Three-body Physics in the Impurity Limit of 39K Bose-Einstein Condensates

TL;DR

This work develops loss spectroscopy to study three-body recombination in a $^{39}$K Bose-Einstein condensate near a Feshbach resonance by exploiting a faster two-body loss channel via an ejection sequence. By reconstructing the medium density from observed losses and spectroscopic signals, the authors extract the impurity–BEC three-body loss coefficient $L_3$ and map its dependence on the scattering length, observing universal $a^4$-type growth with saturation at unitarity. They show consistency between time-resolved reconstruction and spectroscopic density estimates, while revealing additional losses at strong interactions attributable to secondary collisions. A theoretical model incorporating Efimov-inspired contributions and saturation captures the observed $L_3$ behavior, enabling density determinations across interaction strengths and evolution times. The methodology offers a new, quantitative tool for probing collisional physics in strongly interacting ultracold gases and can inform studies of Efimov physics, solitons, and quantum droplets in Bose systems.

Abstract

Loss spectroscopy is a key tool for investigating systems where important system parameters are linked to intrinsic resonant loss processes. We investigate loss processes of impurity atoms embedded in a medium of a Bose-Einstein Condensate close to a Feshbach resonance. In this case, three-body loss processes occur faster than the measurement duration, impeding a direct time-resolved measurement. Here, we discuss how an even faster two-body loss process can be used to probe the system. The time-dependent number of atoms in the medium is reconstructed from such measurements, allowing for the extraction of the three-body loss rate coefficient $L_3$ and its scaling with scattering length. Moreover, the medium atom number is reconstructed from spectroscopic loss measurements. This allows for a comparison of the medium densities based on both the extracted loss rates and the spectroscopically reconstructed atom number. Finally, the number of lost medium atoms per loss event is evaluated and found to exceed 2 at strong interactions, which is attributed to secondary collisions in the medium. These investigations establish the use of a fast loss mechanism as a new tool in the field and provide quantitative measurements of three-body losses at large interaction strengths.

Figures (8)

• Figure 1: Creation and loss measurement in a strongly interacting many-body state. a) The first rf pulse, $\tau$, transfers an admixture of atoms from the BEC state, $\ket{1}$, to the strongly interacting impurity state $\ket{2}$. The most relevant loss between these two states occurs due to three-body recombination between two BEC atoms and one impurity atom. b) The second rf pulse, $\tau_p$, transfers all remaining impurity atoms to the third state, $\ket{3}$. The dominant loss channel between $\ket{1}$ and $\ket{3}$ are two-body spin-exchange collisions.
• Figure 2: a) Overview of the measurement sequence. The two rf pulses are separated by the evolution time, $t_e$, followed by a time $t_o$ until the BEC atom number is observed. During the evolution time, three-body recombination takes place and reduces the number $N$ of BEC atoms. After the second rf probe pulse, two-body collisions take place and further reduce the number of BEC atoms to $N_{obs}$. b) Illustration of the real $N(t)/N_0$ (green solid line) and observed $N_{obs}(t)/N_0$ (red dashed line) medium atom number fractions as a function of the evolution time. The initial atom number is $N_0$ and the assumed impurity fraction is $\chi = 10\%$, leading to the offset value. The green line is the result of pure three-body recombination between medium and impurity atoms. The red dashed line contains the additional loss due to two-body collisions and corresponds to the experimentally observed atom number.
• Figure 3: Observed, $N_\text{obs}(t)/N_0$, (red circles) and reconstructed, $N(t)/N_0$, (gray circles) medium atom number fractions at $a=-200a_0$, fitted with the exponential decay of Eq. \ref{['eq:old_density_obs']} (red dashed line) and the differential equation in Eq. \ref{['eq:Diff_final']} (gray dashed line), respectively. From the latter, the three-body recombination rate coefficient, $L_3$, is extracted.
• Figure 4: Observed medium atom number fraction as a function of the frequency of the ejection probe pulse, $\omega$, relative to the resonance frequency between the $\ket{2}$ and $\ket{3}$ states, $\omega_0$. This spectrum was recorded at an impurity-medium scattering length of $a = -200~a_0$, with impurity fraction $\chi \approx 20\%$, and an evolution time of $t_e = 20$ µs. The observed loss of medium atom numbers is fitted with a Gaussian (solid line). Far off-resonance, the observed loss is due to three-body recombination (dashed line). Close to resonance, the observed loss is a mixture of two-body and three-body losses (dash-dotted line).
• Figure 5: (top) Calculated peak densities for varying evolution time at $1/k_na = -0.35$ using spectroscopic measurements Eq. \ref{['eq:true_atomnumber_ejec']} (blue circles), the loss rate Eq. \ref{['eq:Diff_final']} (green circles), and an empirical method Eq. \ref{['eq:old_density']} (red circles). The densities are only given for the evolution times at which spectroscopic measurements were performed. (bottom) Calculated peak densities for varying interaction strengths at a fixed evolution time of $20$ µs. The result of Eq. \ref{['eq:Diff_final']} (green circles) and Eq. \ref{['eq:old_density']} (red circles) are shown relative to that of Eq. \ref{['eq:true_atomnumber_ejec']} (black dashed line).