Quantum Motion in Real Space

Ciann‐Dong Yang

Paul Bracken

The equation of motion for a particle moving in complex space is obtained and then solved. The interaction between the real and imaginary components of motion can produce what can be regarded as a wave motion in real space. The formation of interference patterns and polarization of a matter wave can be accounted for by the particle’s motion in complex space. The deterministic particle view of a free particle can then be reconciled with its dual probabilistic wave picture but the formulation is entirely in complex space.

Zheng-Yuan Zhang, Han-Chao Chen, Xin Liu +15 more

The quantum Zeno effect (QZE) reveals that frequent measurements can suppress quantum evolution; however, the impact of measurements on the real-space motion of a single atom remains insufficiently explored experimentally. In this work, we employ an optical trap as a measurement pulse and, by monitoring atomic loss, directly observe the QZE in the real-space motion of a single atom. We find that the action of measurement on the atom consists of a projective measurement followed by subsequent periodic unitary evolution, thereby providing an intuitive physical picture of measurement backaction across different timescales. We further investigate the effects of measurement frequency, strength, and spatial position, demonstrating that measurements pulse not only suppress the spatial spreading of the quantum state but also enable deterministic preparation of distinct motional states. Moreover, by dynamically controlling the trap position, we realize measurement-induced directional transport of a single atom, with a velocity exceeding the maximum allowed by the adiabatic condition. Overall, our results provide a direct experimental demonstration of the QZE in real space and establish a versatile framework for measurement-based control of atomic motion, opening new possibilities for motional-state engineering in cold-atom systems.

David F. P. Pile

M. S. Wang

We show that a backward stochastic system with an imaginary diffusion coefficient in complex space is equivalent to a real space quantum system if it obeys a Newtonian-like dynamical law and its final spatial distribution is constrained to be in real space. The ensemble averages of the position, momentum, angular momentum and energy of the stochastic processes are the quantum mechanical expectation values of the corresponding operators. The product of the mean-square deviations of the position and momentum of the stochastic process agreees with the corresponding uncertainty relation of quantum mechanics. The equation of motion is invariant under the combined transformations of changing the time t! ¡ t and taking the complex conjugate of the equation. The stochastic motion reduces to the classical motion in the limit where the de Broglie wavelengh of the particle vanishes. PACS. 03.65.Bz – Foundations, theory of measurement, miscellaneous theories. PACS. 02.50.Ga – Markov processes. PACS. 02.50.Cw – Probability theory.

Daniel M. Greenberger