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arXiv:1802.08702 · Physical Review Letters

Quantum Spin Dynamics of Individual Neutral Impurities Coupled to a Bose-Einstein Condensate

Felix Schmidt, Daniel Mayer, Quentin Bouton, Daniel Adam, Tobias Lausch, Nicolas Spethmann, Artur Widera

Published Sep 25, 2018• 63 citations
arXivHTMLPDF

Abstract

We report on spin dynamics of individual, localized neutral impurities immersed in a Bose-Einstein condensate. Single cesium atoms are transported into a cloud of rubidium atoms and thermalize with the bath, and the ensuing spin exchange between localized impurities with quasispin F_{i}=3 and bath atoms with F_{b}=1 is resolved. Comparing our data to numerical simulations of spin dynamics, we find that, for gas densities in the Bose-Einstein condensate regime, the dynamics is dominated by the condensed fraction of the cloud. We spatially resolve the density overlap of impurities and gas by the spin population of impurities. Finally, we trace the coherence of impurities prepared in a coherent superposition of internal states when coupled to a gas of different densities. For our choice of states, we show that, despite high bath densities and, thus, fast thermalization rates, the impurity coherence is not affected by the bath, realizing a regime of sympathetic cooling while maintaining internal state coherence. Our work paves the way toward the nondestructive probing of quantum many-body systems via localized impurities.

DOI
10.1103/physrevlett.121.130403

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We report on spin dynamics of individual, localized neutral impurities immersed in a Bose-Einstein condensate. Single cesium atoms are transported into a cloud of rubidium atoms and thermalize with the bath, and the ensuing spin exchange between localized impurities with quasispin F_{i}=3 and bath atoms with F_{b}=1 is resolved. Comparing our data to numerical simulations of spin dynamics, we find that, for gas densities in the Bose-Einstein condensate regime, the dynamics is dominated by the condensed fraction of the cloud. We spatially resolve the density overlap of impurities and gas by the spin population of impurities. Finally, we trace the coherence of impurities prepared in a coherent superposition of internal states when coupled to a gas of different densities. For our choice of states, we show that, despite high bath densities and, thus, fast thermalization rates, the impurity coherence is not affected by the bath, realizing a regime of sympathetic cooling while maintaining internal state coherence. Our work paves the way toward the nondestructive probing of quantum many-body systems via localized impurities.
Recent studies on the dynamics of single, neutral impurities immersed in an ultracold gas are reviewed. This paradigmatic model system is realized by the controlled doping of single Caesium atoms into an ultracold Rubidium gas. Interaction between the impurity and the gas in both the motional and internal degrees of freedom is studied for a broad range of bath temperatures in the thermal and quantum‐degenerate regime. Tracing single‐atom diffusion it is found that, even for a granular bath, where the assumption of a continuous medium is not fulfilled, a modified Langevin equation yields excellent predictions for tracer diffusion. Numerical modeling of impurity dynamics in a three‐dimensional superfluid bath shows the emergence of a prethermalized state for intermediate times due to the existence of a superfluid critical momentum, while for lower dimensions the effect of thermal phonons dominates and obstructs the formation of such nonthermal states. Finally, unleashing the quasi‐spin degree of freedom, the authors observe and control spin‐exchange dynamics between individual impurities and the bath. Moreover, a regime of sympathetic impurity cooling is realized, where the internal‐state coherence of the impurity is preserved. In the future, control over the motional and spin‐degree of freedom will enable using individual impurities as thermalized, localized, minimally invasive quantum probes for a quantum fluid.
Abstract We report on the experimental doping of a 87 Rubidium (Rb) Bose–Einstein condensate (BEC) with individual neutral 133 Cesium (Cs) atoms. We discuss the experimental tools and procedures to facilitate Cs-Rb interaction. First, we use degenerate Raman side-band cooling of the impurities to enhance the immersion efficiency for the impurity in the quantum gas. We identify the immersed fraction of Cs impurities from the thermalization of Cs atoms upon impinging on a BEC, where elastic collisions lead to a localization of Cs atoms in the Rb cloud. Second, further enhancement of the immersion probability is obtained by localizing the Cs atoms in a species-selective optical lattice and a subsequent transport into the Rb cloud. Here, impurity-BEC interaction is monitored by position and time-resolved three-body loss of Cs impurities immersed into the BEC. This combination of experimental methods allows for the controlled doping of a BEC with neutral impurity atoms, paving the way to impurity aided probing and coherent impurity-quantum bath interaction.
We discuss the quench dynamics of an isolated system composed of a single spinful impurity in the transverse Rabi field and bath of non-interacting three- and two-dimensional bosons. Specifically, we consider the evolution of bosons and a spin-12\frac{1}{2}21​ particle, initially prepared in a Bose-Einstein condensate state and a magnetic ground state, respectively, with the spin-dependent contact boson-impurity interaction switched on. Applying an original mean-field-like approximation, which naturally reflects the statistical effects of the bosonic bath, we calculate time-dependent components of the average impurity spin and the overlap of the wave function between initial and arbitrary time moments. A key prediction is a substantial speed-up in the decoherence (thermalization) dynamics of the spin degree of freedom compared to results obtained with the Chevy-like ansatz.
We unravel the nonequilibrium dynamics of two fermionic impurities immersed in a one-dimensional bosonic gas following an interspecies interaction quench. Monitoring the temporal evolution of the single-particle density of each species we reveal the existence of four distinct dynamical regimes. For weak interspecies repulsions both species either perform a breathing motion or the impurity density splits into two parts which interact and disperse within the bosonic cloud. Turning to strong interactions we observe the formation of dark-bright states within the mean-field approximation. However, the correlated dynamics shows that the fermionic density splits into two repelling density peaks which either travel toward the edges of the bosonic cloud where they equilibrate or they approach an almost steady state propagating robustly within the bosonic gas which forms density dips at the same location. For these strong interspecies interactions an energy transfer process from the impurities to their environment occurs at the many-body level, while a periodic energy exchange from the bright states (impurities) to the bosonic species is identified in the absence of correlations. Finally, inspecting the one-body coherence function for strong interactions enables us to draw conclusions on the spatial localization of the quench-induced fermionic density humps.
Quantum probes are atomic sized devices mapping information of their environment to quantum-mechanical states. By improving measurements and at the same time minimizing perturbation of the environment, they form a central asset for quantum technologies. We realize spin-based quantum probes by immersing individual Cs atoms into an ultracold Rb bath. Controlling inelastic spin-exchange processes between the probe and bath allows us to map motional and thermal information onto quantum-spin states. We show that the steady-state spin population is well suited for absolute thermometry, reducing temperature measurements to detection of quantum-spin distributions. Moreover, we find that the information gain per inelastic collision can be maximized by accessing the nonequilibrium spin dynamic. Keeping the motional degree of freedom thermalized, individual spin-exchange collisions yield information about the gas quantum by quantum. We find that the sensitivity of this nonequilibrium quantum probing effectively beats the steady-state Cramér-Rao limit by almost an order of magnitude, while reducing the perturbation of the bath to only three quanta of angular momentum. Our work paves the way for local probing of quantum systems at the Heisenberg limit, and moreover, for optimizing measurement strategies via control of nonequilibrium dynamics. © 2020 authors. Published by the American Physical Society.
The physics of quantum impurities coupled to a many-body environment is among the most important paradigms of condensed-matter physics. In particular, the formation of polarons, quasiparticles dressed by the polarization cloud, is key to the understanding of transport, optical response, and induced interactions in a variety of materials. Despite recent remarkable developments in ultracold atoms and solid-state materials, the direct measurement of their ultimate building block, the polaron cloud, has remained a fundamental challenge. We propose and analyze a platform to probe time-resolved dynamics of polaron-cloud formation with an interferometric protocol. We consider an impurity atom immersed in a two-component Bose-Einstein condensate where the impurity generates spin-wave excitations that can be directly measured by the Ramsey interference of surrounding atoms. The dressing by spin waves leads to the formation of magnetic polarons and reveals a unique interplay between few- and many-body physics that is signified by single- and multi-frequency oscillatory dynamics corresponding to the formation of many-body bound states. Finally, we discuss concrete experimental implementations in ultracold atoms.