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arXiv:1012.3813 · Physical Review A

Long-lived periodic revivals of coherence in an interacting Bose-Einstein condensate

M. V. Egorov, R. P. Anderson, Valentin Ivannikov, Bogdan Opanchuk, P. D. Drummond, B. V. Hall, Andrei I. Sidorov

Published Aug 22, 2011• 64 citations
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Abstract

We observe the coherence of an interacting two-component Bose-Einstein condensate (BEC) surviving for seconds in a trapped Ramsey interferometer. Mean-field-driven collective oscillations of two components lead to periodic dephasing and rephasing of condensate wave functions with a slow decay of the interference fringe visibility. We apply spin echo synchronous with the self-rephasing of the condensate to reduce the influence of state-dependent atom losses, significantly enhancing the visibility up to $0.75$ at the evolution time of $1.5$ s. Mean-field theory consistently predicts higher visibility than experimentally observed values. We quantify the effects of classical and quantum noise and infer a coherence time of $2.8$ s for a trapped condensate of $5.5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ interacting atoms.

DOI
10.1103/physreva.84.021605

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The quantum coherence of a Bose-Einstein condensate is studied using the concept of quantum fidelity (Loschmidt echo). The condensate is confined in an elongated anharmonic trap and subjected to a small random potential such as that created by a laser speckle. Numerical experiments show that the quantum fidelity stays constant until a critical time, after which it drops abruptly over a single trap oscillation period. The critical time depends logarithmically on the number of condensed atoms and on the perturbation amplitude. This behavior may be observable by measuring the interference fringes of two condensates evolving in slightly different potentials.

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We observe the coherence of an interacting two-component Bose-Einstein condensate (BEC) surviving for seconds in a trapped Ramsey interferometer. Mean-field-driven collective oscillations of two components lead to periodic dephasing and rephasing of condensate wave functions with a slow decay of the interference fringe visibility. We apply spin echo synchronous with the self-rephasing of the condensate to reduce the influence of state-dependent atom losses, significantly enhancing the visibility up to 0.750.750.75 at the evolution time of 1.51.51.5 s. Mean-field theory consistently predicts higher visibility than experimentally observed values. We quantify the effects of classical and quantum noise and infer a coherence time of 2.82.82.8 s for a trapped condensate of 5.5\ifmmode×\else\texttimes\fi1045.5\ifmmode\times\else\texttimes\fi{}{10}^{4}5.5\ifmmode×\else\texttimes\fi104 interacting atoms.
Ultracold atoms and Bose-Einstein condensates represent a burgeoning and ever exciting area of research which has produced numerous breakthroughs in the last 15 years. Ultracold atoms at nano-Kelvin temperatures, isolated in atom traps from the hot, room temperature environment, exhibit ultimate quantum properties and can serve as pure samples for testing quantum mechanics and performing precision measurements. The research described in this thesis investigates, both theoretically and experimentally, the coherence and dynamical evolution of a two-component Bose-Einstein condensate (BEC). The studies are performed on the |1 › ≡ F = 1,mF = −1 › and |2 › ≡ |F = 2,mF = +1 › hyperfine ground states of a 87Rb BEC trapped on an atom chip. Conventional understanding has been that the fringe contrast in interferometric experiments on a BEC is limited by the mean-field dephasing due to strong interatomic interactions which lead to inhomogeneous collisional shifts. We have discovered using Ramsey interferometry a mean-field driven self-rephasing effect in a trapped twocomponent BEC. When combined with a spin-echo technique, we find that the selfrephasing leads to a coherence time of 2.8 s, the longest ever recorded for an interacting BEC. Secondly, we have developed a new technique based on periodic collective oscillations for precision measurements of the interspecies and intraspecies scattering lengths and derived an analytic mean-field theory for the phase and density dynamics in the twocomponent BEC. This technique has been applied to the measurements of the scattering lengths for the two components, |1i and |2i, in 87Rb with a precision of 0.016%. Additionally, the two-body loss coefficients for these states have been measured. Thirdly, we have developed and applied a new, interferometric method for calibrating the detection system, in order to determine the total atom number precisely for Ramsey interferometric measurements. The calibration coefficient is found to be in a good agreement with that obtained using a conventional calibration technique based on the critical BEC temperature. Finally, we have detected predicted RF-induced Feshbach resonances by monitoring changes in the two-body loss coefficients in the two-component BEC. Conventional Feshbach resonances have been used in many works to tune the s-wave interactions; however, there is no achievable magnetic Feshbach resonance for magnetically trappable states of 87Rb. The RF-induced resonances which we have detected can provide a way to tune the scattering lengths which is important for interferometry and entanglement experiments. The positions of the resonances may provide useful information for predicting the atomic scattering properties of 87Rb.
In our original paper (Altin et al 2011 New J. Phys. 13 065020), we presented the results from a Ramsey atom interferometer operating with an optically trapped sample of up to 10 6 Bose-condensed 87 Rb atoms in the m F = 0 clock states. We were unable to observe projection noise fluctuations on the interferometer output, which we attribute to the stability of our microwave oscillator and background magnetic field. Numerical simulations of the Gross–Pitaevskii equations for our system show that dephasing due to spatial dynamics driven by interparticle interactions accounts for much of the observed decay in fringe visibility at long interrogation times. The simulations show good agreement with the experimental data when additional technical decoherence is accounted for, and suggest that the clock states are indeed immiscible. With smaller samples of 5 × 10 4 atoms, we observe a coherence time of τ = 1.0 +0.5 −0.3 s.
We investigate fidelity for the quantum evolution of a Bose-Einstein condensate (BEC) and reveal its general property with a simple two-component BEC model. We find that, when the initial state is a coherent state, the fidelity decays with time in the ways of exponential, Gaussian, and power law, depending on the initial location, the perturbation strength, as well as the underlying mean-field classical dynamics. In this case we find a clear correspondence between the fast quantum fidelity decay and the dynamical instability of the mean-field system. With the initial state prepared as a maximally entangled state, we find that the behavior of fidelity has no classical correspondence and observe an interesting behavior of the fidelity: periodic revival, where the period is inversely proportional to the number of bosons and the perturbation strength. An experimental observation of the fidelity decay is suggested.
We investigate the coherence dynamics of a two-mode Bose-Einstein condensate coupled with the environment in the mean-field approximation. We give an analytical result of the time-average coherence in the absence of system-environment coupling, and find that the time-average coherence attains its maximum value at the critical point which corresponds to the boundary between the self-trapping regime and the Josephson oscillation regime. The effect of noise on dynamical coherence is also considered by analyzing the couplings of the condensate to the environment. With the first kind of coupling, the coherence finally stabilizes at a fixed value. Meanwhile, we show that the presence of the noise can even enhance the coherence for some particular interaction. With the second kind of coupling as collisional dephasing, the noise leads a sudden transition of the coherence which then subjects to an exponential decay.
The quantum coherence of a Bose-Einstein condensate is studied using the concept of quantum fidelity (Loschmidt echo). The condensate is confined in an elongated anharmonic trap and subjected to a small random potential such as that created by a laser speckle. Numerical experiments show that the quantum fidelity stays constant until a critical time, after which it drops abruptly over a single trap oscillation period. The critical time depends logarithmically on the number of condensed atoms and on the perturbation amplitude. This behavior may be observable by measuring the interference fringes of two condensates evolving in slightly different potentials.