Engineering the Frequency Spectrum of Bright Squeezed Vacuum via Group Velocity Dispersion in an SU(1,1) Interferometer

Bright squeezed vacuum, a promising tool for quantum information, can be generated by high-gain parametric down-conversion. However, its frequency and angular spectra are typically quite broad, which is undesirable for applications requiring single-mode radiation. We tailor the frequency spectrum of high-gain parametric down-conversion using an SU(1,1) interferometer consisting of two nonlinear crystals with a dispersive medium separating them. The dispersive medium allows us to select a narrow band of the frequency spectrum to be exponentially amplified by high-gain parametric amplification. The frequency spectrum is thereby narrowed from $(56.5\pm 0.1)$ to $(1.22\pm 0.02)\mathrm{THz}$ and, in doing so, the number of frequency modes is reduced from approximately 50 to $1.82\pm 0.02$. Moreover, this method provides control and flexibility over the spectrum of the generated light through the timing of the pump.

Figure 1

Principle of the method. A broadband PDC pulse is generated in a strongly pumped nonlinear crystal; the PDC pulse spreads and chirps after propagation in a medium with group velocity dispersion (GVD); the spread and chirped PDC pulse is amplified in another crystal, using the same pump pulse. The frequency spectrum after the second crystal is narrower than that after the first one.

Figure 2

Experimental setup. (a) An attenuator [half-wave plate (HWP) and Glan polarizer (PBS)] and a telescope are used to prepare the pump in power, polarization, and beam diameter. (b) PDC generated in the first pass of the pump in the BBO crystal is stretched temporally in a dispersive medium (GVD) and sent back into the crystal to be amplified. The time of arrival of the pump is carefully tuned with the position of mirror M1, set on a translation stage. (c) The PDC is sent either into a spectrometer or into a photodiode (PD).

Figure 3

Comparison of the spectral densities obtained experimentally for a single pass through the nonlinear crystal (dashed red line), and for the interferometer with a 18.3 cm rod of SF6 (solid black line).

Figure 4

Linewidth of the spectrum (a) and $g^{(2)}$ (b) as functions of the GVD parameter. Experimental points (black) are compared to theoretically calculated values (pink zones and red dashed curves). The red dashed curves correspond to constructive interference between the pump and the PDC at degeneracy. The pink zones denote the region within 1 standard deviation from the mean, which is determined by averaging over 8 different phases for the central frequency from 0 to $2\pi$ by varying the air gaps, considering amplification and deamplification cases. The influence of GVD manifests itself through the narrowing of the spectrum and the increase in $g^{(2)}$.

Figure 5

Experimental spectra when the pump path length is increased by $(1.40\pm 0.01)\mathrm{mm}$ (black solid line) and by $(2.40\pm 0.01)\mathrm{mm}$ (blue dashed line) with respect to the configuration for degeneracy. The red dash-dotted line shows the spectrum calculated for the first case, with a parametric gain of 7. The inset shows the second peak of the calculated spectrum without the convolution to show the interference fringes.