In this dissertation I present experimental work on the measurement and manipulation of the center-of-mass motion of laser-cooled atoms. The first experiment described demonstrates cooling of an atom cloud by 'delta-kick cooling'. A thermal cloud of atoms in a vacuum expands ballistically, generating correlations between position and momentum. An appropriate momentum kick, proportional to position, results in slowing down all the atoms in the cloud. Through this technique a cloud of atoms can be cooled by greater than a factor of 10, preserving phase-space density, but decreasing the number density of atoms. By using laser-cooled atoms, it is also possible to confine atoms in potentials created by the AC-Stark shift of the atomic energy levels. Using interfering lasers to create the Stark shift, atoms are confined in a sinusoidal potential called an optical lattice. After preparing atoms in the lowest-energy band of the lattice, a spatial displacement can create coherent superpositions of many states of the potential. A combination of time delays and secondary displacements allows the measurement of the Q (Husimi) and W (Wigner) quasi-probability distributions, each of which completely characterizes the motional state of the atoms. Alternatively, a shallow lattice that only support two long-lived states can be used. The two-state system may be characterized with far fewer measurements, and furthermore, can be used as a model system for a qubit, a quantum representation of a single bit of information, useful for quantum computation. We demonstrate reconstruction of the density matrix in the 2-state system. The two-state system has be further used to characterize the physical action of an operation. By preparing a complete set of input density matrices we perform quantum process tomography for the intrinsic decoherence of the lattice, and two operations that correspond to single qubit rotations.
In this dissertation I present experimental work on the measurement and manipulation of the center-of-mass motion of laser-cooled atoms. The first experiment described demonstrates cooling of an atom cloud by 'delta-kick cooling'. A thermal cloud of atoms in a vacuum expands ballistically, generating correlations between position and momentum. An appropriate momentum kick, proportional to position, results in slowing down all the atoms in the cloud. Through this technique a cloud of atoms can be cooled by greater than a factor of 10, preserving phase-space density, but decreasing the number density of atoms. By using laser-cooled atoms, it is also possible to confine atoms in potentials created by the AC-Stark shift of the atomic energy levels. Using interfering lasers to create the Stark shift, atoms are confined in a sinusoidal potential called an optical lattice. After preparing atoms in the lowest-energy band of the lattice, a spatial displacement can create coherent superpositions of many states of the potential. A combination of time delays and secondary displacements allows the measurement of the Q (Husimi) and W (Wigner) quasi-probability distributions, each of which completely characterizes the motional state of the atoms. Alternatively, a shallow lattice that only support two long-lived states can be used. The two-state system may be characterized with far fewer measurements, and furthermore, can be used as a model system for a qubit, a quantum representation of a single bit of information, useful for quantum computation. We demonstrate reconstruction of the density matrix in the 2-state system. The two-state system has be further used to characterize the physical action of an operation. By preparing a complete set of input density matrices we perform quantum process tomography for the intrinsic decoherence of the lattice, and two operations that correspond to single qubit rotations.
This dissertation reports on the experimental study of coherent wavepacket dynamics of cesium atoms in the double-well potentials of a one-dimensional, far-off-resonance optical lattice. An optical lattice is the periodic potential produced by the light shift interaction of an atom with the light field of interfering laser beams. With the proper choice of laser parameters and external magnetic fields, an array of double-well potentials is created. Using the techniques of laser cooling, atoms are trapped in the lattice and are prepared in a pure state through a combination of enhanced laser cooling in a near-resonance lattice and state selection in an accelerated far-off-resonance lattice. The atoms are prepared on one side of the double-well potential, and the atomic wavepackets will then oscillate between the left and right localized states of the double-well potential. Entanglement between the internal and external degrees of freedom makes it possible to follow the center-of-mass motion of the atoms by measuring the ground state magnetic populations via Stern-Gerlach analysis. The coherent dynamics of these wavepackets was studied under various combinations of lattice parameters such as lattice depth, applied transverse and longitudinal magnetic fields. There is excellent agreement between the experimentally measured oscillation frequencies and those predicted from a numerical analysis of the bandstructure of the lattice. For certain lattice parameters the total energy of the atom is below the potential barrier and the coherent motion corresponds to tunneling through a classically forbidden barrier. At specific times during the oscillation the atomic wavepacket corresponds to a coherent superposition of the mesoscopically distinct left and right localized states.
Optical lattices are periodic arrangements of laser cooled atoms trapped in potentials created by the interference of multiple laser beams. In this dissertation, we describe a series of experiments performed using optical lattices that exploit the coherence of atoms and we also look at new ways to cool the atoms. With a sudden shift of the optical lattice, atomic wavepackets can be created that evolve much like a classical particle. Using a photon redistribution technique, we have characterized the oscillation of wavepackets in the anharmonic potential wells. Atoms will quantum mechanically tunnel between lattice sites with a sufficiently shallow potential. Due to the structure of the optical lattices that are used, while the atom is tunneling, its internal angular momentum state must change. We use this change to detect and characterize the tunneling. The change in internal state leads to the formation of a new potential that acts on the atom, which is known as a gauge potential, which does not depend on the light intensity, but depends only on the geometry of the lattice. We have for the first time measured and characterized this gauge potential. Finally, by randomly modulating the lattice potential, we have demonstrated that tunneling can be suppressed. We have shown that an enhancement of the Sisyphus cooling process, which localizes atoms in the wells of an optical lattice, is possible using a bichromatic standing wave. A time of flight technique is used to verify the cooling improvement. We combine the techniques developed in these experiments and apply them to the cooling of the trapped atoms using a feedback mechanism, which is analogous to the well known technique of stochastic cooling in the field of beam physics. Lastly, we have laid the theoretical basis for using the ponderomotive force to create optical lattices for laser cooled Rydberg atoms. Rydberg atoms are attractive because of their many extreme properties, and the ability to trap Rydberg atoms into lattice sites will increase the range of experiments and measurements that can be made with them.
In this thesis, detailed experimental studies and numerical simulations are presented of laser cooling mechanisms in dissipative optical lattices and results of the first realized three dimensional Brownian motor in optical lattices. A dissipative optical lattice is a periodic light shift potential, created in the interference patterns of laser beams. In this, atoms can be both cooled and trapped, and the most important relaxation mechanism is generally considered to be “Sisyphus cooling”. However, careful experimental and theoretical investigations indicate the presence of other cooling processes as well. This is studied by varying different parameters such as irradiance and frequency of the lattice light. The time evolution of atoms in optical lattices show strong evidence of a bimodal velocity distribution, where a population transfer between one mode containing “hot” atoms and one mode containing “cold” atoms is evident. The normal diffusion of atoms in optical lattices is characterized by isotrop random fluctuations and exhibit the nature of Brownian motion. We have realized a technique where this motion is rectified and controlled. This is done in a three dimensional double optical lattice. This Brownian motor has control properties for both its speed and its direction in three dimensions. Our three dimensional double optical lattice is created by using laser light, exploiting two transitions, in the D2 line of cesium. Two three dimensional optical lattices are spatially overlapped; each optical lattice traps atoms in one of two hyperfine ground states. The controllability comes about by inducing phase shifts in the lattice laser beams, which displace the lattices relative to each other. This type of highly controlled Brownian motor is of fundamental interest since Brownian motion is present in almost all systems and for the role they play in protein motors and the function of living cells, and for the potential applications in nanotechnology. Brownian motors of this kind also open the way to possible studies of quantum Brownian motors and quantum resonances that are predicted for atomic ratchets. Optical lattices, and especially double optical lattices, have also been suggested as a platform for quantum state manipulations due to the good isolation from environment and ambient effects. Most of the work in this thesis is a first step towards the implementation of quantum manipulation schemes in a double optical lattice.
Summary form only given. The preparation of the quantum state of physical systems and its diagnostics by quantum-state reconstruction has been a subject of large progress in recent years. Various experiments have successfully demonstrated the feasibility of reconstructing the quantum state of optical fields, molecular vibrations, trapped ions, and matter waves. The impressive success in laser cooling of neutral atoms opens new possibilities for preparing quantum states of ensembles of atoms in optical lattices and also quantum computing. In this context, the diagnostics of the quantum state, would provide a very useful tool for studying the accuracy of prepared quantum states or exploring decoherence mechanisms. However, to our knowledge, a reconstruction method for optical lattices that accounts for typical features of optical lattice potentials such as anharmonicity and band structure, is not yet available. We propose such a method, that we think is relatively simple to implement, since only phase shifts of the lattice laser beams and measurements of the band populations in the lattice potential are needed. These techniques are feasible by use of electro/acousto-optical modulators and by measuring the momentum distribution of the atoms after adiabatically turning off the lattice lasers.
This thesis describes recent experiments conducted on a Bose-Einstein condensate in an optical waveguide. This optical potential confines the atoms against gravity in the vertical dimension, guiding them to freely propagate in the horizontal. Being supported against gravity enables long expansion times of hundreds of milliseconds, facilitating techniques such as delta-kick cooling. In an ideal atom interferometer, the beamsplitters would impart a large momentum splitting between the interfering states in order to increase the signal. However, their effective use requires both an even narrower momentum width source and good vibration isolation. Three such techniques were investigated in this thesis: reflection from a repulsive light potential barrier, Bragg transitions from an optical lattice (which are effectively bouncing atoms off a moving grating), and Bloch-acceleration by loading the atoms into such an optical lattice and then accelerating the combined system. It is found that a combination of both Bragg and Bloch provides the most promising route to truly large momentum transfer in a system which is sensitive only to acceleration. Lastly, large-momentum transfer techniques can be used to effectively increase the way in which the output signal scales with time, creating interferometers which generate the same sensitivity faster (increasing the bandwidth of a sensor), or generate a much better sensitivity in the same time. We form a dual condensate of both rubidium-85 an rubidium-87 via sympathetic cooling. The collisional properties of Rubidium-85 can be modified by applying an external magnetic field, at an easy-to-experimentally-reach value of between 150-170G. It turns out that this combination of atomic isotopes is ideal for an interferometric test of the weak equivalence principle, one of the underpinnings of General Relativity. This thesis also presents the results of the first Bose-condensed version of such a dual-species interferometer. By removing any 87Rb left after condensation, we have created a pure 85Rb BEC. Using this we can now explore how the inter-atomic interactions affect the phase shift of a condensed atom interferometer, as we have complete control over the interaction strength. A condensate with no inter-particle interactions should behave like an ideal particle. With a small attractive interaction between atoms, it is possible to create a self-trapped cloud of atoms which propagates dispersionlessly. This cloud is known as a soliton, and it is predicted to have even more interesting quantum mechanical properties. For example it is predicted that by colliding two such solitons, an entangled state can be generated. Our results indicate that the dispersionless character of the soliton out-performs all other interaction strengths in an atom interferometer, including even the non-interacting cloud.
In this thesis, detailed experimental studies and numerical simulations are presented of laser cooling mechanisms in dissipative optical lattices and results of the first realized three dimensional Brownian motor in optical lattices. A dissipative optical lattice is a periodic light shift potential, created in the interference patterns of laser beams. In this, atoms can be both cooled and trapped, and the most important relaxation mechanism is generally considered to be “Sisyphus cooling”. However, careful experimental and theoretical investigations indicate the presence of other cooling processes as well. This is studied by varying different parameters such as irradiance and frequency of the lattice light. The time evolution of atoms in optical lattices show strong evidence of a bimodal velocity distribution, where a population transfer between one mode containing “hot” atoms and one mode containing “cold” atoms is evident. The normal diffusion of atoms in optical lattices is characterized by isotrop random fluctuations and exhibit the nature of Brownian motion. We have realized a technique where this motion is rectified and controlled. This is done in a three dimensional double optical lattice. This Brownian motor has control properties for both its speed and its direction in three dimensions. Our three dimensional double optical lattice is created by using laser light, exploiting two transitions, in the D2 line of cesium. Two three dimensional optical lattices are spatially overlapped; each optical lattice traps atoms in one of two hyperfine ground states. The controllability comes about by inducing phase shifts in the lattice laser beams, which displace the lattices relative to each other. This type of highly controlled Brownian motor is of fundamental interest since Brownian motion is present in almost all systems and for the role they play in protein motors and the function of living cells, and for the potential applications in nanotechnology. Brownian motors of this kind also open the way to possible studies of quantum Brownian motors and quantum resonances that are predicted for atomic ratchets. Optical lattices, and especially double optical lattices, have also been suggested as a platform for quantum state manipulations due to the good isolation from environment and ambient effects. Most of the work in this thesis is a first step towards the implementation of quantum manipulation schemes in a double optical lattice.