[Paper Review] Interaction control and bright solitons in coherently-coupled Bose-Einstein condensates

Jorge Luciano Alió Sanz, A. Frölian+3 more|arXiv (Cornell University)|Dec 12, 2019

Cold Atom Physics and Bose-Einstein Condensates59 references43 citations

TL;DR

This paper demonstrates fast, coherent control of interatomic interactions in a 39K Bose-Einstein condensate using a radio-frequency field to coherently couple two hyperfine states with opposite-sign scattering lengths. By tuning the coupling field, the effective scattering length of the lower dressed state is dynamically controlled over >100 a₀, enabling the observation of bright solitons in the attractive regime and the formation of soliton trains via interaction quench dynamics.

ABSTRACT

We demonstrate fast control of the interatomic interactions in a Bose-Einstein condensate by coherently coupling two atomic states with intra- and inter-state scattering lengths of opposite signs. We measure the elastic and inelastic scattering properties of the system and find good agreement with a theoretical model describing the interactions between dressed states. In the attractive regime, we observe the formation of bright solitons formed by dressed-state atoms. Finally, we study the response of the system to an interaction quench from repulsive to attractive values, and observe how the resulting modulational instability develops into a bright soliton train.

Motivation & Objective

• To achieve fast, flexible, and reversible control of interatomic interactions in a BEC using coherent coupling between atomic states with opposite-sign scattering lengths.
• To experimentally probe the elastic and inelastic scattering properties of dressed states formed by rf coupling in a BEC.
• To demonstrate the stabilization of bright solitons in the attractive regime by engineering the effective scattering length via dressed-state composition.
• To study the dynamics of modulational instability following a rapid quench from repulsive to attractive interactions, leading to soliton train formation.

Proposed method

• Coherent coupling of two 39K hyperfine states (|↑⟩ ≡ |F=1, mF=−1⟩ and |↓⟩ ≡ |F=1, mF=0⟩) using a radio-frequency field to create dressed states |−⟩ and |+⟩.
• Tuning the Rabi frequency and detuning of the rf field to control the mixing angle θ and thus the composition of the dressed states, enabling dynamic control of the effective scattering length a⁻⁻.
• Measuring the effective scattering length a⁻⁻ via time-of-flight expansion imaging and scaling the axial cloud size σₓ⁵/N to infer interaction strength.
• Using Landau-Zener sweeps with ramp rates ≤1 kHz/µs to prepare pure dressed states, with detuning controlled to access different polarization parameters P.
• Performing interaction quench experiments by rapidly switching from repulsive to attractive interaction regimes to trigger modulational instability.
• Employing numerical simulations of the time-dependent Gross-Pitaevskii equation to validate experimental data and correct for deviations in the Thomas-Fermi approximation.

Experimental results

Research questions

• RQ1 Can coherent coupling between atomic states with opposite-sign scattering lengths enable fast and flexible control of effective interactions in a BEC?
• RQ2 How do the elastic and inelastic scattering properties of dressed states depend on the rf coupling parameters, particularly the polarization parameter P?
• RQ3 Can bright solitons be stabilized in the lower dressed state |−⟩ when the effective scattering length is tuned to attractive values?
• RQ4 What is the dynamical evolution of modulational instability following a fast quench from repulsive to attractive interactions in the dressed-state BEC?

Key findings

• The effective scattering length a⁻⁻ of the lower dressed state |−⟩ was experimentally tuned over more than 100 a₀ by varying the rf detuning, with good agreement between experiment and theoretical model.
• A minimum in a⁻⁻ was observed at δ/2π ≈ 6.5 kHz (P ≈ 0.31), consistent with the theoretical prediction due to the attractive inter-state scattering length a↑↓ < 0.
• Bright solitons were directly observed in the lower dressed state |−⟩ when the effective scattering length a⁻⁻ became negative, confirming stabilization via coherent dressing.
• Following a rapid interaction quench from repulsive to attractive interactions, the system exhibited modulational instability that evolved into a train of bright solitons, with dynamics consistent with theoretical expectations.
• The lifetime of the higher dressed state |+⟩ was limited to ∼1 ms due to inelastic collisions, which create correlated atom pairs with opposite momenta and release energy corresponding to the dressed-state energy gap.
• Numerical simulations of the time-dependent Gross-Pitaevskii equation confirmed the experimental scaling of σₓ⁵/N with a⁻⁻ and showed that deviations in the Thomas-Fermi approximation were largest at large negative detuning, where three-body recombination and residual excitations were significant.