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arXiv:1809.02919 · Journal of Physics B Atomic Molecular and Optical Physics

Phase diffusion in trapped-atom interferometers

Valentin Ivannikov, Andrei I Sidorov

Published Sep 7, 2018• 6 citations
arXivHTMLPDF

Abstract

Abstract We evaluate the performance and phase diffusion of trapped 87 Rb atoms in an atom chip sensor with Ramsey interferometry and Hahn’s spin echo in the time and phase domains. We trace out how the phase uncertainty of interference fringes grows with time. The phase-domain spin echo enables us to measure many-second-long phase diffusion with a low-cost local oscillator that otherwise seems unrealistic to obtain with such an oscillator. In the Ramsey experiment we record interference fringes with contrast decaying in 12 s, and with a frequency uncertainty of 80 mHz corresponding to the dephasing time of 2.8 s. A clear distinction is drawn between the decoherence of the atomic ensemble, and the dephasing originating from the local oscillator. Spin echo cancels most of the perturbations affecting the Ramsey experiments, and leaves the residual phase noise of only 19 mHz mostly attributed to the local oscillator frequency instability, yielding the increased coherence time of 11.9 s which coincides with the contrast decay time in the Ramsey sequence. A number of perturbation sources leading to homogeneous and inhomogeneous dephasing is discussed. Our atom chip sensor is useful in probing fundamental interactions, atomtronics, microcantilever, and resonant cavity profiling in situ .

DOI
10.1088/1361-6455/aadfca

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•Jan 1, 2012•2 citations
Abstract We evaluate the performance and phase diffusion of trapped 87 Rb atoms in an atom chip sensor with Ramsey interferometry and Hahn’s spin echo in the time and phase domains. We trace out how the phase uncertainty of interference fringes grows with time. The phase-domain spin echo enables us to measure many-second-long phase diffusion with a low-cost local oscillator that otherwise seems unrealistic to obtain with such an oscillator. In the Ramsey experiment we record interference fringes with contrast decaying in 12 s, and with a frequency uncertainty of 80 mHz corresponding to the dephasing time of 2.8 s. A clear distinction is drawn between the decoherence of the atomic ensemble, and the dephasing originating from the local oscillator. Spin echo cancels most of the perturbations affecting the Ramsey experiments, and leaves the residual phase noise of only 19 mHz mostly attributed to the local oscillator frequency instability, yielding the increased coherence time of 11.9 s which coincides with the contrast decay time in the Ramsey sequence. A number of perturbation sources leading to homogeneous and inhomogeneous dephasing is discussed. Our atom chip sensor is useful in probing fundamental interactions, atomtronics, microcantilever, and resonant cavity profiling in situ .
We have demonstrated a novel atom interferometer which uses a free oscillation of 87Rb BEC atoms in a magnetic harmonic potential on an atom chip. This interferometer can effectively suppress the dephasing due to the trap potential by applying two Bragg laser pulses with an time interval T equal to the oscillation period of the axial mode of the magnetic trap. We observed a high contrast (~30 %) interference fringe signal for T = 58 ms. When we increased the time interval T to 97 ms, an interference fringe was washed out by the random phase fluctuation. We attributed this phase fluctuation to the external vibrational noise from the floor.
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 perform Ramsey interferometry on an ultracold ^{87}Rb ensemble confined in an optical dipole trap. We use a π pulse set at the middle of the interferometer to restore the coherence of the spin ensemble by canceling out phase inhomogeneities and creating a spin echo in the contrast. However, for high atomic densities, we observe the opposite behavior: the π pulse accelerates the dephasing of the spin ensemble leading to a faster contrast decay of the interferometer. We understand this phenomenon as a competition between the spin-echo technique and an exchange-interaction driven spin self-rephasing mechanism based on the identical spin rotation effect. Our experimental data are well reproduced by a numerical model.
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 $5.5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ interacting atoms.
We present a compact atomic clock interrogating ultracold 87Rb magnetically trapped on an atom chip. Very long coherence times sustained by spin self-rephasing allow us to interrogate the atomic transition with 85% contrast at 5 s Ramsey time. The clock exhibits a fractional frequency stability of 5.8×10−135.8\times 10^{-13}5.8×10−13 at 1 s and is likely to integrate into the 1×10−151\times10^{-15}1×10−15 range in less than a day. A detailed analysis of 7 noise sources explains the measured frequency stability. Fluctuations in the atom temperature (0.4 nK shot-to-shot) and in the offset magnetic field (5×10−65\times10^{-6}5×10−6 relative fluctuations shot-to-shot) are the main noise sources together with the local oscillator, which is degraded by the 30% duty cycle. The analysis suggests technical improvements to be implemented in a future second generation set-up. The results demonstrate the remarkable degree of technical control that can be reached in an atom chip experiment.
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.