CAPITULO III METODLOGÍA DE LA INVESTIGACION
3.3. TÉCNICAS E INSTRUMENTOS DE INVESTIGACIÓN.
In our experiment, we analyze the Larmor precession of the angular momentum of a single atom, that is initially prepared in the coherent dark state given by eqn (4.28). After a defined delay time the superposition state detection is performed. Thereby, the precession of atomic angular moment in the magnetic field can be observed as a time dependent change in the transfer efficiency of the atomic state in the STIRAP process.
Magnetic field compensation
For a high visibility of the Larmor-precession, the initial atomic state has to be prepared with high accuracy. In the experiment, the atom is optically pumped into the coherent dark state given by eqn (4.28). A residual magnetic field gives rise to a precession of the atomic states that counteracts the optical pumping process. In order to achieve a suitable pumping efficiency, the precession time has to be smaller than the timescale of the optical pumping process. Therefore, an initial compensation of the magnetic field is required.
4.3. Larmor precession of the atomic angular momentum
Figure 4.21.: Larmor precession of the state defined in eqn (4.28) in a magnetic field oriented along the quantization axis. In a rotating reference frame defined by the quantization axis at the angle ωLt, the atom stays in the |1,0i
eigenstate. The figure shows the representation of the time dependent eigenstate in the laboratory reference frame, as well as the corresponding spin-1 orbital wavefunction.
Therefore, we apply pump light from one direction. The scattering of photons from the pump beam gives rise to a light pressure and a heating of the transversal velocity components of the atom, until it is lost from the trap or is transferred into the dark state. A residual magnetic field gives rise to a Larmor precession of the atom and therefore no stable dark state exists. In essence, higher magnetic fields result in a higher precession frequency and a higher scattering rate of photons, which leads to increased trap losses during the pump sequence. Measuring the survival probability of the atom as a function of the applied magnetic field allows to determine the external magnetic field at the position of the atom. Using different polarizations of the pump field all components of the magnetic field vector can be analyzed. Using these measurements, we were able to compensate the external magnetic field. In the end, we determined a residual magnetic field on the order of 150 mG, corresponding to a Larmor frequency of ωL = 100 kHz, low enough to allow efficient preparation of the initial
superposition states. For a more detailed discussion of the magnetic field compensation see [104, 68].
Experimental process and measurement results
Figure 4.22.: Experimental process for the observation of Larmor precession. Two pump fields – resonant to the transitionsF = 1→F0 = 1 andF = 2→F0 = 1 –
together with the cooling laser, prepare the atom in the initial superposition state|ΨLi(see section 4.2.3). After the preparation, the magnetic moment
undergoes Larmor precession until after a time delay ∆t = 0...5 µs the superposition state detection projects the atom onto the two orthogonal states |ΨLi and |ΨL,⊥i.
In the experiment, the initial state |ΨL(0)i is prepared using optical pumping. After the
preparation, a variable time delay ∆t is inserted before the superpostion state detection (Fig. 4.22). During the time ∆t the magnetic moment of the atom undergoes Larmor precession in the external magnetic field. After the time delay the superposition state detection is per- formed for two different STIRAP polarizations projecting the atomic state onto |ΨL(0)i and
the orthogonal superposition state|ΨL,⊥i.
Figure 4.23 shows the measured transfer probability for both STIRAP light polarizations as a function of the time delay ∆t. In each measurement, we observe an oscillation of the transfer efficiency for both STIRAP polarizations which is a clear signal of Larmor precession of the magnetic moment of the atom. The orientation of the magnetic field in our experiment is not exactly known, but in measurement (a) the z-component of the magnetic field dominates and the observed precession is similar to the theoretically expected behavior (Fig. 4.20). From the precession frequencies we determined the absolute magnetic field values. For the measurements presented in Fig. 4.23 we calculated an absolute magnetic field of (a) 142 mG, (b) 75 mG and (c) 62 mG, respectively.
The observation of the Larmor precession provides an accurate measure for the absolute value of the magnetic field at the position of the atom. Using different initial superposition states also the orientation of the magnetic field can be determined. Therefore, this analysis provides a highly sensitive procedure for the measurement (and compensation) of the magnetic fields in our experiment.
4.3. Larmor precession of the atomic angular momentum
Figure 4.23.: Time dependent overlap of the precessing atomic state with the STIRAP eigenstates |ΨLi (blue curve) and |ΨL,⊥i (red curve) for three different
4.4. Summary
This chapter described the realization of a detection scheme that allows to analyze coherent superpositions of internal atomic Zeeman levels by combining coherent dark state projection with the STIRAP technique. In essence, the polarization of the STIRAP light fields defines which superposition of the Zeeman sublevels mF = ±1 of the F = 1 hyperfine ground level
is transferred to the F = 2 ground level. Together with the hyperfine level detection, this scheme allows to analyze the atomic qubit in arbitrary measurement bases. The accuracy of the detection process was analyzed in detail. Therefrom we obtain a mean detection accuracy – the probability to correctly identify the atomic superposition state – of 95%. The high accuracy recommends the detection scheme for the application in the verification of atom- photon entanglement.
In the last part of this chapter we discussed an application of the state detection process, which allows to observe the precession of the magnetic moment of a single atom in an external magnetic field. The measured precession frequency provides a highly sensitive measure of the residual magnetic fields at the position of the atom and therefore can be used for an accurate compensation of magnetic bias fields.