Squeezed-twin-beam generation in strongly absorbing media

We experimentally demonstrate the generation of squeezed, bright twin beams that arise due to competing gain and absorption, in a medium that is overall transparent. To accomplish this, we make use of a nondegenerate four-wave-mixing process in warm potassium vapor such that one of the twin beams experiences strong absorption. At room temperature and above, due to Doppler broadening and smaller frequency detunings compared to other schemes, the ground-state hyperfine splittings used in the present double-$\mathrm{\Lambda }$ setup are completely overlapped. We show that despite the resulting significant asymmetric absorption of the twin beams, quantum correlations may still be generated. Our results in this regime demonstrate that the simplified model of gain, followed by loss, is insufficient to describe the amount of quantum correlation resulting from the process.

Figure 1

Four-wave mixing in potassium vapor. (a) The pump and probe fields overlap in the center of the vapor cell, and the amplified probe and generated conjugate fields are detected on a balanced photodetector. Here PBS denotes the polarizing beam splitter and GT the Glan-Taylor polarizer. (b) Measured absorption spectrum of the ${}^{39}\mathrm{K}{D}_1$ line (black solid line), a double-Lorentzian model of the hyperfine states based on measurements of the transitions using polarization spectroscopy (black dashed line), and the measured gain lines for the probe (red line) and conjugate (blue line). The arrows indicate the frequency detunings used in the experiment. (c) Energy-level diagram summarizing the four-wave interaction.

Figure 2

Two-mode squeezing via 4WM in potassium vapor. The noise power spectra correspond to (a) the 4WM difference signal for $74\mu \mathrm{W}$ of probe and $62\mu \mathrm{W}$ of conjugate beam powers, (b) the shot-noise limit for $136\mu \mathrm{W}$ of pump light incident on a 50/50 beam splitter and the individual spectra for (c) $62\mu \mathrm{W}$ of conjugate and (d) $74\mu \mathrm{W}$ of probe, respectively.

Figure 3

Measured noise power of our laser light at 3 MHz as a function of the total optical power. The data have been corrected for an offset due to electronic noise.

Figure 4

Measured squeezing compared to the two theoretical models described in the text (DGL, dashed lines, and BS, dash-dotted lines). Data are shown for various levels of gain and measured probe transmissions of $t=0.15$ (blue squares) and $t=0.4$ (red circles), where each data point corresponds to the measured noise power at 3 MHz relative to the SNL. Also shown are the predicted values of squeezing for transmissions of $15\%$ (blue) and $40\%$ (red) using the two theoretical models.

Figure 5

Anticorrelated fluctuations in the probe and conjugate intensities measured over a time scale of 20 s. In this measurement, the experimental parameters are the same as those that lead to the squeezing data shown in Fig. 2.