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InTech eBooks

High Order Momentum States by Light Wave Scattering

Xiaoji Zhou, Xuguang Yue

Published Mar 21, 2012• 0 citations
Publisher

Abstract

Atomic interferometry is very useful in fundamental studies of coherence, decoherence and phase shifts and for practical precision measurements, with the example of gravimeters, gyroscopes, and gradiometers (Cronin et al., 2009). Bose-Einstein Condensate (BEC) based atomic interferometry provides high contrasts, long integration times and the possible use of small devices (Baumgartner et al., 2010; Sapiro et al., 2009a; Torii et al., 2000). In such atomic interferometry, coherent momentum manipulation is very effective for splitting and recombining the condensate (Deng et al., 1999; Kozuma, Deng et al., 1999; Ovchinnikov et al., 1999), for realizing the interference. In some precision measurements, the accumulated phase is positively correlated to the atomic velocity, so that the larger the atomic momentum is, the more precise the measurements can be if the measuring time is unchanged.

DOI
10.5772/35804

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Atomic interferometry is very useful in fundamental studies of coherence, decoherence and phase shifts and for practical precision measurements, with the example of gravimeters, gyroscopes, and gradiometers (Cronin et al., 2009). Bose-Einstein Condensate (BEC) based atomic interferometry provides high contrasts, long integration times and the possible use of small devices (Baumgartner et al., 2010; Sapiro et al., 2009a; Torii et al., 2000). In such atomic interferometry, coherent momentum manipulation is very effective for splitting and recombining the condensate (Deng et al., 1999; Kozuma, Deng et al., 1999; Ovchinnikov et al., 1999), for realizing the interference. In some precision measurements, the accumulated phase is positively correlated to the atomic velocity, so that the larger the atomic momentum is, the more precise the measurements can be if the measuring time is unchanged.
Atomic quantum sensors are a major breakthrough in the technology of time and frequency standards as well as ultra-precise sensing and monitoring of accelerations and rotations. They apply a new kind of optics based on matter waves. Today, atomic clocks are the standard for time and frequency measurement at the highest precisions. Inertial and rotational sensors using atom interferometers have already shown similar potential for replacing state-of-the-art sensors in other fields. With Bose-Einstein condensates, also refered as atom lasers, the traditional experiments with atom interferometers can be greatly improved. Testing of fundamental principles, studies of atomic properties, applications as inertial sensors, and measurements of fundamental constants can benefit from the brightness (intensity and small momentum spread) of these coherent sources. In addition, the coherence properties of condensates may also allow BEC based atom interferometers to approach the Heisenberg detection limit. This corresponds to a measurement precision which scales like 1/N for N atoms and not like 1 / N as for independent measurements on N atoms.
Interferometry with ultracold atoms promises the possibility of ultraprecise and ultrasensitive measurements in many fields of physics, and is the basis of our most precise atomic clocks. Key to a high sensitivity is the possibility to achieve long measurement times and precise readout. Ultracold atoms can be precisely manipulated at the quantum level and can be held for very long times in traps; they would therefore be an ideal setting for interferometry. In this paper, we discuss how the nonlinearities from atom–atom interactions, on the one hand, allow us to efficiently produce squeezed states for enhanced readout and, on the other hand, result in phase diffusion that limits the phase accumulation time. We find that low-dimensional geometries are favorable, with two-dimensional (2D) settings giving the smallest contribution of phase diffusion caused by atom–atom interactions. Even for time sequences generated by optimal control, the achievable minimal detectable interaction energy Δ E min is of the order of 10 −4 μ, where μ is the chemical potential of the Bose–Einstein condensate (BEC) in the trap. From these we have to conclude that for more precise measurements with atom interferometers, more sophisticated strategies, or turning off the interaction-induced dephasing during the phase accumulation stage, will be necessary.
Interferometry with ultracold atoms promises the possibility of ultraprecise and ultrasensitive measurements in many elds of physics, and is the basis of our most precise atomic clocks. Key to a high sensitivity is the possibility to achieve long measurement times and precise readout. Ultra cold atoms can be precisely manipulated at the quantum level, held for very long times in traps, and would therefore be an ideal setting for interferometry. In this paper we discuss how the non-linearities from atom-atom interactions on one hand allow to efficiently produce squeezed states for enhanced readout, but on the other hand result in phase diffusion which limits the phase accumulation time. We find that low dimensional geometries are favorable, with two-dimensional (2D) settings giving the smallest contribution of phase diffusion caused by atom-atom interactions. Even for time sequences generated by optimal control the achievable minimal detectable interaction energy ∆Emin is on the order of 10−4µ, where µ is the chemical potential of the BEC in the trap. From there we have to conclude that for more precise measurements with atom interferometers more sophisticated strategies, or turning off the interaction induced dephasing during the phase accumulation stage, will be necessary. PACS numbers: 37.25.+k,03.75.-b,37.10.Gh,02.60.Pn
Atom interferometers and gyroscopes are highly sensitive atom-optical devices which are capable to measure inertial, gravitational, electric, and magnetic fields and to sense rotations. Theoretically, the signal-to-noise ratio of atomic gyroscopes is about a hundred billion times more than that of their optical counterparts for the same particle flux and the enclosed area. Ultra cold atoms from a Bose-Einstein condensate (BEC) can easily be controlled and coherently manipulated on small chips by laser pulses. Atom-optical devices will therefore play a significant role in fundamental research, precision measurements, and navigation systems. In BEC-based atom interferometers, a BEC in a trap is split by using laser pulses, the split clouds are allowed to evolve, they are reflected, and then recombined by laser pulses to observe interference. The split clouds accumulate spatial phase because of the trap and the nonlinearity caused by atom-atom interactions. A velocity mismatch due to reflection laser pulses also introduces a phase gradient across each cloud. These factors contribute to spatial relative phase between the clouds at recombination, causing the loss of contrast of the interference fringes. The main objective of this dissertation is to study the dynamics of a split condensate in atom Michelson interferometers, investigate the effect of trap frequencies, nonlinearity, and the velocity mismatch on the contrast, and to obtain the best theoretical limit of performance in terms of the experimental parameters: trap frequencies, number of atoms, and the velocity imparted to the clouds by the splitting laser pulses.
The wave nature of particles has been demonstrated in many experiments and it continues to be an active area of research [1]. Optical elements for atoms such as beam splitters and mirrors have been used for the manipulation of atomic deBroglie waves. Many of these elements use light forces which under certain conditions allow the coherent manipulation of the atoms and thus are important for atom interferometry. Atom interferometers have many uses, including the precise measurement of fundamental constants.
Abstract The coherent manipulation of a quantum wave is at the core of quantum sensing. For instance, atom interferometers require linear splitting and recombination processes to map the accumulated phase shift into a measurable population signal. Although Bose Einstein condensates (BECs) are the archetype of coherent matter waves, their manipulation between trapped spatial modes has been limited by the strong interparticle collisions. Here, we overcome this problem by using BECs with tunable interaction trapped in an innovative array of double-well potentials and exploiting quantum tunneling to realize linear beam splitting. We operate several Mach-Zehnder interferometers in parallel, canceling common-mode potential instabilities by a differential analysis, thus demonstrating a trapped-atom gradiometer. Furthermore, by applying a spin-echo protocol, we suppress additional decoherence sources and approach unprecedented coherence times of one second. Our interferometer will find applications in precision measurements of forces with a high spatial resolution and in linear manipulation of quantum entangled states for sensing with sub shot-noise sensitivity.