[Paper Review] Optical control of Feshbach resonances in Fermi gases using molecular dark states

Haibin Wu, J. E. Thomas|arXiv (Cornell University)|Oct 4, 2011

Cold Atom Physics and Bose-Einstein Condensates3 citations

TL;DR

This paper proposes a dark-state optical control method for tuning Feshbach resonances in ultracold Fermi gases using two optical fields to couple multiple closed-channel molecular states, suppressing inelastic losses via quantum interference. The technique enables wide, reversible tuning of the scattering length with minimal loss, achieving up to two orders of magnitude reduction in spontaneous emission compared to single-field methods.

ABSTRACT

We propose a general method for optical control of magnetic Feshbach resonances in ultracold atomic gases with more than one molecular state in an energetically closed channel. Using two optical frequencies to couple two states in the closed channel, inelastic loss arising from spontaneous emission is greatly suppressed by destructive quantum interference at the two-photon resonance, i.e., dark-state formation, while the scattering length is widely tunable by varying the frequencies and/or intensities of the optical fields. This technique is of particular interest for a two-component atomic Fermi gas, which is stable near a Feshbach resonance.

Motivation & Objective

• To address the problem of light-induced inelastic losses and heating in optical Feshbach resonance control, which limits practical application in ultracold quantum gases.
• To enable rapid temporal and high-resolution spatial control of interactions in strongly correlated Fermi gases near Feshbach resonances.
• To exploit destructive quantum interference in a two-level system within the closed channel to suppress spontaneous emission while maintaining broad tunability of the scattering length.
• To extend optical control beyond single-field methods by utilizing multiple molecular states in the closed channel for enhanced stability and precision.
• To provide a viable route for studying nonequilibrium dynamics and unstable many-body systems in ultracold Fermi gases with controllable interactions.

Proposed method

• The method uses two optical fields with frequencies ω₁ and ω₂ and Rabi frequencies Ω₁ and Ω₂ to coherently couple two closed-channel molecular states |g₁⟩ and |g₂⟩ to a common excited state |e⟩, forming a dark state via two-photon resonance.
• The Hamiltonian includes hyperfine coupling Vhf between the open-channel triplet state and |g₁⟩, which mediates the magnetic Feshbach resonance, while |g₂⟩ is decoupled from the open channel.
• Destructive quantum interference at the two-photon resonance condition suppresses spontaneous emission from |e⟩, reducing inelastic losses by suppressing population of the excited state.
• The scattering length is tuned by varying the laser frequencies and intensities, enabling wide control over the effective interaction strength.
• The system is modeled using a Fano-like approach to calculate the s-wave scattering length, with the real and imaginary parts derived from the dressed-state spectrum.
• Stimulated Raman adiabatic passage (STIRAP) is enabled by dynamic control of Ω₁ and Ω₂, allowing coherent population transfer between |g₁⟩ and |g₂⟩ for molecular state engineering.

Experimental results

Research questions

• RQ1 Can two-photon quantum interference in a multi-level closed-channel system suppress inelastic losses during optical Feshbach resonance control in ultracold Fermi gases?
• RQ2 How does the inclusion of multiple molecular states in the closed channel enable broader and more stable tuning of the scattering length compared to single-field methods?
• RQ3 What is the role of the dark state in minimizing spontaneous emission while preserving tunability of the interaction strength?
• RQ4 How does the magnetic field dependence of the scattering length change under the dark-state control scheme compared to conventional Autler-Townes splitting?
• RQ5 Can this method be implemented in realistic experimental systems such as 6Li or 85Rb with existing laser and trapping technology?

Key findings

• The dark-state method reduces the spontaneous scattering rate by up to two orders of magnitude compared to single-field control, with loss suppressed by a factor of ~100 at Ω₂ = 3γₑ.
• The scattering length exhibits a three-peak structure in magnetic field, with a narrow central resonance due to the dark state, enabling high-resolution tuning with small field changes.
• For fixed laser parameters, the real part of the scattering length a′/abg shows a broad, tunable resonance, while the imaginary part a′′/abg reveals a narrow central loss peak, characteristic of dark-state suppression.
• In 6Li, the method is feasible using a 673.7 nm laser for the g₁→e transition with Ω₁ ≈ 0.59 MHz per mW/cm² and γₑ ≈ 12 MHz, enabling practical implementation.
• The background scattering length in 6Li is a_bg = -1405 a₀, and the method allows tuning across the Feshbach resonance with minimal loss.
• The technique enables coherent population transfer between |g₁⟩ and |g₂⟩ via STIRAP, which is essential for preparing ro-vibrational ground-state molecules in ultracold Fermi gases.