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Optics Express

Direct measurement of the Atom number in a Bose condensate

Hung-Wen Cho, Yan-Cheng He, Thorsten Peters, Yi‐Hsin Chen, Han-Chang Chen, Sheng-Chiun Lin, Yi-Chi Lee, Ite A. Yu

Published Jan 1, 2007• 9 citations
Publisher

Abstract

We report on directly measuring the atom number in a Bose- Einstein condensate by the method of optical pumping. Only the branching ratio of the spontaneous decay in the system and the absorption energy of a probe laser beam are required to determine the atom number. The measured absorption energy is not affected by the measurement condition such as the intensity, detuning, and polarization of the probe beam, the magnetic field, etc. We have shown that atom numbers as low as a few thousands can be measured. The atom number is an important parameter in the studies of Bose condensates and its accuracy is greatly improved by this sensitive and robust method.

DOI
10.1364/oe.15.012114

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We report on directly measuring the atom number in a Bose- Einstein condensate by the method of optical pumping. Only the branching ratio of the spontaneous decay in the system and the absorption energy of a probe laser beam are required to determine the atom number. The measured absorption energy is not affected by the measurement condition such as the intensity, detuning, and polarization of the probe beam, the magnetic field, etc. We have shown that atom numbers as low as a few thousands can be measured. The atom number is an important parameter in the studies of Bose condensates and its accuracy is greatly improved by this sensitive and robust method.
All optical techniques used to probe the properties of Bose-Einstein condensates have been based on dispersion and absorption that can be described by a two-level atom. Both phenomena lead to spontaneous emission that is destructive at the low energies involved with ultracold atomic systems. Recently, both were shown to lead to the same limit to the signal to noise ratio for a given destruction. We develop a new method for calculating the phase shift of a laser beam and show that no single-pass optical technique using classical light and a three-level atom can exceed this limit. This puts significant restrictions on potential nondestructive measurement schemes.
The polarization of an atomic Bose-Einstein condensate weakly excited by laser radiation at a nearly resonance frequency is determined. The coefficient of nonlinearity (cubic in field) in the refractive index of the condensate is calculated for the slow decay mode due to the spontaneous emission of excited atoms, as well as for the stationary mode, when the loss of atoms is compensated by the injection of atoms into the trap. In both cases, the cubic nonlinearity coefficients of the condensate are several orders of magnitude larger than the corresponding values for known nonlinear media. The conditions for observing hysteresis in an interferometer containing the condensate in the stationary state in the presence of an incident laser beam are specified.
Bose-Einstein condensates are interesting systems for studying quantum mechanics. Absorption imaging and phase-contrast imaging are two methods that are often used to determine the absolute number of atoms in a condensate. This thesis proposes a third method: holographic imaging. This method relies on the interference of a probe beam, which passes through the condensate, and a reference beam. The phase shift of the light due to the atoms and the optical density of the condensate are reconstructed with the use of Fourier transformation. Up to 300 images can be taken \\textit{in situ}.\n\nThere are two interesting applications of holographic imaging. The first is the refractive index, which can be measured directly with holographic imaging. The Hartree-Fock model is used to relate the real and imaginary part of the refractive index to the degeneracy of the condensate. However, the preliminary results are ambiguous and require further study.\n\nThe second is spin-dependent imaging, in which two orthogonally polarized reference beams are used to reconstruct polarization dependent information. This can be applied to study the dynamics of spinor condensates. In this thesis, a proof of concept for this method is given.
Summary form only given.We have established an experimental and theoretical program focused on understanding photon atom interactions in condensates with the aim of probing the properties of condensates as well as testing our models of the interactions themselves. With a combination of laser and evaporative cooling, we are routinely creating million atom Bose-Einstein condensates of sodium atoms in the newly designed 4D magnet. Our experimental setup incorporates a candlestick atomic beam source, which provides for recirculation of uncollimated sodium atoms, The laser cooling step involves a zero-crossing Zeeman slower, magneto-optic trap, and polarization gradient cooling. The laser-cooled atom cloud is loaded into the 4D magnetic trap and adiabatically compressed to high density and an evaporative cooling process is initiated. Using a RF magnetic resonance technique, hot atoms are ejected through magnetic spin flips. After formation of the condensate in the tightly confining trap, we manipulate the condensate by adiabatically changing the trapping potential and through interaction with photons. We have developed a technique for probing the condensates directly inside the trap using near-resonant absorption imaging. This imaging technique gives high sensitivity to details of the condensate wavefunction and to its surface structure. Images of pure condensates are compared to calculations of the condensate wavefunction based on a Hartree mean field description of the two-body interaction between condensate atoms.
We report our study of the optical pumping effect in absorption imaging of 23Na^{23}\mathrm{Na}23Na atoms in the F=1F=1F=1 hyperfine spin states. Solving a set of rate equations for the spin populations in the presence of a probe beam, we obtain an analytic expression for the optical signal of the F=1F=1F=1 absorption imaging. Furthermore, we verify the result by measuring the absorption spectra of 23Na^{23}\mathrm{Na}23Na Bose-Einstein condensates prepared in various spin states with different probe-beam pulse durations. The analytic result can be used in the quantitative analysis of F=1F=1F=1 spinor condensate imaging and readily applied to other alkali-metal atoms with I=3/2I=3/2I=3/2 nuclear spin such as 87Rb^{87}\mathrm{Rb}87Rb.