In situ Ramsey interferometry and diffraction echo with an atomic Fermi gas

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In situ Ramsey interferometry and diffraction echo with an atomic Fermi gas

C. Marzok, B. Deh, S. Slama, C. Zimmermann, and Ph. W. Courteille

Phys. Rev. A 78, 021602(R) – Published 12 August 2008

Abstract

We report on the observation of Bragg diffraction of a spin-polarized ultracold ${}^{6}{Li}$ Fermi gas and demonstrate a Ramsey-type matter-wave interferometer. Suppression of $s$ -wave collisions by the Pauli principle allows for unperturbed dynamics of the atoms in the trap for longer than $2 s$ . Employing an echo pulse sequence, we observe coherent superpositions of momentum states which do not show any sign of decoherence during the experimentally limited observation time of $100 μ s$ . In contrast, significant decoherence is observed in the presence of a cold cloud of ${}^{87}{Rb}$ atoms. The experiment demonstrates the feasibility of high-resolution atomic interferometry with applications for precision measurements in small volumes and near surfaces.

Received 20 March 2008

DOI:https://doi.org/10.1103/PhysRevA.78.021602

Authors & Affiliations

C. Marzok, B. Deh, S. Slama, C. Zimmermann, and Ph. W. Courteille

Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany

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Issue

Vol. 78, Iss. 2 — August 2008

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Images

Figure 1
(Color online) (a) Time-of-flight absorption images of a $1 μ K$ cold cloud after a single Bragg scattering pulse and a $2 ms$ ballistic expansion period. From top to bottom the Bragg pulse area is varied, $Φ \equiv Ω_{R} τ ∕ 2 π = 0$ , 0.4, and 1. The observed Rabi frequency is $Ω_{R} ∕ 2 π = 58 kHz$ . (b) The black, solid lines show the integration of the time-of-flight absorption images shown in (a) along the radial direction. The red dotted lines show simulations of the axial momentum distributions with no free parameters. (c) False color map of measured momentum distributions for pulse areas varied from 0 to $6 π$ . The radially integrated absorption images appear as rows. (d) False color map of the calculated momentum distributions using the experimental parameters.Reuse & Permissions
Figure 2
(Color online) Periodic revival of the momentum distribution in the trap in the absence (a) and in the presence (b) of ${}^{87}{Rb}$ . The population of the state $2 ℏ q$ is given relative to the total number of atoms in states $0 ℏ q$ and $2 ℏ q$ , denoted $N_{0}$ and $N_{1}$ , respectively. Neighboring peaks are separated by a full trap period. The dashed line gives an array of Gaussian functions, whose amplitudes are decreasing exponentially in time. The fits to the data yield the decay times of $2.4 s$ for (a) and $0.15 s$ for (b). The oscillation frequency is $ω_{z} ∕ 2 π = 142.51 Hz$ and the Rabi frequency $Ω_{R} ∕ 2 π = 58 kHz$ .Reuse & Permissions
Figure 3
(Color online) (a),(b) Time-of-flight absorption images taken after a Ramsey pulse sequence and (c),(d) their radial integrations (black solid line). The times between the Ramsey pulse are (a),(c) $6 μ s$ and (b),(d) $12 μ s$ . The theoretical curves (red dotted line) in (b),(d) are fits based on our model. $ω_{z} ∕ 2 π = 142.51 Hz$ and $Ω_{R} ∕ 2 π = 58 kHz$ are as in Fig. 1.Reuse & Permissions
Figure 4
(Color online) (a) Radially summed absorption images (black solid line) taken after an echo sequence $π ∕ 2 − τ_{1} − π − τ_{2} − π ∕ 2$ for $τ_{1} = 20 μ s$ . Also shown are simulated momentum distributions calculated with experimental parameters (red dotted line). The calculations include trap motion of atoms with different initial positions weighted with a Boltzmann distribution. Coarse graining of the numerical result due to the limited amount of initial positions included for reasons of finite computing power has been smoothed out by a running average along the momentum axis. (b) Difference of the measured (black solid line) and simulated (red dotted line) relative populations of the states $k_{z} = 0 ℏ q$ and $k_{z} = 2 ℏ q$ for varying $τ_{2}$ with different fixed values of $τ_{1}$ . The echo signal washes out for $τ_{1}$ times larger than $50 μ s$ .Reuse & Permissions

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