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Bulletin of the American Physical Society

Bloch-band analysis of optical beam splitters in a matter-wave interferometer

Daniel Gochnauer, Katherine E. McAlpine, Tahiyat Rahman, Subhadeep Gupta

Published May 30, 2019• 0 citations
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Bloch-Zener oscillations

B. M. Breid, D. Witthaut, H. J. Korsch

It is well known that a particle in a periodic potential with an additional constant force performs Bloch oscillations. Modulating every second period of the potential, the original Bloch band splits into two subbands. The dynamics of quantum particles shows a coherent superposition of Bloch oscillations and Zener tunneling between the subbands, a Bloch-Zener oscillation. Such a system is modelled by a tight-binding Hamiltonian, a system of two minibands with an easily controllable gap. The dynamics of the system is investigated by using an algebraic ansatz leading to a differential equation of Whittaker-Hill type. It is shown that the parameters of the system can be tuned to generate a periodic reconstruction of the wave packet and thus of the occupation probability. As an application, the construction of a matter wave beam splitter and a Mach-Zehnder interferometer is briefly discussed. PACS numbers: 03.65.-w, 03.75.Be, 03.75.LmBloch-Zener oscillations 2 1.

•Jan 1, 2006•54 citations
It is well known that a particle in a periodic potential with an additional constant force performs Bloch oscillations. Modulating every second period of the potential, the original Bloch band splits into two sub-bands. The dynamics of quantum particles shows a coherent superposition of Bloch oscillations and Zener tunnelling between the sub-bands, a Bloch–Zener oscillation. Such a system is modelled by a tight-binding Hamiltonian which is a system of two minibands with an easily controllable gap. The dynamics of the system is investigated by using an algebraic ansatz leading to a differential equation of Whittaker–Hill type. It is shown that the parameters of the system can be tuned to generate a periodic reconstruction of the wave packet and thus of the occupation probability. As an application, the construction of a matter wave beam splitter and a Mach–Zehnder interferometer is briefly discussed.
Bloch oscillations (i.e., coherent acceleration of matter waves by an optical lattice) and Bragg diffraction are integrated into light-pulse atom interferometers with large momentum splitting between the interferometer arms, and hence enhanced sensitivity. Simultaneous acceleration of both arms in the same internal states suppresses systematic effects, and simultaneously running a pair of interferometers suppresses the effect of vibrations. Ramsey-Bordé interferometers using four such Bloch-Bragg-Bloch beam splitters exhibit 15% contrast at 24variant Planck's over 2pik splitting, the largest so far (variant Planck's over 2pik is the photon momentum); single beam splitters achieve 88variant Planck's over 2pik. The prospects for reaching 100 s of variant Planck's over 2pik and applications such as gravitational wave sensors are discussed.
It is well known that a particle in a periodic potential with an additional constant force performs Bloch oscillations. Modulating every second period of the potential, the original Bloch band splits into two subbands. The dynamics of quantum particles shows a coherent superposition of Bloch oscillations and Zener tunneling between the subbands, a Bloch-Zener oscillation. Such a system is modelled by a tight-binding Hamiltonian, a system of two minibands with an easily controllable gap. The dynamics of the system is investigated by using an algebraic ansatz leading to a differential equation of Whittaker-Hill type. It is shown that the parameters of the system can be tuned to generate a periodic reconstruction of the wave packet and thus of the occupation probability. As an application, the construction of a matter wave beam splitter and a Mach-Zehnder interferometer is briefly discussed. PACS numbers: 03.65.-w, 03.75.Be, 03.75.LmBloch-Zener oscillations 2 1.