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 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.
This work presents a numerical study of a tunnelingbased interferometer implemented using a Bose-Einstein condensate (BEC) confined in a static double-well potential, where the condensate dynamics are simulated using the one-dimensional Gross-Pitaevskii equation to capture the essential mean-field behavior. By carefully configuring the central barrier parameters, the double well is engineered to act as a coherent matterwave beam splitter. A relative phase is introduced between the two arms of the interferometer, enabling the extraction of phase information through interference. We analyze the resulting interference contrast to determine the best barrier configurations that allow the system to function effectively as an interferometer. It was found that the interferometric contrast remains robust under realistic fluctuations in the barrier parameters, confirming experimental feasibility. Using a fixed barrier for both the splitting and recombination steps, we avoid the need to dynamically ramp the barrier, as in other approaches. This allows us to realize a simple and experimentally accessible interferometry scheme in the double-well potential.
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.
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.
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.
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.