Alejandro González-Tudela
Recent experimental advances enable the fabrication of photonic lattices in which the light propagates with non-trivial energy dispersions. When interfaced with quantum emitters, such systems yield strong collective spontaneous emission phenomena, such as perfect sub-radiance, in which the decay into the bath is completely suppressed, forming bound-states-in-the-continuum. Since such photonic lattices are generally lossy, an alternative way of probing them consists in coherently driving them to an steady-state from which photoluminescence can be extracted. Here, we formalize connections between these two seemingly different situations and use that intuition to predict the formation of non-trivial photonic steady-states in one and two dimensions. In particular, we show that subradiant emitter configurations are linked to the emergence of steady-state light-localization in the driven-dissipative setting, in which the light features the same form than the spontaneously formed bound-states-in-the-continuum. Besides, we also find configurations which leads to the opposite behaviour, an anti-localization of light, that is, it distributes over all the system except for the region defined between the driving lasers. These results shed light on the recently reported optically-defined cavities in polaritonic lattices, and can guide further experimental studies.
Iñaki García-Elcano, Jorge Bravo-Abad, Alejandro González-Tudela
Weyl photons appear when two three-dimensional photonic bands with linear dispersion are degenerate at a single momentum point, labeled as Weyl point. These points have remarkable properties such as being robust topological monopoles of Berry curvature as well as an associated vanishing density of states. In this work, we report on a systematic theoretical study of the quantum optical consequences of such Weyl photons. First, we analyze the dynamics of a single quantum emitter coupled to a Weyl photonic bath as a function of its detuning with respect to the Weyl point and study the corrresponding emission patterns, using both perturbative and exact treatments. Our calculations show an asymmetric dynamical behavior when the emitter is detuned away from the Weyl frequency, as well as different regimes of highly collimated emission, which ultimately translate in a variety of directional collective decays. Besides, we find that the incorporation of staggered mass and hopping terms in the bath Hamiltonian both enriches the observed phenomenology and increases the tunability of the interaction. Finally, we analyze the competition between the coherent and dissipative components of the dynamics for the case of two emitters and derive the conditions under which an effective interacting spin model description is valid.
Zhi-Yuan Wei, Daniel Malz, Alejandro González-Tudela, J. Ignacio Cirac
We show how one can deterministically generate photonic matrix product states with high bond and physical dimensions with an atomic array if one has access to a Rydberg-blockade mechanism. We develop both a quantum gate and an optimal control approach to universally control the system and analyze the photon retrieval efficiency of atomic arrays. Comprehensive modeling of the system shows that our scheme is capable of generating a large number of entangled photons. We further develop a multi-port photon emission approach that can efficiently distribute entangled photons into free space in several directions, which can become a useful tool in future quantum networks.
Mikołaj K. Schmidt, Ruben Esteban, Geza Giedke, Javier Aizpurua, Alejandro González-Tudela
Sep 14, 2020·quant-ph·PDF Frequency-resolved photon correlations have proven to be a useful resource to unveil nonlinearities hidden in standard observables such as the spectrum or the standard (color-blind) photon correlations. In this manuscript, we analyze the frequency-resolved correlations of the photons being emitted from an optomechanical system where light is nonlinearly coupled to the quantized motion of a mechanical mode of a resonator, but where the quantum nonlinear response is typically hard to evidence. We present and unravel a rich landscape of frequency-resolved correlations, and discuss how the time-delayed correlations can reveal information about the dynamics of the system. We also study the dependence of correlations on relevant parameters such as the single-photon coupling strength, the filtering linewidth, or the thermal noise in the environment. This enriched understanding of the system can trigger new experiments to probe nonlinear phenomena in optomechanics, and provide insights into dynamics of generic nonlinear systems.
Eduardo Sánchez-Burillo, Alejandro González-Tudela, Carlos Gonzalez-Ballestero
Mar 20, 2020·quant-ph·PDF We theoretically study a system composed by a waveguide and a moving quantum emitter in the single excitation subspace, treating the emitter motional degree of freedom quantum mechanically. We first characterize single-photon scattering off a single moving quantum emitter, showing both nonreciprocal transmission and recoil-induced reduction of the quantum emitter motional energy. We then characterize the bound states within the bandgap, which display a motion-induced asymmetric phase in real space. We also demonstrate how these bound states form a continuous band with exotic dispersion relations. Finally, we study the spontaneous emission of an initially excited quantum emitter with various initial momentum distributions, finding strong deviations with respect to the static emitter counterpart both in the occupation dynamics and in the spatial distribution of the emitted photons. Our work extends the waveguide-QED toolbox by including the quantum motional degree of freedom of emitters, whose impact in the few-photon dynamics could be harnessed for quantum technologies.
Javier Argüello-Luengo, Alejandro González-Tudela, Tao Shi, Peter Zoller, J. Ignacio Cirac
Feb 21, 2020·quant-ph·PDF Benchmarking numerical methods in quantum chemistry is one of the key opportunities that quantum simulators can offer. Here, we propose an analog simulator for discrete 2D quantum chemistry models based on cold atoms in optical lattices. We first analyze how to simulate simple models, like the discrete versions of H and H$_2^+$, using a single fermionic atom. We then show that a single bosonic atom can mediate an effective Coulomb repulsion between two fermions, leading to the analog of molecular Hydrogen in two dimensions. We extend this approach to larger systems by introducing as many mediating atoms as fermions, and derive the effective repulsion law. In all cases, we analyze how the continuous limit is approached for increasing optical lattice sizes.
Tomás Levy-Yeyati, Carlos Vega, Tomás Ramos, Alejandro González-Tudela
Engineering deterministic photonic gates with simple resources is one of the long-standing challenges in photonic quantum computing. Here, we design a passive conditional gate between co-propagating photons using an array of only two-level emitters. The key resource is to harness the effective photon-photon interaction induced by the chiral coupling of the emitter array to two waveguide modes with different resonant momenta at the emitter's transition frequency. By studying the system's multi-photon scattering response, we demonstrate that, in certain limits, this configuration induces a non-linear $π$-phase shift between the polariton eigenstates of the system without distorting spectrally the wavepackets. Then, we show how to harness this non-linear phase shift to engineer a conditional, deterministic photonic gate in different qubit encodings, with a fidelity arbitrarily close to 1 in the limit of large number of emitters and coupling efficiency. Our configuration can be implemented in topological photonic platforms with multiple chiral edge modes, opening their use for quantum information processing, or in other setups where such chiral multi-mode waveguide scenario can be obtained, e.g., in spin-orbit coupled optical fibers or photonic crystal waveguides.
Cristian Tabares, Christian Kokail, Peter Zoller, Daniel González-Cuadra, Alejandro González-Tudela
Fermionic atoms in optical lattices provide a native implementation of Fermi-Hubbard (FH) models that can be used as analog quantum simulators of many-body fermionic systems. Recent experimental advances include the time-dependent local control of chemical potentials and tunnelings, and thus enable to operate this platform digitally as a programmable quantum simulator. Here, we explore these opportunities and develop ground-state preparation algorithms for different fermionic models, based on the ability to implement both single-particle and many-body, high-fidelity fermionic gates, as provided by the native FH Hamiltonian. In particular, we first design variational, pre-compiled quantum circuits to prepare the ground state of the natively implemented FH model, with significant speedups relative to competing adiabatic protocols. Besides, the versatility of this variational approach enables to target extended FH models, i.e., including terms that are not natively realized on the platform. As an illustration, we include next-nearest-neighbor tunnelings at finite dopings, relevant in the context of $d$-wave superconductivity. Furthermore, we discuss how to approximate the imaginary-time evolution using variational fermionic circuits, both as an alternative state-preparation strategy, and as a subroutine for the Quantum Lanczos algorithm to further improve the energy estimation. We benchmark our protocols for ladder geometries, though they can be readily applied to 2D experimental setups to address regimes beyond the capabilities of current classical methods. These results pave the way for more efficient and comprehensive explorations of relevant many-body phases with existing programmable fermionic quantum simulators.
Carlos Vega, Miguel Bello, Diego Porras, Alejandro González-Tudela
May 26, 2021·quant-ph·PDF Quantum emitters interacting with photonic band-gap materials lead to the appearance of qubit-photon bound states that mediate decoherence-free, tunable emitter-emitter interactions. Recently, it has been shown that when these band-gaps have a topological origin, like in the photonic SSH model, these qubit-photon bound states feature chiral shapes and certain robustness to disorder. In this work, we consider a more general situation where the emitters interact with an extended SSH photonic model with longer range hoppings that displays a richer phase diagram than its nearest-neighbour counterpart, e.g., phases with larger winding numbers. In particular, we first study the features of the qubit-photon bound states when the emitters couple to the bulk modes in the different phases, discern its connection with the topological invariant, and show how to further tune their shape through the use of giant atoms, i.e., non-local couplings. Then, we consider the coupling of emitters to the edge modes appearing in the different topological phases. Here, we show that giant atoms dynamics can distinguish between all different topological phases, as compared to the case with local couplings. Finally, we provide a possible experimental implementation of the model based on periodic modulations of circuit QED systems. Our work enriches the understanding of the interplay between topological photonics and quantum optics.
Eunjong Kim, Xueyue Zhang, Vinicius S. Ferreira, Jash Banker, Joseph K. Iverson, Alp Sipahigil, Miguel Bello, Alejandro Gonzalez-Tudela, Mohammad Mirhosseini, Oskar Painter
While designing the energy-momentum relation of photons is key to many linear, non-linear, and quantum optical phenomena, a new set of light-matter properties may be realized by employing the topology of the photonic bath itself. In this work we investigate the properties of superconducting qubits coupled to a metamaterial waveguide based on a photonic analog of the Su-Schrieffer-Heeger model. We explore topologically-induced properties of qubits coupled to such a waveguide, ranging from the formation of directional qubit-photon bound states to topology-dependent cooperative radiation effects. Addition of qubits to this waveguide system also enables direct quantum control over topological edge states that form in finite waveguide systems, useful for instance in constructing a topologically protected quantum communication channel. More broadly, our work demonstrates the opportunity that topological waveguide-QED systems offer in the synthesis and study of many-body states with exotic long-range quantum correlations.
Miguel Bello, Gloria Platero, Alejandro González-Tudela
Jun 22, 2021·quant-ph·PDF Quantum spin models find applications in many different areas, such as spintronics, high-Tc superconductivity, and even complex optimization problems. However, studying their many-body behaviour, especially in the presence of frustration, represents an outstanding computational challenge. To overcome it, quantum simulators based on cold, trapped atoms and ions have been built, shedding light already on many non-trivial phenomena. Unfortunately, the models covered by these simulators are limited by the type of interactions that appear naturally in these systems. Waveguide QED setups have recently been pointed out as a powerful alternative due to the possibility of mediating more versatile spin-spin interactions with tunable sign, range, and even chirality. Yet, despite their potential, the many-body phases emerging from these systems have only been scarcely explored. In this manuscript, we fill this gap analyzing the ground states of a general class of spin models that can be obtained in such waveguide QED setups. Importantly, we find novel many-body phases different from the ones obtained in other platforms, e.g., symmetry-protected topological phases with large-period magnetic orderings, and explain the measurements needed to probe them.
Yanis Le Fur, Javier Lalueza-Puértolas, Carlos Sánchez Muñoz, Alberto Muñoz de las Heras, Alejandro González-Tudela
Apr 23, 2026·quant-ph·PDF Bosonic quantum error correction enables hardware-efficient protection of quantum information by encoding logical qubits in harmonic oscillators. Bosonic grid states, such as Gottesman-Kitaev-Preskill (GKP) states, are particularly promising due to their potential to correct small displacements and boson loss. However, their generation remains challenging, typically relying on probabilistic protocols or auxiliary qubit systems. Here, we propose deterministic protocols for generating bosonic grid states using programmable nonlinear bosonic circuits composed solely of squeezing, displacement, and Kerr operations. We show that aiming to enforce GKP symmetries in the output of these circuits yields states with competitive performance with respect to current realizations, but whose quality saturates with increasing circuit depth due to imperfect symmetry restoration. Instead, we find that these bosonic circuits naturally give rise to a distinct class of states, that we label as phased-comb states, which are unitarily related to standard grid states but feature an intrinsic phase structure. We demonstrate that these states define a scalable bosonic quantum error-correcting code with near-optimal performance under boson loss comparable to that of approximate GKP states. We further analyze their logical operations and show how to implement a universal gate set for them. Our results establish programmable nonlinear bosonic circuits as a viable route towards the generation of scalable bosonic quantum error-correcting states beyond standard GKP encodings.
Erik P. Navarro-Barón, Herbert Vinck-Posada, Alejandro González-Tudela
Dirac energy-dispersions are responsible of the extraordinary transport properties of graphene. This motivated the quest for engineering such energy dispersions also in photonics, where they have been predicted to lead to many exciting phenomena. One paradigmatic example is the possibility of obtaining power-law, decoherence-free, photon-mediated interactions between quantum emitters when they interact with such photonic baths. This prediction, however, has been obtained either by using toy-model baths, which neglect polarization effects, or by restricting the emitter position to high-symmetry points of the unit cell in the case of realistic structures. Here, we develop a semi-analytical theory of dipole radiation near photonic Dirac points in realistic structures that allows us to compute the effective photon-mediated interactions along the whole unit cell. Using this theory, we are able to find the positions that maximize the emitter interactions and their range, finding a trade-off between them. Besides, using the polarization degree of freedom, we also find positions where the nature of the collective interactions change from being coherent to dissipative ones. Thus, our results significantly improve the knowledge of Dirac light-matter interfaces, and can serve as a guidance for future experimental designs.
Iñaki García-Elcano, Paloma A. Huidobro, Jorge Bravo-Abad, Alejandro González-Tudela
Jun 18, 2024·quant-ph·PDF Long-range interactions are a key resource in many quantum phenomena and technologies. Free-space photons mediate power-law interactions but lack tunability and suffer from decoherence processes due to their omnidirectional emission. Engineered dielectrics can yield tunable and coherent interactions, but typically at the expense of making them both shorter-ranged and sensitive to material disorder and photon loss. Here, we propose a platform that can circumvent all these limitations based on three-dimensional subwavelength atomic arrays subjected to magnetic fields. Our key result is to show how to design the polaritonic bands of these atomic metamaterials to feature a pair of frequency-isolated Weyl points. These Weyl excitations can thus mediate interactions that are simultaneously long-range, due to their gapless nature; robust, due to the topological protection of Weyl points; and decoherence-free, due to their subradiant character. We demonstrate the robustness of these isolated Weyl points for a large regime of interatomic distances and magnetic field values and characterize the emergence of their corresponding Fermi arcs surface states. The latter can as well lead to two-dimensional, non-reciprocal atomic interactions with no analogue in other chiral quantum optical setups.
Carlos Vega, Diego Porras, Alejandro González-Tudela
Topological insulators feature a number of topologically protected boundary modes linked to the value of their bulk invariant. While in one-dimensional systems the boundary modes are zero dimensional and localized, in two-dimensional topological insulators the boundary modes are chiral, one-dimensional propagating modes along the edges of the system. Thus, topological photonic insulators with large Chern numbers naturally display a topologically protected multimode waveguide at their edges. Here, we show how to take advantage of these topologically protected propagating modes by interfacing them with quantum emitters. In particular, using a Harper-Hofstadter lattice, we find situations in which the emitters feature quasiquantized decay rates due to the increasing number of edge modes, and where their spontaneous emission spatially separates in different modes. We also show how using a single $π$-pulse the combination of such spatial separation and the interacting character of the emitters leads to the formation of a single-photon time-bin entangled state with no classical analog, which we characterize computing its entanglement entropy. Finally, we also show how the emitters can selectively interact with the different channels using nonlocal light-matter couplings such as the ones that can be obtained with giant atoms. Such capabilities pave the way for generating quantum gates among topologically protected photons as well as generating more complex entangled states of light in topological channels.
Álvaro Gómez-León, Tomás Ramos, Alejandro González-Tudela, Diego Porras
Sep 22, 2021·quant-ph·PDF 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
Carlos Sánchez Muñoz, Fabrice P. Laussy, Elena del Valle, Carlos Tejedor, Alejandro González-Tudela
Jul 12, 2017·quant-ph·PDF 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.
Mikolaj K. Schmidt, Ruben Esteban, Alejandro Gonzalez-Tudela, Geza Giedke, Javier Aizpurua
Plasmon-enhanced Raman scattering can push single-molecule vibrational spectroscopy beyond a regime addressable by classical electrodynamics. We employ a quantum electrodynamics (QED) description of the coherent interaction of plasmons and molecular vibrations that reveal the emergence of nonlinearities in the inelastic response of the system. For realistic situations, we predict the onset of \textit{phonon-stimulated Raman scattering} and an counter-intuitive dependence of the anti-Stokes emission on the frequency of excitation. We further show that this novel QED framework opens a venue to analyze the correlations of photons emitted at a plasmonic cavity
Alberto Miguel-Torcal, Alejandro González-Tudela, F. J. García-Vidal, Antonio I. Fernández-Domínguez
In recent years, Born-Markov master equations based on tracing out the electromagnetic degrees of freedom have been extensively employed in the description of quantum optical phenomena originating from photon-mediated interactions in quantum emitter ensembles. The breakdown of these effective models, built on assumptions such as ensemble spectral homogeneity, an unstructured photonic density of states, and weak light-matter coupling, has also recently attracted considerable attention. Here, we investigate the accuracy of this well-established framework beyond the most conventional, and extensively explored, spontaneous emission configuration. Specifically, we consider a system comprising two coherently driven and detuned quantum emitters, embedded within a hybrid photonic-plasmonic cavity, formed by a metallic nanorod integrated into a high-refractive-index dielectric microresonator. The local density of photonic states in this structure exhibits a complex frequency dependence, making it a compelling platform for exploring photon-mediated interactions beyond the assumptions above. We benchmark this modeling approach for the quantum dynamics of the emitter pair against exact calculations based on a macroscopic field quantization formalism, providing an illustrative assessment of its validity in significantly structured and dispersive photonic environments. Our analysis reveals four distinct regimes of laser driving and frequency splitting that lead to markedly different levels of accuracy in the effective model.
Miguel Bello, Gloria Platero, Juan Ignacio Cirac, Alejandro González-Tudela
The discovery of topological materials has challenged our understanding of condensed matter physics and led to novel and unusual phenomena. This has motivated recent developments to export topological concepts into photonics to make light behave in exotic ways. Here, we predict several unconventional quantum optical phenomena that occur when quantum emitters interact with a topological waveguide QED bath, namely, the photonic analogue of the Su-Schrieffer-Hegger model. When the emitters frequency lies within the topological band-gap, a chiral bound state emerges, which is located at just one side (right or left) of the emitter. In the presence of several emitters, it mediates topological, long-range tunable interactions between them, that can give rise to exotic phases such as double Néel ordered states. On the contrary, when the emitters' optical transition is resonant with the bands, we find unconventional scattering properties and different super/subradiant states depending on the band topology. We also investigate the case of a bath with open boundary conditions to understand the role of topological edge states. Finally, we propose several implementations where these phenomena can be observed with state-of-the-art technology.