Two Photon Absorption and Coherent Control with Broadband Down-Converted Light

We experimentally demonstrate two-photon absorption with broadband down-converted light (squeezed vacuum). Although incoherent and exhibiting the statistics of a thermal noise, broadband down-converted light can induce two-photon absorption with the same sharp temporal behavior as femtosecond pulses, while exhibiting the high spectral resolution of the narrow band pump laser. Using pulse-shaping methods, we coherently control two-photon absorption in rubidium, demonstrating spectral and temporal resolutions that are 3–5 orders of magnitude below the actual bandwidth and temporal duration of the light itself. Such properties can be exploited in various applications such as spread-spectrum optical communications, tomography, and nonlinear microscopy.

Figure 1

(a) Atomic energy levels of Rb, showing the induced two-photon transition and the resulting cascaded decay. (b) The experimental layout; 3 ns pulses at 516.65 nm were used to pump a 14 mm long beta barium borate (BBO) crystal in a low-finesse resonator. The relative angles between the crystal axis, the pump laser, and the resonator were chosen to obtain broadband phase matching for noncollinear type-I down-conversion. Unlike the signal beam, whose direction of propagation was set by the resonator, the idler beam had a wavelength-dependent angular spread, due to the phase matching conditions in the crystal. Therefore, it was directed through an imaging system that included a transmission grating which compensated for this spread. The signal beam was directed through a pulse shaper and a computer-controlled delay line with $0.1\mu$ resolution and then combined with the idler beam by a dichroic mirror. The pulse shaper separates the spectral components of the beam and utilizes a computer-controlled spatial light modulator (SLM) to introduce the desired spectral phase filter to the light. A photomultiplier tube (PMT) and a digital oscilloscope were used to perform a triggered measurement of the TPA-induced fluorescence.

Figure 2

Experimental TPA with broadband down-converted light, as a function of the signal-idler delay and the pump wavelength. The graphs clearly show a coherent TPA signal that is narrow both temporally and spectrally, superimposed on an incoherent background signal, which is insensitive to both pump wavelength and signal-idler relative delay. In this experiment the pulse shaper was used only to compensate for the dispersion in our system. (a) Calculated (line) and experimental TPA with off-resonance (squares) and on-resonance (circles) pump, as a function of the signal-idler delay. (b) Experimental TPA at zero signal-idler delay (circles), and at 100 fs signal-idler delay (squares), as a function of the pump center wavelength, together with a typical spectrum of the pump (line). The coherent TPA signal appears only when the pump is on-resonance with the $5S-4D$ transition, and exhibits a sharp dependence on the signal-idler delay, exactly as if the interaction was induced by a pair of coherent, 23 fs pulses with the same spectra as the signal and idler beams.

Figure 3

Quantum coherent control of TPA with broadband down-converted light. (a) The square-wave spectral phase filter applied on the signal beam, together with a typical power spectrum of the signal. (b) Experimental (circles) and calculated (line) TPA signal as a function of the signal-idler delay, using the spectral phase filter described in (a). The splitting of the central peak confirms that the coherent TPA behaves exactly as if it was induced by a pair of transform-limited pulses, with one of them temporally shaped by the applied phase filter. (c) Experimental (circles) and calculated (line) TPA signal as a function of the magnitude of the square wave spectral phase filter. The graph shows the periodic annihilation of the coherent TPA at magnitudes of $\pi ,3\pi ,5\pi$, where a complete destructive quantum interference occurs (“dark pulse”), and the complete reconstruction of the TPA signal at amplitudes of $2\pi ,4\pi ,6\pi$, etc.