Non-Markovian polaron dynamics in a trapped Bose-Einstein condensate

Abstract

We study the dynamics of an impurity embedded in a trapped Bose-Einstein condensate, i.e. the Bose polaron problem. This problem is treated by recalling open quantum systems techniques: the impurity corresponds to a particle performing quantum Brownian motion, while the excitation modes of the gas play the role of the environment. It is crucial that the model considers a parabolic trapping potential to resemble the experimental conditions. Thus, we detail here how the formal derivation changes due to the gas trap, in comparison to the homogeneous gas. More importantly, we elucidate all aspects in which the gas trap plays a relevant role, with an emphasis in the enhancement of the non-Markovian character of the dynamics. We first find that the presence of a gas trap leads to a new form of the bath-impurity coupling constant and a larger degree in the super-ohmicity of the spectral density. We then solve the quantum Langevin equation to derive the position and momentum variances of the impurity, where the former is a measurable quantity. For the particular case of an untrapped impurity, the asymptotic behaviour of this quantity is found to be motion superdiffusive. When the impurity is trapped, we find position squeezing, casting the system suitable for implementing quantum metrology and sensing protocols. We detail how both super-diffusion and squeezing can be enhanced or inhibited by tuning the Bose-Einstein condensate trap frequency. Compared to the homogeneous gas case, the form of the bath-impurity coupling constant changes, and this is manifested as a different dependence of the system dynamics on the past history. To quantify this, we introduce several techniques to compare the different amount of memory effects arising in the homogeneous and inhomogeneous gas. We find that it is higher in the second case. This analysis paves the way to the study of non-Markovianity in ultracold gases, and the possibility to exploit such a property in the realization of new quantum devices. arXiv:1803.08946v2 [cond-mat.quant-gas]

Critical slowdown of non-equilibrium polaron dynamics

“…The properties of the Bose polaron is arguably closer to the generic solid-state polaron, since the surrounding BEC has a linear low energy dispersion in analogy with acoustic phonons in a solid. While most of previous efforts have been directed towards the equilibrium properties of the Bose polaron, its dynamics has spawned theoretical work only recently [31][32][33][34][35][36], predicting the formation of phonon-impurity bound states for strongly interacting systems [31] and studying trajectories and momentum relaxation of moving impurities [32][33][34][35], as well as the dynamics of phonon dressing in spinor condensates [36].…”

Fate of the Bose polaron at finite temperature

“…(a) Impurity spectral function at unitarity produced by the three-body ansatz(37) with m = mB, n 1/3 R * = 0.02, and σ = 0.4n 2/3 /mB. Only the energy range around the attractive polaron is plotted.…”

“…(b) Slices through the spectrum (a) at several low temperatures, with a narrower broadening of σ = 0.05n 2/3 /mB. Impurity spectral function at unitarity produced by the three-body ansatz(37) with m/mB → ∞, n 1/3 R * = 0.02, and σ = 0.05n 2/3 /mB. The orange dashed lines are the predicted energies (46) from a low-temperature analysis.…”

Heat current control in trapped Bose–Einstein Condensates

“…(i) Linearization of the impurity-bath coupling, which is achieved by assuming that the impurity is in the middle of its corresponding trap (see equation (6)). This in practice imposes a restriction on the maximum temperature we can consider [35]…”

“…We emphasize that the state of the system-bath is assumed to be a product state as in (35). Hence the average is taken over the thermal state of the bath, while the state of the system is assumed to have reached its unique equilibrium state by considering the long-time, steady state limit  ¥ t which is equivalent to consider that w L L  , L R .…”