[Paper Review] Interferometry with correlated matter-waves

Oksana Streltsova, Alexej I. Streltsov|arXiv (Cornell University)|Dec 12, 2014

Cold Atom Physics and Bose-Einstein Condensates2 references3 citations

TL;DR

This paper proposes a many-body interferometric protocol to directly measure fragmentation in ultra-cold attractive Bose gases by recombining split matter-wave sub-clouds with a laser pulse, demonstrating that the zero-momentum peak population is linearly proportional to the degree of fragmentation. The method enables direct, experimentally accessible measurement of many-body correlations in systems with two-hump density profiles, valid for both attractive and repulsive interactions.

ABSTRACT

Matter-wave interferometry of ultra-cold atoms with attractive interactions is studied at the full many-body level. First, we study how a coherent light-pulse applied to an initially-condensed solitonic system splits it into two matter-waves. The split system looses its coherence and develops correlations with time, and inevitably becomes fragmented due to inter-particle attractions. Next, we show that by re-colliding the sub-clouds constituting the split density together, along with a simultaneous application of the same laser-pulse, one creates three matter-waves propagating with different momenta. We demonstrate that the number of atoms in the sub-cloud with zero-momentum is directly proportional to the degree of fragmentation in the system. This interferometric-based protocol to discriminate, probe, and measure the fragmentation is general and can be applied to ultra-cold systems with attractive, repulsive, short- and long-range interactions.

Motivation & Objective

• To address the open question of how to directly measure fragmentation in ultra-cold quantum systems with attractive interactions.
• To investigate the breakdown of coherence and emergence of fragmentation in matter-wave interferometry beyond mean-field theory.
• To develop a general, experimentally feasible protocol for measuring fragmentation using standard interferometric tools.
• To validate the connection between interferometric visibility and the second natural orbital occupation number in fragmented systems.

Proposed method

• The study uses the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method to solve the time-dependent many-body Schrödinger equation (TDSE) for N=100 attractive bosons in a harmonic trap.
• A laser pulse with wavevector k=5 and π-phase is applied to split an initially coherent, solitonic matter-wave into two sub-clouds, inducing momentum transfer and initiating fragmentation.
• The system is recombined via a second π-phase laser pulse at specific re-collision times, generating three matter-waves with momenta 0, ±2k.
• The population in the zero-momentum channel (ν) is computed by integrating the spatial density over the central region, serving as a proxy for fragmentation.
• A linear relation is derived: n²_intf/N = 1 – (3/2)ν, linking interferometrically measured fragmentation to the second natural orbital occupation number.
• The protocol is tested at multiple re-collision times (t≈7.0, 14.05, 21.08), comparing MCTDHB results with exact diagonalization of the one-body density matrix (DNS).

Experimental results

Research questions

• RQ1 Can fragmentation in ultra-cold attractive Bose gases be directly measured using a standard interferometric setup?
• RQ2 How does the population in the zero-momentum channel relate to the actual degree of fragmentation in a two-hump matter-wave system?
• RQ3 To what extent does many-body physics, beyond the Gross-Pitaevskii mean-field approximation, affect coherence and fragmentation during interferometric splitting and recombination?
• RQ4 Is the linear relationship between interferometric visibility and fragmentation robust across different stages of evolution and re-collision times?

Key findings

• The interferometric protocol successfully measures fragmentation via the zero-momentum peak population, with the interferometric fragmentation n²_intf/N closely matching the exact second natural orbital occupation number n²/N from diagonalization.
• At the first re-collision (t≈7.0), the DNS shows n²/N ≈ 26.4%, and the interferometric measurement yields n²_intf/N ≈ 26.7%, with visibility ν≈0.4889.
• At the second re-collision (t≈14.05), n²/N ≈ 43.7% and n²_intf/N ≈ 42.8%, with ν≈0.3817, confirming the linear relation.
• At the third re-collision (t≈21.08), n²/N ≈ 45.7% and n²_intf/N ≈ 45.0%, with ν≈0.3668, showing consistent agreement across time evolution.
• Small deviations between n²_intf/N and n²/N are attributed to timing mismatches in re-collision detection, not fundamental flaws in the protocol.
• The method is general and applicable to systems with attractive, repulsive, short- and long-range interactions, provided they exhibit two-hump density structures.