Heterodyne measurements

The high sensitivity of this method is related to the fact that we observe a matter-wave interference between the excitation and the condensate, i.e., a heterodyne measurement. Expansion in the inhomogeneous Bogoliubov projection basis confirm this picture [Tozzo 2004] We estimate that this improved sensitivity should give us access to the singly quantized excitation regime. 

The heterodyne measurement is performed as follows. The dye laser excites the trapped ion with frequency (Ol while the fluorescence is observed in a direction of about 54 to the exciting laser beam (see Fig. 2). However, both the observation direction and the laser beam are in a plane perpendicular to the symmetry axis of the trap. Before reaching the ion, a fraction of this laser radiation is removed with a beamsplitter and then frequency shifted (by 137 MHz with an acousto-optic modulator (AOM)) to serve as the local oscillator. The local oscillator and fluorescence radiations are then overlapped and simultaneously focused onto the photodiode where the initial frequency mixing occurs. The frequency difference signal is amplified by a narrow band amplifier and then frequency down-converted to 1 kHz so that it could be analyzed by means of a fast Fourier analyzer (FFT). The intermediate frequency for this mixing of the signal was derived from the same frequency-stable synthesizer which was used to drive the accousto-optic modulator producing the sideband of the laser radiation so that any synthesizer fluctuations are canceled out. 

In conclusion, we have presented the Hrst high-resolution heterodyne measurement of the elastic peak in resonance fluorescence of a single ion. At identical experimental parameters we have also measmed antibunching in the photon correlation of the scattered Held. Together, both measurements show that, in the limit of weak excitation, the fluorescence light differs from the excitation radiation in the second-order correlation but not in the first order correlation. However, the elastic component of resonance fluorescence combines an extremely narrow frequency spectrum with antibunched photon statistics, which means that the fluorescence radiation is not second-order coherent as expected from a classical point of view. This apparent contradiction can be explained easily by taking into accoimt the quantum nature of light, since first-order coherence does not imply second-order coherence for quantized fields (19). The heterodyne and the photon correlation measurement are complementary since they emphasize either the classical wave properties or the quantum properties of resonance fluorescence, respectively. 

Fig. 10.58 Heterodyne measurements of frequency-dependent vibrations of the ear drum and their local variations [1554]...

Heterodyne detection method for the coherent detection of laser signals, which superposes the optical signal with a reference beam from a coherent light source (local oscillator) in contrast to homodyne detection, the local oscillator is operated at a slightly different frequency than the optical signal heterodyne measurements allow for velocity measurements via Doppler effect and are employed, e.g., in electrophoretic light scattering. 

GHz [Ref. 2.1, Table 3-3]. The correct value turned out later to be 239.1 GHz. In fact heterodyne measurements were able to resolve the millimetre line into four components separated only by a few MHz (see Table A in Part II). This is the effect of hyperfine coupling between the nuclear spin of the Iodine nucleus (I = ) and the rotational states (here J = 16 or J = 15). The interested reader is referrred to [Ref. 2.1, Chap. 6]. 

For a number of purposes, the accuracy obtainable by the interferometric measurement of wavelength is not adequate. The most obvious of these purposes is molecular spectroscopy of the lasing molecule itself, which was discussed in Sect. 2. When used as a local oscillator in an astronomical receiver one would also like to know the laser frequency to within a few megahertz so as to know the radial velocity of the observed objects to within a few km/s. In metrology too, where the laser might be used in a chain to link microwave measurements with those made in the optical, high precision is necessary. For such purposes heterodyne measurements, which yield the frequency directly, are to be preferred, and these are now discussed. 

---