This Colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems There is particularly a focus on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian Several aspects of the slow dynamics in driven systems are discussed and the universality of such dynamics in gapless systems with specific focus on dynamics near continuous quantum phase transitions is emphasized Recent progress on understanding thermalization in closed systems through the eigenstate thermalization hypothesis is also reviewed and relaxation in integrable systems is discussed Finally key experiments probing quantum dynamics in cold atom systems are overviewed and put into the context of our current theoretical understanding

Colloquium: Nonequilibrium dynamics of closed interacting quantum systems

It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.

http://absimage.aps.org/image/DAMOP06/MWS_DAMOP06-2006-000603.pdf

A quantum Newton's cradle

The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with results from exactly solvable models and computational approaches, the concept of bosonic Tomonaga-Luttinger liquids relevant for one-dimensional Bose fluids is introduced, and compared with Bose-Einstein condensates existing in dimensions higher than one. The effects of various perturbations on the Tomonaga-Luttinger liquid state are discussed as well as extensions to multicomponent and out of equilibrium situations. Finally, the experimental systems that can be described in terms of models of interacting bosons in one dimension are discussed.

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One dimensional bosons: From condensed matter systems to ultracold gases

We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.

https://iopscience.iop.org/article/10.1088/0034-4885/79/5/056001/pdf

Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.

We consider the time evolution of observables in the transverse-field Ising chain after a sudden quench of the magnetic field. We provide exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter. We employ two complementary approaches based on asymptotic evaluations of determinants and form-factor sums. We prove that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can also be understood in terms of a GGE. We present a conjecture on how these results generalize to particular quenches in other integrable models.

Quantum quench in the transverse-field Ising chain.

We study the non equilibrium time evolution of an integrable field theory in 1+1 dimensions after a sudden variation of a global parameter of the Hamiltonian. For a class of quenches defined in the text, we compute the long times limit of the one point function of a local operator as a series of form factors. Even if some subtleties force us to handle this result with care, there is a strong evidence that for long times the expectation value of any local operator can be described by a generalized Gibbs ensemble with a different effective temperature for each eigenmode.

https://iopscience.iop.org/article/10.1088/1367-2630/12/5/055015/pdf

Quantum quenches in integrable field theories

Quantum Quenches in Integrable Field Theories

We analyze quantum quenches in integrable models and in particular we determine the initial state in the basis of eigenstates of the post-quench Hamiltonian. This leads us to consider the set of transformations of creation and annihilation operators that respect the Zamolodchikov–Faddeev algebra satisfied by integrable models. We establish that the Bogoliubov transformations hold only in the case of quantum quenches in free theories. For the most general case of interacting theories, we identify two classes of transformations. The first class induces a change in the S-matrix of the theory but not in its ground state, whereas the second class results in a 'dressing' of the operators. We consider as examples of our approach the transformations associated with a change of the interaction in the sinh–Gordon model and the Lieb–Liniger model.

http://iopscience.iop.org/article/10.1088/1742-5468/2012/02/P02017/pdf

Zamolodchikov–Faddeev algebra and quantum quenches in integrable field theories

We analyze quantum quenches in integrable models and in particular the determination of the initial state in the basis of eigenstates of the post-quench hamiltonian. This leads us to consider the set of transformations of creation and annihilation operators that respect the Zamolodchikov-Faddeev algebra satisfied by integrable models. We establish that the Bogoliubov transformations hold only in the case of quantum quenches in free theories. In the most general case of interacting theories, we identify two classes of transformations. The first class induces a change in the S-matrix of the theory but not of its ground state, whereas the second class results in a "dressing" of the operators. As examples of our approach we consider the transformations associated with a change of the interaction in the Sinh-Gordon and the Lieb-Liniger model.

Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories

Photonic graph states—quantum light states where multiple photons are mutually entangled—are key resources for optical quantum technologies. They are notably at the core of error-corrected measurement-based optical quantum computing and all-optical quantum networks. In the discrete variable framework, these applications require the high-efficiency generation of cluster states whose nodes are indistinguishable photons. Such photonic cluster states can be generated with heralded single-photon sources and probabilistic quantum gates, yet with challenging efficiency and scalability. Spin–photon entanglement has been proposed to deterministically generate linear cluster states. First demonstrations have been obtained with semiconductor spins, achieving high photon indistinguishability, and most recently with atomic systems with a high collection efficiency and record length. Here we report on the efficient generation of three-partite cluster states made of one semiconductor spin and two indistinguishable photons. We harness a semiconductor quantum dot inserted in an optical cavity for efficient photon collection and electrically controlled for high indistinguishability. We demonstrate two- and three-particle entanglement with fidelities of 80 ± 4% and 63 ± 5%, respectively, with photon indistinguishability of 88 ± 0.5%. Owing to the high operation rate allowed by the quantum-dot platform, the spin–photon and spin–photon–photon entanglement rates exceed, by three and two orders of magnitude, respectively, those of the previous state of the art. Our system and experimental scheme, a monolithic solid-state device controlled with a resource-efficient simple experimental configuration, are very promising for future scalable applications. A three-partite cluster state made of one semiconductor spin and two indistinguishable photons is generated from an InGaAs quantum dot embedded in a pillar microcavity. The three-partite entanglement rate is 0.53 MHz at the output of the device. 

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Davide Fioretto

Papers

Quantum quenches in integrable field theories

Quantum Quenches in Integrable Field Theories

Zamolodchikov–Faddeev algebra and quantum quenches in integrable field theories

Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories

High-rate entanglement between a semiconductor spin and indistinguishable photons