Collisional Transitory Enhancement of the High Momentum Components of a Quantum Wave Packet

Abstract

A classically forbidden, transitory enhancement of the high positive momentum components of a quantum wave packet during its collision with a potential barrier is described. A quantity is defined to measure its importance; the universality of the effect is justified, and its main features are studied with the aid of an analytically solvable model. Its relation to other "anomalously high velocities" is also examined. [S0031-9007(98)07182-8]

Quantum transients

“…An example of interference in momentum representation is the collisional, transitory enhancement of the high momentum components of a wave packet [240,241,199,202]. This enhancement leads to a violation of the classical conservation of energy since the probability of finding the particle with a momentum larger than a given value may exceed the classical bound during the collision.…”

Time-dependent quantum current for independent electrons driven under nonperiodic conditions

“…All this in- formation can provide a fresh view on the old controversial issue of tunneling times. [65][66][67] Much more work is needed to explore all these possibilities mentioned here briefly. In summary, the present approach provides a very useful tool ͑using the time domain, complementary to other energy-domain for-malisms͒ to better understand time-dependent tunneling phenomenology and to study practical high-frequency applications of phase-coherent devices.…”

Momentum-space interferometry with trapped ultracold atoms

“…First, phase imprinting of half of the wavepacket can be regarded as a simple way to realize the interferometry in momentum space that has been previously put forward for more complex scattering processes between cold atoms an weak laser barriers [1,2,3]. Similar to the scattering setting, a central "dark notch" appears in the momentum distribution after phase imprinting, as well as an enhancement of the wings.…”

“…1a, the momentum distribution can change dramatically, vanishing at the center of the distribution, and being enhanced at the wings. This process would violate classical energy-conservation [1], and is due to interference in momentum space between incident and transmitted parts of the wave [2,3].…”