Abstract
We consider the dephasing of two internal states |0⟩ and |1⟩ of a trapped impurity atom, a so-called atomic quantum dot (AQD), where only state |1⟩ couples to a Bose–Einstein condensate (BEC). A direct relation between the dephasing of the internal states of the AQD and the temporal phase fluctuations of the BEC is established. Based on this relation we suggest a scheme to probe BEC phase fluctuations non-destructively via dephasing measurements of the AQD. In particular, the scheme allows to trace the dependence of the phase fluctuations on the trapping geometry of the BEC.
Highlights
The coherence properties of Bose–Einstein condensates (BECs) have attracted considerable theoretical and experimental interest since the first experimental realization of BECs in trapped ultracold clouds of alkali atoms [1, 2]
We propose a scheme to measure temporal phase fluctuations of the BEC based on a single trapped impurity atom coupled to the BEC, hereafter called an atomic quantum dot (AQD) [10]
By identifying the combined system of the AQD and the BEC with an exactly solvable independent boson model [16]–[18], we show that the dephasing of the internal states due to the asymmetric interaction with the BEC is directly related to the temporal phase fluctuations
Summary
The coherence properties of Bose–Einstein condensates (BECs) have attracted considerable theoretical and experimental interest since the first experimental realization of BECs in trapped ultracold clouds of alkali atoms [1, 2]. We propose a scheme to measure temporal phase fluctuations of the BEC based on a single trapped impurity atom coupled to the BEC, hereafter called an atomic quantum dot (AQD) [10]. We consider an AQD with two internal states |0 and |1 , where we assume for simplicity that only state |1 undergoes collisional (s-wave scattering) interactions with the BEC This set-up could be implemented using spin-dependent optical potentials [11], where the impurity atom, trapped separately [12]–[14], and the BEC atoms correspond to different internal atomic states. By identifying the combined system of the AQD and the BEC with an exactly solvable independent boson model [16]–[18], we show that the dephasing of the internal states due to the asymmetric interaction with the BEC is directly related to the temporal phase fluctuations.
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