Optimal preparation of quantum states on an atom-chip device

Abstract

Atom chips provide compact and robust platforms towards practical quantum technologies. A quick and faithful preparation of arbitrary input states for these systems is crucial but represents a very challenging experimental task. This is especially difficult when the dynamical evolution is noisy and unavoidable setup imperfections have to be considered. Here, we experimentally prepare with very high small errors different internal states of a Rubidium Bose-Einstein condensate realized on an atom chip. As a possible application of our scheme, we apply it to improve the sensitivity of an atomic interferometer.Microscopic magnetic traps, as atom chips [1,2], represent an important advance in the field of degenerate quantum gases towards their realization of practical quantum technological devices. Indeed, applications outside the laboratory depend on the compactness and robustness of these setups. Atom chips have already enabled, for instance, the demonstration of miniaturized interferometers [3,4], or the creation of squeezed atomic states [5]. Very recently, they have been also applied to the realization of atom interferometers based on non-classical motional states [6]. Furthermore, atom chips can be integrated with nanostructures [7], or photonic components [8], to implement new quantum information processing tools, or used as novel platforms for quantum simulations [9] and controllable coherent dynamics [10].As in most quantum technological applications, the ability to quickly and faithfully prepare arbitrary input states is of utmost importance. In particular, it is essential to speedup the initialization protocol of these quantum devices in order to reduce the effects of the inevitably present noise and decoherence sources. In this context, quantum optimal control provides powerful tools to tackle this problem by finding the optimal way to transform the system from an experimentally readily prepared initial condition to a desired state with high fidelity from which further quantum manipulations can be performed [11][12][13]. It has been successfully implemented in several physical systems, ranging from cold atoms [14] to molecules [15]. Recently optimal control algorithms have been developed and successfully applied to many-body quantum systems [16][17][18][19][20][21].In addition, optimal control allows one to speed up the state preparation process up to the ultimate bound imposed by quantum mechanics, the so-called quantum speed limit (QSL) [22][23][24][25]. Indeed, the change of a state into a different one cannot occur faster than a time scale that is inversely proportional to the associated energy scale. This is especially relevant for quantum systems like Bose-Einstein condensates (BECs) where it is crucial to perform some desired (coherent) task before dephasing processes unavoidably occur [26]. In this work we present experimental results obtained on a Rubidium ( 87 Rb) BEC, trapped on an atom chip, evolving in a five-level Hilbert space given by the five spin orientations of the F = 2 hyperfine groun...

Ergodicity in randomly perturbed quantum systems

“…In the first step all the atoms are brought into the = = ñ |F m 2, 0 F state (see figure 3) with high fidelity (~95%). This is obtained applying a ms 50 long frequency modulated RF pulse designed with an optimal control strategy [31]. After the RF pulse we transfer the whole = = ñ |F m 2, 0…”

Krotov: A Python implementation of Krotov's method for quantum optimal control

“…The most severe limitations are that Krotov's method requires analytically computable derivatives, see Eq. (12), and it searches only in the local region of the point in the optimization landscape where that derivative is being evaluated (as any gradient-based method does). The optimized pulse thus depends on the guess pulse from which the optimization starts.…”

“…Experimental implementation of the calculated field shapes, using arbitrary waveform generators, has been eased by the latter becoming available commercially. Successful demonstration of quantum operations in various experiments [4,[12][13][14][15][16][17][18][19][20] attests to the level of maturity that quantum optimal control in quantum technologies has reached. In order to calculate optimized external field shapes, two choices need to be made -about the optimization functional and about the optimization method.…”

Experimental proof of quantum Zeno-assisted noise sensing

“…|F 1 . A frequency-modulated RF pulse, designed with an optimal control strategy[46], transfers all the atoms from the initial = =+ ñ…”