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arXiv:2202.05589 · Physical Review A

Creating triple-NOON states with ultracold atoms via chaos-assisted tunneling

Guillaume Vanhaele, Arnd Bäcker, Roland Ketzmerick, Peter Schlagheck

Published Jul 5, 2022• 14 citations
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Abstract

The authors propose a protocol for creating triple-NOON states with ultracold rubidium atoms subject to a periodic driving modulation that facilitates the collective tunneling of the atoms to the other sites. They show that chaos-assisted tunneling can reduce the collective tunneling time without significantly affecting the purity of the superposition.

DOI
10.1103/physreva.106.l011301

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The authors propose a protocol for creating triple-NOON states with ultracold rubidium atoms subject to a periodic driving modulation that facilitates the collective tunneling of the atoms to the other sites. They show that chaos-assisted tunneling can reduce the collective tunneling time without significantly affecting the purity of the superposition.
We investigate theoretically the generation of microscopic atomic NOON states, corresponding to the coherent $|N,0\ensuremath{\rangle}+|0,N\ensuremath{\rangle}$ superposition with $N\ensuremath{\sim}5$ particles, via collective tunneling of interacting ultracold bosonic atoms within a symmetric double-well potential in the self-trapping regime. We show that a periodic driving of the double well with suitably tuned amplitude and frequency parameters allows one to substantially boost this tunneling process without altering its collective character. The timescale to generate the NOON superposition, which corresponds to half the tunneling time and would be prohibitively large in the undriven double well for the atomic populations considered, can thereby be drastically reduced, which renders the realization of NOON states through this protocol experimentally feasible. Resonance- and chaos-assisted tunneling are identified as key mechanisms in this context. A quantitative semiclassical evaluation of their impact on the collective tunneling process allows one to determine the optimal choice for the driving parameters in order to generate those NOON states as fast as possible.
For systems described by the two-site Bose-Hubbard Hamiltonian, I show that a sinusoidal modulation of the tunneling matrix element assists higher-order cotunneling processes. Using this mechanism, I propose an efficient scheme for creating a coherent superposition of states in which all particles are either on one site or all on the other site, the so-called NOON state. This scheme yields an almost perfect NOON state periodically. For larger numbers of particles, further reduction of the time to create the state is possible if more than one modulation frequency is employed. With this scheme, NOON states with a larger number of particles could be realized with state-of-the-art techniques for cold Bose gases in a double-well potential.
We present a protocol for the generation of NOON states with ultracold atoms, leveraging the Bose-Hubbard model in the self-trapping regime. By means of an optimized adiabatic protocol, we achieve a significant reduction in the time required for the preparation of highly entangled NOON states, involving two or more modes. Our method saturates the quantum speed limit, ensuring both efficiency and high fidelity in state preparation. A detailed analysis of the geodesic counterdiabatic driving protocol and its application to the Bose-Hubbard system highlights its ability to expand the energy gap, facilitating faster adiabatic evolution. Through perturbation theory, we derive effective parameters that emulate the counterdiabatic Hamiltonian, enabling experimentally viable implementations with constant physical parameters. This approach is demonstrated to yield exponential time savings compared with standard geodesic driving, making it a powerful tool for creating complex entangled states for applications in quantum metrology and quantum information. Our findings pave the way for scalable and precise quantum state control in ultracold atomic systems.
We present an extension of the chaos-assisted tunneling mechanism to spatially periodic lattice systems. We demonstrate that driving such lattice systems in an intermediate regime of modulation maps them onto tight-binding Hamiltonians with chaos-induced long-range hoppings t_{n}∝1/n between sites at a distance n. We provide a numerical demonstration of the robustness of the results and derive an analytical prediction for the hopping term law. Such systems can thus be used to enlarge the scope of quantum simulations to experimentally realize long-range models of condensed matter.