Schmidt modes in the angular spectrum of bright squeezed vacuum

Abstract

We study the spatial properties of high-gain parametric down-conversion (PDC). From the Hamiltonian we find the Schmidt modes, apply the Bloch-Messiah reduction, and calculate analytically the measurable quantities, such as the angular distributions of photon numbers and photon-number correlations. Our approach shows that the Schmidt modes of PDC radiation can be considered the same as for the low-gain (biphoton) case while the Schmidt eigenvalues strongly depend on the parametric gain. Its validity is confirmed by comparison with several experimental results, obtained by us and by other groups.PACS numbers: 42.65. Lm, 42.65.Yj, 42.50.Lc Introduction. Currently, much interest is attracted to bright squeezed vacuum (BSV), a macroscopic nonclassical state of light that can be obtained via high-gain parametric down conversion (PDC). This is because BSV contains huge photon numbers and at the same time is strongly nonclassical, manifesting entanglement [1] and noise reduction below the standard quantum limit [2]. These features make it interesting for applications such as quantum imaging [3,4] and metrology [5], quantum optomechanics [6] and nonlinear optics with quantum light [7]. Besides, large photon-number correlations arising in BSV are richer than entanglement in two-photon light emitted via low-gain PDC [8].At the same time, theoretical description of BSV presents certain difficulties. In contrast to low-gain PDC, BSV generation cannot be described in the framework of the perturbation theory. The quantum state contains not only two-photon terms but also higher-order Fock components, and its calculation in the Schrödinger picture is difficult. Many recent theoretical investigations of such strong pumping regime are based on the concept of collective input/output modes introduced mostly to describe the spectral properties in the frequency domain [9][10][11][12][13]. In a high-gain regime it is convenient to calculate the observables in the Heisenberg picture. In this case the Schmidt-mode formalism used in the Schroedinger picture for the description of multimode two-photon light [14] is replaced by a similar procedure, called Bloch-Messiah reduction [15]. However beyond the perturbation approach the solution for the field operators was up to now obtained only numerically, usually through a set of integro-differential equations [12,13,[16][17][18].Here we present a fully analytical description of the angular properties of BSV. Our approach is based on the Bloch-Messiah reduction and allows one to obtain the evolution of the photon creation (annihilation) operators both for the Schmidt modes and for the plane-wave modes. After obtaining the evolution of these, we calculate analytically the angular distributions of the inten-

Improving the phase super-sensitivity of squeezing-assisted interferometers by squeeze factor unbalancing

“…The optimal phase sensitivity f D min can be improved this way as visible in the inset of figure 7 which is a zoom into the f = 0 region. For the particular case of the parameters (16) and (17), the best phase sensitivity corresponds to y » 0.2 and approaches the lossless limit (25). In figures 8(a) and (b), we observe the same trend as for the homodyne detection case: by increasing the gain of the second amplifier one can compensate for the effect of external losses on the optimal phase sensitivity and the supersensitivity phase range.…”

“…However, it does not have to be the case in the other realizations of the parametric amplifiers. In particular, it was shown in [25] that the shapes of spatial and temporal modes of the parametric amplifiers based on high-gain parametric down-conversion [26,27] can be considered as gain-independent. The unbalanced regime of an SU(1,1) interferometer was considered in [28], with the conclusion that the best regime is the balanced or close to the balanced one.…”

Single-Mode Parametric-Down-Conversion States with 50 Photons as a Source for Mesoscopic Quantum Optics

“…Two-mode squeezed states with large photon numbers can be considered macroscopic [9] as they exhibit a large Fisher information [10]. Using the process of parametric down-conversion (PDC), bright squeezed states with billions of photons have been demonstrated [11][12][13][14][15][16][17]. However, the multi-mode nature of this approach frequently impairs the direct comparison between theoretical predictions and experimental observations and limits the applications of these states.…”

Experimental reconstruction of spatial Schmidt modes for a wide-field SU(1,1) interferometer

“…Such a modal decomposition describes efficiently the correlations in a bipartite system. In particular, it can be used to describe twin beams (idler and signal) at the output of high-gain PDC [31]. Although a deeper consideration shows that the shapes of the Schmidt modes change with the parametric gain [32], this effect is small.…”