We present theoretical and experimental results on high-fidelity transfer of a trapped Bose-Einstein condensate into its first vibrationally excited eigenstate. The excitation is driven by mechanical motion of the trap, along a trajectory obtained from optimal control theory. Excellent agreement between theory and experiment is found over a large range of parameters. We develop an approximate model to map the dynamics of the many-body condensate wave function to a driven two-level system. PACS numbers: 03.75.-b, 42.50.-p, 67.85.-d arXiv:1212.4173v1 [cond-mat.quant-gas]
We study optimal quantum control of the dynamics of trapped Bose-Einstein condensates: The targets are to split a condensate, residing initially in a single well, into a double well, without inducing excitation, and to excite a condensate from the ground state to the first-excited state of a single well. The condensate is described in the mean-field approximation of the Gross-Pitaevskii equation. We compare two optimization approaches in terms of their performance and ease of use; namely, gradient-ascent pulse engineering (GRAPE) and Krotov's method. Both approaches are derived from the variational principle but differ in the way the control is updated, additional costs are accounted for, and second-order-derivative information can be included. We find that GRAPE produces smoother control fields and works in a black-box manner, whereas Krotov with a suitably chosen step-size parameter converges faster but can produce sharp features in the control fields.
We theoretically investigate protocols based on optimal control theory (OCT) for manipulating Bose-Einstein condensates in magnetic microtraps, using the framework of the Gross-Pitaevskii equation. In our approach we explicitly account for filter functions that distort the computed optimal control, a situation inherent to many experimental OCT implementations. We apply our scheme to the shakeup process of a condensate from the ground to the first excited state, following a recent experimental and theoretical study, and demonstrate that the fidelity of OCT protocols is not significantly deteriorated by typical filters.PACS numbers: 39.20.+q,39.25.+k,02.60.Pn Optimal quantum control aims at the manipulation of a quantum-mechanical wavefunction in a controlled fashion [1][2][3]. External parameters, such as laser fields, can be controlled at will, and allow to steer the wavefunction from a given initial to a desired terminal state. Recent years have seen tremendous research efforts in the realm of quantum control [3]. Quantum chemistry implementations often rely on stochastic optimization techniques, which are particulary appealing for experimental implementations [2]. An alternative approach is provided by optimal control theory (OCT) [1,4,5], that performs a numerical optimization of the control fields through an iterative procedure by solving the dynamic system equations.In Ref. [6,7] we have presented an experimental implementation of optimal quantum control for a BoseEinstein condensate. Ultracold atoms become trapped in the vicinity of an atom chip [8] by the magnetic fields produced by currents running through the wires of the chip, and the magnetic confinement potential can be controlled by changing the currents. We have demonstrated the excitation of the condensate wavefunction from the ground to the first excited state of an anharmonic potential, where the population transfer has been achieved with an efficiency close to 100% by displacing the potential minimum according to a protocol computed with optimal control theory.In this Brief Report, we investigate the effects of filter functions that distort the control parameters computed from optimal control theory. Such filters might be due to electronics and are inherent to many experiments. For sufficiently simple control protocols filter effects can be corrected through a simple deconvolution scheme, but in general it is advantageous to incorporate filtering directly in the OCT approach. In this paper we first develop the methodology for OCT with filtered control parameters, and then apply our scheme to the condensate shakeup investigated in Refs. [6,7]. We find that for realistic filter functions the fidelity of the control process does not become deteriorated significantly. Although in this paper we only focus on Bose-Einstein condensates, the developed methodology is general and might be useful in a much wider context.OCT without filter.-We first briefly review the optimal control implementation of Bose-Einstein condensates formulated in Ref.[9] (see...
In order to meet the challenges of sustainable development, it is of utmost importance to involve all relevant decision makers in this process. These decision makers are diverse, including governments, corporations and private citizens. Since the latter group is the largest and the majority of decisions relevant to the future of the environment is made by that group, great effort has been put into communicating relevant research results to them. The hope is that well-informed citizens make well-informed choices and thus act in a sustainable way. However, this common but drastic simplification that more information about climate change automatically leads to pro-environmental behaviour is fundamentally flawed. It completely neglects the complex social-psychological processes that occur if people are confronted with threatening information. In reality, the defence mechanisms that are activated in such situations can also work against the goal of sustainable development, as experimental studies showed. Based on these findings, we propose an agent-based model to understand the relation between threatening climate change information, anxiety, climate change scepticism, environmental self-identity and pro-environmental behaviour. We find that the exposure to information about climate change, in general, does not increase the pro-environmental intent unless several conditions regarding the individual's values and information density are met.
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