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arXiv:1702.07358 · Quantum Science and Technology

Optimal control of Rydberg lattice gases

Jian Cui, Rick van Bijnen, Thomas Pohl, Simone Montangero, Tommaso Calarco

Published Aug 2, 2017• 35 citations
arXivHTMLPDF

Abstract

Abstract We present optimal control protocols to prepare different many-body quantum states of Rydberg atoms in optical lattices. Specifically, we show how to prepare highly ordered many-body ground states, GHZ states as well as some superposition of symmetric excitation number Fock states, that inherit the translational symmetry from the Hamiltonian, within sufficiently short excitation times minimising detrimental decoherence effects. For the GHZ states, we propose a two-step detection protocol to experimentally verify the optimised preparation of the target state based only on standard measurement techniques. Realistic experimental constraints and imperfections are taken into account by our optimisation procedure making it applicable to ongoing experiments.

DOI
10.1088/2058-9565/aa7daf

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Abstract We present optimal control protocols to prepare different many-body quantum states of Rydberg atoms in optical lattices. Specifically, we show how to prepare highly ordered many-body ground states, GHZ states as well as some superposition of symmetric excitation number Fock states, that inherit the translational symmetry from the Hamiltonian, within sufficiently short excitation times minimising detrimental decoherence effects. For the GHZ states, we propose a two-step detection protocol to experimentally verify the optimised preparation of the target state based only on standard measurement techniques. Realistic experimental constraints and imperfections are taken into account by our optimisation procedure making it applicable to ongoing experiments.
Abstract Ultra-cold atomic gases are unique in terms of the degree of controllability, both for internal and external degrees of freedom. This makes it possible to use them for the study of complex quantum many-body phenomena. However in many scenarios, the prerequisite condition of faithfully preparing a desired quantum state despite decoherence and system imperfections is not always adequately met. To pave the way to a specific target state, we implement quantum optimal control based on Bayesian optimization. The probabilistic modeling and broad exploration aspects of Bayesian optimization are particularly suitable for quantum experiments where data acquisition can be expensive. Using numerical simulations for the superfluid to Mott-insulator transition for bosons in a lattice as well as for the formation of Rydberg crystals as explicit examples, we demonstrate that Bayesian optimization is capable of finding better control solutions with regards to finite and noisy data compared to existing methods of optimal control.
Ultra-cold atomic gases are unique in terms of the degree of controllability, both for internal and external degrees of freedom. This makes it possible to use them for the study of complex quantum many-body phenomena. However in many scenarios, the prerequisite condition of faithfully preparing a desired quantum state despite decoherence and system imperfections is not always adequately met. To pave the way to a specific target state, we implement quantum optimal control based on Bayesian optimization. The probabilistic modeling and broad exploration aspects of Bayesian optimization are particularly suitable for quantum experiments where data acquisition can be expensive. Using numerical simulations for the superfluid to Mott-insulator transition for bosons in a lattice as well as for the formation of Rydberg crystals as explicit examples, we demonstrate that Bayesian optimization is capable of finding better control solutions with regards to finite and noisy data compared to existing methods of optimal control.
Quantum technologies will ultimately require manipulating many-body quantum systems with high precision.Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity.However, this control is still sub-optimal.In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects.Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications.Indeed, it can engineer protocols at the quantum speed limit -the fastest achievable timescale of the transformation.Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices.We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations.
Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity. However, this control is still sub-optimal. In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects. Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications. Indeed, it can engineer protocols at the quantum speed limit - the fastest achievable timescale of the transformation. Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations.
Abstract We examine the adiabatic preparation of crystalline phases of Rydberg excitations in a one-dimensional lattice gas by frequency sweep of the excitation laser, as proposed by Pohl et al (2010 Phys. Rev. Lett. 104 043002 ) and recently realized experimentally by Schauß et al (2015 Science 347 1455 ). We find that the preparation of crystals of a few Rydberg excitations in a unitary system of several tens of atoms requires exceedingly long times for the adiabatic following of the ground state of the system Hamiltonian. Using quantum stochastic (Monte Carlo) wavefunction simulations, we show that realistic decay and dephasing processes affecting the atoms during the preparation lead to a final state of the system that has only a small overlap with the target crystalline state. Yet, the final number and highly sub-Poissonian statistics of Rydberg excitations and their spatial order are little affected by the relaxations.
Motivated by recent progress in the experimental manipulation of cold atoms in optical lattices, we study three different protocols for non-adiabatic quantum state preparation and state transport in chains of Rydberg atoms. The protocols we discuss are based on the blockade mechanism between atoms which, when excited to a Rydberg state, interact through a van der Waals potential, and rely on single-site addressing. Specifically, we discuss protocols for efficient creation of an antiferromagnetic GHZ state, a class of matrix product states including a so-called Rydberg crystal and for the state transport of a single-qubit quantum state between two ends of a chain of atoms. We identify system parameters allowing for the operation of the protocols on timescales shorter than the lifetime of the Rydberg states while yielding high fidelity output states. We discuss the effect of positional disorder on the resulting states and comment on limitations due to other sources of noise such as radiative decay of the Rydberg states. The proposed protocols provide a testbed for benchmarking the performance of quantum information processing platforms based on Rydberg atoms.