Measurements of temperature scaling laws in an optically dense magneto-optical trap

Abstract

We have studied the temperature scaling laws for the conditions under which a cloud of trapped 85 Rb atoms in the + / − configuration makes the transition from the temperature-limited regime to the multiple-scattering regime. Our experimental technique for measuring temperature relies on measuring the ballistic expansion of the cloud after turning off the confining forces and imaging the cloud size as a function of time with two CCD cameras. In the transition regime, the temperature T is shown to depend on the number of atoms N and the peak density n as ͑T − T o ͒ ϰ N 1/3 and as ͑T − T o ͒ ϰ n 2/3 , in a manner consistent with theoretical predictions. Here T o is defined as the equilibrium temperature of a low-density optical molasses. In the multiple-scattering regime we find that T ϰ⍀ 2 / ͑␦⌫͒, where ⍀ and ␦ are the Rabi frequency and the detuning of the trapping laser, respectively, and ⌫ is the natural linewidth of the cycling transition. We have also measured the ratio of temperatures along the axial and radial directions of the magnetic field gradient coils and find that the temperature is isotropic only if the intensities of the three orthogonal trapping beams are equal, and that the ratio is generally independent of trapping laser intensity and magnetic field gradient. Finally we demonstrate a measurement of the gravitational acceleration precise to Ϸ0.1% by tracking the center of the cloud during ballistic expansion.

Measurement of temperature of laser cooled atoms by one-dimensional expansion in a magneto-optical trap

“…We establish the reliability of the present technique in two different ways-firstly, we compare the present measurements of temperature ͑T͒ with those obtained independently with R&R method ͑T RR ͒, and, secondly, we use them to see how well they follow the wellestablished temperature scaling law. 4,11 These results are shown in Fig. 4.…”

“…These include release and recapture 1 ͑R&R͒ and time of flight [2][3][4][5] ͑TOF͒ techniques, and also other more elaborate methods based on forced oscillation of the cloud, 6 fluorescence spectrum analysis, 7 recoil induced resonances, 8 and four wave mixing. 9 A direct method, 10,11 which is an extension of the TOF technique, is used to allow the cold cloud to expand ballistically after abruptly switching off the trapping fields and follow its spatiotemporal evolution by absorption or fluorescence imaging technique with the help of a probe laser beam. The temperature ͑T͒ of the cloud is then determined by fitting the cloud expansion to the wellknown equation 10,11 2 ͑t͒ = 2 ͑0͒ + ͑k B T / M͒t 2 , where ͑t͒ is the rms size of the cloud measured at time t, k B is the Boltzmann constant, and M is the mass of the atom.…”

Trapping of ultracold atoms in a 3He/4He dilution refrigerator

“…The temperature of the ensemble in the magnetic trap was measured to be 90 µK by ballistic expansion in time-of-flight images [30]. Figure 5 We have observed a long term decrease in the trap lifetime which is related to an increase in the vacuum chamber pressure.…”

Demonstration of improved sensitivity of echo interferometers to gravitational acceleration

“…The frequency of the trapping beams (ω 0 -15 MHz) is ramped by an additional 25 MHz below resonance to cool the atoms in an optical molasses. Time of flight CCD images of atoms released from the molasses [42] show that the typical temperature is 20 µK.…”

“…In this case, the frequency ω Typically v L is sensitive to a number of effects such as power imbalances in the laser beams, imperfect circular polarization of the trapping beams, and background magnetic fields. The CCD camera method of measuring the trap temperature monitors both the spatial profile and centroid of the atom cloud [42]. Although the spatial position of the cloud cannot be measured in real-time during the AI experiment, periodic checks showed that v L along the vertical direction can vary by as much as ±2 mm/s over several hours.…”