We present the first measurement of squeezed-state entanglement between the twin beams produced in an Optical Parametric Oscillator (OPO) operating above threshold. Besides the usual squeezing in the intensity difference between the twin beams, we have measured squeezing in the sum of phase quadratures. Our scheme enables us to measure such phase anti-correlations between fields of different frequencies. In the present measurements, wavelengths differ by ≈ 1 nm. Entanglement is demonstrated according to the Duan et al. criterion [Phys. Rev. Lett. 84, 2722] ∆ 2p − + ∆ 2q + = 1.47(2) < 2. This experiment opens the way for new potential applications such as the transfer of quantum information between different parts of the electromagnetic spectrum. [7]. The number of such experiments, however, is still relatively small in comparison with discrete variable systems.The first experimental demonstration of continuous variable entanglement used a continuous-wave (CW) optical parametric oscillator (OPO) operating below threshold [6]. The two squeezed vacuum outputs were shown to possess Einstein Podolsky Rosen (EPR) type correlations. Most recent experiments use a nonlinear interaction to produce squeezed fields, which are then combined in a beamsplitter to generate entanglement [8]. Conversely, a beamsplitter transformation can also be used to generate a squeezed beam from an entangled input [9]. In these experiments, it is mandatory to have fields of the same frequency.In this Letter, we present the first (to our knowledge) measurement of continuous variable entanglement between bright fields of truly different frequencies. Even before the first experiment [6], it was predicted that the above-threshold OPO should produce entangled twin beams [10,11]. So far, this prediction had not yet been verified, owing to the difficulty of measuring phase properties of the twin beams. We have succeeded in measuring quantum correlations between the sum of phase quadratures of non-degenerate twin beams.Bipartite continuous variable entanglement [12] can be tested according to a criterion established by Duan et al. [13] and also by Simon [14]. The criterion is based on the total variance of EPR-type operators. For operatorŝ x i andp i that obey position-momentum commutation relations, they consider the variances of combinations such asx 1 +x 2 andp 1 −p 2 . The quadratures of electromagnetic fields satisfy such commutation relations. We focus here on the so-called amplitudep and phaseq field quadratures, defined by:whereâ is the field annihilation operator, φ is an arbitrary phase and, for a macroscopic field with a welldefined mean amplitude, q = 0. In terms of these operators, inseparability (entanglement) is demonstrated by a violation of the inequality:where the Standard Quantum Level (SQL) is normalized to 1 for each combination of quadratures. In order to simplify notation, we will refer to (p 1 ±p 2 )/ √ 2 asp ± , and to (q 1 ±q 2 )/ √ 2 asq ± [thus, ∆ It is easy to understand why entanglement is expected in the CW OPO operati...

The phenomenon called Electromagnetically Induced Transparency (EIT) may induce different types of correlation between two optical fields interacting with an ensemble of atoms. It is presently well known, for example, that in the vicinity of an EIT resonance the dominant correlations at low powers turn into anti-correlations as power increases. Such correlation spectra present striking power-broadening-independent features, with the best condition for measuring the characteristic linewidth occurring at the highest powers. In the present work we investigate the physical mechanisms responsible for this set of observations. Our approach is first to reproduce these effects in a better controlled experimental setup: a cold atomic ensemble, obtained from a magneto-optical trap. The results from this conceptually simpler system were then compared to a correspondingly simpler theory, which clearly relates the observed features to the interplay between two key aspects of EIT: the transparency itself and the steep normal dispersion near two-photon resonance.

High degrees of intensity correlation between two independent lasers were observed after propagation through a rubidium vapor cell in which they generate Electromagnetically Induced Transparency (EIT). As the optical field intensities are increased, the correlation changes sign (becoming anti-correlation).The experiment was performed in a room temperature rubidium cell, using two diode lasers tuned to the 85 Rb D2 line (λ = 780nm). The cross-correlation spectral function for the pump and probe fields is numerically obtained by modeling the temporal dynamics of both field phases as diffusing processes. We explored the dependence of the atomic response on the atom-field Rabi frequencies, optical detuning and Doppler width. The results show that resonant phase-noise to amplitude-noise conversion is at the origin of the observed signal and the change in sign for the correlation coefficient can be explained as a consequence of the competition between EIT and Raman resonance processes.PACS. 32.80.Qk Coherent control of atomic interactions with photons -42.50.Gy Effects of atomic coherence on propagation, absorption, and amplification of light; electromagnetically induced transparency and absorption

Nonlinear magneto-optical (NMO) resonances occurring for near-zero magnetic field are studied in Rb vapor using light-noise spectroscopy. With a balanced detection polarimeter, we observe high contrast variations of the noise power (at fixed analysis frequency) carried by diode laser light resonant with the 5S 1/2 (F = 2) → 5P 1/2 (F = 1) transition of 87 Rb and transmitted through a rubidium vapor cell, as a function of magnetic field B. A symmetric resonance doublet of anticorrelated noise is observed for orthogonal polarizations around B = 0 as a manifestation of ground state coherence. We also observe sideband noise resonances when the magnetic field produces an atomic Larmor precession at a frequency corresponding to one half of the analysis frequency. The resonances on the light fluctuations are the consequence of phase to amplitude noise conversion owing to nonlinear coherence effects in the response of the atomic medium to the fluctuating field. A theoretical model (derived from linearized Bloch equations) is presented that reproduces the main qualitative features of the experimental signals under simple assumptions.

We report a detailed investigation on the properties of correlation spectra for cold atoms under the condition of Electromagnetically Induced Transparency (EIT). We describe the transition in the system from correlation to anti-correlation as the intensity of the fields increases. Such transition occurs for laser frequencies around the EIT resonance, which is characterized by a correlation peak. The transition point between correlation and anti-correlation is independent of power broadening and provides directly the ground-state coherence time. We introduce a method to extract in real time the correlation spectra of the system. The experiments were done in two distinct magnetooptical traps (MOT), one for cesium and the other for rubidium atoms, employing different detection schemes. A simplified theory is introduced assuming three-level atoms in Λ configuration interacting with a laser with stochastic phase fluctuations, providing a good agreement with the experimental observations.