Bright-soliton quantum superpositions: Signatures of high- and low-fidelity states

Abstract

Scattering quantum bright solitons off barriers has been predicted to lead to nonlocal quantum superpositions, in particular the NOON-state. The focus of this paper lies on signatures of both highand low-fidelity quantum superposition states. We numerically demonstrate that a one-dimensional geometry with the barrier potential situated in the middle of an additional -experimentally typical -harmonic confinement gives rise to particularly well-observable signatures. In the elastic scattering regime we investigate signatures of NOON-states on the N -particle level within an effective potential approach. We show that removing the barrier potential and subsequently recombining both parts of the quantum superposition leads to a high-contrast interference pattern in the center-of-mass coordinate for narrow and broad potential barriers. We demonstrate that the presented signatures can be used to clearly distinguish quantum superpositions states from statistical mixtures and are sufficiently robust against experimentally relevant excitations of the center-of-mass wave function to higher lying oscillator states. For two-particle solitons we extend these considerations to lowfidelity superposition states: even for strong deviations from the two-particle NOON-state we find interference patterns with high contrast.

Progress towards quantum-enhanced interferometry with harmonically trapped quantum matter-wave bright solitons

“…After quasi-instantaneously shifting the harmonic potential by several soliton lengths, we switch on a very narrow repulsive scattering potential in the center of the trap and observe the quantum dynamics for 50:50 splitting after the first collision for two collisions (cf. [29,30,45]). In Fig.…”

“…The minimal distance measurable can be improved by statistical analysis of repeating the experiment N times, giving an improvement of a factor of 1/ √ N for the smallest distance that can be measured [Eq. (30)] for repeated experiments with single particles [47, Sec. "Quantum-Enhanced Parameter Estimation"].…”

Splitting of two-component solitary waves from collisions with narrow potential barriers

“…An object to be probed by the interferometer is placed as an obstacle through which one fragment will pass, which will affect the outcome of the recombination [8][9][10]. Soliton interferometers have been elaborated theoretically in various configurations [11][12][13][14][15][16][17][18][19][20] (including the case when the splitter is inserted as a localized self-repulsive nonlinearity, or its combination with the usual potential barrier [21]) and realized in experiment [9]. Interactions of matter-wave solitons with local potentials have also been studied in other contexts, such as an analytical treatment of the collisions [22], rebound from potential wells [23,24], dynamics of solitons in a dipolar BEC [12], and probing effects of interparticle interactions on tunneling [25,26].…”

Mean-field analog of the Hong-Ou-Mandel experiment with bright solitons

“…Another, potentially rather challenging direction may involve the recently analyzed analogy between the Lieb-Liniger exactly solvable model 1D solutions and their mean-field bright solitonic counterparts in the larger atom number limit [37] to explore the question discussed herein for structures involving different atom numbers. As this control parameter decreases, we can gradually progress from the mean-field limit of the present work to the quantum-mechanical realm of the Lieb-Liniger model and examine how the latter may modify the presently reported phenomenology.…”