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arXiv:2405.09117 · Physical Review Research

Complex-valued three-dimensional atomic spectroscopy with Gaussian-assisted inline holography

Xing Huang, Yuzhuo Wang, Jian Zhao, Saijun Wu

Published Jan 15, 2025• 2 citations
arXivHTMLPDF

Abstract

When a laser-cooled atomic sample is optically excited, the envelope of coherent forward scattering can often be decomposed into a few complex Gaussian profiles. The convenience of Gaussian propagation helps address key challenges in digital holography. In this paper, we develop a Gaussian-decomposition-assisted approach to inline holography for single-shot, simultaneous measurements of absorption and phase-shift profiles of small atomic samples sparsely distributed in three dimensions. The samples' axial positions are resolved with micrometer resolution and their spectroscopy are extracted from complex-valued images recorded at various probe frequencies. The phase-angle readout is not only robust against transition saturation but also insensitive to atom-number and optical-pumping-induced interaction-strength fluctuations. Benefiting from such features, we achieve hundred-kHz-level single-shot resolution to the transition frequency of a Rb 87 D 2 line, with merely hundreds of atoms. We further demonstrate single-shot three-dimensional field sensing by measuring local light shifts to the atomic array with micrometer spatial resolution.

DOI
10.1103/physrevresearch.7.013054

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When a laser-cooled atomic sample is optically excited, the envelope of coherent forward scattering can often be decomposed into a few complex Gaussian profiles. The convenience of Gaussian propagation helps address key challenges in digital holography. In this paper, we develop a Gaussian-decomposition-assisted approach to inline holography for single-shot, simultaneous measurements of absorption and phase-shift profiles of small atomic samples sparsely distributed in three dimensions. The samples' axial positions are resolved with micrometer resolution and their spectroscopy are extracted from complex-valued images recorded at various probe frequencies. The phase-angle readout is not only robust against transition saturation but also insensitive to atom-number and optical-pumping-induced interaction-strength fluctuations. Benefiting from such features, we achieve hundred-kHz-level single-shot resolution to the transition frequency of a Rb 87 D 2 line, with merely hundreds of atoms. We further demonstrate single-shot three-dimensional field sensing by measuring local light shifts to the atomic array with micrometer spatial resolution.
We theoretically develop and experimentally demonstrate a holographic method for imaging cold atoms at the diffraction and photon shot noise limits. Aided by a double point source reference field, a simple iterative algorithm robustly removes the twin image of an 87 Rb cold atom sample during the image reconstruction. Shot-noise limited phase shift and absorption images are consistently retrieved at various probe detunings, and during the laser cooling process. We consistently resolve less than 2 mrad phase shift ( attenuation) of the probe light, outperforming shot-noise limited phase-contrast (absorption) imaging by a factor of 4 or more if the same camera is used without pixel saturation. We discuss the possible extension of this work for precise phase imaging of dense atomic gases, and for off-resonant probing of multiple atoms in optical lattices.
The propagation of light in moving media is dragged by atomic motion. The light-drag effect can be dramatically enhanced by reducing the group velocity with electromagnetically induced transparency (EIT). We develop a systematic procedure to accurately reconstruct the complex wavefront of the slow light with single-shot measurements, enabling precise, photon shot-noise-limited spectroscopic measurements of atomic response across EIT even in the presence of generic atomic number fluctuations. Applying the technique to an expanding cloud of cold atoms, we demonstrate simultaneous inference of the atomic density distribution and the velocity field from the complex imaging data. This inline imaging technique may assist a wide range of cold-atom experiments to access spectroscopic and phase-space information with in situ and minimally destructive measurements.
Multidimensional coherent spectroscopy is a powerful method for studying materials’ optical properties. It also has potential to be used for chemical sensing applications as it allows the measurements of samples’ energy level structures as well as couplings between the excited states resonances. This coupling information is the key to identify whether or not the sample contains a mixture of analytes. Coupling information is not easily accessible using one-dimensional linear or non-linear methods, necessitating more complex multidimensional experimental techniques. However, multidimensional techniques require bulky apparatus, complex stabilization schemes, and/or long acquisition times that prevent them from being used outside the lab. Here we propose and demonstrate a new and simple approach that enables the measurements of the main absorption lines as well as the couplings between the excited states resonances extremely fast (tens to hundreds ofμs\mu \text{s}μs) without measuring the full multidimensional spectra. This approach is based on the Fourier-slice theorem and was inspired by frequency comb technology, particularly dual-comb spectroscopy. Our approach uses free-running lasers and co-linear geometry, and with the development of compact lasers this approach can become field-deployable for sensing applications. We demonstrate the concept on rubidium vapor.
Ordered atomic arrays feature an enhanced collective optical response compared to random atomic ensembles due to constructive interference in resonant dipole-dipole interactions. One consequence of this is the existence of a large shift of the transition with respect to the bare atomic frequency. In the linear optics regime (low light intensity), one observes a spectroscopic shift of the Lorentzian atomic line often called the collective Lamb shift. For stronger driving, many excitations are present in the system rendering the calculation of this shift theoretically challenging, but its understanding is important for instance when performing Ramsey spectroscopy in optical clocks. Here we report on the study of the collective optical response of a one-dimensional array of 30 dysprosium atoms. We drive the atoms on the narrow intercombination transition isolating a two-level system, and measure the atomic state with single-shot state readout using a broad transition. In the linear optics regime, we measure the shift of the resonance in steady state due to dipole interactions, and measure how this shift depends on the interatomic distance. We further resolve at the single atom level how the excitation is distributed over the array. Then, on the same transition we perform Ramsey spectroscopy i.e., away from the linear regime. We observe a time-dependent shift, that allows us to draw the connection between the collective Lamb shift observed in the linear optics regime and in the large-excitation case.
Abstract Three-dimensional (3D) atom localization at subwavelength scales is of critical interest for advanced applications in nanolithography and laser cooling. Despite significant efforts, achieving high spatial resolution in all three dimensions remains a challenging task. In this work, we propose and analytically investigate a novel scheme for 3D subwavelength atom localization using a closed-loop five-level atomic system driven by a phase-controlled microwave field. The localization mechanism is based on the position-dependent absorption of a weak probe field in the presence of three orthogonal standing-wave coupling fields. The inclusion of a magnetically allowed microwave transition introduces a controllable relative phase ( ϕ ), enabling coherent control over the atomic spatial distribution. Our analysis demonstrates that, by judiciously tuning the system parameters—including probe detuning, relative phase, and quantum interference arising from spontaneous emission—the atom can be localized to a highly confined region with a spatial resolution as high as ∼ 0.03 λ , where λ is the optical wavelength. The results highlight the critical role of phase control and coherent field interaction in enhancing the localization precision. This technique offers a robust and versatile tool for achieving high-resolution 3D atom localization and may pave the way for practical implementations in nanoscale fabrication and quantum technologies.
We propose a lens-free nondestructive imaging method for cold atomic clouds using a Gaussian beam accompanied with phase shifting interferometry. This scheme requires no imaging lens. Hence, aberrations associated with it are completely eliminated and mechanical focusing can be avoided. Compared with the common single-beam nondestructive means, our proposed scheme lowers the energy per probe pulse delivered to the cold samples by almost three orders of magnitude, due to signal enhancement inherently provided in the two-beam configuration. Moreover, higher image resolution is attainable by magnifying the far-field interference distribution using a divergent Gaussian beam. We examine this novel lensless detection means for in situ imaging on typical cold atomic clouds under experimentally achievable conditions. Our simulations show the cloud position can be precisely determined, depending upon the cloud size and probe parameters, with an uncertainty from a few hundreds of micrometers to only a few micrometers, and the spatial resolution of the retrieved phase image can reach the diffraction limit.