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arXiv:2105.05667 · PRX Quantum

Quantum State Control of a Bose-Einstein Condensate in an Optical Lattice

Nathan Dupont, Gabriel Chatelain, Lucas Gabardos, Maxime Arnal, Juliette Billy, Bruno Peaudecerf, Dominique Sugny, David Guéry-Odelin

Published Oct 5, 2021• 58 citations
arXivHTMLPDF

Abstract

We report on the efficient design of quantum optimal-control protocols to manipulate the motional states of an atomic Bose-Einstein condensate (BEC) in a one-dimensional optical lattice.Our protocols operate on the momentum comb associated with the lattice.In contrast to previous works also dealing with control in discrete and large Hilbert spaces, our control schemes allow us to reach a wide variety of targets by varying a single parameter, the lattice position.With this technique, we experimentally demonstrate a precise, robust, and versatile control: we optimize the transfer of the BEC to a single or multiple quantized momentum states with full control on the relative phase between the different momentum components.This also allows us to prepare the BEC in a given eigenstate of the lattice band structure, or superposition thereof.

DOI
10.1103/prxquantum.2.040303

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We report on the efficient design of quantum optimal-control protocols to manipulate the motional states of an atomic Bose-Einstein condensate (BEC) in a one-dimensional optical lattice.Our protocols operate on the momentum comb associated with the lattice.In contrast to previous works also dealing with control in discrete and large Hilbert spaces, our control schemes allow us to reach a wide variety of targets by varying a single parameter, the lattice position.With this technique, we experimentally demonstrate a precise, robust, and versatile control: we optimize the transfer of the BEC to a single or multiple quantized momentum states with full control on the relative phase between the different momentum components.This also allows us to prepare the BEC in a given eigenstate of the lattice band structure, or superposition thereof.
We have performed a number of experiments with a Bose-Einstein condensate (BEC) in a one-dimensional optical lattice. Making use of the small momentum spread of a BEC and standard atom optics techniques, a high level of coherent control over an artificial solid-state system is demonstrated. We are able to load the BEC into the lattice ground state with a very high efficiency by adiabatically turning on the optical lattice. We coherently transfer population between lattice states and observe their evolution. Methods are developed and used to perform band spectroscopy. We use these techniques to build a BEC accelerator and a novel, coherent, large-momentum-transfer beam-splitter.
Abstract We apply quantum optimal control to shape the phase-space distribution of Bose–Einstein condensates in a one-dimensional optical lattice. By a time-dependent modulation of the lattice position, determined from optimal control theory, we prepare, in the phase space of each lattice site, translated and squeezed Gaussian states, and superpositions of Gaussian states. Complete reconstruction of these non-trivial states is performed through a maximum likelihood state tomography. As a practical application of our method to quantum simulations, we initialize the atomic wavefunction in an optimal Floquet-state superposition to enhance dynamical tunneling signals.
We numerically study the optimal control of an atomic Bose-Einstein condensate in an optical lattice. We present two generalizations of the gradient-based algorithm, GRAPE, in the non-linear case and for a two-dimensional lattice. We show how to construct such algorithms from Pontryagin’s maximum principle. A wide variety of target states can be achieved with high precision by varying only the laser phases setting the lattice position. We discuss the physical relevance of the different results and the future directions of this work.
We investigate the potential for controlling a noninteracting Bose-Einstein condensate loaded into a one-dimensional optical superlattice. Our control strategy combines Bloch oscillations, originating from accelerating the lattice, with time-dependent control of the superlattice parameters. We investigate two experimentally viable scenarios, very low and very high potential depths, in order to gain a better understanding of matter wave control available within the system. Multiple lattice parameters and a versatile energy band structure allow us to obtain a wide range of control over energy band populations. Finally, we consider several examples of quantum state preparation in the superlattice structure that may be difficult to achieve in a regular lattice.
In this paper, we design and experimentally implement various robust quantum unitary transformations (gates) acting on d -dimensional vectors (qudits) by tuning a single control parameter using optimal control theory. The quantum state is represented by the momentum components of a Bose-Einstein condensate placed in an optical lattice, with the lattice position varying over a fixed duration serving as the control parameter. To evaluate the quality of these transformations, we employ standard quantum process tomography. In addition, we show how controlled unitary transformations can be used to extend state stabilization to global stabilization within a controlled vector subspace. Finally, we apply them to state tomography, showing how the information about the relative phase between distant momentum components can be extracted by inducing an interference process.
We present an effective and fast (few microseconds) procedure for transferring a Bose–Einstein condensate from the ground state in a harmonic trap into the desired bands of an optical lattice. Our shortcut method is a designed pulse sequence where the time duration and the interval in each step are fully optimized in order to maximize robustness and fidelity of the final state with respect to the target state. The atoms can be prepared in a single band with even or odd parity, and superposition states of different bands can be prepared and manipulated. Furthermore, we extend this idea to the case of two-dimensional or three-dimensional optical lattices where the energies of excited states are degenerate. We experimentally demonstrate various examples and show very good agreement with the theoretical model. Efficient shortcut methods will find applications in the preparation of quantum systems, in quantum information processing, in precise measurement and as a starting point to investigate dynamics in excited bands.