The main objective of quantum simulation is an in-depth understanding of many-body physics, which 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. Ultracold defect-free circular atom chains can be prepared by a variant of the evaporative cooling method. This method also leads to the detection of arbitrary spin observables with single-site resolution. The proposed simulator realizes an XXZ spin-1=2 Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kilohertz. All the model parameters can be dynamically 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. The proposed platform already presents unrivaled features for quantum simulation of regular spin chains. We discuss extensions towards more general quantum simulations of interacting spin systems with full control on individual interactions.
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, 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 non-classical states in cavity and circuit Quantum Electrodynamics. PACS numbers:The Rabi oscillations of a two-level atom in a resonant, single-mode coherent field state is one of the simplest phenomena in quantum optics. Nevertheless, it exhibits surprisingly complex features at the mesoscopic scale (few tens of photons) [1][2][3][4]. The oscillations, at an angular frequency Ω 0 √ n, collapse and revive (n is the average photon number in the coherent state; Ω 0 is the vacuum Rabi frequency measuring the atom-field coupling). The collapse, occurring on a time scale T c = 2 √ 2/Ω 0 , results from the quantum field amplitude uncertainty and from the corresponding dephasing of the Rabi oscillations. The (first) revival, around T r = 4π √ n/Ω 0 , results from the rephasing of oscillations associated to different photon numbers [5]. This revival provides a landmark illustration of field amplitude quantization [6]. Between collapse and revival, the field evolves into an entangled atom-field state, involving two coherent states with different phases [7,11,[35][36][37]. It is called a "cat state" in memory of Schrödinger's metaphor. Close to t = T r /2, the atomic state factors out of a field "cat", superposition of coherent states with opposite phases [5].These phenomena can be observed in systems implementing the Jaynes and Cummings model, a spin-1/2 coupled to a one-dimensional harmonic oscillator [12]. Ions in traps [13,14], cavity quantum electrodynamics (CQED) [3,6] and circuit quantum electrodynamics (cQED) [16, 39] are thus ideal platforms for this observation.Nevertheless, revival observations have so far been limited to small photon numbers since experiments face formidable challenges. For microwave CQED with superconducting cavities crossed by fast Rydberg atoms, the interaction time is limited to a few vacuum Rabi periods, 2π/Ω 0 . Revivals have been observed only for n 1 [6,17]. Early revivals induced by a time-reversal of the collapse can be observed for larger n values (about 10), but the maximum separation of the cat compo-nents is small [18,19]. Ion traps have similar limitations [13,20]. In cQED, the limited coherence time of tunable superconducting qubits makes it difficult to observe long-term dynamics in the resonant regime [21]. Large cat-state preparation so far relie...
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