This chapter describes the Bose--Einstein condensate (BEC) interferometry. We first introduce the optical interferometer, briefly discussing the role of fringe contrast in observing interference patterns. Next, we examine a BEC interferometer in a Michelson geometry that consists of a BEC in a trapping potential well. The BEC cloud in the potential well is put into a linear superposition of two clouds that travel along different paths in the trap and are recombined using the same light beams. By studying the population of atoms in the different motional states of the BEC clouds that emerge after recombination, we obtain information about the relative phase shift accumulated by the two traveling superposed condensates during the interferometry. We then characterize the atom distribution that is found in the output of the interferometer by finding the probability density distribution and calculating the features of the probability density such as the mean, the variance, and the interference fringe contrast. Finally, we parameterize the effect of two-body collisional interactions on the observed interference fringes in a way that can be directly controlled in an experiment.
This chapter describes the Bose--Einstein condensate (BEC) interferometry. We first introduce the optical interferometer, briefly discussing the role of fringe contrast in observing interference patterns. Next, we examine a BEC interferometer in a Michelson geometry that consists of a BEC in a trapping potential well. The BEC cloud in the potential well is put into a linear superposition of two clouds that travel along different paths in the trap and are recombined using the same light beams. By studying the population of atoms in the different motional states of the BEC clouds that emerge after recombination, we obtain information about the relative phase shift accumulated by the two traveling superposed condensates during the interferometry. We then characterize the atom distribution that is found in the output of the interferometer by finding the probability density distribution and calculating the features of the probability density such as the mean, the variance, and the interference fringe contrast. Finally, we parameterize the effect of two-body collisional interactions on the observed interference fringes in a way that can be directly controlled in an experiment.
An atom interferometer is a sensitive device that has potential for many useful applications. Atoms are sensitive to electromagnetic fields due to their electric and magnetic moments and their mass allows them to be deflected in a gravitational field, thereby making them attractive for measuring inertial forces. The narrow momentum distribution of Bose-Einstein condensate (BEC) is a great asset in realizing portable atom interferometers. An example is a guided-wave atom interferometer that uses a confining potential to guide the motion of the condensate. Despite the promise of guided-wave atom interferometry with BEC, spatial phase and phase diffusion limit the contrast of the interference fringes. The control of these phases is required for successful development of a BEC-based guided-wave atom interferometer. This thesis analyses the guided-wave atom interferometer, where an atomic BEC cloud at the center of a confining potential is split into two clouds that move along different arms of the interferometer. The clouds accumulate relative phase due to the environment, spatially inhomogeneous trapping potential and atom-atom interactions within the condensate. At the end of the interferometric cycle, the clouds are recombined producing a cloud at rest and moving clouds. The number of atoms in the clouds that emerge depends on the relative phase accumulated by the clouds during propagation. This is investigated by deriving an expression for the probability of finding any given number of atoms in the clouds that emerge after recombination. Characteristic features like mean, standard deviation and cross-correlation function of the probability density distribution are calculated and the contrast of the interference fringes is optimized. This thesis found that optimum contrast is achieved through the control of total population of atoms in the condensate, trap frequencies, s-wave scattering length, and the duration of the interferometric cycle.
Precision interferometry with atomic wavepackets confined in a one-dimensional optical lattice is an emergent paradigm in quantum sensing of forces and fields, with applications in gravimetry, accelerometry, geophysics, and fundamental physics tests. We report on the realization of a lattice-trapped interferometer where the two arms are sourced from a weakly-interacting ytterbium Bose-Einstein condensate, coherently split and trapped by pulsed optical standing waves before recombination. We directly observe atomic interactions through contrast changes and phase shifts of the interferometer. By changing either the atom number or the sample volume to vary the density, we demonstrate control over interactions and optimize interferometer performance. Our observations are effectively captured by a mean-field theoretical model of the system. This work experimentally probes the boundary where improved performance from source brightening through higher phase space density transitions into a regime beyond single-atom physics in lattice-trapped atom interferometry, and opens a door to incorporating many-body effects for metrological advances in such platforms.
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.
Bose–Einstein condensates of particles behave in many ways like coherent radiation fields, and the realization of Bose–Einstein condensation in dilute gases has opened up the experimental study of interactions between coherent matter waves. In addition, the existence of these dilute trapped quantum gases has prompted a re-examination of a number of theoretical issues. In Sec. 13.1 we discuss Josephson tunnelling of a condensate between two wells and the role of fluctuations in particle number and phase. The number and phase variables play a key role in the description of the classic interference experiment, in which two clouds of atoms are allowed to expand and overlap (Sec. 13.2). Rather surprisingly, an interference pattern is produced even though initially the two clouds are completely isolated. Density fluctuations in a Bose gas are studied in Sec. 13.3, where we relate atomic clock shifts to the two-particle correlation function. The ability to manipulate gaseous Bose–Einstein condensates by lasers has made possible the study of coherent matter wave optics and in Sec. 13.4 we describe applications of these techniques to observe solitons, Bragg scattering, and non-linear mixing of matter waves. How to characterize Bose–Einstein condensation in terms of the density matrix is the subject of Sec. 13.5, where we also consider fragmented condensates.
Interferometry with trapped atomic Bose-Einstein condensates (BECs) requires the development of techniques to recombine the two paths of the interferometer and map the accumulated phase difference to a measurable atom number difference. We have implemented and compared two recombining procedures in a double-well-based BEC interferometer. The first procedure utilizes the bosonic Josephson effect and controlled tunneling of atoms through the potential barrier, similar to laser light in an optical fiber coupler. The second one relies on the interference of the reflected and transmitted parts of the BEC wave function when impinging on the potential barrier, analogous to light impinging on a half-silvered mirror. Both schemes were implemented successfully, yielding an interferometric contrast of similar to 20% and 42% respectively. Building efficient matter-wave recombiners represents an important step towards the coherent manipulation of external quantum superposition states of BECs.
Interferometry with trapped atomic Bose-Einstein condensates (BECs) requires the development of techniques to recombine the two paths of the interferometer and map the accumulated phase difference to a measurable atom number difference. We have implemented and compared two recombining procedures in a double-well-based BEC interferometer. The first procedure utilizes the bosonic Josephson effect and controlled tunneling of atoms through the potential barrier, similar to laser light in an optical fiber coupler. The second one relies on the interference of the reflected and transmitted parts of the BEC wave function when impinging on the potential barrier, analogous to light impinging on a half-silvered mirror. Both schemes were implemented successfully, yielding an interferometric contrast of $\ensuremath{\sim}20$% and 42% respectively. Building efficient matter-wave recombiners represents an important step towards the coherent manipulation of external quantum superposition states of BECs.