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Rydberg impurities control and probe superpositions of Bose-Einstein Condensates

S. Rammohan, Shiva Kant Tiwari, Adya Prasad Mishra, Abhijit Pendse, Anil Kumar Chauhan, Rejish Nath, Alexander Eisfeld, Sebastian Wüster

Published Nov 22, 2020• 0 citations
OpenAlex

Abstract

We show that two major facets of the decoherence paradigm are experimentally accessible for a single impurity atom embedded in a Bose-Einstein condensate, when the impurity is brought into an electronic superposition of two Rydberg states. Not only can the electronic decoherence of the Rydberg atom be read out by microwave interferometry, the platform also provides unique access to the accompanying entangled state of the environment. We theoretically demonstrate signatures of the latter in total atom densities during the transient time in which the impurity is becoming entangled with the medium but the resultant decoherence is not complete yet. The Rydberg impurity thus provides a handle to initiate and read-out mesoscopically entangled superposition states of Bose atom clouds affecting about 500 condensate atoms. We find that the time-scale for its creation and decoherence can be tuned from the order of nanoseconds to microseconds by choice of the excited Rydberg principal quantum number $\nu$, and that Rydberg decoherence dynamics is typically non- Markovian.

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We show that two major facets of the decoherence paradigm are experimentally accessible for a single impurity atom embedded in a Bose-Einstein condensate, when the impurity is brought into an electronic superposition of two Rydberg states. Not only can the electronic decoherence of the Rydberg atom be read out by microwave interferometry, the platform also provides unique access to the accompanying entangled state of the environment. We theoretically demonstrate signatures of the latter in total atom densities during the transient time in which the impurity is becoming entangled with the medium but the resultant decoherence is not complete yet. The Rydberg impurity thus provides a handle to initiate and read-out mesoscopically entangled superposition states of Bose atom clouds affecting about 500 condensate atoms. We find that the time-scale for its creation and decoherence can be tuned from the order of nanoseconds to microseconds by choice of the excited Rydberg principal quantum number ν\nuν, and that Rydberg decoherence dynamics is typically non- Markovian.
Decoherence affects all quantum systems, natural or artificial, and is the primary obstacle impeding quantum technologies. We show theoretically that for a Rydberg q-bit in a Bose condensed environment, experiments can image the system-environment interface that is central for decoherence. High precision absorption images of the condensed environment will be able to capture transient signals that show the real time build up of a mesoscopic entangled state in the environment. This is possible before decoherence sources other than the condensate itself can kick in, since q-bit decoherence time-scales can be tuned from the order of nanoseconds to microseconds by choice of the excited Rydberg principal quantum number ν\nuν. Imaging the interface will allow detailed explorations of open quantum system concepts and may offer guidance for coherence protection in challenging scenarios with non-Markovian environments.
Decoherence affects all quantum systems, natural or artificial, and is the primary obstacle impeding quantum technologies. We show theoretically that for a Rydberg qubit in a Bose condensed environment, experiments can image the system-environment interface that is central for decoherence. High-precision absorption images of the condensed environment will be able to capture transient signals that show the real-time buildup of a mesoscopic entangled state in the environment. This is possible before decoherence sources other than the condensate itself can kick in, since qubit decoherence timescales can be tuned from the order of nanoseconds to microseconds by a choice of the excited Rydberg principal quantum number $\ensuremath{\nu}$. Imaging the interface will allow detailed explorations of open quantum system concepts and may offer guidance for coherence protection in challenging scenarios with non-Markovian environments.
Experiments have demonstrated that the excitation of atoms embedded in a Bose-Einstein condensate to Rydberg states is accompanied by phonon creation. Here we provide the theoretical basis for the description of phonon-induced decoherence of the superposition of two different Rydberg states. To this end, we determine Rydberg-phonon coupling coefficients using a combination of analytical and numerical techniques. From these coefficients, we calculate bath correlation functions, spectral densities, and reorganization energies. These quantities characterize the influence of the environment and form essential inputs for followup open quantum system approaches. We find that the amplitude of bath correlations scales like the power law ${\ensuremath{\nu}}^{\ensuremath{-}6}$ with the principal quantum number $\ensuremath{\nu}$, while reorganization energies scale exponentially, reflecting the extreme tunability of Rydberg atomic properties.
We show how the phase profile of Bose-Einstein condensates can be engineered through its interaction with localized Rydberg excitations. The interaction is made controllable and long range by off-resonantly coupling the condensate to another Rydberg state with laser light. Our technique allows the mapping of entanglement generated in systems of few strongly interacting Rydberg atoms onto much larger atom clouds in hybrid setups. As an example we discuss the creation of a spatial mesoscopic superposition state from a bright soliton. Additionally, the phase imprinted onto the condensate using the Rydberg excitations is a diagnostic tool for the latter. For example, a condensate time-of-flight image would permit reconstructing the pattern of an embedded Rydberg crystal.
Abstract Recent experiments with Bose–Einstein condensates have entered a regime in which thousands of ground-state condensate atoms fill the Rydberg-electron orbit. After the excitation of a single atom into a highly excited Rydberg state, scattering off the Rydberg electron sets ground-state atoms into motion, such that one can study the quantum-many-body dynamics of atoms moving within the Rydberg atom. Here we study this many-body dynamics using Gross–Pitaevskii and truncated Wigner theory. Our simulations focus in particular on the scenario of multiple sequential Rydberg excitations on the same rubidium condensate which has become the standard tool to observe quantum impurity dynamics in Rydberg experiments. We investigate to what extent such experiments can be sensitive to details in the electron–atom interaction potential, such as the rapid radial modulation of the Rydberg molecular potential, or p-wave shape resonance. We demonstrate that both effects are crucial for the initial condensate response within the Rydberg orbit, but become less relevant for the density waves emerging outside the Rydberg excitation region at later times. Finally we explore the local dynamics of condensate heating. We find that it provides only minor corrections to the mean-field dynamics. Combining all these insights, our results suggest Bose–Einstein condensates as a viable platform for the in situ and real time interrogation of ultra-cold chemistry dynamics involving Rydberg states.
Rydberg atoms immersed in a Bose-Einstein condensate interact with the quantum gas via electron-atom and ion-atom interaction. To suppress the typically dominant electron-neutral interaction, Rydberg states with a principal quantum number up to n=190 are excited from a dense and tightly trapped micron-sized condensate. This allows us to explore a regime where the Rydberg orbit exceeds the size of the atomic sample by far. In this case, a detailed line shape analysis of the Rydberg excitation spectrum provides clear evidence for ion-atom interaction at temperatures well below a microkelvin. Our results may open up ways to enter the quantum regime of ion-atom scattering for the exploration of charged quantum impurities and associated polaron physics.