An atom interferometer for measuring loss of coherence from an atom mirror

We describe an atom interferometer to study the coherence of atoms reflected from an evanescent wave mirror. The interferometer is sensitive to the loss of phase coherence induced by the defects in the mirror. The results are consistent with and complementary to recent measurements of specular reflection. PACS. 03.75.Be Atom and neutron optics – 03.75.Dg Atom and neutron interferometry – 39.20.+q Atom interferometry techniques In the past 10 years, atom interferometry has found a number of applications. Notable examples are atom gyrometers, gravimeters and accelerometers, measurements of forward scattering amplitudes for elastic collisions, and investigations of the Aharanov-Casher effect [1]. Here we demonstrate a new application: interferometric characterization of an atomic mirror. Using either dipole forces or magnetic fields, it is not difficult to make a “mirror”, i.e. a steep reflecting barrier, strong enough to reflect atoms with velocities of order 1 m/s, the velocity acquired in ∼5 cm of free fall. Both dipole and magnetic force mirrors can be coupled with a high quality substrate to guarantee a well defined overall flatness or curvature, thus giving rise to the evanescent wave mirror [2,3], or to the magnetic mirror [4]. It is now well-known however, that a fundamental difficulty of atomic mirrors is loss of coherence due to various sources of roughness in the reflecting potential [5–8]. The extremely small de Broglie wavelength associated with the typical velocities (λdB ∼ 5 nm in the case of Rb at 1 m/s), imposes severe constraints on the small scale roughness of the substrate — it must be much better than λdB/2π [9] before the reflection can be considered specular, and therefore coherent. In this experiment, we use an atomic mirror within an interferometer and thus give a true demonstration of its coherence. In a previous paper [10], we reported measurements of the velocity distribution of atoms from an atom mirror and measured the fraction of specularly reflected atoms, as well as the transverse velocity profile of the diffusely reflected ones. The resolution of this measurement however, a e-mail: [email protected] b The Laboratoire Charles Fabry is part of the Federation LUMAT, FR2764 du CNRS. was insufficient to study the lineshape of the specularly reflected distribution — a crucial aspect characterizing the effect of the mirror on the coherence. Here we discuss a related measurement which is able to focus in more detail on the shape of the specularly reflected fraction. We have developed an atom interferometer which gives information complementary to velocity distribution measurements. We observe fringes whose contrast as a function of path difference corresponds to the coherence function of the atomic mirror, in other words to the Fourier transform of the transverse velocity distribution induced by the mirror. This measurement is particularly sensitive to the long distance behavior of the coherence function or to the velocity distribution in the specular peak, where direct velocity distribution measurements are impractical. Narrower velocity selection implies fewer atoms and worse signal to noise. The signal to noise in the interferometric technique is practically independent of the velocity resolution. It is the analog of Fourier transform spectroscopy with de Broglie waves. A diagram of the experiment is shown in Figure 1. Atoms from a MOT are subjected to two π/2 pulses which transfer 2 recoil momenta to the atoms. Their time separation is T . Only one of the internal atomic states is reflected by the mirror as shown by the solid line paths. After reflection the two paths are recombined by repeating the Raman pulse sequence with the same separation time. The result is an interferometer in which the two possible paths bounce off different parts of the mirror, separated by l = 2vRT , where vR is the recoil velocity. By detecting atoms in only one of the two internal states, interference fringes as a function of the time T are visible as shown in Figure 2. The actual atomic trajectories are parabolic, but we have suppressed this feature in the figure because R ap id e N ot e H ighlt Paper 488 The European Physical Journal D Fig. 1. Diagram of the interferometer. The arrows represent Raman π/2 pulses which create superpositions of different internal states and momenta. The atomic mirror is an evanescent wave at the surface of a glass prism represented by the trapezoid. The dashed lines correspond to paths which are eliminated, either during the bounce or during the detection. The letters a, b, c and d, label the 4 possible paths discussed in the text. The path lengths are not a realistic representation of the trajectory lengths. the only role played by gravity is to determine the de Broglie wavelength of the atoms at the moment they hit the mirror. The interferometer most resembles one first discussed in reference [11] and demonstrated in reference [12]. The differences here are that we use 2 photon Raman transitions rather than 1 photon transitions [13] and, more importantly, that we have placed an atomic mirror within the interferometer and use the fringes to study the influence of the mirror on the spatial coherence of the reflected atoms. We isolate the effect of the mirror by comparing these fringes to those obtained by applying all four pulses before the atoms hit the mirror. These fringes are also shown in Figure 2. It is evident that the mirror strongly reduces the fringe contrast, and we will discuss the information this reduction gives us below. But first we will give some experimental details of our setup. The apparatus is the same as that used in reference [10], and the laser pulse sequence is very similar. We refer the reader to Figure 1 of that paper for the energy level scheme. A Rb MOT is loaded with approximately 10 atoms in 2 s. The atoms are prepared in the F = 2 level by turning off the 2 → 3 repumping laser before the trapping beams. They fall under gravity towards a glass prism 20 mm below. Starting 8 ms after the atoms begin to fall, two counter–propagating Raman beams are pulsed on twice for 25 μs, with a period T between the start of the two pulses. The two–photon detuning of the first pulse pair is δ1 = ωa −ωb −ωHFS where ωb and ωa are the frequencies of the two Raman lasers, ωHFS is the hyperfine splitting in Rb, corrected for the atomic recoils involved in the transition. The laser parameters are such that the π/2 condition is fulfilled for δ1 = 0. 1.50