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

Vanhaele, Guillaume; Bäcker, Arnd; Ketzmerick, Roland; Schlagheck, Peter

doi:10.1103/physreva.106.l011301

Cited by 9 publications

(4 citation statements)

References 69 publications

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“…In the molecular context, examples come from high-resolution spectra wherein "clumps" of spectral lines are associated with the vibrational superexchange mechanism [4,5] and related to quantum vibrational energy flow in molecules [6][7][8]. Additional examples include the generation of NOON states in ultracold bosonic atoms [9,10], the efficacy of coherent control in driven [11][12][13][14] and kicked [15,16] systems, stability of quantum discrete breathers [17,18], and fragmentation of trapped Bose-Einstein condensates [19,20]. Furthermore, dynamical tunneling has been shown to play a crucial role in a variety of "engineered" systems [21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Tunneling in More than Two Degrees of Freedom

Keshavamurthy

2024

Entropy

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Recent progress towards understanding the mechanism of dynamical tunneling in Hamiltonian systems with three or more degrees of freedom (DoF) is reviewed. In contrast to systems with two degrees of freedom, the three or more degrees of freedom case presents several challenges. Specifically, in higher-dimensional phase spaces, multiple mechanisms for classical transport have significant implications for the evolution of initial quantum states. In this review, the importance of features on the Arnold web, a signature of systems with three or more DoF, to the mechanism of resonance-assisted tunneling is illustrated using select examples. These examples represent relevant models for phenomena such as intramolecular vibrational energy redistribution in isolated molecules and the dynamics of Bose–Einstein condensates trapped in optical lattices.

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Section: Introductionmentioning

confidence: 99%

Dynamical Tunneling in More than Two Degrees of Freedom

Keshavamurthy

2024

Entropy

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“…On the whole, this field is not directly aimed at the challenge posed by quantum chaos, where exponential instability is converted from hindrance to resource. Nevertheless, there are a few works [30][31][32][33][34][35][36], but none address general approaches to optimal coherent targeting in quantum chaotic many-body systems.…”

Section: Introductionmentioning

confidence: 99%

Controlling many-body quantum chaos: Bose–Hubbard systems

Beringer,

Steinhuber,

Diego Urbina

et al. 2024

New J. Phys.

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This work develops a quantum control application of many-body quantum chaos for ultracold bosonic gases trapped in optical lattices. It is long known how to harness exponential sensitivity to changes in initial conditions for control purposes in classically chaotic systems. In the technique known as targeting, instead of a hindrance to control, the instability becomes a resource. Recently, this classical targeting has been generalized to quantum systems either by periodically countering the inevitable quantum state spreading or by introducing a control Hamiltonian, where both enable localized states to be guided along special chaotic trajectories toward any of a broad variety of desired target states. Only strictly unitary dynamics are involved; i.e. it gives a coherent quantum targeting. In this paper, the introduction of a control Hamiltonian is applied to Bose–Hubbard systems in chaotic dynamical regimes. Properly selected unstable mean field solutions can be followed particularly rapidly to states possessing precise phase relationships and occupancies. In essence, the method generates a quantum simulation technique that can access rather special states. The protocol reduces to a time-dependent control of the chemical potentials, opening up the possibility for application in optical lattice experiments. Explicit applications to custom state preparation and stabilization of quantum many-body scars are presented in one- and two-dimensional lattices (three-dimensional applications are similarly possible).

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“…There have been some forays into controlling specifically quantum chaotic systems, such as the quantization of turnstiles leading to chaotic wave packet revivals [26], using weak control fields to quantize Ulam's control conjecture [27], and the creation of NOON states via chaos-assisted tunneling [28,29]. None of these address general schemes for optimal coherent targeting in quantum chaotic systems, which if fully developed might offer some important capabilities.…”

Section: Introductionmentioning

confidence: 99%

Controlling quantum chaos: Time-dependent kicked rotor

Tomsovic,

Urbina,

Richter

2023

Phys. Rev. E

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One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent Letter [Phys. Rev. Lett. 130, 020201 (2023)], a generalization of this targeting method to quantum systems was demonstrated using successive unitary transformations that counter the natural spreading of a quantum state. In this paper further details are given and an important quite general extension is established. In particular, an alternate approach to constructing the coherent control dynamics is given, which introduces a time-dependent, locally stable control Hamiltonian that continues to use the chaotic heteroclinic orbits previously introduced, but without the need of countering quantum state spreading. Implementing that extension for the quantum kicked rotor generates a much simpler approximate control technique than discussed in the Letter, which is a little less accurate, but far more easily realizable in experiments. The simpler method's error can still be made to vanish as h → 0.

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

Cited by 9 publications

References 69 publications

Dynamical Tunneling in More than Two Degrees of Freedom

Dynamical Tunneling in More than Two Degrees of Freedom

Controlling many-body quantum chaos: Bose–Hubbard systems

Controlling quantum chaos: Time-dependent kicked rotor

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