Chemistry of a Light Impurity in a Bose-Einstein Condensate

Similar to an electron in a solid, an impurity in an atomic Bose-Einstein condensate (BEC) is dressed by excitations from the medium, forming a polaron quasiparticle with modified properties. This impurity can also undergo chemical recombination with atoms from the BEC, a process resonantly enhanced when universal three-body Efimov bound states cross the continuum. To study the interplay between these phenomena, we use a Gaussian state variational method able to describe both Efimov physics and arbitrarily many excitations of the BEC. We show that the polaron cloud contributes to bound state formation, leading to a shift of the Efimov resonance to smaller interaction strengths. This shifted scattering resonance marks the onset of a polaronic instability towards the decay into large Efimov clusters and fast recombination, offering a remarkable example of chemistry in a quantum medium.

Figure 1

Qualitative energy landscape. Illustration of the energy $E$ of an impurity immersed in a BEC as a function of the number of excitations $N_{\mathrm{ex}}$ surrounding it. The local minimum corresponds to the polaron. It is separated by a barrier from states much lower in energy, represented by bound clusters containing a large number of particles. Experimentally, the formation of these clusters leads to fast recombination and loss. The barrier height is dependent on the density of the BEC and the scattering length. The barrier disappears at the density-dependent critical scattering length $a^{*}$, leading to a complete instability of the polaron. The black circle and square are discussed in the context of Fig. 4.

Figure 2

Efimov cluster formation. Contour plot of the binding energy per particle $E/⟨\widehat{N}⟩$ (in units of ${\mathrm{\Lambda }}^2/M$) as a function of the expectation value of the number of particles $⟨\widehat{N}⟩$ and scattering length $a$, for mass ratio $M/m=6/133$. The bold line indicates the critical scattering length $a_c$ at which a bound state first appears. The noninteger particle numbers follow from our variational wave function being a superposition of different particle number eigenstates.

Figure 3

Polaron instability and shifted Efimov scattering resonance. The critical scattering length $a^{*}$ at which the polaron breaks down (black solid) as a function of the mean interparticle distance $n_0^{-1/3}\mathrm{\Lambda }$, for $M/m=6/133$ and $a_B\mathrm{\Lambda }=0.1$. The color map shows the quasiparticle weight $Z$. Dashed lines indicate $Z_{\mathrm{MF}}$ from mean field theory.

Figure 4

Mechanism of the resonance shift. The number of excitations in the polaron cloud $N_{\mathrm{ex}}$ (dashed lines) as a function of scattering length $a\mathrm{\Lambda }$ at various densities $n_0$ (indicated by color). The number of excitations needed to form a bound state with lower energy than the polaron energy is shown using solid lines. Crosses indicate the points at which the polaron destabilizes. Parameters as in Fig. 3.