Cold Atom Workshop Barcelona

25 Jan 2024, 09:00 → 26 Jan 2024, 23:00 Europe/Madrid

Aula Enric Casassas (UB Physics Faculty)

Two-day meeting of the Cold Atom Physics community in Spain

List of Invited Speakers 

• Veronica Ahufinger (Universitat Autònoma de Barcelona)
• Aitor Alaña (Universidad del País Vasco / EHU)
• Maria Arazo (Universitat de Barcelona)
• Javier Argüello Luengo (ICFO-The Institute of Photonic Sciences)
• Enes Aybar (ICFO-The Institute of Photonic Sciences)
• Daniel Barredo (CINN-CSIC, Asturias)
• Raúl Bombín (Universitat Politècnica de Catalunya)
• Sandra Buob (ICFO-The Institute of Photonic Sciences)
• Pierpaolo Fontana (Universitat Autònoma de Barcelona)
• Miguel Ángel Garcia-March (Universitat Politècnica de València)
• Daniel Goncalves (ICFO-The Institute of Photonic Sciences)
• Rosario González-Férez (Universidad de Granada)
• Tobias Grass (DIPC-Donostia Inernational Physics Center)
• Sarah Hirthe (ICFO-The Institute of Photonic Sciences)
• Chen-How Huang (DIPC-Donostia Inernational Physics Center)
• Michele Modugno (Universidad del País Vasco UPV/EHU & IKERBASQUE)
• Alberto Muñoz de las Heras (CSIC, Madrid)
• Juan Ramón Muñoz de Nova (Universidad Complutense de Madrid)
• Diego Porras Torre (CSIC, Madrid)
• Fabio Revuelta (Universidad Politécnica de Madrid)
• Juan Sánchez (Universitat Politècnica de Catalunya)
• Fernando Sols (Universidad Complutense de Madrid)
• Antonio Tiene (Universidad Autónoma de Madrid)
• Romain Veyron (ICFO-The Institute of Photonic Sciences)
• Yuma Watanabe (ICFO-The Institute of Photonic Sciences)

When

January 25-26, 2024

Local Organizing Committee 

• Anna Argudo (Administrative Staff, ICCUB)
• Mariona Moreno-Cardoner (chair, ICCUB)
• Montserrat Guilleumas (ICCUB)
• Bruno Julia-Diaz (ICCUB)
• Esther Pallarès (Administrative Staff, ICCUB)
• Alessio Celi (Coordinator of RED2018-102488-T (CAPS network) )
• Fernando Sols (Coordinator of FFAF - RSEF)
• Michele Modugno (Secretary of FFAF - RSEF) 

 

  

Acknowledgements

This event is partly funded by RED2018-102488-T(MCIU - AEI) .

 

Formulari_dinscripcio._Informacio_detallada_english.pdf

Thursday 25 January

1 Registration

2 Welcome

Speaker: Eugeni Graugés (Dean of the Faculty of Physics, UB), Fernando Sols (Coordinator RSEF-FFAF), Maria Moreno-Cardoner (organizer)

Day 1: Session I (Chair: Anna Sanpera, Universitat Autònoma de Barcelona)

3 Bosonic orbital Su-Schrieffer-Heeger model in a lattice of rings

We study the topological properties of interacting and non-interacting bosons loaded in the orbital angular momentum states l = 1 in a lattice of rings with alternating distances [Phys. Rev. A 108, 023317 (2023)]. At the single-particle level, the two circulation states within each site lead to two decoupled Su-Schrieffer-Heeger lattices with correlated topological phases. We characterize the topological configuration of these lattices in terms of the alternating distances, as well as their single-particle spectrum and topologically protected edge states. Secondly, we add on-site interactions for the two-boson case, which lead to the appearance of multiple bound states and edge bound states. We investigate the doublon bands in terms of a strong-link model and we analyze the resulting subspaces using perturbation theory in the limit of strong interactions. All analytical results are benchmarked against exact diagonalization simulations.

Speaker: Verònica Ahufinger (Universitat Autònoma de Barcelona)

4 Topological phase diagram of optimally shaken honeycomb lattices

By means of a simple non-perturbative numerical approach, we compute the topological phase diagram for ultracold atoms in shaken honeycomb lattices, under the optimal driving discussed by A. Verdeny and F. Mintert [Phys. Rev. A 92, 063615 (2015)]. These results are used to provide a general discussion of different approaches for computing the effective Floquet Hamiltonian of periodically driven systems.

Speaker: Michele Modugno (Universidad del País Vasco UPV/EHU & IKERBASQUE)

5 Phononic Topological Dissipative Phases in Trapped Ions

Trapped ions can be used to simulate a rich variety of bosonic many-body phases that can be implemented with the vibrational degrees of freedom. We will show that by using parametric couplings, phonons in trapped ions can undergo topological dissipative phase transitions. The latter are the phononic counterparts of topological amplifiers, and can be used for sensing ultraweak forces and electric fields. We will present a theoretical framework for the description of dissipative topological phases that goes beyond trapped ions and can be used in other optomechanical, photonic, or ultracold atom systems.

Speaker: Diego Porras (CSIC-Madrid)

6 Bosons in a flat band

Different systems with (nearly) dispersion-free energy bands have appeared in the past years, from magic angle twisted bilayer graphene to optical lattices with exotic lattice geometries, such as the Lieb lattice or the Kagome lattice. Flat bands provide a fascinating arena for strongly correlated many-body phenomena, since their physics is automatically dominated by interactions. In the context of bosonic systems, an intriguing question arises: Will bosons in flat bands condense, and if yes, where? We have analyzed flat band condensates numerically and via a mean-field description. Our results do not only confirm that condensation in the flat band of a Kagome lattice is possible, but also that the condensate may even carry topological properties induced by interactions.

Speaker: Tobias Grass (DIPC-Donostia Inernational Physics Center)

11:20 Coffee Break

Day 1: Session II (Chair: Leticia Tarruell, ICFO-The Institute of Photonic Sciences)

7 Exploring quantum magnetism and spin squeezing with Rydberg atom arrays

Rydberg atoms in arrays of optical tweezers offer new perspectives for applications in quantum simulation, quantum computation, and quantum metrology. In this talk, I will describe our recent efforts to control dipolar interactions between Rydberg states to engineer a 2D XY spin Hamiltonian. In this model, we adiabatically prepare low-temperature states of both the XY ferro- and antiferromagnet. In the ferromagnetic case, we observe the presence of long-range order enabled by long-range interactions [1]. I will further show that by performing quantum quenches we can probe the dispersion relation of the excitations in the system [2]. Finally, I will illustrate that, by carefully steering the out-of-equilibrium dynamics, we can generate sizable spin squeezing, which could be used for metrological applications [3].

References:
[1] Chen et al., Nature 616, 691 (2023).
[2] Chen et al., arXiv:2311.11726.
[3] Bornet et al., Nature 621, 728 (2023)."

Speaker: Daniel Barredo (CINN - CSIC Asturias)

8 A strontium quantum-gas microscope in a clock-magic lattice

Quantum-gas microscopy is a powerful tool to study individual particle behavior in quantum many-body systems. Realizing those systems with alkaline-earth atoms such as strontium gives rise to exciting phenomena. For example, bosonic strontium in sub-wavelength atomic arrays exhibits strong cooperative effects in atom-photon scattering. The fermionic isotope in the optical lattice enables studying SU(N ≤ 10)-Fermi systems which give rise to exotic magnetic phases beyond the limits of natural materials.

We have realized a strontium quantum-gas microscope which will allow us to study these systems experimentally. We produce quantum-degenerate clouds of bosonic strontium by evaporative cooling in an elliptical sheet beam which provides confinement in a two-dimensional plane. Then, we load the gas into a square optical lattice of 575nm spacing which arises from the four-fold interference of the bow-tie configuration of the lattice beams. Both the lattice and the sheet beam are operated at 813nm, the clock-magic wavelength of strontium, and have a combined power of around 3W. For imaging, we capture photons scattered at the 461nm transition with a high-NA objective while exploiting the narrow 689nm transition for efficient Sisyphus cooling. We obtain high signal-to-noise-ratio single-site resolved images where the atoms can be imaged for several tens of seconds without observing significant hopping. Furthermore, we detect evidence of superfluid 84Sr in the optical lattice with our quantum-gas microscope.

Speaker: Sandra Buob (ICFO - The Institute of Photonic Sciences)

9 Quantum jump photo-detection and quantum trajectory analysis in a single atom experiment

Speaker: Romain Veyron (ICFO - The Institute of Photonic Sciences)

10 Out-of-equilibrium quantum phase separation in free-space atomic ensembles

The driven Dicke model, wherein an ensemble of atoms is driven by an external field and undergoes collective spontaneous emission due to coupling to a leaky cavity mode, is a paradigmatic model that exhibits a driven dissipative phase transition as a function of driving power. Recently, a highly analogous phase transition was experimentally observed, not in a cavity setting, but rather in a free-space atomic ensemble. Motivated by this, we present our ongoing efforts to better characterize the free-space problem, and understand possible differences compared to the cavity version. We specifically discuss a cavity QED model with weak local dissipation as a minimal model for the free space. We find that the presence of local dissipation dramatically changes the properties of the phase transition. In particular, we present preliminary arguments that suggest that the free-space case might exhibit a smooth crossover rather than a true phase transition in the thermodynamic (large atom number) limit.

Speaker: Daniel Goncalves (ICFO - The Institute of Photonic Sciences)

13:10 Lunch Break

Day 1: Session III (Chair: Miguel Ángel Cazalilla, Donostia International Physics Center)

11 Exploring the supersolid stripe phase in a spin-orbit coupled BEC

Supersolids are an exotic phase of matter that combines seemingly opposing characteristics of solids and superfluids. They display spontaneous translational symmetry breaking manifesting in crystalline order, while also possessing superfluid properties like frictionless flow. Supersolids were originally predicted over fifty years ago in the context of solid Helium, but were first observed only few years ago in ultracold atomic systems. Cavity-mediated interactions, dipolar interactions, or optically induced spin-orbit coupling can spontaneously break translational symmetry in a Bose-Einstein condensate. Here, we characterize supersolidity in a spin-orbit coupled Bose-Einstein condensate of potassium. We optically dress the system to engineer a single-particle dispersion relation with two minima at distinct momenta. Matter-wave interference between the condensates in the two minima gives rise to a density modulation, which constitutes the spontaneous breaking of translational symmetry and thus realizes the so-called supersolid stripe phase. We are able to observe this spontaneous density modulation in-situ, by employing a matter-wave lensing technique to magnify the density stripes. We achieve a spatial period larger than our optical imaging resolution, which allows us to characterize the crystalline structure of the stripe phase.

Speaker: Sarah Hirthe (ICFO - The Institute of Photonic Sciences)

12 Supersolid Phase in Multi-Band Bose-Hubbard Model with Long-Range Interactions

Ultracold bosons in optical lattices provide a fertile platform for studying strongly-correlated many-body systems in a highly controllable manner. Bose-Hubbard (BH) models well describe bosons in optical lattices and have been widely investigated theoretically and experimentally. The conventional BH model consists of the nearest neighbor hopping and on-site interaction between bosons confined in the lowest-Bloch band and exhibits the quantum phase transition between the superfluid and the Mott-insulator, which has been witnessed experimentally with ultracold atoms. Theoretical works have also examined generalizations of the standard BH model, leading to enriched many-body physics. A paradigmatic example concerns long-range interactions — these lead to novel phases, such as the Haldane insulator in 1-dimension, density waves, and the most intriguing supersolid phase. While the experimental realization of long-range interacting Bose Hubbard models has been challenging, recent progress has been made with both cold atomic systems and excitons in semiconductor devices. Interestingly, in the last year, a multi-band extended Bose Hubbard model was realized in a GaAs double well device describing strongly interacting indirect (dipolar) excitons forming a density wave state in a two-dimensional square lattice. Motivated by these experimental breakthroughs, we theoretically investigate two-band physics with on-site and nearest-neighbor interactions in an extended one-dimensional BH model. In particular, we focus on “proximity” effects due to the interplay of the two bands. With this aim, we consider the case where the intraband parameters of the two bands considered independently support different phases and study the effects of inter-band interactions. We find that coupling a density wave state in one band to a superfluid state in the other can lead to lattice supersolids. Depending on the filling of the bands and the interband interaction strength, the supersolid phase competes with phase separation, superfluid order, or insulating density-wave orders. Interestingly, our results point to a novel possibility of stabilizing a supersolid phase by thermally exciting one of the two bands, which counterintuitively gives rise to a supersolid obtained from heating.

Speaker: Yuma Watanabe (ICFO - The Institute of Photonic Sciences)

13 Supersolid formation time shortcut and excitation reduction by manipulating the dynamical instability

Supersolids are a phase of matter exhibiting both superfluidity and a periodic density modulation typical of crystals. When formed via quantum phase transition from a superfluid, they require a formation time before their density pattern develops. Some protocols/schemes are proposed for experimental applications, building on earlier descriptions of the role roton instability plays in the supersolid formation process and the associated formation time. In particular, the Parachutejump scheme sought to lessen the excitation produced when crossing the phase transition, and the Bang-Bang method sought to shorten the formation time. The proposed schemes are able to fulfill their objectives successfully as both the shortening of the formation process and the reduction of excitation are achieved within the framework of extended Gross Pitaevskii theory.

Speaker: Aitor Alaña (Universidad del País Vasco / EHU)

14 Modeling Particle Loss in Open Systems using Keldysh Path Integral and Second Order Cumulant Expansion

For open quantum systems, integration of the bath degrees of freedom using the second order cumulant expansion in the Keldysh path integral provides an alternative derivation of the effective action for systems coupled to general baths. The baths can be interacting and not necessarily Markovian. Using this method in the Markovian limit, we compute the particle loss dynamics in various models of ultra-cold atomic gases including a one-dimensional Bose-Hubbard model with two-particle losses and a multi-component Fermi gas with interactions tuned by an optical Feshbach resonance. We explicitly demonstrate that the limit of strong two-body losses can be treated by formulating an indirect loss scheme to describe the bath-system coupling. The particle-loss dynamics thus obtained is valid at all temperatures. For the one-dimensional Bose-Hubbard model, we compare it to solutions of the phenomenological rate equations. The latter are shown to be accurate at high temperatures.

Speaker: Chen-How Huang (DIPC-Donostia Inernational Physics Center)

16:20 Coffee Break

Day 1: Session I (Chair: Grigory Astrakharchik, Universitat Politècnica de Barcelona)

15 Multiple polaron quasiparticles with dipolar fermions in a bilayer

We study the impurity problem with dipolar Fermi atoms in a bilayer geometry. By evaluating the polaron spectrum, we disclose the appearance of a Rydberg-like series of attractive branches when the distance between the layers becomes smaller. We relate them to the appearance of newly bound molecular states by evaluating their orbital angular momentum component. We observe an interchange of orbital character between these states when the system parameters such as the gas density or the interlayer distance change.

Speaker: Antonio Tiene (Universidad Autónoma de Madrid)

16 Dysprosium density functional: A Quantum Monte Carlo based functional to study dipolar droplets and supersolidity

We present the Dysprosium density functional (Dy-DF), a density functional to describe droplet formation and supersolidity in dipolar systems.
Making use of quantum Monte Carlo we compute with accuracy the equation of state of $^{162}$Dy. The quantum correlation energy contribution is used to modify the usual Lee-Huang-Yang term that accounts for quantum correlations in the widely used extended Gross Pitaievskii equation (eGPE).
To validate our functional we show that it reproduces the available experimental data for the minimum critical number of atoms needed to form a droplet.
Due to its critical nature, the prediction of this quantity is challenging and many theories only achieve a qualitative approximation. Furthermore, we show that our functional can be used also to study the BEC-supersolid transition in these systems. The Dy-DF functional outperforms the state-of-the-art eGPE description without increasing the computational cost.

Speaker: Raúl Bombín (Universitat Politècnica de Catalunya)

17 Effects of curved geometry and finite temperature in dipolar Bose Einstein Condensates

We explore the thermal effects in the phase diagram of a dipolar BEC confined in a tubular geometry, and show that temperature significantly shifts the low density point where the order of the phase transition between the supersolid and fluid phases changes. We also investigate the effect of a shell-shaped confinement in dipolar physics at zero temperature, and show that it leads to the emergence of a rich variety of ring-shaped solids and supersolids.

Speaker: Juan Sánchez-Baena (Universitat Politècnica de Catalunya)

18 TBA (Spinor Condensate Experiment)

Speaker: Enes Aybar (ICFO - The Institute of Photonic Sciences)

18:10 Poster Session

21:00 Conference Dinner at Restaurant Pelai (City Center)

Friday 26 January

Day 2: Session I (Chair: Giulia De Rosi, Universitat Politècnica de Barcelona)

19 Rydberg blockade due to the charge-dipole interaction between an atom and a polar molecule



Speaker: Rosario González-Férez (Universidad de Granada)

20 Superfluidity from correlations in driven boson systems

We investigate theoretically the superfluidity of a one-dimensional boson system whose hopping energy is periodically modulated with a zero time average, which results in the suppression of first-order single-particle hopping processes. The dynamics of this Floquet-engineered flat-band system is entirely driven by correlations and described by exotic Hamiltonian and current operators. We employ exact diagonalization and compare our results with those of the conventional, undriven Bose–Hubbard system. We focus on the two main manifestations of superfluidity, the Hess-Fairbank effect and the metastability of supercurrents, with explicit inclusion of an impurity when relevant. Among the novel superfluid features, we highlight the presence of a cat-like ground state, with branches that have opposite crystal momentum but carry the same flux-dependent current, and the essential role of the interference between the collective components of the ground-state wave function. Calculation of the dynamic form factor reveals the presence of an acoustic mode that guarantees superfluidity in the thermodynamic limit.

Speaker: Fernando Sols (Universidad Complutense de Madrid)

21 Quantum correlations in mixtures of a few ultracold bosons

Speaker: Miguel Ángel Garcia-March (Universitat Politècnica de València)

22 Chiral currents in Bose-Einstein condensates subject to current-density interactions

Persistent currents in quasi-one-dimensional Bose-Einstein condensates become chiral in the presence of current-density interactions. This phenomenon is explored in ultracold atoms loaded in a rotating ring geometry, where diverse current-carrying stationary states are analytically found to generalize previously known solutions to the mean-field equations of motion. Their dynamical stability is tested by numerical simulations that show stable currents for states with both constant and modulated density profiles, while decaying currents appear only beyond a unidirectional velocity threshold. Recent experiments in the field place these states within experimental reach.

Speaker: Maria Arazo (Universitat de Barcelona / ICCUB)

23 Multiple symmetry breaking in spontaneous Floquet states

We study multiple symmetry-breaking in many-body systems, focusing on the specific case of an atomic condensate. We discuss the quantization procedure of the Goldstone mode associated to each broken symmetry. This quantization involves a Berry-Gibbs connection which depends on the macroscopic conserved charges associated to each broken symmetry and is not invariant under generalized gauge transformations. Our results suggest that some traveling solutions in a ring can be potentially misidentified as time crystals since they do not arise from a genuine breaking of time-translation symmetry but rather from a spatial-translation symmetry breaking plus some constant drift. We extend the formalism to a spontaneous Floquet state, a periodic state which breaks continuous time-translation symmetry. We find that each broken symmetry now has an associated Floquet-Goldstone mode with zero quasi-energy. Thus, the temporal Floquet-Goldstone mode arising from the continuous time-translation symmetry-breaking is the characteristic signature of a spontaneous Floquet state, absent in conventional (driven) Floquet systems, and its quantum amplitude provides a rare realization of a time operator in Quantum Mechanics. We apply this formalism to the CES state, which breaks U(1) and time-translation symmetries, providing a temporal analogue of a supersolid. Using numerical simulations based on the Truncated Wigner method, we show that the temporal Floquet-Goldstone can be measured from the density-density correlations.

Speaker: Juan Ramon Muñoz de Nova (Universidad Complutense de Madrid)

11:10 Coffee Break + Group Picture

Day 2: Session VI (Chair: Cesar Cabrera, University of Hamburg)

24 Analog simulators for high harmonic generation

The demanding experimental access to the ultrafast dynamics of materials challenges our understanding of their electronic response to applied strong laser fields. In this work, we show that trapped ultracold atoms with highly controllable potentials can become an enabling tool to describe phenomena in a scenario where some effects are more easily accessible and twelve orders of magnitude slower. For this purpose, we characterize the mapping between the attoscience platform and atomic simulators, and propose an experimental protocol to simulate the emission yield of High Harmonic Generation, a regime that has so far been elusive to cold atom simulation. As we illustrate, the benchmark offered by these simulators can provide new insights on the conversion efficiency of extended and short nuclear potentials, as well as the response to applied elliptical polarized fields or ultrashort few-cycle pulses. We will also review recent work done in the group where long-range interactions can lead to new phenomena in problems related to quantum transport, ultrafast processes and frustrated phases of matter.

Speaker: Javier Argüello-Luengo (ICFO - The Institute of Photonic Sciences)

25 Efficient formulations of non-Abelian lattice gauge theories

Speaker: Pierpaolo Fontana (Universitat Autònoma de Barcelona)

26 Variational quantum algorithms for quantum optical systems

Variational quantum algorithms (VQAs) have emerged as a powerful tool to make the best out of the quantum hardware available nowadays. The key idea is to use a classical optimizer to find the set of parameters of a parametrized quantum circuit implemented on the hardware such that it minimizes a given cost function. Beyond digital architectures, VQAs also hold great promise for analog quantum optical simulators, i.e., systems in which ensembles of quantum emitters (e.g., neutral atoms, ions, or excitons) interact with photons.
In the first part of this talk, we will adiabatically eliminate the photons, which give rise to effective interations between the emitters. I will illustrate the power of such interactions in creating wave function Ansätze that capture accurately the ground state of quantum critical spin models (XXZ and Ising) [1].
In the second part, we will focus on the photons. By employing the quantum and classical Fisher information as cost function, I will show how to deterministically generate metrologically-relevant states with large photon numbers exploiting tunable quantum optical non-linearities [2].

References:
[1] C. Tabares, AMH, L. Tagliacozzo, et al., Phys. Rev. Lett. 131, 073602 (2023).
[2] AMH, C. Tabares, J. T. Schneider, et al., arXiv:2309.09841 (2023).

Speaker: Alberto Muñoz de las Heras (IFF - CSIC Madrid)

27 Inelastic confinement-induced resonances under 3D confinement

Inelastic confinement-induced resonances (ICIRs) [1] offer an alternative way to control atom-atom scattering besides Feshbach resonances [2]. These resonances have their origin in the coupling between the center-of-mass and the relative motion due to the anharmonicities in the optical confinement, irrespective of its shape (optical lattice, optical tweezer, etc.), and of the interatomic potential.

Since the first experimental observation of ICIRs under quasi-1D confinement, their existence has CIRs been also demonstrated under quasi-2D confinement [4] and even in mixed dimensional systems [5]. In this communication [6], we report on the observation of confinement-induced resonances for strong 3D confinement. Starting from a Mott-insulator state with predominantly single-site occupancy, we detect loss and heating features at specific values for the confinement length and the 3D scattering length. Two independent models predict the resonance positions to a good approximation, suggesting a universal behavior. The relation of our work with that recently reported in the Ref. [7] will be also discussed.

Our results extend confinement-induced resonances to any dimensionality and open up an alternative method for interaction tuning and controlled molecule formation under strong 3D confinement.

[1] S. Sala, P.-I. Schneider, and A. Saenz, Phys. Rev. Lett. 109, 073201 (2012); S.-G. Peng, H. Hu, X.-J. Liu, and P. D. Drummond, Phys. Rev. A 84, 043619 (2011).
[2] C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010).
[3] E. Haller, M. J. Mark, R. Hart, J. G. Danzl, L. Reichsöllner, V. Melezhik, P. Schmelcher, H.-C. Nägerl, Phys. Rev. Lett. 104, 153203 (2010).
[4] B. Fröhlich, M. Feld, E. Vogt, M. Koschorreck, W. Zwerger, and M. Köhl, Phys. Rev. Lett. 106, 105301 (2011).
[5] G. Lamporesi, J. Catani, G. Barontini, Y. Nishida, M. Inguscio, and F. Minardi, Phys. Rev. Lett. 104, 153202 (2010).
[6] D. Capecchi, C. Cantillano, M. J. Mark, F. Meinert, A. Schindewolf, M. Landini,1 Alejandro Saenz, F. Revuelta, H.-C. Nägerl, arXiv:2209,12504 (accepted in Phys. Rev. Lett.).
[7] Y. Kyung Lee, H. Lin, W. Ketterle, arXiv:2208,06054 (accepted in Phys. Rev. Lett.).

Speaker: Fabio Revuelta (Universidad Politécnica de Madrid)

28 Closing Remarks

13:15 Lunch Break

15:30 Barcelona Historic Guided Tour (City Center)