A bright-solitary matter wave (a non-dispersive wavepacket of an attractive Bose-Einstein condensate in a quasi-one-dimensional waveguide) can be split on a narrow repulsive optical barrier and recombined at the same barrier, realizing the beam-splitter and recombiner of a soliton interferometer. The 2020 experiment of Wales et al. (Commun. Phys. 3, 51) demonstrated interference-mediated recombination of a bright-solitary 85Rb matter wave but could not directly observe the predicted oscillatory dependence of the recombined fraction A(zoff)A(z_{\rm off}) on the barrier offset: the independently measured 1.3±0.3 µm shot-to-shot fluctuation of the magnetic axial trap relative to the barrier is comparable to the fringe spacing, and genuine thermal or beyond-mean-field decoherence could not be excluded. The open problem is to resolve these interference fringes directly — which requires roughly 0.1 µm relative barrier-trap stability, achievable for example through an all-optical axial potential or a more resilient species or geometry — and to quantitatively separate extrinsic position-noise averaging from intrinsic decoherence, together with a predictive theory beyond the quasi-1D mean-field description in the regimes where it breaks down (wider barriers, slow interactions, thermal and quantum-field effects).

Background

Bright solitons are non-dispersive wavepackets that arise in Bose-Einstein condensates (BECs, dilute ultracold gases occupying a single macroscopic quantum state) when the interatomic interaction is sufficiently attractive to exactly compensate wavepacket spreading. They are realized with species such as 85Rb or 7Li by tuning the s-wave scattering length asa_s — the strength and sign of the low-energy two-body contact interaction — to a small negative value using a magnetic Feshbach resonance (a resonant coupling of two-atom collision channels that renders asa_s magnetic-field-tunable). In a quasi-one-dimensional (quasi-1D) waveguide a few thousand atoms form a single 'bright-solitary matter wave' whose shape is preserved as it moves; because it does not spread, it can in principle be interrogated interferometrically for far longer than a dilute cloud, motivating soliton matter-wave interferometry for inertial and rotation sensing.

A repulsive optical barrier (a laser beam detuned above the atomic resonance — 'blue-detuned' — so that it repels atoms, focused across the waveguide) acts as a beam splitter for a soliton: the incident soliton splits into two daughter solitons that separate, oscillate back in the axial harmonic trap, and meet again at the barrier, where they are recombined. Founding theory showed that scattering an attractive condensate from a barrier can create a mesoscopic quantum superposition of the whole cloud being left and right of the barrier (Weiss and Castin, 2009; Streltsov, Alon and Cederbaum, 2009). Mean-field analyses within the Gross-Pitaevskii equation (GPE, the standard nonlinear Schrödinger-type description of a condensate) mapped soliton splitting, recombination, and collisions at Gaussian barriers in quasi-1D and 3D (Cuevas et al., 2013). Multiconfigurational quantum simulations (many-body simulations representing the condensate with several coupled orbitals) established that barrier splitting can entangle the atoms, with a quantum-to-classical transition between genuine many-body superpositions and classical mixtures (Helm, Rooney, Weiss and Gardiner, 2014; Martin and Ruostekoski, 2012), and quantum phase diffusion — the build-up of relative-phase uncertainty between soliton fragments driven by number fluctuations and interactions — was identified as a fundamental noise limit of soliton interferometers (Haine, 2018). Proposals include soliton interferometers with Rosen-Morse barriers (smoothed, analytically solvable potential barriers; Polo and Ahufinger, 2013), nonlinear density-dependent splitters (Sakaguchi and Malomed, 2016), and ring-trap Sagnac interferometers, in which counter-propagating matter waves probe rotation through the Sagnac phase shift (Helm, Cornish and Gardiner, 2015). Experimentally, a solitonic atom interferometer was first realized in 85Rb using Bragg-pulse beam splitters (light pulses that diffract the matter wave into a superposition of two momenta) in a horizontal optical waveguide (McDonald et al., 2014).

In this setting, Wales et al. (Commun. Phys. 3, 51 (2020)) demonstrated, for the first time in the barrier geometry, controlled splitting of a bright-solitary 85Rb matter wave (~2500 atoms, asa_s Feshbach-tuned, axial trap frequency ωz/2π\omega_z/2\pi of order 1.5 Hz) on a repulsive Gaussian barrier (532-nm beam; narrow-barrier width ~3.6 µm) and its recombination at the same barrier. For a wide barrier the recombination is dominated by velocity filtering (the faster fraction transmits, the remainder reflects); for a narrow barrier, interference between the reflected and transmitted parts dominates, evidenced by enhanced population fluctuations after the second barrier interaction. Quasi-1D and 3D GPE simulations with no free fitting parameters predict strong oscillations of the recombined fraction A(zoff)A(z_{\rm off}) — the fraction of atoms found on one side of the barrier after recombination — as the barrier offset zoffz_{\rm off} from the trap centre is varied over a few micrometres. However, the experiment could not resolve these fringes: the independently measured shot-to-shot RMS fluctuation of the magnetic axial trap centre relative to the barrier, 1.3±0.3 µm (attributable to a stray magnetic field of only ~3 mG), is comparable to the fringe spacing, so each run samples a random portion of the oscillation. Resolving the fringes requires relative barrier-trap stability and control at the ~0.1 µm level; the authors propose an all-optical axial potential, generated for example by acousto-optic deflectors (AODs, laser-beam steering devices) or a digital micromirror device (DMD, a programmable micromirror array that 'paints' arbitrary optical potentials), noting that their existing optical potentials already exhibit ~0.3 µm stability. A quasi-1D classical-field simulation (a GPE supplemented by stochastically populated thermal modes, used to approximate finite-temperature effects beyond pure mean field) gave a worst-case thermal estimate of the splitting standard deviation of 0.047, compared with the measured 0.064 that also contains imaging noise (the absorption-image atom-number measurement itself contributes about 150 atoms for a 2500-atom soliton) — so thermal decoherence can be neither confirmed nor excluded. The analytic quasi-1D model additionally breaks down for wider barriers and slower barrier interactions, and a full three-dimensional, non-equilibrium, beyond-mean-field treatment (accounting for correlations and fluctuations beyond the single-condensate GPE description) of the soliton-production and splitting process was deemed not feasible by the authors. As alternative routes they suggest lower-mass lithium (broader fringes, larger solitons, suppressed velocity filtering) and ring traps for soliton Sagnac interferometry.

Problem Statement

The problem is to directly observe and quantitatively account for the coherent recombination of a bright-solitary matter wave that has been split on a narrow repulsive barrier.

  1. Directly resolve the predicted oscillatory dependence of the recombined fraction A(zoff)A(z_{\rm off}) — the fraction of atoms found on one side of the barrier after recombination — on the barrier offset zoffz_{\rm off} relative to the trap centre (the interference fringes) — the definitive signature of coherent splitting and phase-sensitive recombination in the barrier geometry. This requires shot-to-shot relative barrier-trap stability and control of order 0.1 µm (the 2020 experiment had 1.3±0.3 µm), achievable for example by replacing the magnetically generated axial potential with an all-optical potential (acousto-optic deflectors or a digital micromirror device), or by using a species or geometry for which the requirement is relaxed (for example lower-mass lithium, where the fringes are broader and the solitons larger, or a ring trap).

  2. Quantitatively explain the observed fringe contrast: separate extrinsic averaging (the ideal fringes convolved with the measured shot-to-shot offset-noise distribution) from genuine intrinsic decoherence — thermal excitations and beyond-mean-field effects — and measure or bound the intrinsic contribution, for example through controlled variation of temperature and of the offset noise against mean-field (GPE) predictions.

As its theory counterpart, the problem includes extending the predictive description of this splitting-recombination process beyond the quasi-1D mean-field approximation in the regimes where it fails: wider barriers, slow barrier interactions, and three-dimensional thermal and quantum-field effects.

Any species, apparatus, or theoretical route addressing these goals may be used; the problem is not tied to 85Rb or to the specific magnetic-trap apparatus of the source experiment.

The three components above are jointly required: direct resolution of the fringes, separation of extrinsic averaging from intrinsic decoherence, and the beyond-mean-field predictive description. 'Any species, apparatus, or theoretical route' concerns the choice of implementation rather than waiving any component. For the fringe-observation component, a written resolution is expected to give an experimentally concrete scheme that predicts the offset-dependent fringes, together with a quantitative contrast budget and an explicit path to the required relative barrier-trap stability (of order 0.1 µm); an actual laboratory measurement is not required.

References

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