the laser. The richness provided by the biexcitonic level structure allows to reach a variety of regimes, from antibunched and bunched photon pairs with polarization orthogonal to the driving field, to polarization entangled two-photon emission. This evidences that the general paradigm of two-photon emission from a ladder of dressed states can find interesting, particular implementations in a variety of systems.

The violation of the Cauchy-Schwarz and Bell inequalities ranks among the major evidences of the genuinely quantum nature of an emitter. We show that by dispensing from the usual approximation of mode correlations and studying directly correlations between the physical reality -the photons- these violations can be optimized. This is achieved by extending the concept of photon correlations to all frequencies in all the possible windows of detections, with no prejudice to the supposed origin of the photons. We identify the regions of quantum emission as rooted in collective de-excitation involving virtual states instead of, as previously assumed, cascaded transitions between real states.