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The density broadening in a sodium F=2 condensate detected by a pulse train
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Image of FIG. 1.

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FIG. 1.

(Color online) (a)-(e) represent the number of microwave pulses and the shape of the pulses. (a) A Rabi pulse; (b) The Ramsey sequence; (c) Five pulses; (d) 100 pulses. (e) The calculated intensity as a function of the frequency detuning, ω. The number of pulses are labeled on the top right of this plot. 1 pulse [(−− −), black dashed line]; 2 pulses [(−· − · −), green dashed-dotted line]; 5 pulses [(· · ·), blue dotted line]; and 100 pulses [(—), red solid line]. (f) The excitation probabilities calculated at three different powers using the five-pulse train as shown in (c). The powers are given in terms of the area under five pulses: 1π [(—), black solid line], 1.5π [(•), red dot] and 2π [(△), green triangle].

Image of FIG. 2.

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FIG. 2.

(Color online) The power dependence measurements with three pulses. This power dependence can be generalized to N pulses. The black squares (■) are measured data at two different microwave powers and the red solid lines are the calculated transition probabilities by three pulses at two different powers [(—), red solid line]. (a) The power is 1.33π. (b) The power is 1.11π. In both cases, the pulse-width=the interval between pulses=1 ms. (c) Comparing the single pulse with a continuous power variation [(—), red solid line] and the 3-pulse tain with the same power variation [(−− −), black dashed line]. The area under the single pulse and the area under the 3-pulse train are π and the length of the single pulse and the total length of the 3-pulse train are 100 s. The pulse shapes are plotted on the top-left corner, the single pulse, and the top-right corner, a 3-pulse train.

Image of FIG. 3.

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FIG. 3.

(Color online) (a)The data are taken with three pulses [(■), black square], the same data as plotted in Fig. 2(b), and five pulses [(○), red circle]. The solid lines are simulations with the dipole-dipole interaction: three pulses [(—), black solid line] and five pulses [(—), red solid line]. Both calculations use π pulses and the amplitudes are rescaled by the number of atoms. In both cases, the pulse-width=the interval between pulses=1 ms and the powers are close to π. Both scans are taken at the same density. (b) The dipole-blockade effect. Both data are calculated with five pulses and the powers are π. The red solid line (—) is calculated without any interactions. In other words, we assume the atoms are isolated. The black dashed line (−− −) is calculated with the two-body dipole-dipole interaction.

Image of FIG. 4.

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FIG. 4.

(Color online) (a) Two microwave scans taken at densities: 3.6 × 1013cm−3 and 1.7 × 1013cm−3. The pulse-train used is shown in Fig. 1(c). The microwave scans are taken at the center peak as shown in Fig. 1(f). (b) The Lorentzian fitted linewidth as a function of the atomic density. (c) The peak frequency as a function of the peak atomic density.


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The dipole-blockaded sodiumclock transition has been detected by high resolution microwave spectroscopy, the multiple-pulse spectroscopy. This spectroscopic technique has been first used to detect the density broadening and shifting in a Sodium Bose Einstein Condensate (BEC) by probing the sodium clock-transition. Moreover, by narrowing the pulse-width of the pulses, some of the broadening mechanisms can be partially reduced. The results reported here are essential steps toward the ground-statequantum computing, few-body spectroscopy, spin squeezing and quantum metrology.


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Scitation: The density broadening in a sodium F=2 condensate detected by a pulse train