We report an experiment in which an atomic excitation is localized to a spatial width that is a factor of 8 smaller than the wavelength of the incident light. The experiment utilizes the sensitivity of the dark state of electromagnetically induced transparency (EIT) to the intensity of the coupling laser beam. A standing-wave coupling laser with a sinusoidally varying intensity yields tightly confined Raman excitations during the EIT process. The excitations, located near the nodes of the intensity profile, have a width of 100 nm. The experiment is performed using ultracold 87 Rb atoms trapped in an optical dipole trap, and atomic localization is achieved with EIT pulses that are approximately 100 ns long. To probe subwavelength atom localization, we have developed a technique that can measure the width of the atomic excitations with nanometer spatial resolution.
We present a proof-of-principle experiment in which the population of an atomic level is spatially localized using the technique of electromagnetically-induced transparency (EIT). The key idea is to utilize the sensitive dependence of the dark state of EIT on the intensity of the coupling laser beam. By using a sinusoidal intensity variation (standing-wave), we demonstrate that the population of a specific hyperfine level can be localized much tighter than the spatial period.It is well-known that traditional optical techniques cannot resolve or write features smaller than half the wavelength of light. This barrier, known as the diffraction limit, has important implications for a variety of scientific research areas including biological microscopy and quantum computation. As an example, in a neutralatom quantum computing architecture, the diffraction limit prohibits high-fidelity manipulation of individual atoms if they are separated by less than the wavelength of light. Recently, Agarwal and others [1][2][3] have proposed to use the dark state of electromagnetically induced transparency (EIT) [4,5] to address atoms at potentially nanometer spatial scales. This technique relies on the sensitive dependence of the dark state to the intensities of the driving probe and coupling laser beams. If a standing-wave coupling laser is used, the population of the excited Raman level can be very tightly localized near the intensity nodes, allowing for sub-wavelength control. In this letter, we present a proof-of-principle experiment that demonstrates the key ideas of this approach. By using ultracold Rubidium (Rb) atoms in a magneto-optical trap (MOT) and pulsed coherent transfer, we demonstrate atomic localization to spots much smaller than the spatial period of the coupling-laser intensity profile. Although due to imaging limitations we have used a large spatial period in this work (≈ 600 µm), our results will likely scale to the sub-wavelength regime in the future.Before proceeding, we cite important prior work leading up to this experiment. In their pioneering work, Thomas and colleagues have suggested and experimentally demonstrated sub-wavelength position localization of atoms using spatially varying energy shifts [6][7][8]. Zubairy and coworkers have discussed atom localization using resonance fluorescence and phase and amplitude control of the absorption spectrum [9][10][11]. Knight and colleagues discussed localization via quantum interference at the probability amplitude of the excited electronic state [12]. Li et. al. have experimentally demonstrated probe narrowing beyond the diffraction limit using a spatially-varying coupling laser profile in a vapor cell [13]. There has also been remarkable progress in utilizing the position dependent stimulated emission to achieve nanoscale resolution [14,15]. This last approach, also known as stimulated-emission depletion microscopy, is now a widely used technique in biological imaging. We note that our approach of using the dark state for atomic localization has the followin...
We experimentally demonstrate the localization of excitation between hyperfine ground states of 87 Rb atoms to as small as λ/13 wide spatial regions. We use ultracold atoms trapped in a dipole trap and utilize electromagnetically induced transparency (EIT) for the atomic excitation.The localization is achieved by combining a spatially varying coupling laser (standing-wave) with the intensity dependence of EIT. The excitation is fast (150 ns laser pulses) and the dark-state fidelity can be made higher than 94% throughout the standing wave. Because the width of the localized regions is much smaller than the wavelength of the driving light, traditional optical imaging techniques cannot resolve the localized features. Therefore, to measure the excitation profile, we use an auto-correlation-like method where we perform two EIT sequences separated by a time delay, during which we move the standing wave. 1 I. 1. INTRODUCTIONThe diffraction limit, which posits that traditional optical techniques cannot resolve or write features smaller than about half the wavelength of light, is an important barrier for a variety of research areas. For example, a number of quantum computing implementations, such as those utilizing trapped neutral atoms, use focused laser beams to trap, initialize, and manipulate qubits [1][2][3][4][5]. In a neutral-atom quantum computing architecture, the qubit spacing has to be larger than half the wavelength, which limits the two-qubit interaction energies that can be obtained (for example through Rydberg dipole-dipole interaction). The necessary qubit spacing in turn limits the fidelity and the speed of the two-qubit gates. A technique to address atoms with high fidelity in sub-wavelength spatial scales would greatly improve the performance of the two-qubit gates. In this work, we use the dark state of electromagnetically induced transparency (EIT) [6][7][8][9] to address atoms in regions much smaller than the diffraction limit. We use a standing wave coupling laser and demonstrate efficient transfer between the ground levels of 87 Rb in regions with widths as small as λ/13. The transfer is fast (150 ns laser pulses) and the fidelity for the atomic system to be in the dark state can be made higher than 94% at all spatial points along the standing wave. We perform these experiments using ultracold 87 Rb atoms trapped in a far-off-resonant dipole trap at a temperature of ≈ 1 µK. Although other techniques have been investigated that achieve sub-wavelength resolution, using the dark state provides key advantages for quantum computing. The atoms are coherently transferred [9], keeping their phase relationship with other qubits intact. The dark state can be prepared with little population transfer to a radiative excited state, which reduces heating and decoherence from spontaneous emission.Because the excitation is coherent, dark-state based localization can be achieved using short and intense laser pulses, allowing fast quantum gates to be constructed.There has been other important work related to address...
The growth of online learning has created a need for instructors who can competently teach online. This literature review explores the research questions, program recommendations, and future research suggestions related to professional development for online instructors. Articles were selected and coded based on date of publication and the context of the professional development. Results indicate that most research questions focused on (a) professional development programs, (b) instructors, and (c) instructors’ online courses. Most program recommendations focused on (a) professional development programs, (b) context of professional development, and (c) instructors’ activity during professional development. Future recommendations for research topics focused on professional development programs and instructors, while future recommendations for research methods focused on research design and institutional settings. The findings suggest that while professional development for online instructors is important, consistency in both design and delivery is lacking. Future research is needed to provide guidance to programs, instructors, and institutions leading to satisfaction and success for more online students.
We analyze a general approach for suppressing inhomogeneous broadening of atomic transitions and thereby increasing the strength of the interaction between the atomic system and near-resonant light. The key idea is to compensate for the frequency shift due to the broadening process by using an intense laser to produce an equal and opposite Stark shift.
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