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Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

Matter wave sidebands from a complex potential with temporal helicity

Stefan Bernet, Roland Abfalterer, Claudia Keller, Jörg Schmiedmayer, Anton Zeilinger

Published Apr 8, 1999• 6 citations
Publisher

Abstract

Atoms are diffracted at tailored time–modulated complex potential gratings made of light. Modulating both real and imaginary parts separately, the potential winds like a corkscrew in complex space. This temporal helicity induces energy transfers only in one single direction. As a result we present the first observation of asymmetric frequency sidebands of atomic matter waves.

DOI
10.1098/rspa.1999.0370

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Atoms are diffracted at tailored time–modulated complex potential gratings made of light. Modulating both real and imaginary parts separately, the potential winds like a corkscrew in complex space. This temporal helicity induces energy transfers only in one single direction. As a result we present the first observation of asymmetric frequency sidebands of atomic matter waves.
Temporal light modulation methods which are of great practical importance in optical technology, are emulated with matter waves. This includes generation and tailoring of matter-wave sidebands, using amplitude and phase modulation of an atomic beam. In the experiments atoms are Bragg diffracted at standing light fields, which are periodically modulated in intensity or frequency. This gives rise to a generalized Bragg situation under which the atomic matter waves are both diffracted and coherently shifted in their de Broglie frequency. In particular, we demonstrate creation of complex and non-Hermitian matter-wave modulations. One interesting case is a potential with a time-dependent complex helicity $[V\ensuremath{\propto}\mathrm{exp}(i\ensuremath{\omega}t)],$ which produces a purely lopsided energy transfer between the atoms and the photons, and thus violates the usual symmetry between absorption and stimulated emission of energy quanta. Possible applications range from atom cooling over advanced atomic interferometers to a new type of mass spectrometer.
Atoms interacting with standing light waves are a model system for the propagation of waves in static and time varying periodic media. We present here experiments studying the coherent motion of atomic deBroglie waves in periodic potentials made from on and off resonant light. We observe anomalous transmission of atoms through resonant standing light waves and experimentally confirm that atoms fulfilling the Bragg condition form a standing matter wave pattern. We furthermore demonstrate how Bragg diffraction of atomic matter waves at a time-modulated thick standing light wave can be used to coherently shift the deBroglie frequency of the diffracted atoms. Our frequency shifter for atomic matter waves is similar to an acousto-optic frequency shifter for photons.
Cesium atoms prepared in a state of well-defined total energy have been reflected from a vibrating mirror, causing the matter waves to be phase modulated. The mirror is an evanescent light wave whose intensity is modulated in time at a frequency $\ensuremath{\nu}$ in the range 0 to 2 MHz; the atoms are reflected at normal incidence. The resulting beam consists of a ``carrier'' plus various sidebands corresponding to de Broglie waves propagating at different velocities. The precision and flexibility of this technique make it a promising tool in atom optics.
Bragg diffraction of atoms at thick standing light waves requires that the wave-matching condition is fulfilled. This usually means that the atomic beam crosses the light wave exactly at the Bragg angle. Nevertheless, our experiments also demonstrate Bragg diffraction at detuned angles if the amplitude of the standing light wave is temporally modulated with an appropriate frequency. If, on the other hand, the phase of the light wave is modulated no diffraction is observed. Both modulation processes produce frequency sidebands which set up `slowly travelling standing waves' in front of a retro-reflection mirror. Atoms are diffracted at these `almost standing' light waves in a similar way to photons at the travelling sound waves in an acousto-optic modulator. The frequency of the diffracted de Broglie waves is assumed to be shifted by the intensity modulation frequency. The different results using amplitude- and phase-modulated light waves are due to interference between the diffraction contributions of the individual frequency sidebands contained in the standing light wave.