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Tunneling Dynamics of a Bose-Einstein Condensate

Shreyas Potnis

Published Jun 1, 2016• 1 citation
OpenAlex

Abstract

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.

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Tunnelling Time of a Bose-Einstein condensate

Jesus Ramon Ramos Benitez

Tunnelling is one of the phenomena at the heart of quantum mechanics. Despite its central role in physics, the duration of the tunnelling process has been debated since the development of quantum theory without a definite answer. In this thesis, the question of how long a particle takes to tunnel is investigated experimentally using ultracold atoms. These systems provide an ideal platform to address this question due to their isolation from the external environment and the ability to create almost arbitrary potentials for the atoms. As the tunnelling time experiment requires low temperatures, the realization and characterization of wave packets below the nanokelvin regime are studied first. A 16x reduction of the effective temperature of the atoms is obtained through delta-kick cooling. However, the achieved temperatures are so low that a new method, dubbed the “knife-edge technique”, is developed to characterize the final atomic state accurately. Through this new method, a final temperature of 900 ± 200 pK is found. Finally, the tunnelling time is investigated using a Bose-Einstein condensate in a one dimensional waveguide intersected by a 1.3 μm barrier. As the atoms tunnel through the thin potential, their spins time the tunnelling event through the Larmor precession induced by a pseudo-magnetic field localized inside the barrier. The precession angle is found by performing tomography on the spin state of the tunnelling atoms. With the knowledge of the Larmor frequency and the rotation angles, we find a tunnelling time of 0.65(7) ms. This experiment achieves a long-sought tunnelling time measurement with a clear interpretation, and its results show good quantitative agreement with theory based on the weak measurement formalism.

•Nov 1, 2019•0 citations

Analysis of dynamical tunneling experiments with a Bose-Einstein condensate

W. K. Hensinger, Amaury Mouchet, Paul S. Julienne +3 more

Dynamical tunneling is a quantum phenomenon where a classically forbidden process occurs that is prohibited not by energy but by another constant of motion. The phenomenon of dynamical tunneling has been recently observed in a sodium Bose-Einstein condensate. We present a detailed analysis of these experiments using numerical solutions of the three-dimensional Gross-Pitaevskii equation and the corresponding Floquet theory. We explore the parameter dependency of the tunneling oscillations and we move the quantum system towards the classical limit in the experimentally accessible regime.

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Analysis of dynamical tunnelling experiments with a Bose-Einstein condensate

W. K. Hensinger, A Mouchet (13669555), P S Julienne (16105424) +3 more

Dynamical tunneling is a quantum phenomenon where a classically forbidden process occurs that is prohibited not by energy but by another constant of motion. The phenomenon of dynamical tunneling has been recently observed in a sodium Bose-Einstein condensate. We present a detailed analysis of these experiments using numerical solutions of the three-dimensional Gross-Pitaevskii equation and the corresponding Floquet theory. We explore the parameter dependency of the tunneling oscillations and we move the quantum system towards the classical limit in the experimentally accessible regime

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Interaction-Assisted Quantum Tunneling of a Bose-Einstein Condensate Out of a Single Trapping Well

Shreyas Potnis, Ramón Ramos, Kenji Maeda +2 more

We experimentally study tunneling of Bose-condensed ^{87}Rb atoms prepared in a quasibound state and observe a nonexponential decay caused by interatomic interactions. A combination of a magnetic quadrupole trap and a thin 1.3 μm barrier created using a blue-detuned sheet of light is used to tailor traps with controllable depth and tunneling rate. The escape dynamics strongly depend on the mean-field energy, which gives rise to three distinct regimes-classical spilling over the barrier, quantum tunneling, and decay dominated by background losses. We show that the tunneling rate depends exponentially on the chemical potential. Our results show good agreement with numerical solutions of the 3D Gross-Pitaevskii equation.

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Tunnelling Dynamics of a Bose-Einstein Condensate through Single and Double Barriers

Manju Perumbil

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.

•Jan 1, 2020•0 citations

Quantum tunneling dynamics of an interacting Bose-Einstein condensate through a Gaussian barrier

Manju Perumbil, Kyle S. Hardman, M. A. Sooriyabandara +5 more

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.

arXiv:1808.07196•Physical Review A•Nov 26, 2018•22 citations
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.
Tunnelling is one of the phenomena at the heart of quantum mechanics. Despite its central role in physics, the duration of the tunnelling process has been debated since the development of quantum theory without a definite answer. In this thesis, the question of how long a particle takes to tunnel is investigated experimentally using ultracold atoms. These systems provide an ideal platform to address this question due to their isolation from the external environment and the ability to create almost arbitrary potentials for the atoms. As the tunnelling time experiment requires low temperatures, the realization and characterization of wave packets below the nanokelvin regime are studied first. A 16x reduction of the effective temperature of the atoms is obtained through delta-kick cooling. However, the achieved temperatures are so low that a new method, dubbed the “knife-edge technique”, is developed to characterize the final atomic state accurately. Through this new method, a final temperature of 900 ± 200 pK is found. Finally, the tunnelling time is investigated using a Bose-Einstein condensate in a one dimensional waveguide intersected by a 1.3 μm barrier. As the atoms tunnel through the thin potential, their spins time the tunnelling event through the Larmor precession induced by a pseudo-magnetic field localized inside the barrier. The precession angle is found by performing tomography on the spin state of the tunnelling atoms. With the knowledge of the Larmor frequency and the rotation angles, we find a tunnelling time of 0.65(7) ms. This experiment achieves a long-sought tunnelling time measurement with a clear interpretation, and its results show good quantitative agreement with theory based on the weak measurement formalism.
Dynamical tunneling is a quantum phenomenon where a classically forbidden process occurs that is prohibited not by energy but by another constant of motion. The phenomenon of dynamical tunneling has been recently observed in a sodium Bose-Einstein condensate. We present a detailed analysis of these experiments using numerical solutions of the three-dimensional Gross-Pitaevskii equation and the corresponding Floquet theory. We explore the parameter dependency of the tunneling oscillations and we move the quantum system towards the classical limit in the experimentally accessible regime.
Dynamical tunneling is a quantum phenomenon where a classically forbidden process occurs that is prohibited not by energy but by another constant of motion. The phenomenon of dynamical tunneling has been recently observed in a sodium Bose-Einstein condensate. We present a detailed analysis of these experiments using numerical solutions of the three-dimensional Gross-Pitaevskii equation and the corresponding Floquet theory. We explore the parameter dependency of the tunneling oscillations and we move the quantum system towards the classical limit in the experimentally accessible regime
We experimentally study tunneling of Bose-condensed ^{87}Rb atoms prepared in a quasibound state and observe a nonexponential decay caused by interatomic interactions. A combination of a magnetic quadrupole trap and a thin 1.3 μm barrier created using a blue-detuned sheet of light is used to tailor traps with controllable depth and tunneling rate. The escape dynamics strongly depend on the mean-field energy, which gives rise to three distinct regimes-classical spilling over the barrier, quantum tunneling, and decay dominated by background losses. We show that the tunneling rate depends exponentially on the chemical potential. Our results show good agreement with numerical solutions of the 3D Gross-Pitaevskii equation.
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 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.