Nondestructive Probing of Rabi Oscillations on the Cesium Clock Transition near the Standard Quantum Limit

We report on the nondestructive observation of Rabi oscillations on the Cs clock transition. The internal atomic state evolution of a dipole-trapped ensemble of cold atoms is inferred from the phase shift of a probe laser beam as measured using a Mach-Zehnder interferometer. We describe a single color as well as a two-color probing scheme. Using the latter, measurements of the collective pseudospin projection of atoms in a superposition of the clock states are performed and the observed spin fluctuations are shown to be close to the standard quantum limit.

Figure 1

Schematic drawing of the experimental setup. A probe laser beam enters the Mach-Zehnder interferometer via a port of the beam splitter BS1. One part of the beam propagates through the Cs atoms as they interact with the radiation field of the microwave source MW. The other part of the beam propagates on a reference path with no atoms. The two parts are recombined at the beam splitter BS2 and the phase shift from the atoms is detected as the differential signal of detectors D1 and D2 at the two output ports of BS2.

Figure 2

Rabi oscillations (average of 10 experimental cycles) on the clock transition for an ensemble of Cs atoms [optically pumped towards the ($F=4$, $m_F=0$) state] as inferred from the phase shift of probe laser light. The oscillations are recorded using probe pulses with a repetition period of $6\mu \mathrm{s}$ and duration of $0.5$ and $1.0\mu \mathrm{s}$, respectively. In the latter case a pronounced damping of oscillations is observed, however, with coherent dynamics at longer times (see inset). In the former case the fringe contrast for the normalized phase shift is limited to about 54% as result of $\sim 30\%$ remaining atoms in ($F=4$, $m_F\ne 0$) states.

Figure 3

Purified sample of atoms (a) Rabi cycling on the clock transition recorded using $0.2\mu \mathrm{s}$ probe pulses with a repetition period of $2.3\mu \mathrm{s}$. Oscillations are still visible after a time of 8 ms (a running average filter over 8 pulses has been included at this point of time to enhance the oscillations) corresponding to having applied $\sim 3500$ probe pulses. The trace is an average of 50 realizations of the experiment. (b) A single experiment recording of Rabi oscillations during the first millisecond. (c) A zoom-in on the first millisecond of the trace in (a), i.e., an average of 50 traces as shown in (b). At time 0 ms the phase shift is zero as a result of all the atoms being transferred to the ($F=3$, $m_F=0$) clock state and the probe only being sensitive to atoms in the $F=4$ states.

Figure 4

The fluctuations in the interferometer phase for ensembles in an equal superposition of the clock states as a function of the interferometer phase shift with all atoms at a pole of the Bloch sphere (this phase shift is proportional to the atom number). The quantum projection noise estimated from our experimental parameters is shown as a line. The inset shows the distribution of the measured pseudospin projection, its width increasing with atom number.