Amplitude and Phase of Wave Packets in a Linear Potential

Abstract

We theoretically study and successfully observe the evolution of Gaussian and Airy surface gravity water wave packets propagating in an effective linear potential. This potential results from a homogeneous and time-dependent flow created by a computer-controlled water pump. For both wave packets we measure the amplitudes and the cubic phases appearing due to the linear potential. Furthermore, we demonstrate that the self-acceleration of the Airy surface gravity water wave packets can be completely canceled by a linear potential.

Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves

“…An additional important feature of Airy wave packets is the accumulation of phase proportional to ξ 3 . This cubic-phase offset was predicted more than 40 years ago [35,46] and was measured in water waves for the first time [18], see Figure 6e. It should be stressed that in quantum mechanics and in optics, the measurement of the phase of a wave packet is practically impossible, since only the signal intensity of the high carrier frequency can be measured and therefore the information on the phase is lost [47].…”

“…However, quite often the propagation of those waves is described by the same set of mathematical equations resulting in shared physical behavior in different systems [6][7][8]. Experiments on gravity wave packets on a surface of a classical fluid, which are analogous in many aspects to wave packets in quantum mechanics or optics, opened a new field of exciting opportunities to study the quantum mechanical phenomena in easily accessible classical systems [9][10][11][12][13][14][15][16][17][18][19][20][21]. We overview here various types of wave packets in physical experiments in different media.…”

T3 Stern-Gerlach Matter-Wave Interferometer

“…Our SGI is unique in three aspects: (i) Although the gradient fields act on the atom continuously during its flight through the interferometer, as in the Humpty-Dumpty configuration [7][8][9], we obtain a remarkably high contrast. (ii) The observed phase shift scales [13] with the cube of the time the atom spends in the SGI, and thus represents the first interferometric measurement of the Kennard phase [14][15][16] predicted in 1927. (iii) The lack of light pulses to split and recombine the beams in combination with the Kennard phase makes our interferometer a perfect probe for magnetic as well as other properties of surfaces.…”

Stern-Gerlach Interferometry with the Atom Chip

“…Let us begin by comparing experimental parameters used in the ultra-cold atomic environment in our laboratory, typically achieved with BECs of 87 Rb, with corresponding state-of-the-art parameters for atomic beams. Table 14.1 summarizes parameters that are most relevant for these experiments.…”

“…In order to apply Stern-Gerlach splitting, our ultra-cold atomic sample needs to have at least two spin states. However, our initial atomic sample is purely in the |F, m F = |2, 2 state of 87 Rb. After preparing a BEC on the atom chip, our SG implementation therefore begins by first releasing the magnetic trap, and then applying a radio-frequency (RF) π/2 Rabi pulse to create an equal superposition of the two internal spin states 1 √ 2 (|1 + |2 ), where |1 and |2 represent the m F = 1 and m F = 2 Zeeman sub-levels of the F = 2 manifold in the ground electronic state [66].…”