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arXiv:1302.6208 · Journal of Physics B Atomic Molecular and Optical Physics

Microwave control of atomic motional states in a spin-dependent optical lattice

Noomen Belmechri, Leonid Förster, Wolfgang Alt, Artur Widera, Dieter Meschede, Andrea Alberti

Published May 9, 2013• 58 citations
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Abstract

Spin-dependent optical potentials allow us to use microwave radiation to manipulate the motional state of trapped neutral atoms (Förster et al 2009 Phys. Rev. Lett. 103 233001). Here, we discuss this method in greater detail, comparing it to the widely employed Raman sideband coupling method. We provide a simplified model for sideband cooling in a spin-dependent potential, and we discuss it in terms of the generalized Lamb–Dicke parameter. Using a master equation formalism, we present a quantitative analysis of the cooling performance for our experiment, which can be generalized to other experimental settings. We additionally use microwave sideband transitions to engineer motional Fock states and coherent states, and we devise a technique for measuring the population distribution of the prepared states.

DOI
10.1088/0953-4075/46/10/104006

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Spin-dependent optical potentials allow us to use microwave radiation to manipulate the motional state of trapped neutral atoms (Förster et al 2009 Phys. Rev. Lett. 103 233001). Here, we discuss this method in greater detail, comparing it to the widely employed Raman sideband coupling method. We provide a simplified model for sideband cooling in a spin-dependent potential, and we discuss it in terms of the generalized Lamb–Dicke parameter. Using a master equation formalism, we present a quantitative analysis of the cooling performance for our experiment, which can be generalized to other experimental settings. We additionally use microwave sideband transitions to engineer motional Fock states and coherent states, and we devise a technique for measuring the population distribution of the prepared states.
The subject of this work is the control of the quantum mechanical motional state of trapped neutral Cesium atoms. This is accomplished using a rarely considered method based on microwave radiation in combination with a spin dependent optical lattice potential. The setup used was designed to trap and to store on the order of ten atoms in a one dimensional optical lattice. Fluorescence imaging allows to determine both, the number and the position of the atoms. The spin degree of freedom is manipulated using microwave radiation and the trapping potential allows to shift the atoms to the 'left' or to the 'right' along the potential axis, depending on their spin orientation. A microwave spectrum with a slightly displaced lattice exhibits sideband peaks corresponding to a change of the vibrational quantum number. This is the mechanism which introduces coupling between the spin and the motional degree of freedom. The work draws parallels to the usually used sideband technique based on optical transitions instead of microwaves and exploiting the photon recoil instead of a state dependent potential. Similar to the optical method the microwave based approach allows for the realization of a resolved-sideband cooling technique which efficiently prepares the atomic ensemble in the motional ground state. Starting from this purified quantum mechanical state, other interesting states are prepared using successive sideband transitions. The result of the preparation is probed by implementing filtering schemes for the motional state. With this control technique the experimental setup in total is capable to control the spin, the position along the one dimensional periodic potential and the vibrational state of the atoms.
We control the quantum mechanical motion of neutral atoms in an optical lattice by driving microwave transitions between spin states whose trapping potentials are spatially offset. Control of this offset with nanometer precision allows for adjustment of the coupling strength between different motional states, analogous to an adjustable effective Lamb-Dicke factor. This is used both for efficient one-dimensional sideband cooling of individual atoms to a vibrational ground state population of 97% and to drive coherent Rabi oscillation between arbitrary pairs of vibrational states. We further show that microwaves can drive well resolved transitions between motional states in maximally offset, shallow lattices, and thus in principle allow for coherent control of long-range quantum transport.
This thesis gives an account of work done on semi-classical and quantum Monte Carlo simulations in far-detuned optical lattices. Firstly, the basic principles of laser cooling of atoms are presented including a short introduction to optical lattices in the near and far-detuned regime. A detailed analysis is made of the band-structure of optical lattices, using the Bloch formalism, and of the bound-state population distribution appropriate for a thermal sample of trapped atoms. Secondly, a general overview is given of the quantum Monte Carlo method for simulating the dynamics of atom-light interactions. This is followed by a detailed study of the concept of Raman cooling, which is a useful tool to prepare atoms in the ground motional state of the lattice and an important first step to achieving quantum state control with ultra-cold atoms. A simplified model of Raman cooling is introduced and simulated using the quantum Monte Carlo wave-function approach. Then the implementation of simulations of resolved-sideband Raman cooling based on this model is discussed as is how the results were used to optimize the experimental work done by our group. The results of these simulations show for the first time that the quantum Zeno effect has a crucial impact on the efficiency of Raman cooling experiments. Also the experimental measurements of the temperature of Raman sideband cooled atoms for a range of parameters are compared with theoretical results and shows a good qualitative agreement. Thirdly, the results of semi-classical numerical simulations of parametric excitation in optical lattices are presented. It is shown that the modulation of the potential can result in selective parametric excitation of trapped atoms. The theoretical results show good qualitative agreement with experiment. The thesis is concluded with a description of possible avenues for future studies on quantum state control in optical lattices.
Optical lattices induced by light detuned far from the frequency of any atomic resonance transition are ideal systems in which to develop techniques for the coherent control of atomic motional and internal states. Decoherence arising from spontaneous emission can be eliminated to an arbitrary degree by varying the detuning of the optical field. The atoms trapped in these lattices are to a large extent isolated from environmental disturbances and from each other. The first step towards the coherent control of atoms in a far-detuned lattice is their preparation in a single motional state. In this thesis the preparation of atoms in the ground vibrational state of a two-dimensional far-detuned optical lattice via resolved-sideband Raman cooling is presented. This sideband-cooling scheme involves stimulated Raman transitions between bound vibrational states of a pair of magnetic ground state sublevels, followed by an irreversible step due to optical pumping, resulting in a net loss of one quantum of vibrational energy per cooling cycle. This process provides efficient cooling in two-dimensions and leads to the accumulation of a large fraction of atoms in the 2-D ground vibrational state of a potential well associated with a single Zeeman substate. Experiments aimed at improving and monitoring the characteristics of the lar-detuned lattice and the sideband-Raman cooling efficiency are also described. Parametric excitation experiments and modelling are employed to investigate the degree of anharmonicity of the optical potential and the importance of heating induced by laser intensity noise, whilst Zeeman-state analysis of the sample is performed for monitoring the distribution of atoms over different magnetic sub- states. Finally, spin-polarization experiments are carried out in order to study the paramagnetic properties of the lattice and lead to an evaluation of a spin-temperature for the sample.
Summary form only given. Optical microtraps provide a strong spatial confinement for laser-cooled atoms. They can, e.g., be realized with strongly focused trapping light beams or the optical near fields of nano-scale waveguides and photonic nanostructures. Atoms in such traps often experience strongly spatially varying AC Stark shifts which are proportional to the magnetic quantum number of the respective energy level. These inhomogeneous fictitious magnetic fields can cause a displacement of the trapping potential that depends on the Zeeman state. Hitherto, this effect was mainly perceived as detrimental. However, it also provides a means to probe and to manipulate the motional state of the atoms in the trap by driving transitions between Zeeman states. Furthermore, by applying additional real or fictitious magnetic fields, the state-dependence of the trapping potential can be controlled. Here, using laser-cooled atoms that are confined in a nanofiber-based optical dipole trap [1], we employ this control in order to tune the microwave coupling of motional quantum states. We record corresponding microwave spectra which allow us to infer the trap parameters as well as the temperature of the atoms. Finally, we reduce the mean number of motional quanta in one spatial dimension to {n}=0.3±0.1, close to the motional ground state, by using microwave sideband cooling. Our work shows that the inherent fictitious magnetic fields in optical microtraps expand the experimental toolbox for interrogating and manipulating cold atoms.
We trap neutral Cs atoms in a two-dimensional optical lattice and cool them close to the zero point of motion by resolved-sideband Raman cooling. Sideband cooling occurs via transitions between the vibrational manifolds associated with a pair of magnetic sublevels, and the required Raman coupling is provided by the lattice potential itself. We obtain mean vibrational excitations ${\overline{n}}_{x}\ensuremath{\approx}{\overline{n}}_{y}<0.024$, corresponding to a population >95>95%>95 in the vibrational ground state. Atoms in the ground state of an optical lattice provide a new system in which to explore quantum state control and subrecoil laser cooling.