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Absorption imaging of a quasi-two-dimensional gas: A multiple scattering analysis

Lauriane Chomaz, Laura Corman, Tarik Yefsah, Rémi Desbuquois, Jean Dalibard

Published May 1, 2012• 86 citations
Publisher

Abstract

Absorption imaging with quasi-resonant laser light is a commonly used technique for probing ultra-cold atomic gases in various geometries. In this paper, we investigate some non-trivial aspects of this method when applying the method to in situ diagnosis of a quasi-two-dimensional (2D) gas. Using Monte Carlo simulations we study the modification of the absorption cross-section of a photon when it undergoes multiple scattering in the gas. We determine the variations of the optical density with various parameters, such as the detuning of the light from the atomic resonance and the thickness of the gas. We compare our results to the known 3D result (the Beer–Lambert law) and outline the specific features of the 2D case.

DOI
10.3929/ethz-b-000049792

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Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis

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Absorption imaging with quasi-resonant laser light is a commonly used technique for probing ultra-cold atomic gases in various geometries. In this paper, we investigate some non-trivial aspects of this method when applying the method to in situ diagnosis of a quasi-two-dimensional (2D) gas. Using Monte Carlo simulations we study the modification of the absorption cross-section of a photon when it undergoes multiple scattering in the gas. We determine the variations of the optical density with various parameters, such as the detuning of the light from the atomic resonance and the thickness of the gas. We compare our results to the known 3D result (the Beer–Lambert law) and outline the specific features of the 2D case.

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Quantitative absorption imaging: The role of incoherent multiple scattering in the saturating regime

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In this paper, we study the modification of coherent scattering processes in dense ensembles. Using absorption imaging, we experimentally demonstrate that the absorption cross section in dense $^{87}\mathrm{Rb}$ cold atom ensembles is reduced, with respect to the single-particle response. This reduction is linearly dependent on the optical density and well reproduced by a one-dimensional model of coherent field propagation in an ensemble of quantum two-level systems that self-consistently incorporates multiple scattering contribution. Our model shines light upon the key role of incoherent scattering on the modification of the optical response of dense ensembles and leads to a generalization of the Beer-Lambert law. Our result applies to any effective two-level system ensemble and allows for quantitative and absolute in situ absorption imaging.

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Quasi two-dimensional 6Li Fermi gas

Paul Dyke

Quasi-2D degenerate Fermi gases provide a rich physical environment to explore since many effects that are present do not exist in 3D. This thesis describes the first experiments carried out in a quasi-2D Fermi gas across the broad 6Li Feshbach resonance at 834 G. A description of the apparatus used to form molecular Bose-Einstein condensates and degenerate Fermi gases in the two lowest hyperfine states of 6Li, |F = 1/2,mf = 1/2i and |F = 1/2,mf = −1/2i, is presented. An anisotropic 2D optical potential is formed by an elliptical Gaussian beam produced by tightly focusing a circular Gaussian beam in one direction with a cylindrical lens. The trapping frequencies are ∼3 kHz in the axial direction and ∼50 Hz in the radial direction giving an aspect ratio of ∼60. For a non-interacting Fermi gas this allows ∼1700 atoms to populate the lowest transverse harmonic oscillator state and to be considered as quasi-2D. We present the transition from a three dimensional gas to a two dimensional gas at ∼2000 atoms agreeing within experimental uncertainty with the non-interacting atom number. The observations are made through measuring the radial and axial widths of the gas at three different magnetic fields, 810 G, 834 G, and 991 G. The widths σ are then plotted against the atom number N. The curve, log σ(N) = n logN+a, is then fit to the data in the 3D regime and in the 2D regime. The expansion of a non-interacting Fermi gas in the 2D regime changes from a scaling of N1/4 to N1/6 in the 3D regime and for a Bose gas it changes to N1/5. A value for n is extracted in each of these regimes. For each magnetic field we then obtain in the 2D regime: n = 0.27(0.04) at 810 G, n = 0.23(0.02) at 834 G and n = 0.26(0.01) at 991 G. In the 3D regime we obtain: n = 0.195(0.01) at 810 G, n = 0.154(0.01) at 834 G and n = 0.175(0.01 at 991 G. We also observe a change in the aspect ratio as we approach the 2D regime which is not present in our 3D single beam optical dipole trap and is absent in any 3D system. These first results indicate that we have a quasi-2D Fermi gas. The main experimental results are the first indications of a confinement induced resonance in a 6Li Fermi gas through the measurement of the cloud width in the tightly confined direction after a fixed expansion time. We observe a significant deviation in the transverse width of the 2D interacting Fermi gas from the 3D case due to the increased tight confinement. The confinement induced resonance should appear when the 3D scattering length approaches the transverse harmonic oscillator length, az = p~/mωz, where m is the mass and ωz is the tight transverse trapping frequency. For our experimental parameters this leads to a 3D scattering length of 1.03 μm, where the observation is at 819(1) G. In the weakly confined direction there is no such increase in the width due to the free motion in the xy plane. Instead the cloud width across the Feshbach resonance increases monotonically, similar to that of a 3D gas and as described theoretically for a quasi-2D Fermi gas by Lin et al. [1].

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Narrowing of sub-Doppler saturated-absorption resonances in multilayer gas cells

А. Ч. Измайлов

We have studied theoretically nontrivial specific features of sub-Doppler resonances of saturated absorption in a multilayer gas cell with a rarefied gas medium, which is a compact analog of a large number of plane-parallel atomic beams. Spatially separated saturating and probing monochromatic laser beams that co- and counterpropagate (at the same frequency) in this cell have been considered. In this situation, the action of the light radiation of the saturating beam on the probing beam is determined by optically pumped atoms that fly between the beams under conditions that the longitudinal components of their velocities experience selection due to a specific geometry of the multilayer cell. Such a selection leads to a narrowing of the sub-Doppler resonance in the absorption of the probing beam and decreases the difference between the structures of this resonance for the cases of co- and counterpropagation of the saturating radiation. We have found that, in the considered multilayer cell, the effective width of the sub-Doppler resonance can be smaller (by a factor of about 1.5) than the extremely narrow characteristic width of the well-known Lamb dip in spectroscopy of saturated absorption in the standard gas cell. Results of this study can be used in atomic spectroscopy of ultrahigh resolution and for the laser-frequency stabilization.

Optics and Spectroscopy•Jul 1, 2014•0 citations
Absorption imaging with quasi-resonant laser light is a commonly used technique for probing ultra-cold atomic gases in various geometries. In this paper, we investigate some non-trivial aspects of this method when applying the method to in situ diagnosis of a quasi-two-dimensional (2D) gas. Using Monte Carlo simulations we study the modification of the absorption cross-section of a photon when it undergoes multiple scattering in the gas. We determine the variations of the optical density with various parameters, such as the detuning of the light from the atomic resonance and the thickness of the gas. We compare our results to the known 3D result (the Beer–Lambert law) and outline the specific features of the 2D case.
Absorption imaging with quasi-resonant laser light is a commonly used technique for probing ultra-cold atomic gases in various geometries. In this paper, we investigate some non-trivial aspects of this method when applying the method to in situ diagnosis of a quasi-two-dimensional (2D) gas. Using Monte Carlo simulations we study the modification of the absorption cross-section of a photon when it undergoes multiple scattering in the gas. We determine the variations of the optical density with various parameters, such as the detuning of the light from the atomic resonance and the thickness of the gas. We compare our results to the known 3D result (the Beer–Lambert law) and outline the specific features of the 2D case.
In this paper, we study the modification of coherent scattering processes in dense ensembles. Using absorption imaging, we experimentally demonstrate that the absorption cross section in dense 87Rb^{87}\mathrm{Rb}87Rb cold atom ensembles is reduced, with respect to the single-particle response. This reduction is linearly dependent on the optical density and well reproduced by a one-dimensional model of coherent field propagation in an ensemble of quantum two-level systems that self-consistently incorporates multiple scattering contribution. Our model shines light upon the key role of incoherent scattering on the modification of the optical response of dense ensembles and leads to a generalization of the Beer-Lambert law. Our result applies to any effective two-level system ensemble and allows for quantitative and absolute in situ absorption imaging.
Quasi-2D degenerate Fermi gases provide a rich physical environment to explore since many effects that are present do not exist in 3D. This thesis describes the first experiments carried out in a quasi-2D Fermi gas across the broad 6Li Feshbach resonance at 834 G. A description of the apparatus used to form molecular Bose-Einstein condensates and degenerate Fermi gases in the two lowest hyperfine states of 6Li, |F = 1/2,mf = 1/2i and |F = 1/2,mf = −1/2i, is presented. An anisotropic 2D optical potential is formed by an elliptical Gaussian beam produced by tightly focusing a circular Gaussian beam in one direction with a cylindrical lens. The trapping frequencies are ∼3 kHz in the axial direction and ∼50 Hz in the radial direction giving an aspect ratio of ∼60. For a non-interacting Fermi gas this allows ∼1700 atoms to populate the lowest transverse harmonic oscillator state and to be considered as quasi-2D. We present the transition from a three dimensional gas to a two dimensional gas at ∼2000 atoms agreeing within experimental uncertainty with the non-interacting atom number. The observations are made through measuring the radial and axial widths of the gas at three different magnetic fields, 810 G, 834 G, and 991 G. The widths σ are then plotted against the atom number N. The curve, log σ(N) = n logN+a, is then fit to the data in the 3D regime and in the 2D regime. The expansion of a non-interacting Fermi gas in the 2D regime changes from a scaling of N1/4 to N1/6 in the 3D regime and for a Bose gas it changes to N1/5. A value for n is extracted in each of these regimes. For each magnetic field we then obtain in the 2D regime: n = 0.27(0.04) at 810 G, n = 0.23(0.02) at 834 G and n = 0.26(0.01) at 991 G. In the 3D regime we obtain: n = 0.195(0.01) at 810 G, n = 0.154(0.01) at 834 G and n = 0.175(0.01 at 991 G. We also observe a change in the aspect ratio as we approach the 2D regime which is not present in our 3D single beam optical dipole trap and is absent in any 3D system. These first results indicate that we have a quasi-2D Fermi gas. The main experimental results are the first indications of a confinement induced resonance in a 6Li Fermi gas through the measurement of the cloud width in the tightly confined direction after a fixed expansion time. We observe a significant deviation in the transverse width of the 2D interacting Fermi gas from the 3D case due to the increased tight confinement. The confinement induced resonance should appear when the 3D scattering length approaches the transverse harmonic oscillator length, az = p~/mωz, where m is the mass and ωz is the tight transverse trapping frequency. For our experimental parameters this leads to a 3D scattering length of 1.03 μm, where the observation is at 819(1) G. In the weakly confined direction there is no such increase in the width due to the free motion in the xy plane. Instead the cloud width across the Feshbach resonance increases monotonically, similar to that of a 3D gas and as described theoretically for a quasi-2D Fermi gas by Lin et al. [1].
Quantum gas microscopes have become a major element for quantum simulations using ultra-cold atoms in optical lattices. They are for example used to observe long-range order such as anti-ferromagnetic correlations in far field optical lattices using density and spin resolved microscopy. Decreasing the period of such lattice offer interesting perspective to increase atom-atom interaction energies and engineer atom-light coupling that our group tackles via the hybridization of cold atoms and nano-structured surfaces.In this poster, we will present how such type of sub-wavelength lattice potentials can be generated by trapping atoms in proximity (tens to hundreds of nanometers) of a nano-structured surface. At such atom to surface distance, the attractive Casimir-Polder force can be compensated by a doubly dressed state trapping method that I will discuss. Such method additionally offers solutions to overcome the diffraction limit of conventional imaging that become critical for sub-wavelength lattices. In this work, I will present the experimental characterization of a sub-wavelength resolution absorption imaging applicable to quantum gas detection. This method requires a quantitative determination of the atom number of dense clouds which has been characterized in this work and demonstrate that the scattering cross section reduces linearly with the optical density. Modelling the propagation of light in dense cloud we show that this reduction can be attributed to re-scattering of the incoherent part of the resonant fluorescence spectrum.The poster will additionally present an update on our recent work on the spectroscopy of Acetylene in sealed hollow core fibers.
We present a complete recipe to extract the density–density correlations and the static structure factor of a two-dimensional (2D) atomic quantum gas from in situ imaging. Using images of non-interacting thermal gases, we characterize and remove the systematic contributions of imaging aberrations to the measured density–density correlations of atomic samples. We determine the static structure factor and report the results on weakly interacting 2D Bose gases, as well as strongly interacting gases in a 2D optical lattice. In the strongly interacting regime, we observe a strong suppression of the static structure factor at long wavelengths.
We have studied theoretically nontrivial specific features of sub-Doppler resonances of saturated absorption in a multilayer gas cell with a rarefied gas medium, which is a compact analog of a large number of plane-parallel atomic beams. Spatially separated saturating and probing monochromatic laser beams that co- and counterpropagate (at the same frequency) in this cell have been considered. In this situation, the action of the light radiation of the saturating beam on the probing beam is determined by optically pumped atoms that fly between the beams under conditions that the longitudinal components of their velocities experience selection due to a specific geometry of the multilayer cell. Such a selection leads to a narrowing of the sub-Doppler resonance in the absorption of the probing beam and decreases the difference between the structures of this resonance for the cases of co- and counterpropagation of the saturating radiation. We have found that, in the considered multilayer cell, the effective width of the sub-Doppler resonance can be smaller (by a factor of about 1.5) than the extremely narrow characteristic width of the well-known Lamb dip in spectroscopy of saturated absorption in the standard gas cell. Results of this study can be used in atomic spectroscopy of ultrahigh resolution and for the laser-frequency stabilization.