Coherence properties of high-gain twin beams

Abstract

Twin-beam coherence properties are analyzed both in the spatial and spectral domains at high-gain regime including pump depletion. The increase of the size of intensity auto-and cross-correlation areas at increasing pump power is replaced by a decrease in the pump depletion regime. This effect is interpreted as a progressive loss in the mode selection occurring at high-gain amplification. The experimental determination of the number of spatio-spectral modes from g (2) -function measurements confirms this explanation. The process of parametric down-conversion (PDC) in bulk nonlinear crystals generates twin-beam states of light that are naturally multi-mode both in spectrum and space [1]. Many works, performed in the single-photon regime, have highlighted the correlations and coherence properties of photon pairs either in spectrum or space [2][3][4][5][6][7][8][9]. In the past ten years, also high-gain PDC, leading to a large number of photons per mode, has been the object of several studies for its interesting properties of subshot-noise spatial intensity correlations [10][11][12][13] and macroscopic entanglement [14][15][16][17][18][19]. More recently, the spectral features of macroscopic twin-beam states have been investigated in the collinear interaction geometry close to frequency degeneracy [20]. Moreover, in the high-gain regime, the X-shaped coherence of the PDC output field [21] and the X-shaped spatio-temporal twin beam near-field correlations [22][23][24], originating from the space-time coupling in the phase-matching, have been demonstrated. The high-gain PDC process is also in the focus of attention for its potential applications. For instance, high-gain PDC has been used for quantum imaging [25], ghost imaging [26], and absolute calibration of photo-detectors [27,28]. The possibility to involve such bright states in interactions with material quantum objects (atoms, molecules, quantum dots) has been also addressed. Also the application of twin beams to quantum memories has been recently suggested [29].In this paper, we present a joint investigation of spatial and spectral features of twin-beam states produced in the high-gain regime with non-negligible pump depletion. The coherence properties at different values of pump mean power are inferred by evaluating the intensity auto-and cross-correlation functions on single-shot images of the far-field (θ, λ) speckle-like pattern of the PDC radiation. The initial increase with PDC gain of the size of coherence areas, both in spectrum and space, gradually stops and, at a certain pump power, is replaced by a decrease. This behavior is due to the occurrence of a progressive pump depletion, which is testified by the evolution of the spatial and spectral pump beam profiles. A possible explanation can be given in terms of the varying population of Schmidt paired modes [30] that 'diagonalize' the nonlinear interaction. The number of effectively populated modes is experimentally accessed by the measurement of spatio-spectral intensity g (2) -correlation function. T...

Schmidt modes in the angular spectrum of bright squeezed vacuum

“…3b). The FWHM of the covariance increases with the parametric gain, as observed in the experiments by Brida et al [30] and Allevi et al [31]. However it appears to be limited by the size of the lowest Schmidt mode which is the only one that remains in the high-gain limit.…”

Coherence and dimensionality of intense spatiospectral twin beams

“…According to Eqs. (46), the twin beam is spectrally composed of independent single-mode signal and idler fields in this high-intensity (classical) limit. We note that one dominant paired mode constitutes the twin beam also in the transverse wave-vector plane and the crystal output plane.…”

“…As the number of transverse modes is large, we can introduce quasicontinuum of the Schmidt eigenvalues with its probability function ̺ λ defined in Eq. (45). The probability function ̺ λ is plotted in Fig.…”

“…Recently, the first experimental investigations of ultraintense twin beams have been reported both for multimode [17,[44][45][46][47][48] as well as single-mode (bright squeezedvacuum states) fields [49]. The effects of pump-field depletion have been observed.…”

“…Also back-flow of energy from the twin beam into the pump field may occur. These processes affect spectra as well as transverse profiles of the twin beams [45][46][47]. Here, we restrict our attention to the case of un-depleted pump fields (parametric approximation).…”