Quantum speed limit and optimal control of many-boson dynamics

Abstract

We extend the concept of quantum speed limit -the minimal time needed to perform a driven evolution -to complex interacting many-body systems. We investigate a prototypical many-body system, a bosonic Josephson junction, at increasing levels of complexity: (a) within the two-mode approximation corresponding to a nonlinear two-level system, (b) at the mean-field level by solving the nonlinear Gross-Pitaevskii equation in a double well potential, and (c) at an exact many-body level by solving the time-dependent many-body Schrödinger equation. We propose a control protocol to transfer atoms from the ground state of a well to the ground state of the neighbouring well. Furthermore, we show that the detrimental effects of the inter-particle repulsion can be eliminated by means of a compensating control pulse, yielding, quite surprisingly, an enhancement of the transfer speed because of the particle interaction -in contrast to the self-trapping scenario. Finally, we perform numerical optimisations of both the nonlinear and the (exact) many-body quantum dynamics in order to further enhance the transfer efficiency close to the quantum speed limit.

Emergence of junction dynamics in a strongly interacting Bose mixture

“…Different methods have been employed to tackle the many-body problem of bosons in a double-well, even outside the mean-field regime [43][44][45][46][47]. Addressing the subject from a few-body perspective [48][49][50][51][52], however, might lead to new insight on the properties of these systems. Here we show that, in the regime where the repulsion between the impurity and the background is dominant, the system can exhibit non-trivial dynamical effects: the impurity undergoes Josephson-like oscillations when initialized at the edge of the system, and can have its tunneling enhanced when a barrier is present.…”

Amplification of the parametric dynamical Casimir effect via optimal control

“…We use and compare two strategies to optimize the visibility of the DCE: a multi step heuristic method employing bang-bang switches of the qubit frequency from the off-resonance regime to the resonance regime and back out of resonance, and optimal control theory which has been proven to be able to successfully control circuit quantum electrodynamics processes [2,[22][23][24][25][26][27][28]. In particular, we employ the dressed chopped random basis algorithm (dCRAB) which has been already applied successfully to various theoretical and experimental atomic and condensed matter control problems to meet various control goals, including state-transfer, gate synthesis, observable control, and fast quantum phase transition crossing [29][30][31][32][33][34][35]. For the problem studied here, the control function is the time-dependent modulation of the qubit frequency and the figure of merit is the expectation value of the number of photons that are generated in the cavity by parametric amplification of the DCE: This amounts to finding an optimal setup for the detection of the DCE.…”

Optimal nonlinear coherent mode transitions in Bose-Einstein condensates utilizing spatiotemporal controls

“…Early work utilized Krotov optimization to study the optimal control of loading a BEC onto an optical lattice and preserving its global phase [10]. Additional optimal control simulations have been performed with magnetic fields described by small sets of control parameters for effective splitting of condensates [11,12], number squeezing [13], and time-optimal controlled transformations of many-boson systems [14]. The numerical aspects of BEC optimization have also been studied, in particular, the comparisons of optimal control algorithms [15] and numerical software for studying controlled BEC dynamics [12].…”