Matter-wave coherence

It is worthwhile to note that the charged Bose gas trapped in the double well potential Ua of Eq. 50 behaves as an inverted Josephson junction (N-S-S-N). The super-current, which accompanies the matter wave coherence, is induced between the degenerate resonance states of the adjacent wells at the frequency of the tunnel splitting A response time, as is typical of tunnel junctions (whose frequency cutoff is much smaller than the vibrational frequency even for nano junctions). The coherent oscillations of the Josephson current can be observed by virtue of their slow frequency A V which is robustly controlled by the bias voltage. 

Ultrafast laser excitation gives excited systems prepared coherently, as a coherent superposition of states. The state wave function (aprobabihty wave) is a coherent sum of matter wave functions for each molecule excited. The exponential terms in the relevant time-dependent equation, the phase factors, define phase relationships between constituent wave functions in the summation. 

The matter wave function is formed as a coherent superposition of states or a state ensemble, a wave packet. As the phase relationships change the wave packet moves, and spreads, not necessarily in only one direction the localized launch configuration disperses or propagates with the wave packet. The initially localized wave packets evolve like single-molecule trajectories. 

Excitations of molecules with femtosecond laser pulses lead to excited-state matter wave packets coherently, launching them with such well-defined spatial resolution and coherence in nuclear motions that they evolve like single-molecule trajectories. Both electronically excited and vibrationally excited ground-state species may be studied. The structural change versus time profile of a reaction turns out to be compatible with classical modes of thinking. 

S. Inouye et al., Phase-Coherent Amphfication of Atomic Matter Waves, Nature 402, 641-644 (1999). 

Formally, we describe the state of the particle during the propagation as a coherent superposition of states, in particular of position states, that are classically mutually exclusive. A classical object will either take one or the other path for sure. A quantum object cannot be said to do that since the intrinsic information content of the quantum system is insufficient to allow such a description [Brukner 2002], Matter wave interferometers prove this experimentally. The intriguing part is that a full interference visibility can only be obtained if we exclude all possibilities of detecting, even in principle, the... 

Bose-Einstein condensate a state of matter, produced in laboratories, in which atoms are packed so close together that their wavefunctions become correlated similar to those of photons in a laser beam, and coherent matter waves can be formed. 

Atomic particles moving with the momentum p can be characterized by their de Broglie wavelength A, = h/p. If beams of such particles can be split into coherent partial beams, which are recombined after traveling different path lengths, matter-wave interferometry becomes possible. This has been demonstrated extensively for electrons and neutrons, and recently also for neutral atoms [1278, 1279]. 

The increasing research on laser cooling of atoms and molecules and many experiments with Bose-Einstein condensates have brought about some remarkable results and have considerably increased our knowledge about the interaction of light with matter on a microscopic scale and the interatomic interactions at very low temperatures. Also the realization of coherent matter waves (atom lasers) and investigations of interference effects between matter waves have proved fundamental aspects of quantum mechanics. 

Ginsberg NS, Gamer SR, and Hau LV. Coherent control of optical information with matter wave dynamics. Nature 2007 Feb 8 445 623-626. 

Fig. 9.75. Pulses of coherent matter waves generated from a Bose-Binstein condensate [9.462]...

S. Inouye, T. Pfau, S. Gupta, A.P. Chikkatur, A. Gorlitz, D.E. Pritchard, W. Ketterle Phase-coherent amplification of atomic matter waves. Natnre 402, 641 (1999)... 

An almost forgotten issue is the proposed relativistic nature of an electron as elucidated by Lorentz. The electron was seen as a flexible spherical unit of charge which distorts as it contracts in the direction of any motion. To account for the relativistic contraction of macroscopic bodies Lorentz further assumed that the electrical forces which bind atoms together were essentially states of stress and strain in the aether. Countless prominent scientists have expressed similar views without trying to develop a coherent theory of matter. The Lorentz electron model antedates de Broglie s postulate of matter waves and the development... 

The concept of coherent control, which we have developed with isolated molecules in the gas phase, is universal and should apply to condensed matter as well. We anticipate that the coherent control of wave functions delocalized over many particles in solids or liquids will be a useful tool to track the temporal evolution of the delocalized wave function modulated by many-body interactions with other particles surrounding itself. We may find a clue to better understand the quantum-classical boundary by observing such dynamical evolution of wave functions of condensed matter. In the condensed phase, however, the coherence lifetime is in principle much shorter than in the gas phase, and the coherent control is more difficult accordingly. In this section, we show our recent efforts to develop the coherent control of condensed matter. 

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