The transmission of an interacting Bose-Einstein condensate incident on a repulsive Gaussian barrier is investigated through numerical simulation. The dynamics associated with interatomic interactions are studied across a broad parameter range not previously explored. Effective one-dimensional Gross-Pitaevskii equation (GPE) simulations are compared to classical Boltzmann-Vlasov equation (BVE) simulations in order to isolate purely coherent matter-wave effects. Quantum tunneling is then defined as the portion of the GPE transmission not described by the classical BVE. An exponential dependence of transmission on barrier height is observed in the classical simulation, suggesting that observing such an exponential dependence is not a sufficient condition for quantum tunneling. Furthermore, the transmission is found to be predominately described by classical effects, although interatomic interactions are shown to modify the magnitude of the quantum tunneling. Interactions are also seen to affect the amount of classical transmission, producing transmission in regions where the noninteracting equivalent has none. This theoretical investigation clarifies the contribution quantum tunneling makes to overall transmission in many-particle interacting systems, potentially informing future tunneling experiments with ultracold atoms.
The transmission of an interacting Bose-Einstein condensate incident on a repulsive Gaussian barrier is investigated through numerical simulation. The dynamics associated with interatomic interactions are studied across a broad parameter range not previously explored. Effective one-dimensional Gross-Pitaevskii equation (GPE) simulations are compared to classical Boltzmann-Vlasov equation (BVE) simulations in order to isolate purely coherent matter-wave effects. Quantum tunneling is then defined as the portion of the GPE transmission not described by the classical BVE. An exponential dependence of transmission on barrier height is observed in the classical simulation, suggesting that observing such an exponential dependence is not a sufficient condition for quantum tunneling. Furthermore, the transmission is found to be predominately described by classical effects, although interatomic interactions are shown to modify the magnitude of the quantum tunneling. Interactions are also seen to affect the amount of classical transmission, producing transmission in regions where the noninteracting equivalent has none. This theoretical investigation clarifies the contribution quantum tunneling makes to overall transmission in many-particle interacting systems, potentially informing future tunneling experiments with ultracold atoms.
This thesis presents a theoretical investigation into the transmission and tunneling dynamics of a Bose-Einstein condensate (BEC) through single and double barriers. We show how quantum tunneling differs from transmission and provide a method for separating them out. We then focus on finding an experimentally-realisable parameter regime for making an atomic Fabry-Perot interferometer (FPI) using two repulsive barriers and study how interatomic interactions affect the dynamics of resonant transmission. Finally, we show that an atomic FPI can be used as an acceleration sensor and we compare its sensitivity to that of a Mach-Zehnder atom interferometer. We first investigate the transmission of an interacting BEC incident on a repulsive Gaussian barrier through numerical simulation. We study the dynamics associated with interatomic interactions across a broad parameter range not previously explored. Comparing effective one-dimensional Gross-Pitaevskii equation (GPE) simulations to classical Boltzmann-Vlasov equation (BVE) simulations, we isolate purely coherent matterwave effects. We then define quantum tunneling as the portion of the GPE transmission not described by the classical BVE. Transmission shows an exponential dependence on barrier height in the classical simulation, suggesting that observing such an exponential dependence is not a sufficient condition for quantum tunneling. Furthermore, we find that the transmission is predominately described by classical effects, although interatomic interactions modify the magnitude of the quantum tunneling. We show that the interactions also affect the amount of classical transmission, producing transmission in regions where the non-interacting equivalent has none. This theoretical investigation clarifies the contribution quantum tunneling makes to overall transmission in many-particle interacting systems, potentially informing future tunneling experiments with ultracold atoms. In the second part, we numerically demonstrate atomic Fabry-Perot resonances for a pulsed interacting BEC source transmitting through double Gaussian barriers. These resonances are observable for an experimentally-feasible parameter choice. By simulating an effective one-dimensional GPE, we investigate the effect of atom number, scattering length, and BEC momentum width on the resonant transmission peaks. For Rb-85 atomic sources with the current experimentally-achievable momentum width, we show that reasonably high contrast Fabry-Perot resonant transmission peaks can be observed using a) non-interacting BECs of 100000 atoms, b) interacting BECs of 100000 atoms with s-wave scattering lengths a_s= +-0.1a_0, and c) interacting BECs of 1000 atoms with a_s=+-1.0a_0. Our theoretical investigation impacts any future experimental realisation of an atomic Fabry-Perot interferometer with an ultracold atomic source. Finally, we explore the possibility of using an atomic FPI as an acceleration sensor. Using Fisher information, we quantify the acceleration sensitivity of the system. We study the dependence of sensitivity on various parameters of the system and determine the optimum parameter regime that gives the best sensitivity. For a BEC with infinitely narrow momentum width, the sensitivity can be improved without limit by increasing cavity length. However, when the atomic cloud has a finite momentum width, there exists an optimum cavity length corresponding to each momentum width. By comparing the sensitivity of the atomic FPI to that of a Mach-Zender interferometer with similar parameters, we show that the sensitivity of the atomic FPI overcomes that of the Mach-Zehnder interferometer in low device length and low momentum width regimes. In short, we demonstrate that an atomic FPI can be successfully used for sensing acceleration and the sensitivity of the device can be increased by reducing its length and by using a BEC with lower momentum width compared to the cavity linewidth.
The ground state of Bose-Einstein condensates with attractive particle interactions is metastable. One of the decay mechanisms of the condensate is a collapse by macroscopic quantum tunneling, which can be described by the bounce trajectory as a solution of the time-dependent Gross-Pitaevskii equation in imaginary time. For condensates with an electromagnetically induced gravity-like interaction, the bounce trajectory is computed with an extended variational approach using coupled Gaussian functions and is simulated numerically exact within the mean-field approach on a spacetime lattice. It is shown that the variational computations converge very rapidly to the numerically exact result with increasing number of Gaussians. The tunneling rate of the condensate is obtained from the classical action and additional parameters of the bounce trajectory. The converged variational and numerically exact results drastically improve by several orders of magnitude the decay rates obtained previously with a simple variational approach using a single Gaussian-type orbital for the condensate wave function.
We investigate macroscopic quantum tunneling of a Bose-Einstein condensate, and how it is affected by the interatomic interaction. We study the dynamics of a condensate falling under gravity and scattering on a Gaussian potential barrier that models a mirror formed by a far-detuned sheet of light. We observe bouncing, interference, and quantum tunneling of the condensate. We find that the tunneling rate is very sensitive to the interatomic interaction and to the shape of the condensate. Under many conditions the tunneling rate is strongly enhanced by the interaction as achieved, for instance, by increasing the number of condensed particles. In a quasi one-dimensional situation the tunneling pulse displays two peaks. The quantum tunneling can be quasiperiodic, and in this way one could generate coherent Bose-Einstein condensed atomic pulses.
We show theoretically the existence of a metastable state and the possibility of decay to the ground state through macroscopic quantum tunneling in two-component Bose-Einstein condensates with repulsive interactions. Numerical analysis of the coupled Gross-Pitaevskii equations clarifies the metastable states whose configuration preserves or breaks the symmetry of the trapping potential, depending on the interspecies interaction and the particle number. We calculate the tunneling decay rate of the metastable state by using the collective coordinate method under the WKB approximation. Then the height of the energy barrier is estimated by the saddle point solution. It is found that macroscopic quantum tunneling is observable in a wide range of particle numbers. Macroscopic quantum coherence between two distinct states is discussed; this might give an additional coherent property of two-component Bose condensed systems. Thermal effects on the decay rate are estimated.
The simplicity and versatility of ultra-cold atoms make it an ideal system for studying Quantum Mechanical phenomenon like tunneling. This thesis describes progress towards experimentally measuring the time spent by a tunneling particle in the classically forbidden region. A detailed analysis of the experimental requirements to measure the tunneling time is presented along with the experimental tools developed to meet these requirements. These include a thin \SI{1.3}{\micro m} optical tunnel barrier, a smooth atomic waveguide, and a Larmor clock to measure the tunneling time. Delta-kick cooling is used to achieve the extremely low temperatures required for the tunneling time experiments. A 2.4x reduction in the atomic velocity spread is demonstrated, reducing the rms velocity spread to \SI{0.46(5)}{mm/s}. This corresponds to cooling to an effective temperature of \SI{2.0(4)}{nK}. The thin optical barrier opens up the possibility to study the decay of quasi-bound condensates via tunneling. We develop a novel trapping configuration for this purpose, in which the barrier acts as one of the walls of the trap. Inter-atomic interactions strongly dictate the escape dynamics of the condensate out of this trap, giving rise to three distinct regimes--- classical over the barrier spilling, quantum tunneling driven by interactions, and decay dominated by background losses. We show that in the tunneling regime, the decay rate depends exponentially with the chemical potential of the condensate. Experimental results show good agreement with numerical solutions of the 3D Gross-Pitaevskii equation.
An atomic Bose-Einstein condensate (BEC) is often described as a macroscopic object which can be approximated by a coherent state. This, on the surface, would appear to indicate that its behavior should be close to being classical. In this paper, we clarify the extent of how "classical" a BEC is by exploring the semiclassical equations for BECs under the mean field Gaussian approximation. Such equations describe the dynamics of a condensate in the classical limit in terms of the variables < x > and < p > as well as their respective variances. We compare the semiclassical solution with the full quantum solution based on the Gross-Pitaevskii Equation (GPE) and find that the interatomic interactions which generate nonlinearity make the system less "classical." On the other hand, many qualitative features are captured by the semiclassical equations, and the equations to be solved are far less computationally intensive than solving the GPE which make them ideal for providing quick diagnostics, and for obtaining new intuitive insight.