1 4 Se p 20 06 Time invariance violation is a physical base of atomic Bloch oscillations in an optical lattice

The physical mechanism of phenomenon is explained as a result of inequality of forward and reversed processes in optics. The importance of experimental study of its invariance relation is discussed. There is rather usual situation in nonlinear optics when a phenomenon has mathematical description, but clear explanation of its physical mechanism is absent. Clear physical sense appears if we use the concept of inequality of forward and reversed processes in optics. Such approach has quite reliable basis [1]. In this note we shall discuss the situation with explanation of the Bloch oscillation of ultracold atoms in a vertical optical lattice, formed by two coun-terpropagating beams [2-4]. Under action of gravity the atoms perform a cyclic motion in the vertical direction. The measurement of oscillating frequency allows a sensitive determination of the acceleration of gravity or forces at the micrometer length scale. According to the existing theoretical concept the physical base of the Bloch oscillations is the polarization interaction of the atoms with the standing optical wave. The corresponding theoretical description is very complex and non-intuitive [5, 6]. It gives for the Bloch oscillations frequency following expression: ν B = mgλ 2h (1) where m is the atomic mass, g is the acceleration of gravity, λ is the wavelength of the light, and h is Planck constant [2]. Below we shall deduce the formula (1) by very simple and quite intuitive way. We also shall give the alternative physical explanation of origin of the phenomenon. When the magneto-optical trap is switched off, the ultracold atoms start to fall down under action of the gravity (Fig.1). At the certain moment of time the Raman optical transition takes place and the atoms receive a double recoil moment in the opposite direction. The obtained recoil energy (2E R) allows for atoms to return in the initial point. The amplitude (height) of atomic