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Fig. 1. Noise reduction factor versus the parametric gain coefficient for two-colour squeezed vacuum.

In the absence of input radiation, a strongly pumped non-degenerate optical parametric amplifier (NOPA) emits only noise, which, however, manifests remarkable statistical properties. It is known as two-mode squeezed vacuum (SV); at weak pumping it becomes two-photon light, while at strong pumping it is essentially multiphoton and can be called macroscopic. Its two frequency components have strongly fluctuating intensities but ideally the difference of these intensities is completely free of noise. Until recently, observation of noise reduction of macroscopic SV remained a challenge. We discovered that the clue is the collection of many transverse and longitudinal modes [1]. In a pulsed NOPA we generated two-colour SV with up to 2000 photons per mode. The insets show the output photon numbers versus the pump power. The noise reduction factor (NRF), the conventional measure of twin-beam squeezing, remained about 4 dB and almost constant (a) up to gain values of 2 (13 photons per mode). Higher gain was achieved by pump focusing at lower pump power, leading to fewer collected modes. Still, NRF remained below unity (b) for gain values up to 4.1 (900 photons per mode).

Three experimental configurations have been realized. In the first one, the optical parametric oscillator (OPA) is frequency non-degenerate, and the twin beams have different wavelengths [1]. In the second configuration, by using two frequency-degenerate OPAs in orthogonal polarization modes, we obtain squeezing in a given Stokes parameter [2]. In both these configurations, two-mode squeezing is measured.

The third version of the setup combines wavelength and polarization degrees of freedom and therefore provides generation of a four-mode SV. In this setup, two OPAs are placed into a Mach-Zehnder interferometer and pumped by coherent beams. With the OPAs aligned for collinear frequency-degenerate phase matching, we produce ‘macroscopic Bell States’, which are high-gain analogues of the two-photon Bell states. Of special interest is the ‘macroscopic singlet state’, which has the following remarkable qualities: (1) although it is pure, it is completely non-polarized, i.e., invariant to polarization transformations; (2) it has noise in all polarization observables suppressed below the shot-noise limit.

Fig. 2. Intensities in polarization modes and their NRFs for the 'macroscopic single state', as functions of polarization transformation performed with a half-wave plate (left) and a quarter-wave plate (right). Vertical lines correspond to the measurement of different Stokes observables: blue dashed line, S1; green dotted line, S2; red solid line, S3.

Figure 2 demonstrates both these features. It shows the intensities in mutually orthogonal polarization modes (small empty blue squares and filled red circles), as well as the NRF for their difference (large empty green circles), as a function of polarization transformation performed by a half-wave plate (left) and a quarter-wave plate (right). All dependencies are nearly flat, which indicates polarization invariance. At the same time, NRF remains well below unity (the shot-noise level, shown by black dotted lines) for all orientations of the waveplates. In particular, blue dashed vertical lines in Fig.2 correspond to the measurement of the Stokes observable S1, green dotted vertical lines, to the measurement of S2, and red solid vertical lines, to the measurement of S3. For all these observables, about 30% suppression of noise has been measured. Precise figures obtained are: NRF(S1)=0.720.01, NRF(S2)=0.700.01, NRF(S3)=0.690.01 [3].

[1] I.N. Agafonov, M.V. Chekhova, and G. Leuchs, Two-Color Bright Squeezed Vacuum. Phys. Rev. A 82, 011801(R) (2010).
[2] Timur Iskhakov, Maria V. Chekhova, and Gerd Leuchs, Generation and Direct Detection of Broadband Mesoscopic Polarization-Squeezed Vacuum. PRL 102, 183602 (2009).
[3] Timur Iskhakov, Maria V. Chekhova, Georgy O. Rytikov , and Gerd Leuchs, Macroscopic Pure State of Light Free of Polarization Noise. PRL 106, 113602 (2011).