We report the creation of thermal, Fock, coherent, and squeezed states of motion of a harmonically bound {sup 9}Be{sup +} ion. The last three states are coherently prepared from an ion which has been initially laser cooled to the zero point of motion. The ion is trapped in the regime where the coupling between its motional and internal states, due to applied (classical) radiation, can be described by a Jaynes-Cummings-type interaction. With this coupling, the evolution of the internal atomic state provides a signature of the number state distribution of the motion. {copyright} {ital 1996 The American Physical Society.}

Generation of Non-classical Motional States of a Trapped Atom

Recent decades have witnessed great developments in the field of quantum simulation—where synthetic systems are built and studied to gain insight into complicated, many-body real-world problems. Systems of individually controlled neutral atoms, interacting with each other when excited to Rydberg states, have emerged as a promising platform for this task, particularly for the simulation of spin systems. Here, we review the techniques necessary for the manipulation of neutral atoms for the purpose of quantum simulation—such as quantum gas microscopes and arrays of optical tweezers—and explain how the different types of interactions between Rydberg atoms allow a natural mapping onto various quantum spin models. We discuss recent achievements in the study of quantum many-body physics in this platform, and some current research directions beyond that. This Review Article outlines the techniques necessary for the manipulation of neutral atoms and making use of their interactions, when excited to Rydberg states, to achieve the goal of quantum simulation of many-body physics.

https://hal.archives-ouvertes.fr/hal-02488244/document

Many-body physics with individually controlled Rydberg atoms

Over the last decade, systems of individually-controlled neutral atoms, interacting with each other when excited to Rydberg states, have emerged as a promising platform for quantum simulation of many-body problems, in particular spin systems. Here, we review the techniques underlying quantum gas microscopes and arrays of optical tweezers used in these experiments, explain how the different types of interactions between Rydberg atoms allow a natural mapping onto various quantum spin models, and describe recent results that were obtained with this platform to study quantum many-body physics.

Many-Body Physics with Individually-Controlled Rydberg Atoms

After many years of development of the basic tools, quantum simulation with ultracold atoms has now reached the level of maturity at which it can be used to investigate complex quantum processes. Planning of new experiments and upgrading of existing set-ups requires a broad overview of the available techniques, their specific advantages and limitations. This Technical Review aims to provide a comprehensive compendium of the state of the art. We discuss the basic principles, the available techniques and their current range of applications. Focusing on the simulation of various phenomena in solid-state physics through optical lattice experiments, we review their basics, the necessary techniques and the accessible physical parameters. We outline how to control and use interactions with external potentials and interactions between the atoms, and how to design new synthetic gauge fields and spin–orbit coupling. We discuss the latest progress in site-resolved techniques that use quantum gas microscopes, and describe the unique features of quantum simulation experiments with two-electron atomic species. Quantum simulation with ultracold atomic gases is an established platform for investigating complex quantum processes. Focusing on optical lattice experiments, this Technical Review overviews the available tools and their applications to the simulation of solid-state physics problems.

Tools for quantum simulation with ultracold atoms in optical lattices

After many years of development of the basic tools, quantum simulation with ultracold atoms has now reached the level of maturity where it can be used to investigate complex quantum processes. Planning of new experiments and upgrading existing set-ups depends crucially on a broad overview of the available techniques, their specific advantages and limitations. This Technical Review aims to provide a comprehensive compendium of the state of the art. We discuss the basic principles, the available techniques and their current range of applications. Focusing on the simulation of varied phenomena in solid-state physics using optical lattice experiments, we review their basics, the necessary techniques and the accessible physical parameters. We outline how to control and use interactions with external potentials and between the atoms, and how to design new synthetic gauge fields and spin-orbit coupling. We discuss the latest progress in site-resolved techniques using quantum gas microscopes, and describe the unique features of quantum simulation experiments with two-electron atomic species.

The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic approaches to many-body systems are limited and the huge size of their Hilbert space makes numerical simulations on classical computers intractable. A quantum simulator avoids these limitations by transcribing the system of interest into another, with the same dynamics but with interaction parameters under control and with experimental access to all relevant observables. Quantum simulation of spin systems is being explored with trapped ions, neutral atoms and superconducting devices. We propose here a new paradigm for quantum simulation of spin-1/2 arrays providing unprecedented flexibility and allowing one to explore domains beyond the reach of other platforms. It is based on laser-trapped circular Rydberg atoms. Their long intrinsic lifetimes combined with the inhibition of their microwave spontaneous emission and their low sensitivity to collisions and photoionization make trapping lifetimes in the minute range realistic with state-of-the-art techniques. Ultra-cold defect-free circular atom chains can be prepared by a variant of the evaporative cooling method. This method also leads to the individual detection of arbitrary spin observables. The proposed simulator realizes an XXZ spin-1/2 Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kHz. All the model parameters can be tuned at will, making a large range of simulations accessible. The system evolution can be followed over times in the range of seconds, long enough to be relevant for ground-state adiabatic preparation and for the study of thermalization, disorder or Floquet time crystals. This platform presents unrivaled features for quantum simulation.

Towards Quantum Simulation with Circular Rydberg Atoms

Towards quantum simulation with circular Rydberg atoms

The simple resonant Rabi oscillation of a two-level system in a single-mode coherent field reveals complex features at the mesoscopic scale, with oscillation collapses and revivals. Using slow circular Rydberg atoms interacting with a superconducting microwave cavity, we explore this phenomenon in an unprecedented range of interaction times and photon numbers. We demonstrate the efficient production of cat states, which are the quantum superposition of coherent components with nearly opposite phases and sizes in the range of few tens of photons. We measure cuts of their Wigner functions revealing their quantum coherence and observe their fast decoherence. This experiment opens promising perspectives for the rapid generation and manipulation of nonclassical states in cavity and circuit quantum electrodynamics.

https://hal.archives-ouvertes.fr/hal-02323657/document

Fédéric Assemat

Papers

Towards Quantum Simulation with Circular Rydberg Atoms

Towards quantum simulation with circular Rydberg atoms

Quantum Rabi Oscillations in Coherent and in Mesoscopic Cat Field States