Multipass configuration for improved squeezed vacuum generation in hot Rb vapor

We study a squeezed vacuum field generated in hot Rb vapor via the polarization self-rotation effect. Our previous experiments showed that the amount of observed squeezing may be limited by the contamination of the squeezed vacuum output with higher-order spatial modes, also generated inside the cell. Here, we demonstrate that the squeezing can be improved by making the light interact several times with a less dense atomic ensemble. With optimization of some parameters we can achieve up to $-2.6$ dB of squeezing in the multipass case, which is a 0.6 dB improvement compared to the single-pass experimental configuration. Our results show that, other than the optical depth of the medium, the spatial mode structure and the cell configuration also affect the squeezing level.

Figure 1

(a) Experimental setup for generation and measurement of PSR quantum noise in a single-pass configuration. SMPM is a single-mode-polarization-maintaining fiber, $\lambda /2$ is a half-wave plate, GP is a Glan-laser polarizer, PBS is a polarizing beam splitter, PhR is a phase-retarding wave plate, and BPD is a balanced photodetector. Panels (b) and (c) show the modification of the experiment for the double- and quadruple-pass arrangements, correspondingly.

Figure 2

Experimental optimization of squeezed vacuum in the parameter space of the pump beam power and atomic density for (a) single-, (b) double-, and (c) quadruple-pass configurations. The shading represents the value of the minimum quantum noise suppression below the shot noise level (see the scale on the right), with the darkest areas in each plot representing the “island” of optimal conditions for squeezing. Note the difference in horizontal scaling between the three graphs.

Figure 3

Measured dependencies of minimum quadrature noise on the effective optical depth for single-, double-, and quadruple-pass configurations. The laser pump power for all three traces was 11 mW, shown in Fig. 2 to provide the best value of squeezing for all three geometries.

Figure 4

Transverse intensity distribution of the pump field (a) and the absolute values of the calculated deconvolution coefficients $|c_p|$ of the Laguerre-Gaussian modes $L_p^{\ell =0}$, defined in Eq. (1) after the cell at room temperature ($T={26}^{\circ }\mathrm{C}, N={10}^{10}{\mathrm{cm}}^{-3}$). Small beam contamination due to diffraction gives rise to a nonzero $c_2$ coefficient, even if atoms are not present. Corresponding results for the pump beam after the interaction with Rb vapor at high temperature ($T={91}^{\circ }\mathrm{C}, N=2.6\times {10}^{12}{\mathrm{cm}}^{-3}$) are shown in (c) and (d).

Figure 5

The calculated relative amplitudes of the first few higher-order Laguerre-Gaussian modes $L_p^{\ell =0}$ as (a) atomic density $N$ gradually increases or as (b) the length of the atomic medium $L$ (in the units of the Rayleigh radius $z_R$) is increased.

Figure 6

A modified experimental setup with two independent vapor cells. All the abbreviations are the same as in Fig. 1.

Figure 7

A measurement of squeezing dependence on the second cell density in the two-cell system. In (a) the atom density of the first cell is $9.3\times {10}^{11}{\mathrm{cm}}^{-3}$ and in (b) it is $4.3\times {10}^{11}{\mathrm{cm}}^{-3}$. Crosses represent the squeezing amount in total, and circles correspond to the case when a PBS is inserted after the first cell so that the first-cell-generated squeezing is filtered.

Figure 8

The dependence of squeezing amount on position of the first (circles) and second cell (crosses). Black represents measured squeezing when both cells are present. Red (light gray) is when an addition PBS is placed after the first cell and filters the squeezed field generated in the first cell. In panels (a) and (b) the atomic density in both cells is $4.3\times {10}^{11}{\mathrm{cm}}^{-3}$. In panels (c) and (d) atomic density in the first cell is $4.3\times {10}^{11}{\mathrm{cm}}^{-3}$ and in the second is $9.3\times {10}^{11}{\mathrm{cm}}^{-3}$. In panels (e) and (f) the atomic density in both cells is $9.3\times {10}^{11}{\mathrm{cm}}^{-3}$. In the top row, the position of the first cell is $-2.5$ cm. In the bottom row, the positions of the second cell are each $-2.5$ cm in (b), 0 cm in (d), and 1.3 cm in (f), which are the optimal positions found in the top row.