[Paper Review] Sagnac interferometry based on ultra-slow polaritons in cold atomic vapors

Frank Zimmer, Michael Fleischhauer|CERN Bulletin|Dec 23, 2003

Cold Atom Physics and Bose-Einstein Condensates4 citations

TL;DR

This paper proposes a hybrid Sagnac interferometer that combines the large area of optical gyroscopes with the high rotational sensitivity per unit area of matter-wave gyroscopes by using ultra-slow light in cold atomic vapors via electromagnetically induced transparency (EIT). The momentum transfer from slow light to atoms creates a coherent matter-wave component, enhancing the Sagnac phase shift by up to 10^11 times compared to conventional optical interferometers, especially when atoms are cooled to sub-recoil temperatures.

ABSTRACT

The advantages of light and matter-wave Sagnac interferometers -- large area on one hand and high rotational sensitivity per unit area on the other -- can be combined utilizing ultra-slow light in cold atomic gases. While a group-velocity reduction alone does not affect the Sagnac phase shift, the associated momentum transfer from light to atoms generates a coherent matter-wave component which gives rise to a substantially enhanced rotational signal. It is shown that matter-wave sensitivity in a large-area interferometer can be achieved if an optically dense vapor at sub-recoil temperatures is used. Already a noticeable enhancement of the Sagnac phase shift is possible however with much less cooling requirements.

Motivation & Objective

• To overcome the trade-off between large interferometer area (optical gyroscopes) and high rotational sensitivity per unit area (matter-wave gyroscopes).
• To leverage the coherence and momentum transfer in ultra-slow light propagation via EIT in cold atomic vapors to generate a matter-wave component.
• To demonstrate that ultra-slow light enables a substantial enhancement of the Sagnac phase shift through coherent matter-wave excitation.
• To identify practical limits on group velocity reduction due to absorption and collisional decoherence in atomic samples.
• To determine the cooling requirements necessary to achieve maximal sensitivity enhancement in such a hybrid system.

Proposed method

• Utilizes a ring interferometer with a cold atomic vapor cell or trap attached to a rotating frame, where light propagates along the periphery.
• Employs a Λ-type three-level atomic system with probe and control fields to induce electromagnetically induced transparency (EIT), reducing the group velocity of light.
• Models the system in the rotating frame using a Hamiltonian transformed via the generator of rotation, incorporating angular momentum coupling.
• Derives coupled equations of motion for the probe field and atomic matter-wave components, showing coherent conversion of light to matter waves via momentum transfer.
• Analyzes the Sagnac phase shift including contributions from light propagation, matter-wave motion, and absorption due to atomic velocity distribution.
• Evaluates signal-to-noise ratio limitations using the absorption coefficient κL, derived from atomic temperature, density, and group velocity.

Experimental results

Research questions

• RQ1 Can ultra-slow light in cold atomic vapors be used to create a coherent matter-wave component that enhances rotational sensitivity in a Sagnac interferometer?
• RQ2 What is the maximum achievable enhancement of the Sagnac phase shift in such a hybrid light-matter-wave system compared to conventional optical or matter-wave interferometers?
• RQ3 How do absorption losses and collisional decoherence limit the minimum group velocity (or maximum sensitivity) in this setup?
• RQ4 What cooling temperature is required to achieve the full 10^11-fold sensitivity enhancement predicted by the matter-wave limit?
• RQ5 Does the Sagnac phase shift depend on the group velocity of light in the medium, or is it invariant as in conventional optics?

Key findings

• The Sagnac phase shift is enhanced by the momentum transfer from ultra-slow light to atoms, which generates a coherent matter-wave component that increases rotational sensitivity.
• The maximum sensitivity enhancement of 10^11 is achievable only when the atomic sample is cooled to the recoil temperature or below, corresponding to the matter-wave regime.
• Even with moderate cooling (T ≈ 10^3 T_rec), a few orders of magnitude enhancement over pure optical Sagnac interferometers is possible.
• Absorption losses increase sharply as the group velocity decreases (ξ → 0), limiting the minimum usable group velocity to maintain a signal-to-noise ratio > 1.
• The minimum group velocity is constrained by collisional decoherence: v_gr,min / v_rec ≈ 0.1–10 × √(T/T_rec), depending on atomic density and collision cross-section.
• The system remains robust against phase noise from the atomic velocity distribution as long as the absorption coefficient κL ≤ 1, which sets a practical bound on achievable sensitivity.