The use of interferometry for measuring the wavelength of a radiation field is probably one of its older applications. Nowadays the concept of interferometry has been extended. It has become possible to observe experimentally the interference for one particle and even for multiparticle wave fields. The two-photon field produced in the parametric down-conversion, have been extensively utilized in many of the so-called multiparticle interferometry experiments [1, 2].
In this new type of interference, it is not possible to ignore the quantum aspects of the electromagnetic field. In quantum interferometry, it is also possible to associate interference patterns to the wavelength of a field. For single photon fields, classical and quantum interpretations of the interference experiments lead to the same wavelength. For multi-photon or multi-particle fields however, the wavelength can be dependent on the way the measurement is performed, and a classical interpretation is no longer possible. Thinking of two-photon wavepackets, for example, if we can make the two photons travel together through an interferometer as they were contained in one packet, we can measure a wavelength corresponding to an entity with the energy two times larger than the single photon one [3, 4]. This concept is quite general in quantum physics and it can be extended to any particle or field and the DeBroglie wavelength will be associated to the total energy of the system.
In this paper we study the two photon interference from the point of view of the measurement of the wavelength. We present an experiment whose configuration is capable to produce quantum interference without the use of material interferometers, in the sense that no double-slits and no beam-splitters are used. It consists of a transverse version of interferometers of the type of Mandel's  and Zeilinger's . It is also similar to the interferometer presented by Klyshko et al. in Ref., but without the double-slits and with the possibility of detecting signal and idler photons in completely independence, as it will be shown. This is the main difference from previous transverse interferometers [8, 9, 10, 11]. Another experiment recently performed by Fonseca et al., utilizes the same principle for measuring a non-local wavelength for a two-photon wavepacket. The configuration presented here is similar to that presented by White et al. for producing polarization entangled states with high intensities, however in our case the polarization state is not entangled. Twin photons from the parametric down-conversion process are used. These photons have been called biphotons as a reference to their strong correlation at the quantum level. The interference fringes are obtained by measuring coincidence counts and the frequency of the oscillation of the patterns are associated to wavelengths for the biphotons. It is shown that this frequency can be arbitrarily varied, depending on the way the measurements are performed. It is also shown, that the measured wavelengths can be assigned to single and to two-photon wavepackets, for two kinds of measurement. Attempts to connecting the oscillation frequency and the biphoton wavelengths for other kinds of measurements indicate that special care must be taken in defining and measuring wavelengths in multiparticle interferometry. On the other hand, this interferometer can be used in the production and manipulation of position entangled states and has potential for applications in measurements of diffraction indexes. A single mode quantum theory is enough to explain the behavior of the frequency of the patterns and it is in agreement with the experimental data.