scholarly journals Probing the edge between integrability and quantum chaos in interacting few-atom systems

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 486
Author(s):  
Thomás Fogarty ◽  
Miguel Ángel García-March ◽  
Lea F. Santos ◽  
Nathan L. Harshman
Keyword(s):  
Quantum Chaos ◽  
Cold Atoms ◽  
Quantum Systems ◽  
Particle Interactions ◽  
Body System ◽  
Many Body ◽  
One Dimensional ◽  
The Core ◽  
Emergence Of Chaos ◽  
Number Of Particles

Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.

scholarly journals How many particles make up a chaotic many-body quantum system?

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Guy Zisling ◽  
Lea Santos ◽  
Yevgeny Bar Lev
Keyword(s):  
Long Range ◽  
Quantum Chaos ◽  
Short Range ◽  
Many Body ◽  
Interacting Particles ◽  
One Dimensional ◽  
Long Range Interactions ◽  
Minimum Number ◽  
Many Particles ◽  
Number Of Particles

We numerically investigate the minimum number of interacting particles, which is required for the onset of strong chaos in quantum systems on a one-dimensional lattice with short-range and long-range interactions. We consider multiple system sizes which are at least three times larger than the number of particles and find that robust signatures of quantum chaos emerge for as few as 4 particles in the case of short-range interactions and as few as 3 particles for long-range interactions, and without any apparent dependence on the size of the system.

scholarly journals Dynamical Thermalization of Interacting Fermionic Atoms in a Sinai Oscillator Trap

2019 ◽  
Vol 4 (3) ◽  
pp. 76
Author(s):  
Klaus M. Frahm ◽  
Leonardo Ermann ◽  
Dima L. Shepelyansky
Keyword(s):  
Quantum Chaos ◽  
Cold Atoms ◽  
Particle Dynamics ◽  
Body System ◽  
Many Body ◽  
Fermionic Atoms ◽  
Dirac Distribution ◽  
Initial States

We study numerically the problem of dynamical thermalization of interacting cold fermionic atoms placed in an isolated Sinai oscillator trap. This system is characterized by a quantum chaos regime for one-particle dynamics. We show that, for a many-body system of cold atoms, the interactions, with a strength above a certain quantum chaos border given by the Åberg criterion, lead to the Fermi–Dirac distribution and relaxation of many-body initial states to the thermalized state in the absence of any contact with a thermostate. We discuss the properties of this dynamical thermalization and its links with the Loschmidt–Boltzmann dispute.

scholarly journals Fast scrambling on sparse graphs

2019 ◽  
Vol 116 (14) ◽  
pp. 6689-6694 ◽  
Author(s):  
Gregory Bentsen ◽  
Yingfei Gu ◽  
Andrew Lucas
Keyword(s):  
Quantum Chaos ◽  
Degrees Of Freedom ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Body System ◽  
Many Body ◽  
Sparse Graphs ◽  
Local Quantum ◽  
Sparse Connectivity ◽  
Infinite Temperature

Given a quantum many-body system with few-body interactions, how rapidly can quantum information be hidden during time evolution? The fast-scrambling conjecture is that the time to thoroughly mix information among N degrees of freedom grows at least logarithmically in N. We derive this inequality for generic quantum systems at infinite temperature, bounding the scrambling time by a finite decay time of local quantum correlations at late times. Using Lieb–Robinson bounds, generalized Sachdev–Ye–Kitaev models, and random unitary circuits, we propose that a logarithmic scrambling time can be achieved in most quantum systems with sparse connectivity. These models also elucidate how quantum chaos is not universally related to scrambling: We construct random few-body circuits with infinite Lyapunov exponent but logarithmic scrambling time. We discuss analogies between quantum models on graphs and quantum black holes and suggest methods to experimentally study scrambling with as many as 100 sparsely connected quantum degrees of freedom.

scholarly journals Equivalence of Dissipative and Dissipationless Dynamics of Interacting Quantum Systems With Its Application to the Unitary Fermi Gas

2021 ◽  
Vol 9 ◽  
Author(s):  
Masaaki Tokieda ◽  
Shimpei Endo
Keyword(s):  
Quantum Dynamics ◽  
Cold Atoms ◽  
Fermi Gas ◽  
Quantum Systems ◽  
Harmonic Potential ◽  
Particle Interactions ◽  
Dissipative Dynamics ◽  
Strongly Interacting ◽  
Unitary Fermi Gas

We analytically study quantum dissipative dynamics described by the Caldirola-Kanai model with inter-particle interactions. We have found that the dissipative quantum dynamics of the Caldirola-Kanai model can be exactly mapped to a dissipationless quantum dynamics under a negative external harmonic potential, even when the particles are strongly interacting. In particular, we show that the mapping is valid for the unitary Fermi gas, which is relevant for cold atoms and nuclear matters.

scholarly journals Interaction instability of localization in quasiperiodic systems

2018 ◽  
Vol 115 (18) ◽  
pp. 4595-4600 ◽  
Author(s):  
Marko Žnidarič ◽  
Marko Ljubotina
Keyword(s):  
Transport Properties ◽  
Quantum Systems ◽  
Theoretical Physics ◽  
Solvable Models ◽  
Many Body ◽  
Small Perturbations ◽  
One Dimensional ◽  
Quasiperiodic Potential ◽  
Quasiperiodic Systems ◽  
Small Interactions

Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport properties discontinuously change from localization to diffusion upon switching on interaction. This demonstrates an inherent instability of a possible many-body localization in a quasiperiodic potential at small interactions. We also show how the transport properties can be strongly modified by engineering potential at only a few lattice sites.

scholarly journals Hubbard-Stratonovich-like Transformations for Few-Body Interactions

2018 ◽  
Vol 175 ◽  
pp. 11012
Author(s):  
Christopher Körber ◽  
Evan Berkowitz ◽  
Thomas Luu
Keyword(s):  
Perturbation Theory ◽  
Great Accuracy ◽  
Quantum Systems ◽  
Collective Phenomena ◽  
Many Body ◽  
Chiral Perturbation ◽  
Body Level ◽  
The Many ◽  
Three Body ◽  
Number Of Particles

Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary fields via the Hubbard-Stratonovich transformation. This transformation effectively reduces two-body interactions to interactions of one particle with the auxiliary field, thereby improving the computational scaling of the respective algorithms. The relevance of collective phenomena and interactions grows with the number of particles. For many theories, e.g. Chiral Perturbation Theory, the inclusion of three-body forces has become essential in order to further increase the accuracy on the many-body level. In this proceeding, the an-alytical framework for establishing a Hubbard-Stratonovich-like transformation, which allows for the systematic and controlled inclusion of contact three-and more-body inter-actions, is presented.

scholarly journals Experimentally Accessible Witnesses of Many-Body Localization

2019 ◽  
Vol 1 (1) ◽  
pp. 50-62 ◽  
Author(s):  
Marcel Goihl ◽  
Mathis Friesdorf ◽  
Albert H. Werner ◽  
Winton Brown ◽  
Jens Eisert
Keyword(s):  
Statistical Physics ◽  
Optical Lattices ◽  
Cold Atoms ◽  
Quantum Statistical Mechanics ◽  
Quantum Systems ◽  
Many Body ◽  
Physical Systems ◽  
Tensor Network ◽  
Distinct Features ◽  
Flight Measurements

The phenomenon of many-body localized (MBL) systems has attracted significant interest in recent years, for its intriguing implications from a perspective of both condensed-matter and statistical physics: they are insulators even at non-zero temperature and fail to thermalize, violating expectations from quantum statistical mechanics. What is more, recent seminal experimental developments with ultra-cold atoms in optical lattices constituting analog quantum simulators have pushed many-body localized systems into the realm of physical systems that can be measured with high accuracy. In this work, we introduce experimentally accessible witnesses that directly probe distinct features of MBL, distinguishing it from its Anderson counterpart. We insist on building our toolbox from techniques available in the laboratory, including on-site addressing, super-lattices, and time-of-flight measurements, identifying witnesses based on fluctuations, density–density correlators, densities, and entanglement. We build upon the theory of out of equilibrium quantum systems, in conjunction with tensor network and exact simulations, showing the effectiveness of the tools for realistic models.

scholarly journals Entanglement spreading and quasiparticle picture beyond the pair structure

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Alvise Bastianello ◽  
Mario Collura
Keyword(s):  
Quantum Systems ◽  
One Dimension ◽  
Many Body ◽  
Initial State ◽  
Perfect Agreement ◽  
Quasi Particle ◽  
Simple Assumption ◽  
The Common ◽  
Quasiparticle Picture ◽  
Number Of Particles

The quasi-particle picture is a powerful tool to understand the entanglement spreading in many-body quantum systems after a quench. As an input, the structure of the excitations' pattern of the initial state must be provided, the common choice being pairwise-created excitations. However, several cases exile this simple assumption. In this work we investigate weakly-interacting to free quenches in one dimension. This results in a far richer excitations' pattern where multiplets with a larger number of particles are excited. We generalize the quasi-particle ansatz to such a wide class of initial states, providing a small-coupling expansion of the Rényi entropies. Our results are in perfect agreement with iTEBD numerical simulations.

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