deletions | additions       diff --git a/section_Experimental_Setup_An_optimal__.tex b/section_Experimental_Setup_An_optimal__.tex  index d900f7d..4636290 100644  --- a/section_Experimental_Setup_An_optimal__.tex  +++ b/section_Experimental_Setup_An_optimal__.tex 
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As mentioned, one obstacle for most quantum implementation of BS is technical noise, in the form of spurious non-linear and Raman processes \cite{Lefrancois_2015}. Modulation instability (MI) (purple in figure \ref{fig:tech_noise}) is a competing FWM process, its gain profile given by $G_{MI} = 1 + (\gamma P / g_{MI})^2 \sinh^2(g_{MI} L)$ where $g_{MI} = \sqrt{(\gamma P)^2 - (k_{MI} + \gamma P)^2}$ and $\kappa_{MI} = \left[\beta(\omega_p + \delta\omega) + \beta(\omega_p - \delta\omega) - 2 \beta(\omega_p)\right]/2$ are respectively the MI wavevector and linear phasematching term for a frequency detuning $\delta \omega$ from the a strong pump set at $\omega_p$. Modulation instability affects BS in multiple ways, either by depleting the pump and generating spurious sidebands, or amplifying the vacuum fluctuations and generating pairs of energy correlated photons. It can be managed placing the pump on the normal dispersion, where parametric gain is forbidden and the bandwidth for pair generation is minimized, as well as detuning the signal far from the pump frequencies.  Spontaneous and Stimulated Raman Scattering are processes that couple light with the thermal phonons bath of the medium. Scattering strength depends on the density of occupied states as well as the Raman spectrum $g_r(\delta\omega)$. The probability of a spontaneous Stokes scattering (i.e. the photon losing energy) is given by $p_S = g_r(\delta\omega) \frac{1}{1-exp(-\delta\omega \hbar/ k_b T)}$ while for anti-Stokes it is $p_S = g_r(\delta\omega) \frac{exp(-\delta\omega \hbar/ k_b T)}{1-exp(-\delta\omega \hbar/ k_b T)}$  The spectrum depends on the material: amorphous materials have a broad spectrum (i.e. for glass it extends to about $40$ THz \cite{Stolen_1973}), while crystalline materials have strong, sharp features. Both processes become less probable for very large detuning, though the anti-Stoke probability depends exponentially on the temperature when $-\delta\omega \hbar \gg k_b T$ ($6$ THz for room temperature), so that cooling the fiber can further reduce the noise by several order of magnitude (red $300$ K and blue $90$ K on in  figure \ref{fig:tech_noise}) \cite{Li_2004, Takesue_2008}. In both cases, noise is reduced the farther we place the signal from the pumps: because of to the BS phasematching flexibility, there are no limitations on the amount of detuning $\Delta\Omega$ \cite{M_chin_2006} between pumps and signal, the only fundamental parameter being $\omega_{ZDW}$ (rather than $\beta^{(3)}$ ), easily tunable via dispersion engineering.  We operate using a dispersion-shifted fiber (Vistacor, Corning): although the fiber is not optimized for nonlinear interactions ( $\gamma \simeq 3$ W/km), a sufficiently long spool makes up for the reduced nonlinear parameter. Measurement of the dispersion (shown in figure \ref{fig:dispersion}) measures , ?, ?  with $\lambda_{ZDW} = 1420 $ nm that corresponds to a $\omega_{ZDW} = 1330 $ THz, with the signal/idler and the pumps placed respectively in the O-Band (1260 nm - 1320 nm ) and the C-Band (1530 nm - 1565 nm) ΔΩ for a $\Delta \Omega  ~ 120 120$  THz . This is an attractive configuration because it enables the large detuning needed for a low-noise operation, while still operating at wavelengths where off-the-shelf equipment is available. For $\delta\omega = 5 $ THz (~6.5 nm for pumps and ~4.3 nm for the signal/idler) the calculated  acceptance bandwidth is ( FWHM). The experimental setup is depicted in figure \ref{fig:setup}: to generate the pump fields, we use temperature stabilized laser diodes(DFB, QPhotonics)  that are current modulated via a pulse generator, producing pulses of duration τ = 1-10 ns and peak power 5 mW. The pumps are amplified with cascaded C-band erbium-doped fiber amplifier (EDFA). The last EDFA (Keopsys) is optimized for high power pulsed amplification at low duty cycle (output P out = 30 dBm at 100/1 duty cycle). Both pulses are temporally separated when traversing the EDFA to avoid mutual nonlinear effects in the gain medium, and synchronized afterward using an unbalance combination of 1551.7 nm fiber wavelength division multiplexers (WDM). Signal and pumps are coupled together using O-Band/C-band WDM, temporally synchronized and injected in the nonlinear fiber. The polarization of each field is independently controlled to ensure parallel polarization in the nonlinear fiber.   The 100 m of nonlinear fiber is spooled and placed in a cryogenic container. Signal losses through the setup are as low as 2.6 dB, due to splices, connectors and WDMs. Since the second WDM removes > 30dbB of pump power, we consider most of the Raman noise generated between the two WDMs, and we take care of placing as much amount of fiber as possible in the cryostat. At the end of the interaction, a second WDM removes most of the pumps, and the signal is sent to the detection stage.