Adriano Angelone, Tao Ying, Fabio Mezzacapo, Guido Masella, Marcello Dalmonte, Guido Pupillo
We investigate the out-of-equilibrium physics of monodisperse bosonic ensembles on a square lattice. The effective Hamiltonian description of these systems is given in terms of an extended Hubbard model with cluster-forming interactions relevant to experimental realizations with cold Rydberg-dressed atoms. The ground state of the model, recently investigated in Phys. Rev. Lett. 123, 045301 (2019), features, aside from a superfluid and a stripe crystalline phase occurring at small and large interaction strength $V$, respectively, a rare first-order transition between an isotropic and an anisotropic stripe supersolid at intermediate $V$. By means of quantum Monte Carlo calculations we show that the equilibrium crystal may be turned into a glass by simulated temperature quenches and that out-of-equilibrium isotropic (super)solid states may emerge also when their equilibrium counterparts are anisotropic. These out-of-equilibrium states are of experimental interest, their excess energy with respect to the ground state being within the energy window typically accessed in cold atom experiments. We find, after quenching, no evidence of coexistence between superfluid and glassy behavior. Such an absence of superglassiness is qualitatively explained.
Johannes Schachenmayer, Guido Pupillo, Andrew J. Daley
We analyse the time-dependence of currents in a 1D Bose gas in an optical lattice. For a 1D system, the stability of currents induced by accelerating the lattice exhibits a broad crossover as a function of the magnitude of the acceleration, and the strength of the inter-particle interactions. This differs markedly from mean-field results in higher dimensions. Using the infinite Time Evolving Block Decimation algorithm, we characterise this crossover by making quantitative predictions for the time-dependent behaviour of the currents and their decay rate. We also compute the time-dependence of quasi-condensate fractions which can be measured directly in experiments. We compare our results to calculations based on phase-slip methods, finding agreement with the scaling as the particle density increases, but with significant deviations near unit filling.
Guido Pupillo, Carl J. Williams, Nikolay V. Prokof'ev
We investigate the effects of finite temperature on ultracold Bose atoms confined in an optical lattice plus a parabolic potential in the Mott insulator state. In particular, we analyze the temperature dependence of the density distribution of atomic pairs in the lattice, by means of exact Monte-Carlo simulations. We introduce a simple model that quantitatively accounts for the computed pair density distributions at low enough temperatures. We suggest that the temperature dependence of the atomic pair statistics may be used to estimate the system's temperature at energies of the order of the atoms' interaction energy.
Xin Lu, Chang-Qin Wu, Andrea Micheli, Guido Pupillo
We study the structure and melting of a classical bilayer system of dipoles, in a setup where the dipoles are oriented perpendicular to the planes of the layers and the density of dipoles is the same in each layer. Due to the anisotropic character of the dipole-dipole interactions, we find that the ground-state configuration is given by two hexagonal crystals positioned on top of each other, independent of the interlayer spacing and dipolar density. For large interlayer distances these crystals are independent, while in the opposite limit of small interlayer distances the system behaves as a two-dimensional crystal of paired dipoles. Within the harmonic approximation for the phonon excitations, the melting temperature of these crystalline configurations displays a non-monotonic dependence on the interlayer distance, which is associated with a re-entrant melting behavior in the form of solid-liquid-solid-liquid transitions at fixed temperature.
Nóra Sándor, Rosario González-Férez, Paul S. Julienne, Guido Pupillo
We propose a novel scheme to efficiently tune the scattering length of two colliding ground-state atoms by off-resonantly coupling the scattering-state to an excited Rydberg-molecular state using laser light. For the s-wave scattering of two colliding ${^{87}}\mathrm{Rb}$ atoms, we demonstrate that the effective optical length and pole strength of this Rydberg optical Feshbach resonance can be tuned over several orders of magnitude, while incoherent processes and losses are minimised. Given the ubiquity of Rydberg molecular states, this technique should be generally applicable to homo-nuclear atomic pairs as well as to atomic mixtures with s-wave (or even p-wave) scattering.
Anoop Thomas, Eloïse Devaux, Kalaivanan Nagarajan, Thibault Chervy, Marcus Seidel, David Hagenmüller, Stefan Schütz, Johannes Schachenmayer, Cyriaque Genet, Guido Pupillo, Thomas W. Ebbesen
Light-matter interactions have generated considerable interest as a means to manipulate material properties. Light-induced superconductivity has been demonstrated using pulsed lasers. An attractive alternative possibility is to exploit strong light-matter interactions arising by coupling phonons to the vacuum electromagnetic field of a cavity mode as has been suggested and theoretically studied. Here we explore this possibility for two very different superconductors, namely YBCO (YBa$_2$Cu$_3$O$_{6+x}$) and Rb$_3$C$_{60}$, coupled to surface plasmon polaritons, using a novel cooperative effect based on the presence of a strongly coupled vibrational environment allowing efficient dressing of the otherwise weakly coupled phonon bands of these compounds. By placing the superconductor-surface plasmon system in a SQUID magnetometer, we find that the superconducting transition temperatures ($T_{c}$) for both compounds are modified in the absence of any external laser field. For YBCO, $T_{c}$ decreases from 92 K to 86 K while for Rb$_3$C$_{60}$, it increases from 30 K to 45 K at normal pressures. In the latter case, a simple theoretical framework is provided to understand these results based on an enhancement of the electron-phonon coupling. This proof-of-principle study opens a new tool box to not only modify superconducting materials but also to understand the mechanistic details of different superconductors.
Alejandro Mendoza-Coto, Rogelio Díaz-Méndez, Guido Pupillo
We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real time dynamics of a large class of classical markovian chains, and particularly to short-time situations where the exact evolution is relevant.
Guido Pupillo, Ana Maria Rey, Gavin Brennen, Carl J. Williams, Charles W. Clark
Several proposals for quantum computation utilize a lattice type architecture with qubits trapped by a periodic potential. For systems undergoing many body interactions described by the Bose-Hubbard Hamiltonian, the ground state of the system carries number fluctuations that scale with the number of qubits. This process degrades the initialization of the quantum computer register and can introduce errors during error correction. In an earlier manuscript we proposed a solution to this problem tailored to the loading of cold atoms into an optical lattice via the Mott Insulator phase transition. It was shown that by adding an inhomogeneity to the lattice and performing a continuous measurement, the unit filled state suitable for a quantum computer register can be maintained. Here, we give a more rigorous derivation of the register fidelity in homogeneous and inhomogeneous lattices and provide evidence that the protocol is effective in the finite temperature regime.
Guido Pupillo, Ana Maria Rey, Carl J. Williams, Charles W. Clark
We present a model that generalizes the Bose-Fermi mapping for strongly correlated 1D bosons in an optical lattice, to cases in which the average number of atoms per site is larger than one. This model gives an accurate account of equilibrium properties of such systems, in parameter regimes relevant to current experiments. The application of this model to non-equilibrium phenomena is explored by a study of the dynamics of an atom cloud subject to a sudden displacement of the confining potential. Good agreement is found with results of recent experiments. The simplicity and intuitive appeal of this model make it attractive as a general tool for understanding bosonic systems in the strongly correlated regime.
Simone Montangero, Rosario Fazio, Peter Zoller, Guido Pupillo
We study the dynamics of a non-integrable system comprising interacting cold bosons trapped in an optical lattice in one-dimension by means of exact time-dependent numerical DMRG techniques. Particles are confined by a parabolic potential, and dipole oscillations are induced by displacing the trap center of a few lattice sites. Depending on the system parameters this motion can vary from undamped to overdamped. We study the dipole oscillations as a function of the lattice displacement, the particle density and the strength of interparticle interactions. These results explain the recent experiment C.D. Fertig et al., Phys. Rev. Lett. 94, 120403 (2005).
Marina Litinskaya, Edoardo Tignone, Guido Pupillo
We demonstrate theoretically that photon-photon attraction can be engineered in the continuum of scattering states for pairs of photons propagating in a hollow-core photonic crystal fiber filled with cold atoms. The atoms are regularly spaced in an optical lattice configuration and the photons are resonantly tuned to an internal atomic transition. We show that the hard-core repulsion resulting from saturation of the atomic transitions induces bunching in the photonic component of the collective atom-photon modes (polaritons). Bunching is obtained in a frequency range as large as tens of GHz, and can be controlled by the inter-atomic separation. We provide a fully analytical explanation for this phenomenon by proving that correlations result from a mismatch of the quantization volumes for atomic excitations and photons in the continuum. Even stronger correlations can be observed for in-gap two-polariton bound states. Our theoretical results use parameters relevant for current experiments with Rb atoms excited on the D2-line.
Ana Maria Rey, Guido Pupillo, Charles W. Clark, Carl J. Williams
We discuss interacting and non-interacting one dimensional atomic systems trapped in an optical lattice plus a parabolic potential. We show that, in the tight-binding approximation, the non-interacting problem is exactly solvable in terms of Mathieu functions. We use the analytic solutions to study the collective oscillations of ideal bosonic and fermionic ensembles induced by small displacements of the parabolic potential. We treat the interacting boson problem by numerical diagonalization of the Bose-Hubbard Hamiltonian. From analysis of the dependence upon lattice depth of the low-energy excitation spectrum of the interacting system, we consider the problems of "fermionization" of a Bose gas, and the superfluid-Mott insulator transition. The spectrum of the noninteracting system turns out to provide a useful guide to understanding the collective oscillations of the interacting system, throughout a large and experimentally relevant parameter regime.
Alberto Giuseppe Catalano, Francesco Mattiotti, Jérôme Dubail, David Hagenmüller, Tomaž Prosen, Fabio Franchini, Guido Pupillo
Dec 15, 2022·quant-ph·PDF We analyze the propagation of excitons in a $d$-dimensional lattice with power-law hopping $\propto 1/r^α$ in the presence of dephasing, described by a generalized Haken-Strobl-Reineker model. We show that in the strong dephasing (quantum Zeno) regime the dynamics is described by a classical master equation for an exclusion process with long jumps. In this limit, we analytically compute the spatial distribution, whose shape changes at a critical value of the decay exponent $α_{\rm cr} = (d+2)/2$. The exciton always diffuses anomalously: a superdiffusive motion is associated to a Lévy stable distribution with long-range algebraic tails for $α\leqα_{\rm cr}$, while for $α> α_{\rm cr}$ the distribution corresponds to a surprising mixed Gaussian profile with long-range algebraic tails, leading to the coexistence of short-range diffusion and long-range Lévy-flights. In the many-exciton case, we demonstrate that, starting from a domain-wall exciton profile, algebraic tails appear in the distributions for any $α$, which affects thermalization: the longer the hopping range, the faster equilibrium is reached. Our results are directly relevant to experiments with cold trapped ions, Rydberg atoms and supramolecular dye aggregates. They provide a way to realize an exclusion process with long jumps experimentally.
Rogelio Diaz-Mendez, Fabio Mezzacapo, Fabio Cinti, Wolfgang Lechner, Guido Pupillo
We study the phases and dynamics of a gas of monodisperse particles interacting via soft-core potentials in two spatial dimensions, which is of interest for soft-matter colloidal systems and quantum atomic gases. Using exact theoretical methods, we demonstrate that the equilibrium low-temperature classical phase simultaneously breaks continuous translational symmetry and dynamic space-time homogeneity, whose absence is usually associated with out-of-equilibrium glassy phenomena. This results in an exotic self-assembled cluster crystal with coexisting liquid-like long-time dynamical properties, which corresponds to a classical analog of supersolid behavior. We demonstrate that the effects of quantum fluctuations and bosonic statistics on cluster-glassy crystals are separate and competing: zero-point motion tends to destabilize crystalline order, which can be restored by bosonic statistics.
Guido Masella, Adriano Angelone, Fabio Mezzacapo, Guido Pupillo, Nikolay V. Prokof'ev
Strong, long-range interactions present a unique challenge for the theoretical investigation of quantum many-body lattice models, due to the generation of large numbers of competing states at low energy. Here, we investigate a class of extended bosonic Hubbard models with off-site terms interpolating between short and infinite range, thus allowing for an exact numerical solution for all interaction strengths. We predict a novel type of stripe crystal at strong coupling. Most interestingly, for intermediate interaction strengths we demonstrate that the stripes can turn superfluid, thus leading to a self-assembled array of quasi-one-dimensional superfluids. These bosonic superstripes turn into an isotropic supersolid with decreasing the interaction strength. The mechanism for stripe formation is based on cluster self-assembling in the corresponding classical ground state, reminiscent of classical soft-matter models of polymers, different from recently proposed mechanisms for cold gases of alkali or dipolar magnetic atoms.
Stefan Schütz, Johannes Schachenmayer, David Hagenmüller, Gavin K. Brennen, Thomas Volz, Vahid Sandoghdar, Thomas W. Ebbesen, Claudiu Genes, Guido Pupillo
Apr 18, 2019·quant-ph·PDF We discuss a technique to strongly couple a single target quantum emitter to a cavity mode, which is enabled by virtual excitations of a nearby mesoscopic ensemble of emitters. A collective coupling of the latter to both the cavity and the target emitter induces strong photon non-linearities in addition to polariton formation, in contrast to common schemes for ensemble strong coupling. We demonstrate that strong coupling at the level of a single emitter can be engineered via coherent and dissipative dipolar interactions with the ensemble, and provide realistic parameters for a possible implementation with SiV$^{-}$ defects in diamond. Our scheme can find applications, amongst others, in quantum information processing or in the field of cavity-assisted quantum chemistry.
David Wellnitz, Stefan Schütz, Shannon Whitlock, Johannes Schachenmayer, Guido Pupillo
We propose a mechanism to realize high-yield molecular formation from ultracold atoms. Atom pairs are continuously excited by a laser, and a collective decay into the molecular ground state is induced by a coupling to a lossy cavity mode. Using a combination of analytical and numerical techniques, we demonstrate that the molecular yield can be improved by simply increasing the number of atoms, and can overcome efficiencies of state-of-the-art association schemes. We discuss realistic experimental setups for diatomic polar and nonpolar molecules, opening up collective light matter interactions as a tool for quantum state engineering, enhanced molecule formation, collective dynamics, and cavity mediated chemistry.
David Wellnitz, Guido Pupillo, Johannes Schachenmayer
Nov 12, 2020·quant-ph·PDF We study a simple model for photoinduced electron transfer reactions for the case of many donor-acceptor pairs that are collectively and homogeneously coupled to a photon mode of a cavity. We describe both coherent and dissipative collective effects resulting from this coupling within the framework of a quantum optics Lindblad master equation. We introduce a method to derive an effective rate equation for electron transfer, by adiabatically eliminating donor and acceptor states and the cavity mode. The resulting rate equation is valid both for weak and strong coupling to the cavity mode, and describes electronic transfer through both the cavity coupled bright states and the uncoupled dark states. We derive an analytic expression for the instantaneous electron transfer rate that depends non-trivially on the time-varying number of pairs in the ground state. We find that under proper resonance conditions, and in the presence of an incoherent drive, reaction rates can be enhanced by the cavity. This enhancement persists, and can even be largest, in the weak light-matter coupling regime. We discuss how the cavity effect is relevant for realistic experiments.
David Wellnitz, Guido Pupillo, Johannes Schachenmayer
Jul 13, 2021·quant-ph·PDF Collectively coupling molecular ensembles to a cavity has been demonstrated to modify chemical reactions akin to catalysis. Theoretically understanding this experimental finding remains to be an important challenge. In particular the role of quantum effects in such setups is an open question of fundamental and practical interest. Theoretical descriptions often neglect quantum entanglement between nuclear and electro-photonic degrees of freedom, e.g.~by computing Ehrenfest dynamics. Here we discover that disorder can strongly enhance the build-up of this entanglement on short timescales after incoherent photo-excitation. We find that this can have direct consequences for reaction coordinate dynamics. We analyze this phenomenon in a disordered Holstein-Tavis-Cummings model, a minimal toy model that includes all fundamental degrees of freedom. Using a numerical technique based on matrix product states we simulate the exact quantum dynamics of more than 100 molecules. Our results highlight the importance of beyond Born-Oppenheimer theories in polaritonic chemistry.
Davide Vodola, Luca Lepori, Elisa Ercolessi, Guido Pupillo
We analyze the quantum phases, correlation functions and edge modes for a class of spin-1/2 and fermionic models related to the 1D Ising chain in the presence of a transverse field. These models are the Ising chain with anti-ferromagnetic long-range interactions that decay with distance $r$ as $1/r^α$, as well as a related class of fermionic Hamiltonians that generalise the Kitaev chain, where both the hopping and pairing terms are long-range and their relative strength can be varied. For these models, we provide the phase diagram for all exponents $α$, based on an analysis of the entanglement entropy, the decay of correlation functions, and the edge modes in the case of open chains. We demonstrate that violations of the area law can occur for $α\lesssim1$, while connected correlation functions can decay with a hybrid exponential and power-law behaviour, with a power that is $α$-dependent. Interestingly, for the fermionic models we provide an exact analytical derivation for the decay of the correlation functions at every $α$. Along the critical lines, for all models breaking of conformal symmetry is argued at low enough $α$. For the fermionic models we show that the edge modes, massless for $α\gtrsim 1$, can acquire a mass for $α< 1$. The mass of these modes can be tuned by varying the relative strength of the kinetic and pairing terms in the Hamiltonian. Interestingly, for the Ising chain a similar edge localization appears for the first and second excited states on the paramagnetic side of the phase diagram, where edge modes are not expected. We argue that, at least for the fermionic chains, these massive states correspond to the appearance of new phases, notably approached via quantum phase transitions without mass gap closure. Finally, we discuss the possibility to detect some of these effects in experiments with cold trapped ions.