Coherent Superposition of Feshbach Dimers and Efimov Trimers

A powerful experimental technique to study Efimov physics at positive scattering lengths is demonstrated. We use the Feshbach dimers as a local reference for Efimov trimers by creating a coherent superposition of both states. Measurement of its coherent evolution provides information on the binding energy of the trimers with unprecedented precision and yields access to previously inaccessible parameters of the system such as the Efimov trimers’ lifetime and the elastic processes between atoms and the constituents of the superposition state. We develop a comprehensive data analysis suitable for noisy experimental data that confirms the trustworthiness of our demonstration.

Figure 1

Illustration of the energy levels and of the interferometer. (a) Dimer (orange) and trimer (blue) energy levels (not to scale) are shown schematically as a function of the inverse scattering length. The grey arrow indicates the parameter regime of our work and illustrates the effect of the modulation pulse. (b),(c) Two pulse sequence results in constructive (b) or destructive (c) interference.

Figure 2

Observation of oscillations. The number of free atoms $N$ after the interferometer sequence is measured as a function of the free evolution time $t$. Each data point is the average of 2–8 measurements and the error bar is $1\sigma$ of the mean error. (a) Data for $t\in [80,220]\mu \mathrm{s}$. Green line indicates the best fit to a cosine Eq. (1). (b) Data for $t\in [240,400]\mu \mathrm{s}$. Red dashed line in (a) and (b) indicates (one and the same) best fit to a damped cosine Eq. (2).

Figure 3

Data analysis using three free parameters. I. The results of a three-parameter fit using the data of Fig. 2 and Eq. (1): (a) $A(\nu )$ and (b) $\phi (\nu )$. Error bars are $1\sigma$ fitting uncertainties and they are also depicted in (c)–(e) as a function of $\nu$. Parameters indicated by the green square are used for the green fit in Fig. 2. II. Same as (I) for the data of Fig. 2.

Figure 4

Data analysis using three free parameters and a damped cosine. Same as Fig. 3, but for the entire data set [Figs. 2 and 2] and using Eq. (2) for the fit. Parameters indicated by the red square are used for the red (dashed) fit in Fig. 2.