Feshbach resonances and transition rates for cold homonuclear collisions betweenK39andK41

Abstract

We report results from close-coupling calculations for homonuclear ultracold collisions between potassium atoms, using the most up-to-date Born-Oppenheimer potential curves. The present study includes both of the bosonic isotopes 39 K and 41 K. The s-wave scattering lengths as functions of the magnetic field strength for collisions between atoms in identical and different hyperfine states are obtained. Several Feshbach resonances are located and characterized for both isotopes. Comparison with experiments, where such data are available, show excellent agreement. We also study weakly bound molecular states of the K 2 molecule in close relation to the calculated Feshbach resonances. Another objective of the present work is to study inelastic collisions in which the hyperfine states of the colliding atoms are changed. From this type of calculation we obtain transition rates as functions of the magnetic field strength. Finally, we discuss how such transition rates might be of importance for experimental work.

Quantum Mechanical Stabilization of a Collapsing Bose-Bose Mixture

“…A very promising candidate is the mixture of the second and third lowest hyperfine states, F = 1, m F = 0 (state 1) and F = 1, m F = −1 (state 2), of 39 K. The corresponding scattering lengths a ij as functions of the magnetic field have been studied theoretically [23,24] and experimentally [23]. In particular, the condition a 12 = − √ a 11 a 22 is satisfied at B 0 ≈ 56.77G where a 11 ≈ 84.3a Bohr , a 22 ≈ 33.5a Bohr , and the quantity ∂(a 12 + √ a 11 a 22 )/∂B ≈ 12.09a Bohr /G.…”

Three-Body Interacting Bosons in Free Space

“…However, they should be very close in absolute values and have opposite signs: a ↑↑ > 0 and a ↑↓ = −a ↑↑ (1 + 2ξ). Lysebo and Veseth [49] predict rich possibilities for tuning interactions in between various hyperfine states of 39 K. In particular, states F = 1, m F = 0 and F = 1, m F = −1 in the magnetic field region from 50 to 60 Gauss can potentially give the desired effect, but one has to generalize the above theory to the case a ↑↑ = a ↓↓ .…”

Two- and three-body contacts in the unitary Bose gas

“…On resonance a diverges and one reaches the unitary regime, in which the interactions are as strong as allowed by quantum mechanics. This regime has been extensively studied in Fermi gases [2][3][4], while the unitary Bose gas represents a new experimental frontier [5][6][7][8][9][10].In these systems, universal properties of the short-range particle correlations imply universal thermodynamic relations between macroscopic observables such as the momentum distribution, energy, and the spectroscopic response [11][12][13][14][15][16][17][18][19]. In the case of (mass-balanced) two-component Fermi gases, at the heart of these relations is a single fundamental thermodynamic parameter, the two-body contact density C 2 , which measures the strength of two-particle correlations.…”

“…We tune the ↑↑ scattering length a using a Feshbach resonance centred on B 0 = 402.70(3) G [31]. In all our experiments |a| > 300 a 0 while the moduli of the ↑↓ and ↓↓ scattering lengths are < 10 a 0 [32], where a 0 is the Bohr radius. Near B 0 the bare splitting of the ↑ and ↓ states is ≈ 99 MHz.…”

“…On resonance a diverges and one reaches the unitary regime, in which the interactions are as strong as allowed by quantum mechanics. This regime has been extensively studied in Fermi gases [2][3][4], while the unitary Bose gas represents a new experimental frontier [5][6][7][8][9][10].…”