Wien filter: A wave-packet-shifting device for restoring longitudinal coherence in charged-matter-wave interferometers

This chapter introduces cavity quantum optomechanics with levitated nanospheres with some emphasis on preparing mesoscopic quantum superpositions and testing collapse models. It is divided into three parts: levitated quantum optomechanics: atoms vs. sphere; decoherence in levitated nanospheres; and wave-packet dynamics: coherence vs. decoherence. It is first shown how the master equation describing the dynamics of a polarizable object in a cavity along the cavity axis and that of the cavity mode is derived. Optical levitation is also discussed. It is then shown how most of the decoherence sources in levitated nanospheres can be cast into a relatively simple master equation describing position localization type of decoherence. Such decoherence tends to suppress the centre-of-mass position coherences. Finally, a discussion of wave-packet dynamics is given, with the motivation of using levitated nanospheres for matter-wave interferometry, that is, to create macroscopic quantum superpositions for testing quantum mechanics in unprecedented parameter regimes.

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Localization of a matter wave packet in a disordered potential

Physical Review A ◽

10.1103/physreva.83.031603 ◽

2011 ◽

Vol 83 (3) ◽

Cited By ~ 30

Author(s):

M. Piraud ◽

P. Lugan ◽

P. Bouyer ◽

A. Aspect ◽

L. Sanchez-Palencia

Keyword(s):

Wave Packet ◽

Matter Wave

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Observing the Phase Space Trajectory of an Entangled Matter Wave Packet

Physical Review Letters ◽

10.1103/physrevlett.105.263602 ◽

2010 ◽

Vol 105 (26) ◽

Cited By ~ 30

Author(s):

U. Poschinger ◽

A. Walther ◽

K. Singer ◽

F. Schmidt-Kaler

Keyword(s):

Phase Space ◽

Wave Packet ◽

Matter Wave ◽

Phase Space Trajectory

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Low-workfunction field-emission source for high-resolution EELS

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100125592 ◽

1987 ◽

Vol 45 ◽

pp. 132-133

Author(s):

P. E. Batson

Keyword(s):

High Resolution ◽

Energy Loss ◽

Electron Probe ◽

Collection Efficiency ◽

Electron Sources ◽

Wien Filter ◽

Half Angle ◽

Thermal Emitter ◽

Electron Energy Loss ◽

Intrinsic Energy

In recent years,instrumentation for electron energy loss spectroscopy (EELS) has been steadily improved to increase energy resolution and collection efficiency. At present 0.40eV at 10mR collection half angle is available with commercial magnetic sectors (e.g. Gatan, Inc. and VG Microscopes, Ltd.), and 70meV at 10mR has been demonstrated by use of a Wien filter within a large deceleration field. When these high resolution spectrometers are coupled to the modern small electron probe instrument, we obtain a tool which promises to reveal local changes in bandstructure and bonding near defects and interfaces in heterogeneous materials.Unfortunately, typical electron sources have intrinsic energy widths which limit attainable spectroscopic resolution in the absence of some monochromation system. For instance, the W thermal emitter has a half width of about 1eV.

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Interferometric (Fourier-Spectroscopic) Measurement of Electron Energy Distributions

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100134144 ◽

1990 ◽

Vol 48 (2) ◽

pp. 110-111 ◽

Cited By ~ 1

Author(s):

F. Hasselbach ◽

A. Schäfer

Keyword(s):

Group Velocity ◽

Wave Packets ◽

Index Of Refraction ◽

Electron Wave ◽

Fringe Contrast ◽

Faraday Cage ◽

Optical Index ◽

Wien Filter ◽

Coherent Wave ◽

Electric And Magnetic Fields

Möllenstedt and Wohland proposed in 1980 two methods for measuring the coherence lengths of electron wave packets interferometrically by observing interference fringe contrast in dependence on the longitudinal shift of the wave packets. In both cases an electron beam is split by an electron optical biprism into two coherent wave packets, and subsequently both packets travel part of their way to the interference plane in regions of different electric potential, either in a Faraday cage (Fig. 1a) or in a Wien filter (crossed electric and magnetic fields, Fig. 1b). In the Faraday cage the phase and group velocity of the upper beam (Fig.1a) is retarded or accelerated according to the cage potential. In the Wien filter the group velocity of both beams varies with its excitation while the phase velocity remains unchanged. The phase of the electron wave is not affected at all in the compensated state of the Wien filter since the electron optical index of refraction in this state equals 1 inside and outside of the Wien filter.

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