Dynamic matter-wave pulse shaping

Abstract

In this paper we discuss possibilities to manipulate a matter-wave with time-dependent potentials. Assuming a specific setup on an atom chip, we explore how one can focus, accelerate, reflect, and stop an atomic wave packet, with, for example, electric fields from an array of electrodes. We also utilize this method to initiate coherent splitting or an arbitrary wave form. Special emphasis is put on the robustness of the control schemes. We begin with the wave packet of a single atom, and extend this to a BEC, in the Gross-Pitaevskii picture. In analogy to laser pulse shaping with its wide variety of applications, we expect this work to form the base for more complex time-dependent potentials eventually leading to matter-wave pulse shaping with numerous applications.

Atom interferometry using a shaken optical lattice

“…While we use a GA to optimize the shaking, the interferometer sequence may also be found through use of an optimal control algorithm such as the Krotov [11,12] or CRAB methods [13]. Similar methods have been used to solve problems in other atomic systems, such as matter wave pulse shaping [14] or state inversion of a BEC [15]. Optimization methods have been used in atom interferometers, as in the Ramsey interferometry scheme of (Fig.…”

Time-varying Bose–Einstein condensates

“…The standard mechanisms for the control of a BEC over time include changing the strength of the external potential [8][9][10][11][12][13]36,61], changing the strength of the self-interaction/the scattering length [15,16,[18][19][20]62], or changing the dispersion [21,22]. A change in the strength of the potential will be akin to a change in the value of α over time.…”

“…Theoretical work on BECs often makes use of the Gross-Pitaevskii equation (GPE) [6,7], which models the time evolution of the macroscopic BEC wavefunction. While most studies on the GPE consider static external potentials, it is possible to vary the strength or form of a potential in time [8][9][10][11] in order to modify the shape of BEC matter-waves [12][13][14]. In addition to the external potential, both the scattering length [15][16][17][18][19][20] and dispersion [21,22] can be taken to vary in time.…”

A Thermofield-based Multilayer Multiconfigurational Time-Dependent Hartree Approach to Non-Adiabatic Quantum Dynamics at Finite Temperature

“…We close by noting, that stochastic approaches in the MCTDH framework, e.g., in Refs. 56,57 , require several system-dependent realizations of an imaginary-time propagation of a randomly created initial state followed by a real-time propagation to properly converge a timedependent ensemble average. For many DoFs and large numbers of realizations, this approach presumably becomes numerically prohibiting.…”

“…Moreover, also the finite temperature regime has been accessed by directly propagating the density operator [50][51][52][53][54] , which is generally restricted to a small set of system DoFs. Additionally, wave function based stochastic sampling approaches to the evaluation of thermal ensemble averages [55][56][57][58][59] have been considered, which potentially suffer from a large number of necessary realizations to properly sample the initial thermal state rendering them costly for large systems.…”