Control of particle propagation beyond the uncertainty limit by interference between position and momentum

Abstract

As shown in Phys. Rev. A 96, 020101(R) (2017), it is possible to demonstrate that quantum particles do not move along straight lines in free space by increasing the probability of finding the particles within narrow intervals of position and momentum beyond the "either/or" limit of 0.5 using constructive quantum interference between a component localized in position and a component localized in momentum. The probability of finding the particle in a corresponding spatial interval at a later time then violates the lower bound of the particle propagation inequality which is based on the validity of Newton's first law. In this paper, the problem of localizing the two state components in their respective target intervals is addressed by introducing a set of three coefficients that describe the localization of arbitrary wavefunctions quantitatively. This characterization is applied to a superposition of Gaussians, obtaining a violation of the particle propagation inequality by more than 5 percent if the width of the Gaussian wavefunction is optimized along with the size of the position and momentum intervals. It is shown that the violation of the particle propagation inequality originates from the fundamental way in which quantum interferences relate initial position and momentum to the future positions of a particle, indicating that the violation is a fundamental feature of causality in the quantum limit.

Quantum Causality Relations and the Emergence of Reality from Coherent Superpositions

“…Quantum corrections of classical causality relations can only be observed if both state preparation and measurement are sufficiently precise, since neither one has any physical meaning of its own. The quantitative nature of quantum corrections of causality can then be observed and quantified in terms of the statistical relations between different measurement outcomes, an example of which has been given in [44][45][46] for the failure of Newton's first law in the case of particle propagation in free space. A closer inspection of the relation between causality and quantum coherence can thus result in the systematic development of new means of control beyond the least action approximation.…”

Quantum causality relations and the emergence of reality from coherent superpositions

“…Quantum corrections of classical causality relations can only be observed if both state preparation and measurement are sufficiently precise, since neither one has any physical meaning of its own. The quantitative nature of quantum corrections of causality can then be observed and quantified in terms of the statistical relations between different measurement outcomes, an example of which has been given in [44][45][46] for the failure of Newton's first law in the case of particle propagation in free space. A closer inspection of the relation between causality and quantum coherence can thus result in the systematic development of new means of control beyond the least action approximation.…”

Probability flow for a free particle: new quantum effects

“…The phenomenon was subsequently described in detail and quantified for that case [2], and has been widely discussed in its own right since [3][4][5][6][7][8][9][10][11][12]. It has also been generalized in various other directions [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], and is of continuing interest in the time of arrival context [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44].…”