[Paper Review] First observation of feshbach resonances at very low magnetic field in a 133Cs fountain

H. Marion, S. Bize+10 more|ArXiv.org|Jul 13, 2004

Cold Atom Physics and Bose-Einstein Condensates4 citations

TL;DR

This paper reports the first observation of Feshbach resonances in a 133Cs atomic fountain at extremely low magnetic fields (5 ± 1 mG, corresponding to ~500 ± 100 nK), achieved using adiabatic passage to prepare controlled atomic samples. The study reveals collision-induced frequency shifts dominated by the βγ channel, with precise constraints on magnetic field and collision parameters, enabling sub-10⁻¹⁶ uncertainty in primary frequency standards.

ABSTRACT

One of the main limitations of cesium atomic fountains has been the cold collision frequency shift. By using a method based on a transfer of population by adiabatic passage allowing to prepare cold atomic samples with a well defined ratio of atomic density as well as atom number the collisional shift is controlled at the 10E-3 of its value. A calibration of Zeeman sub-states contribution to the clock shift as a function of the field has been performed. Feshbach resonances have been observed for the first time at very low magnetic field and with a very good resolution. A Monte Carlo simulation has been performed and could fit properly some of experimental data. This constrains some parameters of the theory of collisions.

Motivation & Objective

• To control and measure cold collision shifts in cesium atomic fountains, a major source of uncertainty in primary frequency standards.
• To observe Feshbach resonances at very low magnetic fields, previously unexplored in cesium fountains.
• To use adiabatic passage to prepare atomic samples with well-defined density and atom number for precise collision measurements.
• To constrain theoretical parameters of cold collisions in 133Cs using experimental data and Monte Carlo simulations.
• To achieve sub-10⁻¹⁶ uncertainty in atomic clocks by suppressing collisional shifts through magnetic field tuning.

Proposed method

• Adiabatic passage (AP) was employed to prepare cold atomic samples with controlled density and atom number, minimizing shot noise and enabling precise measurement of collision shifts.
• A double atomic fountain at the Paris Observatory was used, with improved 2D optical molasses for transverse beam collimation, increasing loading rate by a factor of ~10.
• A sapphire cryogenic oscillator (SCO) provided ultra-stable microwave signals with phase noise below 5×10⁻¹⁶ at 1 s, enhancing frequency stability.
• Differential measurements alternated high (Nₐₜ) and low (Nₐₜ/2) atom number configurations to isolate collisional shifts.
• Monte Carlo simulations modeled the velocity and density distribution, fitting the observed resonance shapes to extract parameters like B₀, Δμ, Cₑ, and Γᵢ.
• Theoretical modeling of Feshbach resonances included energy distribution effects and inelastic loss rates (Γᵢ), with resonance condition defined by vanishing energy difference between molecular bound state and continuum.

Experimental results

Research questions

• RQ1 What is the lowest magnetic field at which Feshbach resonances can be observed in a 133Cs atomic fountain?
• RQ2 How do collisional shifts in cesium fountains depend on magnetic field and atomic density, and can they be precisely controlled?
• RQ3 To what extent do inelastic processes (Γᵢ) and velocity distributions affect the observed resonance shape and position?
• RQ4 Which hyperfine channel (αγ or βγ) dominates the Feshbach resonance in the |m_F|=3 state, and how does this affect the clock shift sign?
• RQ5 Can the background scattering length be reliably extracted when including linear and quadratic field-dependent terms?

Key findings

• The first observation of Feshbach resonances in 133Cs at magnetic fields as low as 5 ± 1 mG (500 ± 100 nK) was achieved, representing the lowest energy molecular bound state observed in such resonances to date.
• The resonance in the |m_F|=3 state is dominated by the βγ channel involving the |4;0⟩ and |3;3⟩ states, with the clock shift sign inverted relative to the αγ channel.
• The background scattering length was found to be insensitive to small magnetic field variations, with no significant linear or quadratic field dependence detected within the measurement uncertainty.
• The effective collision energy parameter Cₑ was constrained to ~0.2×E_rec/k_rec, indicating that the resonance width is primarily determined by the atomic velocity distribution at low Cₑ.
• The inelastic loss rate Γᵢ was found to be ≤0.2×E_rec, suggesting minimal impact of inelastic processes on the observed resonance shape.
• The magnetic field at resonance, B₀ = 5 ± 1 mG, is tightly constrained and well-decorrelated from other parameters, enabling precise control of collision shifts.