Generation of 87^{87}Rb-resonant bright two-mode squeezed light with four-wave mixing

Squeezed states of light have found their way into a number of applications in quantum-enhanced metrology due to their reduced noise properties. In order to extend such an enhancement to metrology experiments based on atomic ensembles, an efficient light-atom interaction is required. Thus, there is a particular interest in generating narrow-band squeezed light that is on atomic resonance. This will make it possible not only to enhance the sensitivity of atomic based sensors, but also to deterministically entangle two distant atomic ensembles. We generate bright two-mode squeezed states of light, or twin beams, with a non-degenerate four-wave mixing (FWM) process in hot $^{85}$Rb in a double-lambda configuration. Given the proximity of the energy levels in the D1 line of $^{85}$Rb and $^{87}$Rb, we are able to operate the FWM in $^{85}$Rb in a regime that generates two-mode squeezed states in which both modes are simultaneously on resonance with transitions in the D1 line of $^{87}$Rb, one mode with the $F=2$ to $F'=2$ transition and the other one with the $F=1$ to $F'=1$ transition. For this configuration, we obtain an intensity difference squeezing level of $-3.5$ dB. Moreover, the intensity difference squeezing increases to $-5.4$ dB and $-5.0$ dB when only one of the modes of the squeezed state is resonant with the D1 $F=2$ to $F'=2$ or $F=1$ to $F'=1$ transition of $^{87}$Rb, respectively

Geomorphic and landform survey of northern Appennini

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Quantization of classical integrable systems. Part IV: systems of resonant oscillators

By applying methods already discussed in a previous series of papers by the same authors, we construct here classes of integrable quantum systems which correspond to n fully resonant oscillators with nonlinear couplings. The same methods are also applied to a series of nontrivial integral sets of functions, which can be constructed when additional symmetries are present due to the equality of some of the frequencies. Besides, for n=3 and resonance 1:1:2, an exceptional integrable system is obtained, in which integrability is not explicitly connected with this type of symmetry. In this exceptional case, quantum integrability can be realized by means of a modification of the symmetrization procedure.Comment: 23 page