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A quantum control protocol is proposed for the creation of NOON states with $N$ ultracold bosonic atoms on two modes, corresponding to the coherent superposition $\vert N,0\rangle + \vert 0,N\rangle$. This state can be prepared by using a third mode where all bosons are initially placed and which is symmetrically coupled to the two other modes. Tuning the energy of this third mode across the energy level of the other modes allows the adiabatic creation of the NOON state. While this process normally takes too much time to be of practical usefulness, due to the smallness of the involved spectral gap, it can be drastically boosted through counterdiabatic driving which allows for efficient gap engineering. We demonstrate that this process can be implemented in terms of static parameter adaptations that are experimentally feasible with ultracold quantum gases. Gain factors in the required protocol speed are obtained that increase exponentially with the number of involved atoms and thus counterbalance the exponentially slow collective tunneling process underlying this adiabatic transition., Comment: 7 + 3 pages, 4 + 2 figures

We compare two different numerical methods to integrate in time spatially delocalized initial densities using the Schr\"odinger-Poisson equation system as the evolution law. The basic equation is a nonlinear Schr\"odinger equation with an auto-gravitating potential created by the wave function density itself. The latter is determined as a solution of Poisson's equation modelling, e.g., non-relativistic gravity. For reasons of complexity, we treat a one-dimensional version of the problem whose numerical integration is still challenging because of the extreme long-range forces (being constant in the asymptotic limit). Both of our methods, a Strang splitting scheme and a basis function approach using B-splines, are compared in numerical convergence and effectivity. Overall, our Strang-splitting evolution compares favourably with the B-spline method. In particular, by using an adaptive time-stepper rather large one-dimensional boxes can be treated. These results give hope for extensions to two spatial dimensions for not too small boxes and large evolution times necessary for describing, for instance, dark matter formation over cosmologically relevant scales., Comment: Converged 1D solutions of Schr\"odinger-Poisson model including spatial expansion, comparison between various methods and optimisation of integrators

Quantum walks have gained significant attention over the past decades, mainly because of their variety of implementations and applications. Atomic quantum walks are typically subject to spontaneous emissions arising from the control fields. We investigate spontaneous emission in an atom optics kicked rotor quantum walk. Here, spontaneous emission occurs naturally due to the driving by the kicks, and it is generally viewed as a nuisance in the experiment. We find, however, that spontaneous emission may induce asymmetries in an otherwise symmetric quantum walk. Our results underscore the utility of spontaneous emission and the application of the asymmetric evolution in the walker's space, i.e. for the construction of a quantum walk ratchet or for Parrondo-like quantum games. This highlights the potential for reinterpreting seemingly adverse effects as beneficial under certain conditions, thus broadening the scope of quantum walks and their applications.

We review a scheme for the systematic design of quantum control protocols based on shortcuts to adiabaticity in few-level quantum systems. The adiabatic dynamics is accelerated by introducing high-frequency modulations in the control Hamiltonian, which mimic a time-dependent counterdiabatic correction. We present a number of applications for the high-fidelity realization of quantum state transfers and quantum gates based on effective counterdiabatic driving, in platforms ranging from superconducting circuits to Rydberg atoms., Comment: Review on effective counterdibatic driving

A shortcut-to-adiabatic protocol for the realization of a fast and high-fidelity controlled-phase gate in Rydberg atoms is developed. The adiabatic state transfer, driven in the high-blockade limit, is sped up by compensating nonadiabatic transitions via oscillating fields that mimic a counterdiabatic Hamiltonian. High fidelities are obtained in wide parameter regions. The implementation of the bare effective counterdiabatic field, without original adiabatic pulses, enables to bypass gate errors produced by the accumulation of blockade-dependent dynamical phases, making the protocol efficient also at low blockade values. As an application toward quantum algorithms, how the fidelity of the gate impacts the efficiency of a minimal quantum-error correction circuit is analyzed., Comment: Cover story of Annalen der Physik, Volume 535, Issue 12

We theoretically propose a quantum simulation scheme for the toric-code Hamiltonian, the paradigmatic model of a quantum spin liquid, based on time-periodic driving. We develop a hybrid continuous-digital strategy that exploits the commutativity of different terms in the target Hamiltonian. It allows one to realize the required four-body interactions in a nonperturbative way, attaining strong coupling and the suppression of undesired processes. In addition, we design an optimal protocol for preparing the topologically ordered ground states with high fidelity. A proof-of-principle implementation of a topological device and its use to simulate the topological phase transition are also discussed. The proposed scheme finds natural implementation in architectures of superconducting qubits with tuneable couplings., Comment: 21 pages, 9 figures

We propose quantum control protocols for the high-fidelity preparation of target states in systems with Autler-Townes splitting. We investigate an approximated three-level system obtained from a four-level one by adiabatically eliminating a state that does not participate in the evolution. In our work we use linear, arctan, and Roland-Cerf functions for transferring population between two eigenstates of the system obtaining a high fidelity for long evolution times. Additionally, in order to overcome the restriction given by the lifetimes of the experimental setup, we propose an accelerated adiabatic evolution with a shortcut to adiabaticity protocol, which allows us to reach fidelities close to one but much faster.

We present a concrete theoretical proposal for detecting topological phase transitions in double kicked atom-optics kicked rotors with internal spin-1/2 degree of freedom. The implementation utilizes a kicked Bose-Einstein condensate evolving in one-dimensional momentum space. To reduce influence of atom loss and phase decoherence we aim to keep experimental durations short while maintaining a resonant experimental protocol. Experimental limitations induced by phase noise, quasimomentum distributions, symmetries, and the AC-Stark shift are considered. Our results thus suggest a feasible and optimized procedure for observing topological phase transitions in quantum kicked rotors.

We investigate the possibility of implementing a sequence of quantum walks whose probability distributions give an overall positive winning probability, while it is negative for the single walks (Parrondo's paradox). In particular, we have in mind an experimental realisation with a Bose-Einstein condensate in which the walker's space is momentum space. Experimental problems in the precise implementation of the coin operations for our discrete-time quantum walks are analysed in detail. We study time-dependent phase fluctuations of the coins as well as perturbations arising from the finite momentum width of the condensate. We confirm the visibility of Parrondo's paradox for experimentally available time scales of up to a few hundred steps of the walk.

Over the last decade there have been many advances in studies of quantum walks (QWs) including a momentum-space QW recently realized in our spinor Bose-Einstein condensate system. This QW possessed behaviors that generally agreed with theoretical predictions; however, it also showed momentum distributions that were not adequately explained by the theory. We present a theoretical model which proves that the coherent dynamics of the spinor condensate is sufficient to explain the experimental data without invoking the presence of a thermal cloud of atoms as in the original theory. Our numerical findings are supported by an analytical prediction for the momentum distributions in the limit of zero-temperature condensates. This current model provides more complete explanations to the momentum-space QWs that can be applied to study quantum search algorithms and topological phases in Floquet-driven systems., Comment: experimental and theoretical paper on discrete-time quantum walks

We present a classical approximation for the peaks of survival resonances occurring when diffracting matter waves from absorption potentials. Generally our simplified model describes the absorption-diffraction process around the Talbot time very well. Classical treatments of this process are presently lacking. For purely imaginary potentials, the classical model duplicates quantum mechanical calculations. The classical model allows for simple evolution of phase-space probability densities, which in the limit of the effective Planck's constant going to zero allows for a compact analytical expression of the survival probability as a function of remaining parameters. Our work extends the range of processes that can be described through classical analogues.

The relative energetic stability of the structural phases of common antiferromagnetic transition-metal oxides (MnO, FeO, CoO, and NiO) within the semilocal and hybrid density functionals are fraught with difficulties. In particular, MnO is known to be the most difficult case for almost all common semilocal and hybrid density approximations. Here, we show that the meta-generalized gradient approximation (meta-GGA) constructed from the cuspless hydrogen model and Pauli kinetic energy density (MGGAC) can lead to the correct ground state of MnO. The relative energy differences of zinc-blende (zb) and rock-salt (rs) structures as computed using MGGAC are found to be in nice agreement with those obtained from high-level correlation methods like the random phase approximation or quantum Monte Carlo techniques. Besides, we have also applied the onsite hybrid functionals (closely related to DFT+U ) based on GGA and meta-GGA functionals, and it is shown that a relatively high amount of Hartree-Fock exchange is necessary to obtain the correct ground-state structure. Our present investigation suggests that the semilocal MGGAC and onsite hybrids, both being computationally cheap, as methods of choice for the calculation of the relative stability of antiferromagnetic transition-metal oxides having potential applications in solid-state physics and structural chemistry.

Cu K edge X-ray absorption spectra of overdoped superconducting $YSr_2Cu_{2.75}Mo_{0.25}O_{7.54}$ and $Sr_2CuO_{3.3}$ show a remarkably strong correlation of their superconductivity with the local dynamics of their Cu-Sr and Cu-apical-O pairs. This finding that the entire alkaline earth cation-apical O "dielectric" layer has an active role in the unusual electronic properties of cuprates has not been previously considered and has far reaching implications. We develop this idea of a possible role for the apical oxygen charge dynamics via a soft mode of the Sr by applying Kuramoto's synchronization technique to exact diagonalization calculations of two neighboring Cu-apical O pairs bridged by Sr and a planar O atom. These calculations show a first order phase transition to a synchronized state of the Internal Quantum Tunneling Polarons (IQTPs) in which a fraction of the hole originally confined to the apical O atoms of the cluster is transferred onto the planar O. This combination of experimental results and theory demonstrates that the Sr-O dielectric layer of cuprates most likely plays an important role in high temperature superconductivity via its collective charge dynamics that extends into the $CuO_2$ conducting planes., Comment: 17 pages, 7 figures

A major open topic in cuprates is the interplay between the lattice and electronic dynamics and the importance of their coupling to the mechanism of high-temperature superconductivity (HTSC). As evidenced by Extended X-ray Absorption Fine Structure experiments (EXAFS), anharmonic structural effects are correlated with the charge dynamics and the transition to a superconducting phase in different HTSC compounds. Here we describe how structural anharmonic effects can be coupled to electronic and lattice dynamics in cuprate systems by performing the exact diagonalization of a prototype anharmonic many-body Hamiltonian on a relevant six-atom cluster and show that the EXAFS results can be understood as a Kuramoto synchronization between coupled internal quantum tunneling polarons associated with the two-site distribution of the copper-apical-oxygen ($Cu-O_{ap}$) pair in the dynamic structure. Furthermore, we find that this first order, anti-phase synchronization transition can be fine tuned by temperature and anharmonicity of the lattice vibrations, and promotes the pumping of charge, initially stored at the apical oxygen reservoirs, into the copper-oxide planes. Simultaneously, the internal quantum tunneling polaron extends to the copper-planar-oxygen ($Cu-O_{pl}$) pair. All these findings support an interpretation of the EXAFS data in terms of an effective, quantum mechanical triple-well-potential, which accurately represents the anti-phase synchronization of apical oxygens displacements and lattice-assisted charge transfer to the $CuO_2$ plane., Comment: 13 pages, 5 figures. Submitted to Physical Review B

We have realized a quantum walk in momentum space with a rubidium spinor Bose-Einstein condensate by applying a periodic kicking potential as a walk operator and a resonant microwave pulse as a coin toss operator. The generated quantum walks appear to be stable for up to ten steps and then quickly transit to classical walks due to spontaneous emissions induced by laser beams of the walk operator. We investigate these quantum to classical walk transitions by introducing well controlled spontaneous emissions with an external light source during quantum walks. Our findings demonstrate a scheme to control the robustness of the quantum walks and can also be applied to other cold atom experiments involving spontaneous emissions.

Experimental imperfections induce phase and population errors in quantum systems. We present a method to compensate unitary errors affecting also the population of the qubit states. This is achieved through the interaction of the target qubit with an additional control qubit. We show that our approach works well for single-photon and two-photon excitation schemes. In the first case, we study two reduced models (i) a two-level system in which the interaction corresponds to an effective level shift and (ii) a three-level one describing two qubits in the Bell triplet subspace. In the second case, instead, a double-STIRAP process is presented with comparable compensation efficiency with respect to the single-photon case., Comment: Version 2, comments are very welcome

Molecular Nanomagnets may enable the implementation of qudit-based quantum error-correction codes which exploit the many spin levels naturally embedded in a single molecule, a promising step towards scalable quantum processors. To fully realize the potential of this approach, a microscopic understanding of the errors corrupting the quantum information encoded in a molecular qudit is essential, together with the development of tailor-made quantum error correction strategies. We address these central points by first studying dephasing effects on the molecular spin qudit produced by the interaction with surrounding nuclear spins, which are the dominant source of errors at low temperatures. Numerical quantum error correction codes are then constructed, by means of a systematic optimisation procedure based on simulations of the coupled system-bath dynamics, that provide a striking enhancement of the coherence time of the molecular computational unit. The sequence of pulses needed for the experimental implementation of the codes is finally proposed., Comment: 11 pages, 7 figures

This paper investigates the feasibility of simulating Fuzzy Dark Matter (FDM) with a reduced number of spatial dimensions. Our aim is to set up a realistic, yet numerically inexpensive, toy model in $(1+1)$-dimensional space time, that - under well controlled system conditions - is capable of realizing important aspects of the full-fledged $(3+1)$-FDM phenomenology by means of one-dimensional analogues. Based on the coupled, nonlinear and nonlocal $(3+1)$-Schr\"odinger-Poisson equation under periodic boundary conditions, we derive two distinct one-dimensional models that differ in their transversal matter distribution and consequently in their nonlocal interaction along the single dimension of interest. We show that these discrepancies change the relaxation process of initial states as well as the asymptotic, i.e., thermalized and virialized, equilibrium state. Our investigation includes the dynamical evolution of artificial initial conditions for non-expanding space, as well as cosmological initial conditions in expanding space. The findings of this work are relevant for the interpretation of numerical simulation data modelling nonrelativistic fuzzy cold dark matter in reduced dimensions, in the quest for testing such models and for possible laboratory implementations of them., Comment: 24 pages, 14 figures, accepted for publication in Physical Review D

We investigate finite-size quantum effects in the dynamics of $N$ bosonic particles which are tunneling between two sites adopting the two-site Bose-Hubbard model. By using time-dependent atomic coherent states (ACS) we extend the standard mean-field equations of this bosonic Josephson junction, which are based on time-dependent Glauber coherent states. In this way we find $1/N$ corrections to familiar mean-field (MF) results: the frequency of macroscopic oscillation between the two sites, the critical parameter for the dynamical macroscopic quantum self trapping (MQST), and the attractive critical interaction strength for the spontaneous symmetry breaking (SSB) of the ground state. To validate our analytical results we perform numerical simulations of the quantum dynamics. In the case of Josephson oscillations around a balanced configuration we find that also for a few atoms the numerical results are in good agreement with the predictions of time-dependent ACS variational approach, provided that the time evolution is not too long. Also the numerical results of SSB are better reproduced by the ACS approach with respect to the MF one. Instead the onset of MQST is correctly reproduced by ACS theory only in the large $N$ regime and, for this phenomenon, the $1/N$ correction to the MF formula is not reliable., Comment: 8 pages, 4 figures, improved version

The realization of effective Hamiltonians featuring many-body interactions beyond pairwise coupling would enable the quantum simulation of central models underpinning topological physics and quantum computation. We overcome crucial limitations of perturbative Floquet engineering and discuss the highly accurate realization of a purely three-body Hamiltonian in superconducting circuits and molecular nanomagnets., Comment: 6+8 pages, 3+4 figures

We study the quantum tunneling of two one-dimensional quasi-condensates made of alkali-metal atoms, considering two different tunneling configurations: side-by-side and head-to-tail. After deriving the quasiparticle excitation spectrum, we discuss the dynamics of the relative phase following a sudden coupling of the independent subsystems. In particular, we calculate the coherence factor of the system, which, due to the nonzero tunneling amplitude, it exhibits dephasing-rephasing oscillations instead of pure dephasing. These oscillations are enhanced by a higher tunneling energy, and by higher system densities. Our predictions provide a benchmark for future experiments at temperatures below $T \lesssim 5 \, \mbox{nK}$., Comment: 15 pages, 4 figures

The atom-optics kicked rotor can be used to prepare specific momentum distributions on a discrete basis set. We implement a continuous-time quantum walk and a quantum search protocol in this momentum basis. In particular we propose ways to identify a specific marked state from the final momentum distribution after the walker's evolution. Our protocol is guided by current experimental possibilities making it accessible to experimentally implemented quantum walks with Bose-Einstein condensates.

When driven by a potential bias between two finite reservoirs, the particle current across a quantum system evolves from an initial loading through a coherent, followed by a metastable phase, and ultimately fades away upon equilibration. We formulate a theory which fully accounts for the associated, distinct time scales, and identifies the parameter dependence of the decay rate which ultimately controls the convergence towards equilibrium. Our formalism guarantees total particle number conservation and fundamental consistency between macroscopic and internal currents flowing in the system. We furthermore establish a clear imprint of the fermionic or bosonic particle character on the resulting conductance., Comment: 6 pages, 4 figures

We present a formalism to study many-particle quantum transport across a lattice locally connected to two finite, non-stationary (bosonic or fermionic) reservoirs, both of which are in a thermal state. We show that, for conserved total particle number, a system of nonlinear quantum-classical master equations describes the concurrent many-particle time evolution on the lattice and in the reservoirs. The finiteness of the reservoirs makes a macroscopic current emerge, which decreases exponentially in time, and asymptotically drives the many-particle configuration into an equilibrium state where the particle flow ceases. We analytically derive the time scale of this equilibration process, and, furthermore, investigate the imprint of many-particle interferences on the transport process., Comment: 15 pages, 12 figures