Mach-Zehnder atom interferometer

One example of an application is the measurement of the gravitational acceleration g on earth with an accuracy of 3 x 10 g with a light-pulse atomic interferometer [1291]. Laser-cooled wave packets of sodium atoms in an atomic fountain (Sect. 9.1.9) are irradiated by a sequence of three light pulses with properly chosen intensities. The first pulse is chosen as 7r/2-pulse, which creates a superposition of two atomic states 1) and 2) and results in a splitting of the atomic fountain beam at position 1 in Fig. 9.71 into two beams because of photon recoil. The second pulse is a tt-pulse, which deflects the two partial beams into opposite directions the third pulse finally is again a tt/2-pulse, which recombines the two partial beams and causes the wave packets to interfere. This interference can, for example, be detected by the fluorescence of atoms in the upper state 2). 

For momentum transfer stimulated Raman transitions between the two hyperfine levels 1 and 2) of the Na(3 5 i/2) state are used, which are induced by two laser pulses with light frequencies coi and o)2 (o) —002 = hfs) traveling into opposite directions (Fig. 9.71b). Each transition transfers the momentum Ap 2hk. The gravitational field causes a deceleration of the upwards moving atoms in the fountain. This changes their velocity, which can be detected as a Doppler shift of the Raman transitions. Because the Raman resonance a)i—a)2 = has an extremely narrow 

Matter-wave interferometry has found wide applications for testing basic laws of physics. One advantage of interferometry with massive particles, for instance, is the possibility of studying gravitational effects. Compared to the neutron interferometer, atomic interferometry can provide atomic fluxes that are many orders of magnitude higher than thermalized neutron fluxes from reactors. The sensitivity is therefore higher and the costs are much lower. 

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In this paper, we propose an experiment to test neutrality of isolated lithium atoms. Atom interferometry has been shown to be the ideal technique to measure weak interactions of an atom with its environment [1,2]. In particular, in 1991, Kasevich and Chu have mentionned the test of neutrality of atoms as a possible utilisation of their atomic interferometer [2], As far as we know, no further details have been published. The experimental set-up we propose is based on a Mach-Zehnder atom interferometer like the ones developped by the research groups of D. Pritchard [3], Siu Au Lee [4], A. Zeilinger [5] and the one under construction in our group [6]. If the same uniform electric field E is applied on both arms of the interferometer, a phase shift of the interferometric signal will appear. This phase shift will be proportional to the residual charge of lithium atom and to the electric field E. 

Fig. 1. The experimental set-up proposed to test neutrality of lithium atom is based on a Mach-Zehnder atom interferometer working in the Bragg configuration. Gi, G2, G3 are the three diffraction gratings and the detector is placed in front of one of the two complementary exits. The capacitor of length Lc extends from 2 = zm to z = zout-Some plates defining the zero potential in a symmetrical way are not represented...

A Mach-Zehnder atom interferometer is not the only atom interferometer that could be used. One could also use a Ramsey-Borde interferometer [12] to test neutrality of atoms. The capacitor should then be set where trajectories are parallel and atoms are in the same internal state in both paths, so that the phase shift depends only on atomic charge. A possible disadvantage of these interferometers is that the observed contrast is around 20 % according to [12] and that many atoms of the source are lost in extra interferometers also present in the apparatus. 

In the case of a space separation of the laser beams (i.e. if the atomic velocity is perpendicular to the direction of the laser beams), the interferometer is in a Mach-Zehnder configuration. Then, the interferometer is also sensitive to rotations, as in the Sagnac geometry (Sagnac, 1913) for light interferometers. For a Sagnac loop enclosing area A, a rotation Q, produces a phase shift ... 

The experiments were carried out in a high vacuum chamber where a beam of atomic potassium K (4s) intersects perpendicularly with the femtosecond laser pulses leading to photoionization. The released photoelectrons are detected employing a magnetic bottle time-of-flight electron spectrometer. The 785 nm, 30 fs FWHM laser pulses provided by an amplified 1 kHz Ti sapphire laser system are split into two beams using a Mach-Zehnder interferometer. In the first experiment the time delay r is varied in a range of 80 to 100 fs with 0.2 fs resolution at a... 

The very first demonstration of molecule interference dates back to the days of Estermann and Stern [Estermann 1930] who demonstrated experimentally diffraction of 11-2 at a LiF crystal surface in 1930. Further experiments with diatomic molecules had to await progress and interest in atom optics. A Ramsey-Borde interferometer was realized for the iodine dimer in 1994 [Borde 1994] and was recently used [Lisdat 2000] with K. Similarly, a Mach-Zehnder interferometer was demonstrated [Chapman 1995 (a)] for Na2. The nearfield analog to the Mach-Zehnder interferometer, a Talbot-Lau interferometer, was recently applied to experiments with L12 [Berman 1997], Diffraction at nanofabricated gratings also turned out to be the most effective way to prove the existence of weakly bound helium dimer [Schollkopf 1996] and to measure its binding energy [Grisenti 2000],... 

Schrodinger kittens) [30]. Of course, the problem of practical realization of the system arises. At this point one should emphasize that the most commonly proposed practical realization is that in which a nonlinear medium is located inside one arm of the Mach-Zehnder interferometer [26]. However, models of a quantum nonlinear oscillator can be achieved in various ways. For instance, systems comprising trapped ions [31], trapped atoms [32], or cavities with moving mirrors [16] can be utilized to generate states of our interest. 

Fig. 9.71 (a) Paths of the atom in a Mach-Zehnder-type atomic interferometer (b) momentum transfer by stimulated Raman transitions applied to rubidium atoms in an atomic fountain where the atoms move parallel to the laser beams [1291] (c) level scheme for Raman transitions... 

The Mach-Zehnder interferometer has been used in spectroscopy to measure the refractive index of atomic vapors in the vicinity of spectral lines (Sect. 3.1). The... 

We know of many types of optical interferometer (the simple double-slit Young interferometer, the Mach-Zehnder interferometer, the Fabry-Perot interferometer, the Talbot interferometer, etc.). A similar situation occurs in atom interferometry. Artificial laboratory devices exploit various types of structure for atom interferometry both material bodies (slits and gratings) and nonmaterial light structures. All these atom interferometers will be considered very briefly we refer readers for details to the book by Berman (1997) and reviews by Baudon et al. (1999), Kasevich (2002), and Chu (2002). 

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