Further info on the lecture venue can be found here.
In Memory of Lev Petrovich Pitaevskii
Gregory Astrakharchik (UPC & UB, Barcelona)
This is a short talk in memory of an outstanding scientist: Lev Petrovich Pitaevskii. I briefly comment on his academic and scientific trajectory, from writing a letter to Lev Landau for being admitted to PhD exams in Moscow, getting accepted, and up to the later period when Lev Petrovich moved to Trento, Italy, where I did my PhD study under his supervision. Lev Petrovich is known worldwide as one of the authors and editors of probably the most celebrated course on Theoretical Physics. In addition, he wrote a number of seminal works on Casimir forces, the excitation spectrum of superfluid helium (“Pitaevskii plateau”), plasma physics, dilute gases (Gross-Pitaevskii theory), and more. The talk contains a collection of photographs showing different periods of his prodigious life as well as my personal recollections.
References
[1] Berestetskii, Lifshitz & Pitaevskii, Relativistic Quantum Theory, Vol. 4 (1971)
[2] Landau, Lifshitz & Pitaevskii, Electrodynamics of Continuous Media, Vol. 8 (1984)
[3] Lifshitz & Pitaevskii, Statistical Physics, Part 2: Theory of the Condensed State, Vol. 9 (1980)
[4] Lifshitz & Pitaevskii, Physical Kinetics, Vol. 10 (1981)
[5] Novikov, Manakov, Pitaevskii & Zakharov, Theory of Solitons: The Inverse Scattering Method Springer Science & Business Media (1984)
[6] Pitaevskii & Stringari, Bose-Einstein Condensation (2018)
Keywords: Pitaevskii, Gross-Pitaevskii equation, Pitaevskii plateau
Quantum Optics with Matter Waves
Alejandro González-Tudela (IFF, CSIC, Madrid)
Experimental advances in state-dependent optical lattices enable the exploration of quantum optical phenomena by replacing the role of photons with matter waves [1]. In this talk, I will explain how such systems can be used to explore quantum optical phenomena difficult to observe in standard
light-matter interfaces, such as the formation of atom-photon bound states, which allow one to mediate tunable and long-range interactions [2], the emergence of novel super/subradiance phenomena [3], or the exploration of topological light-matter interfaces [4].
References
[1] Nature 559, 589–592 (2018)
[2] Phys. Rev. X 6 (2), 021027 (2016); Nature Photonics 9 (5), 320-325 (2015); PNAS, 201603777 (2016); Phys. Rev. A 97 (4), 043831 (2018)
[3] Phys. Rev. Lett. 119 (14), 143602 (2017); Phys. Rev. A 96 (4), 043811 (2017); Quantum 2, 97 (2018)
[4] Science Advances 5 (7), eaaw0297 (2019); Phys. Rev. Lett. 125 (16), 163602 (2020)
Keywords: Quantum Optics, Quantum Simulation, Non-Markovian Dynamics, Topological Quantum Optics
González-Tudela’s Lecture Notes
Dynamics of integrable many-body quantum systems: from Newton’s cradle to Gibbs’ grave
Jean-Sébastien Caux (University of Amsterdam)
Many-body quantum systems are a theorist’s nightmare due to their complexity, but an experimentalist’s dream due to their potential for displaying new physics.
Recent progress has shown that a special class of systems, known as integrable systems, benefit from a mathematical richness which opens up the door to the computation of many physical properties of experimental relevance. Besides their elaborate equilibrium dynamics, such systems also host relaxation and equilibration behaviour which does not fit traditional textbook understanding.
This course will provide an overview of this area of research, starting from fundamental motivations, introducing models and methods, discussing how these can be applied in real situations (with a special focus on cold atomic systems), and ending with some perspectives on future possibilities.
References
[1] Heisenberg chains [2] Lieb-Liniger [3] Quenches
Keywords: Integrability, Bethe Ansatz, Cold Atoms, Lieb-Liniger Model, Spin
Chains, Heisenberg Model, Correlation Functions, Bragg Spectroscopy, Neutron Scattering, Quantum Quenches, Equilibration and Thermalization, Solitons, Generalized Hydrodynamics, Floquet Driving
Caux’s Lecture Notes (KeyNote)
Ultracold atomic Fermi gases in the strongly correlated regime
Francesco Scazza (University of Trieste & CNR-INO)
One of the most promising applications of ultracold atomic gases is the study of strongly correlated Fermi systems, for which accurate theoretical predictions are challenging even for state-of-the-art approaches. In this lecture, I will first introduce ultracold atomic Fermi gases and how their collective behaviour dramatically changes when inter-atomic interactions are enhanced in the vicinity of a Feshbach resonance, realizing paradigmatic quantum fluids. This introduction will serve to delve into the physics of the famous strongly correlated BEC-BCS crossover and its low-temperature phases, i.e. crossover superfluids. I will then present a number of techniques to experimentally probe such strongly interacting atomic Fermi gases, gaining access to both their equilibrium and transport properties. In the last part of the lecture, I will focus on the regimes of high spin imbalance and repulsive interactions, somewhat complementary to fermion pair superfluidity, introducing Fermi polarons and the competing instabilities in repulsive atomic Fermi systems. I will end with some perspectives in the field, highlighting novel approaches to the analog quantum simulation of fermionic many-body systems.
References
[1] Crossover superfluid [2] Repulsive Fermi gases [3] Fermi polarons
Keywords: Degenerate Fermi gases, BEC-BCS Crossover, Superfluid Transport, Josephson effect, Fermi Polarons, Repulsive Fermi Gases
The Lieb-Liniger model in cold atom experiments
Isabelle Bouchoule (Lab. Charles-Fabry, CNRS, Palaiseau)
One-dimensional (1D) quantum systems have very peculiar properties. In particular, the effects of interactions are typically enhanced in those systems and strongly interacting regimes are obtained in the dilute regime. Note also the possibility to map a bosonic system to a fermionic one. In cold atoms experiments, one-dimensional gases are realized when transverse degrees of freedom are frozen. In particular, the model of one-dimensional bosons with contact interactions, called the Lieb-Liniger model, is realized on different experimental cold-atoms platforms. Out-of-equilibrium dynamics in this model has been investigated in such experiments. The remarkable recent result is the experimental validation of Generalized Hydrodynamics, a new effective theory developed for integrable systems, a class to which the Lieb-Liniger model belongs to. My lectures will be devoted to the presentation of the study of the Lieb-Liniger model, both at equilibrium and out-of-equilibrium, in the context of cold atoms experiments.
During the lecture, I will first discuss briefly the two-body physics in one dimension with contact interactions and make the link with the three-dimensional collisional properties of the atoms. I will then present the Lieb-Liniger model and the form of its eigenstates, which take the Bethe-Ansatz form and are parametrized by wave numbers called rapidities. The latter can be measured by a 1D expansion and experimental results of such a measurement will be presented. We will then concentrate on relaxed states and emphasize the crucial role of the rapidity distribution. Thermal states are in particular relaxed states and I will present experimental results that are in very good agreement with exact theoretical predictions of thermal states. I will then introduce the Generalized Hydrodynamic theory, which assumes local relaxation and describes long wave-length slow dynamics, and present
the two experiments that successfully tested this theory.
In the second part of my lecture, I will discuss several approximate theories, valid in asymptotic regimes, which offer a simplified description of the Lieb-Liniger model and which permit simple calculation of correlation functions and of out-of-equilibrium dynamics. The descriptions we will consider are the classical field approximation, the Bogoliubov approximation, and the Luttinger Liquid description. Experimental results well described by those approaches
will be presented. Finally, I finish with a rapid presentation of a recent theoretical result making the connexion between the Luttinger Liquid description and the exact description in terms of Bethe-Ansatz states.
References
Keywords: Contact interactions, Lieb-Liniger model, Integrability, Relaxation, Generalized Gibbs ensemble, Long wave-length Dynamics, Generalized Hydrodynamics
Quantum simulation and computation with arrays of cold
Rydberg atoms
Daniel Barredo (CINN, El Entrego)
Cold Rydberg atoms are currently the focus of a renewed interest because of their applications in quantum technologies. In these lectures, we will review their exotic properties and interactions. We will present a versatile platform which is nowadays experiencing a great expansion from the perspective of quantum simulation of many body problems and quantum computation [1]. We will report on our efforts to control Rydberg interactions to explore different types of Hamiltonians. Through recent experimental results, we will illustrate the implementation of the Ising [2] and XY [3] Hamiltonians to study quantum magnetism. We will show the ability of these systems to engineer topological systems with strong interactions and the observation of new phases of matter [4]. Finally, I will show our first steps to scale up the atom numbers in our platform by using a cryogenic environment [5], and the state of the art of this platform for quantum computation tasks [6, 7].
References
[1] Nat. Phys. 16, 132 (2020)
[2] Nature 595, 233 (2021)
[3] PRX Quantum 3, 020303 (2022)
[4] Science 365, 775 (2019)
[5] Phys. Rev. Applied 16, 034013 (2021)
[6] Nature 604, 451 (2022)
[7] Nature 604, 457 (2022)
Keywords: Rydberg Atoms, Quantum Simulation, Quantum Computing, Cold Atoms, Atom Arrays, Optical Tweezers
Barredo’s Lecture Notes 1 (pdf)
Barredo’s Lecture Notes 1(PowerPoint)
Bose-Einstein condensation, quantum geometry and quasiparticles
Georg Bruun (University of Aarhus)
In this set of lectures, we will cover two topics. The first is Bose-Einstein condensation in lattices with flat bands. When these bands arise due to interference effects between sublattice hoppings, it turns out that the quantum geometric properties of the Bloch functions have profound effects on the properties of the condensate. The speed of sound in the BEC is determined by the quantum metric tensor around the condensate, and the quantum fluctuations and stability of the condensate are determined by the quantum distance of Bloch states to the condensate.
Our attention is then turned to mobile impurities in BECs, which represent a highly tuneable realisation of quasiparticles. Surprisingly, there are only two regimes where we have controlled results for these quasiparticles: A static impurity in an ideal BED, and when the interactions are weak. We then discuss different methods to approach the strongly interacting regime, which include predictions of a bosonic orthogonality catastrophe. We end by comparing the different theories with experiments.
References
[1] Phys. Rev. Lett. 127, 170404 (2021)
[2] Phys. Rev. B 104, 144507 (2021)
[3] Phys. Rev. A 103, 013317 (2021) [4] Phys. Rev. Lett. 115, 160401 (2015) [6] Phys. Rev. A 99, 063607 (2019)
Keywords: Bose-Einstein Condensation, Flat Band Lattices, Quantum Geometry, Quasiparticles, Orthogonality Catastrophe, Perturbation and Variational Theory
Quantum simulation with quantum gases in optical lattices
Juliette Simonet (University of Hamburg)
Quantum gases in optical lattices have proven to be a powerful tool for the investigation of various phenomena related to the field of many-body physics [1, 2]. Increasingly sophisticated preparation and probing schemes have further boosted quantum simulation in optical lattices. A paradigm example of this advancement is the development of quantum gas microscopes that allow probing Hubbard models with unprecedented accuracy. In the past years, great effort has been spent to develop methods for tailoring new properties so far lacking for quantum simulation of solid-state systems. In this context, time-periodic driving, subsumed under Floquet engineering, constitutes a powerful technique [3].
We will discuss the recent achievements in realizing new classes of Hamiltonians including artificial gauge fields or topological band structures. A strong motivation for developing these methods is the prospect to study the interplay between topology and interactions in a system where both ingredients are fully tunable.
References
[1] Rev. Mod. Phys. 80, 885 (2008)
[2] Lewenstein, Sanpera & Ahufinger, Ultracold atoms in optical lattices (2012)
[3] Nat. Phys. 17, 1342 (2021)
Keywords: Ultracold Atoms in Optical Lattices, Hubbard Models, Floquet Engineering, Artificial Gauge Fields, Topological Properties in Optical Lattices