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arXiv:2008.12156 · Physical Review A

NOON states with ultracold bosonic atoms via resonance- and chaos-assisted tunneling

Guillaume Vanhaele, Peter Schlagheck

Published Jan 19, 2021• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.103.013315

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We investigate theoretically the generation of microscopic atomic NOON states, corresponding to the coherent ∣N,0\ensuremath⟩+∣0,N\ensuremath⟩|N,0\ensuremath{\rangle}+|0,N\ensuremath{\rangle}∣N,0\ensuremath⟩+∣0,N\ensuremath⟩ superposition with N\ensuremath∼5N\ensuremath{\sim}5N\ensuremath∼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.
We introduce a scheme to generate NOON states of few-body bosonic vortices and demonstrate their application as high-precision rotation sensors. Our approach is based on cold atoms in a weakly anisotropic two-dimensional harmonic trap, where the single-particle p orbitals define an effective two-mode Bose-Hubbard model with vortex modes (px±ipy)(\mathrm{p}_x\pm\mathrm{i}\mathrm{p}_y)(px​±ipy​) carrying opposite circulation. In the self-trapping regime, we show that the NOON manifold becomes spectrally isolated, and collective tunneling processes give rise to highly entangled vortex NOON states. However, these states emerge on prohibitively long timescales. To overcome this limitation, we develop two complementary acceleration strategies: geodesic counterdiabatic driving for small particle numbers, and resonance- and chaos-assisted tunneling in the semiclassical regime at larger particle numbers. Both approaches enable the generation of NOON states on experimentally relevant timescales while preserving near-unit fidelities. Finally, we quantify the metrological advantage of vortex NOON states by introducing an interferometric protocol that exploits their intrinsic sensitivity to rotation, enabling the detection of infinitesimal external rotations at the Heisenberg limit. Our work opens the door to rotation sensors based on atomic NOON states, generically realizable in bosonic Josephson junctions with vortex-type orbitals.
This thesis investigates the fast and controlled generation of highly entangled many-body quantum states in systems of ultracold bosonic atoms. We focus in particular on the preparation of NOON states and their multimode generalizations, which constitute central resources for quantum metrology due to their enhanced sensitivity to parameter estimation. Working within Bose-Hubbard models in the self-trapping regime, where interaction effects dominate the dynamics, we exploit collective tunneling phenomena to isolate effective subspaces suitable for state engineering. To overcome the intrinsic slowness of adiabatic protocols, we introduce a control strategy based on the combined use of geodesic control and counterdiabatic driving, referred to as \textit{geodesic counterdiabatic driving}. This approach enables accelerated state preparation using time-independent and experimentally accessible control parameters, while reaching the quantum speed limit. We demonstrate the efficiency and robustness of the method for generating high-fidelity NOON states in optical lattices. Finally, we extend the framework to the creation of NOON states with vortices in two-dimensional harmonic traps and discuss applications to quantum-enhanced metrology, highlighting the feasibility of rotation sensing beyond classical limits.
Abstract We study the tunneling dynamics of N = 10 one-dimensional interacting bosons confined in a temporally driven double well potential that imitates a quantum seesaw and how we can manipulate these dynamics by changing the drive of the seesaw potential. We emulate the seesaw with a driven double well potential and consider two driving protocols: an harmonic constant-frequency drive and a chirped drive with linearly increasing frequency. We consider the time-dependent many-body Schrödinger equation of a repulsively interacting quasi-one-dimensional few-boson system. We solve it by using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) as implemented in the MCTDH-X software. For an harmonic drive and at small values of the driving amplitude, the dynamics of the particles become very slow rendering a stationary-like state. In a phase-space picture the population imbalance between the wells follows a trajectory which is restricted to a comparatively small region of space. For an harmonic drive at intermediate amplitudes, the dynamics become periodic in nature, implying that the bosons populate each of wells periodically. At comparatively large amplitudes of the harmonic drive, the dynamics show features of chaos in phase-space representation. For the chirped drive with a driving frequency increasing linearly in time, the imbalance of the atoms in the seesaw, however, has a temporal evolution that is faster for certain frequency ranges. The tunneling dynamics in such cases, for small amplitudes, show the appearance of quasi-periodicity with simultaneously present slow and fast oscillations. Increasing the amplitude of the chirped drive, we observe that the dynamics, although being periodic, become severely damped in their amplitude. Our study establishes that by tuning the temporal evolution of the quantum seesaw, a precise control of tunneling dynamics of the correlated bosons can be achieved. Since harmonic driving and chirp frequency modulation of the seesaw are experimentally achievable, our simulations can be experimentally realized in laboratories dealing with cold atomic gases.
We study macroscopic superpositions in the orbital rather than the spatial degrees of freedom, in a three-dimensional, double-well system. We show that the ensuing dynamics of NNN interacting excited ultracold bosons, which, in general, requires at least eight single-particle modes and (N+7N)(\genfrac{}{}{0pt}{}{N+7}{N})(NN+7​) Fock vectors, is described by a surprisingly small set of many-body states. An initial state with half the atoms in each well, and purposely excited in one of them, gives rise to the tunneling of axisymmetric and transverse vortex structures. We show that transverse vortices tunnel orders of magnitude faster than axisymmetric ones and are therefore more experimentally accessible. The tunneling process generates macroscopic superpositions only distinguishable by their orbital properties and within experimentally realistic times.
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.