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arXiv:0706.3072 · Physical Review A

Efficient vibrational state coupling in an optical tilted-washboard potential via multiple spatial translations and application to pulse echoes

Samansa Maneshi, J. F. Kanem, Chao Zhuang, Matthew J. Partlow, Aephraim M. Steinberg

Published Feb 5, 2008• 11 citations
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Abstract

We measure the application of simple and compound pulses consisting of time-dependent spatial translations to coupling vibrational states of ultracold $^{85}\text{R}\text{b}$ atoms in a far-detuned 1D optical lattice. The lattice wells are so shallow as to support only two bound states, and we prepare the atoms in the ground state. The lattice is oriented vertically, leading to a tilted-washboard potential analogous to those encountered in condensed-matter systems. Experimentally, we find that a square pulse consisting of lattice displacements and a delay is more efficient than single-step pulses or Gaussian pulses. This is described as an example of coherent control. It is striking that contrary to the intuition that soft pulses minimize loss, the Gaussian pulse is outperformed by the square pulse. Numerical calculations are in strong agreement with our experimental results and show the superiority of the square pulse to the single-step pulse for all lattice depths and to the Gaussian pulse for lattice depths greater than seven lattice recoil energies. We also compare the effectiveness of these pulses for reviving oscillations of atoms in vibrational superposition states using the pulse-echo technique. We find that the square and Gaussian pulses result in higher echo amplitudes than the single-step pulse. These improved echo pulses allow us to probe coherence at longer times than in the past, measuring a plateau which has yet to be explained. In addition, we show numerically that the vibrational state coupling due to such lattice manipulations is more efficient in shallow lattices than in deep lattices. The coupling probability for an optimized single-step pulse approaches $1/e$ as the depth goes to infinity (harmonic-oscillator limit), while in shallow lattices with large anharmonicity, the coupling probability reaches a maximum value of 0.51 for a lattice depth of five recoil energies. For square and Gaussian pulses the coupling in the lattice is even stronger, reaching maxima of 0.64 at 6 recoil energies and 0.67 at 5 recoil energies, respectively.

DOI
10.1103/physreva.77.022303

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In this thesis, I report on experiments with cold 85Rb atoms in a far-detuned one-dimensional optical lattice. These experiments are focused on creating efficient coupling between the quantized vibrational states of atoms in the optical lattice, on controlling and maintaining coherence between the vibrational states, and on developing a spectroscopy method to characterize the decay of coherence. First, I present an experimental study of the application of simple and compound pulses consisting of time-dependent spatial translations to coupling vibrational states of ultracold 85Rb atoms in the optical\nlattice. Experimental results show that a square pulse consisting of lattice displacements and a delay is more efficient than single-step and Gaussian pulses. The square pulse can be seen as an example of coherent control. Numerical calculations are in strong agreement with the experimental results. In addition, it is shown numerically that the vibrational state coupling due to such lattice manipulations is more efficient in shallow lattices than in deep lattices, in which the coupling probability approaches the harmonic\noscillator limit. Next, the effectiveness of these pulses in reviving oscillations of atoms in vibrational superposition states using a pulse-echo technique is examined. Experimental results show that the square and Gaussian pulses result in higher echo amplitudes than the single-step pulse. These echo amplitudes are an order of magnitude larger than the echo amplitudes observed previously for the motional states of atoms in optical lattices.\nWith the aim of the optimized square echo pulse, echo amplitude is measured at much\nlonger times, where a surprising coherence freeze (plateau) is observed. To investigate \nmechanisms responsible for the observed echo decay and the coherence freeze, we developed\na new two-dimensional pump-probe spectroscopy technique to monitor the evolution of frequency-frequency correlations in the system, a necessary input for understanding the decay of coherence. Through this 2D technique, we have characterized the temporal decay of frequency memory and through our simulations we find that coherence freeze is related to the shape of this memory loss function. This technique is general in that it can be applied in a variety of quantum information candidate systems to probe the nature of their decoherence.
Summary form only given. The investigation of coherent superposition states for atoms interacting with external potentials allows a completely new class of experiments directed towards coherent trapping and guiding of neutral atoms. In addition, the process of decoherence, i.e., the collapse of superposition states, is one of the basic concepts for our understanding of the connection between classical and quantum physics. We study the creation and decay of superpositions of different components of the center-of-mass wavefunction of rubidium atoms in a one-dimensional near-resonant optical lattice. This makes it possible to gain insight into the dependence of decoherence processes on the coupling of the atoms to the light field. We discuss the dependence of the wave packet oscillations and echoes on experimental parameters (potential depth, light intensity and detuning, time delay, size of the shift, etc.). We compare our experimental results with numerical simulations of the echo effect. The observation of this new effect in the coherent wave packet motion of atoms trapped in optical potentials will allow us to selectively study the decoherence process and measure the decoherence time in regimes where this was previously impossible.
This dissertation reports on quantum state preparation of cesium atoms in a two-dimensional optical lattice, by resolved-sideband Raman cooling. An optical lattice is a periodic potential produced by the light shift interaction between an atom and light field. Laser cooled atoms can become strongly localized about the bottom of potential wells in an optical lattice, where they occupy a discrete spectrum of bound vibrational energy levels. The distribution over vibrational levels of atoms in the lattice is characterized by the mean vibrational excitation, n . In an optical lattice, absorption and emission of photons from lattice beams causes n to increase in time. This source of heating is always present, but its rate can be greatly reduced in a lattice detuned far from the atomic resonance. Sideband cooling is an efficient means of transferring atoms from higher into lower-lying vibrational levels and, thus, it reduces n for the ensemble. If the sideband cooling rate is much greater than the heating rate, then n approaches zero and virtually all atoms are in the lowest vibrational level in their potential wells. Our sideband cooling scheme involves stimulated Raman transitions between bound states in the potential wells of a pair of magnetic sublevels, followed by optical pumping, for a net loss of one quantum of vibration per cooling cycle. The process accumulates 98% of atoms in the ground vibrational level of a potential well associated with a single Zeeman substate. Each atom in the lattice is then very close to a pure state. For two-dimensional lattice with sideband cooling we find nx≈ny≈0.008 &parl0;16&parr0; . Various issues related to state preparation and sideband cooling are also discussed in the context of a one dimensional lin ⊥ lin optical lattice. These include improvement of laser cooling in a near resonance lattice by application of weak magnetic fields, transfer of atoms from near into far off-resonance lattices, and heating rates in far off-resonance lattices.
Raman lasers are used as a spectroscopic probe of the state of atoms confined in a shallow one-dimensional (1D) vertical lattice. For sufficiently long laser pulses, resolved transitions in the bottom band of the lattice between Wannier Stark states corresponding to neighboring wells are observed. Couplings between such states are measured as a function of the lattice laser intensity and compared to theoretical predictions, from which the lattice depth can be extracted. Limits to the linewidth of these transitions are investigated. Transitions to higher bands can also be induced, as well as between transverse states for tilted Raman beams. All these features allow for a precise characterization of the trapping potential and for an efficient control of the atomic external degrees of freedom.
In this thesis, I present an experimental study of quantum control techniques for transferring population between vibrational states of atoms trapped in an optical lattice. Results from a range of techniques are compared, including techniques tested previously in the same system. In the study of the Adiabatic Rapid Passage (ARP) technique, control of population transfer is realized through varying the chirp rate and modulation amplitude of a frequency-chirped sinusoidal displacement of the lattice. Meanwhile, dependence of population transfer on the chirp direction is observed, which is explained by a model of ARP in a 3-level system. In the study of the coherent control technique, interference between a one-phonon transition at 2\omega and a two-phonon transition at omega is experimentally demonstrated. The omega and 2\omega transitions are realized by sinusoidally displacing the optical lattice at omega and sinusoidally modulating the lattice depth at 2\omega, respectively. The branching ratio of transitions to the first excited state and to higher excited states is controlled by varying the relative phase between these two pathways. The highest measured branching ratio of 17\pm2 is achieved among all the experiments using this coherent control scheme. In the study of the GRadient Ascent Pulse Engineering (GRAPE) technique, a "pulse" involving both displacement and depth-modulation of the lattice is used to transfer population. This pulse is theoretically engineered with the GRAPE algorithm to optimize the fidelity between the first excited state and the final state, when the lattice Hamiltonian without gravity for a specific lattice depth is considered. The experimental result shows that there is almost no excitation into higher excited states during population transfer from the ground to the first excited state, even when this process is affected by gravity and inhomogeneous broadening in reality. By comparing all the techniques, the GRAPE technique is found to be the best in terms of increasing population transfer into the first excited state while reducing excitation into higher excited states. On the other hand, the ARP technique creates the highest normalized population inversion, a ratio of the difference to the sum of the ground and the first excited state populations.
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.