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Journal of the Optical Society of America B

Sub-microwave wavelength localization of Rydberg superatoms

Rahmatullah Rahmatullah, Ziauddin Ziauddin, You-Lin Chuang, Ray‐Kuang Lee, Sajid Qamar

Published Sep 21, 2018• 9 citations
Publisher

Abstract

With the interaction among one optical probe field and pairs of standing microwaves in the configuration of Rydberg-dressed electromagnetically induced transparency, we study theoretically the sub-microwave wavelength localization of Rydberg superatoms in two and three dimensions. Composited by an ensemble of Rydberg atoms with strong dipole–dipole interactions, a superatom can be localized within the microwave wavelength through the position-dependent atom–field interaction. By measuring the absorption spectrum from the optical probe field, a single position of Rydberg superatoms with high precision can be obtained, depending on the probe field detuning and phase shifts associated with the standing microwaves.

DOI
10.1364/josab.35.002588

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With the interaction among one optical probe field and pairs of standing microwaves in the configuration of Rydberg-dressed electromagnetically induced transparency, we study theoretically the sub-microwave wavelength localization of Rydberg superatoms in two and three dimensions. Composited by an ensemble of Rydberg atoms with strong dipole–dipole interactions, a superatom can be localized within the microwave wavelength through the position-dependent atom–field interaction. By measuring the absorption spectrum from the optical probe field, a single position of Rydberg superatoms with high precision can be obtained, depending on the probe field detuning and phase shifts associated with the standing microwaves.
Large dipole moments between high Rydberg states have been utilized to measure microwave electric fields based on electromagnetically induced transparency, while nonlocal Rydberg interactions are not suitably addressed yet in most relevant works. Here we adopt a mean-field superatom model to investigate the main restrictions of Rydberg microwave electrometry due to nonlocal interactions in atomic samples of appropriate densities. It is found that accurate microwave measurements can be attained in the linear regime only for dilute enough atomic samples and not too strong probe fields, which jointly determine whether Rydberg excitations are insignificant. This then leads to the critical lines of atomic density and probe intensity, below which the discrepancy between measured and real values is negligible due to vanishing Rydberg interactions, for a fixed microwave or coupling field. Our findings are instructive to identify the optimal conditions for Rydberg microwave electrometry by reaching a compromise between high precisions and high accuracies, requiring, respectively, large and small numbers of Rydberg excitations, when measuring weaker microwave fields.
We discuss electromagnetically induced transparency in a cold ensemble of atoms optically excited to the Rydberg states. Strong dipole-dipole or van der Waals interactions between the atomic Rydberg states translate into large nonlocal nonlinearities for a propagating probe field. In the case of weak quantum fields, this can be used to attain a conditional phase shift of π between pairs of single photons realizing a deterministic photonic phase gate. For stronger fields, long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our calculations reproduce and interpret the results of recent experiments.
Rydberg atoms have been widely investigated due to their large size, long radiative lifetime, huge polarizability and strong dipole-dipole interactions. The position information of Rydberg atoms provides more possibilities for quantum optics research, which can be obtained under the localization method. We study the behavior of three-dimensional (3D) Rydberg atom localization in a four-level configuration with the measurement of the spatial optical absorption. The atomic localization precision depends strongly on the detuning and Rabi frequency of the involved laser fields. A 100% probability of finding the Rydberg atom at a specific 3D position is achieved with precision of ∼0.031λ. This work demonstrates the possibility for achieving the 3D atom localization of the Rydberg atom in the experiment.
Interaction of the internal states of an atom with spatially dependent standing-wave cavity field can impart position information of the atom passing through it leading to subwavelength atom localization. We recently demonstrated a different regime of atom localization [Phys. Rev. A 72, 013820 (2005)], namely sub-half-wavelength localization through phase control of electromagnetically induced transparency. This regime corresponds to extreme localization of atoms within a chosen half-wavelength region of the standing-wave cavity field. Here we present further investigation of the simplified model considered earlier and show interesting features of the proposal. We show how the model can be used to simulate a variety of energy-level schemes. Furthermore, the dressed-state analysis is employed to explain the emergence and suppression of the localization peaks, and the peak positions and widths. The range of parameters for obtaining clean sub-half-wavelength localization is identified.
A scheme for two-dimensional (2D) atom localization via probe absorption in a three-level $\ensuremath{\Lambda}$-type atomic system is suggested. The required atom-field configuration is obtained when the atom interacts with a weak probe field and two orthogonal standing-wave fields where each standing-wave field is obtained from the superposition of the two standing-wave fields along the corresponding directions. We study the effect of the probe field detuning and phase shifts associated with the standing-wave fields. Two equally probable position information of the single atom are observed in the conditional position probability distribution. However, a unique position of the single atom in the 2D xyxyxy plane is observed for some arbitrary choices of the phases associated with standing-wave fields and by selecting slightly different wavelengths of standing-wave fields.
We present a realistic and efficient scheme for sub-half-wavelength atom localization. This scheme is based on the phase-dependent electromagnetically induced transparency in a four-level system in the double-Λ configuration. We use a strong bichromatic field (one component of which is standing-wave field) as the driving components, and a weak bichromatic field as the probe components. By choosing the collective phase of the four applied components, the atom is localized in either of the two half-wavelength regions with 50% detecting probability when the absorption to the probe fields is detected.