Effect of atomic noise on optical squeezing via polarization self-rotation in a thermal vapor cell

The traversal of an elliptically polarized optical field through a thermal vapor cell can give rise to a rotation of its polarization axis. This process, known as polarization self-rotation (PSR), has been suggested as a mechanism for producing squeezed light at atomic transition wavelengths. We show results of the characterization of PSR in isotopically enhanced rubidium-87 cells, performed in two independent laboratories. We observed that, contrary to earlier work, the presence of atomic noise in the thermal vapor overwhelms the observation of squeezing. We present a theory that contains atomic noise terms and show that a null result in squeezing is consistent with this theory.

Figure 1

Two orthogonal ${\sigma }_{+}$ and ${\sigma }_{-}$ circularly polarized light fields interacting with a four-level atomic system.

Figure 2

(Color online) Schematic of the experimental setup. All polarizing optics are of the Glan-Thompson type. FI: Faraday isolator. BS: beam splitter. Pol.: polarizer. PBS: polarizing beam splitter. $\lambda ∕4$: quarter-wave plate. $\lambda ∕2$: half-wave plate. PZT: piezoelectric actuator.

Figure 3

(Color online) False color contour plot of the normalized transmission results for the $D_2$ line as a function of input beam intensity and laser frequency detuning. Zero frequency corresponds to the $\mid 5^2{S}_{1∕2},F_g=2⟩$ to $\mid 5^2{P}_{3∕2},F_e=3⟩$ energy levels.

Figure 4

(Color online) False color contour plot of $\mathcal{G}l$ for the $D_2$ line, normalized to the input beam ellipticity of 2°, as a function of input beam intensity and laser frequency detuning. Zero frequency corresponds to the $\mid 5^2{S}_{1∕2},F_g=2⟩$ to $\mid 5^2{P}_{3∕2},F_e=3⟩$ energy levels.

Figure 5

(Color online) The normalized transmission and $\mathcal{G}l$ results for the $D_2$ line are shown in (a) and (b), respectively. The (i) red curves are the theoretical fits to the experimental results [(ii) green curve]. Input beam $\text{intensity}=31.5\mathrm{mW}$, and zero frequency corresponds to the $\mid 5^2{S}_{1∕2},F_g=2⟩$ to $\mid 5^2{P}_{3∕2},F_e=3⟩$ energy levels.

Figure 6

(Color online) False color contour plot of the normalized transmission results for the $D_1$ line, as a function of input beam intensity and laser frequency detuning. Zero frequency corresponds to the $\mid 5^2{S}_{1∕2},F_g=2⟩$ to $\mid 5^2{P}_{1∕2},F_e=1⟩$ energy levels.

Figure 7

(Color online) False color contour plot of $\mathcal{G}l$ for the $D_1$ line, normalized to the input beam ellipticity of 2°, as a function of input beam intensity and laser frequency detuning. Zero frequency corresponds to the $\mid 5^2{S}_{1∕2},F_g=2⟩$ to $\mid 5^2{P}_{1∕2},F_e=1⟩$ energy levels.

Figure 8

(Color online) The normalized transmission and $\mathcal{G}l$ results for the $D_1$ line are shown in (a) and (b), respectively. The (i) red curves are the theoretical fits to the experimental results [(ii) green curve]. Input beam $\text{intensity}=22.3\mathrm{mW}$, and zero frequency corresponds to the $\mid 5^2{S}_{1∕2},F_g=2⟩$ to $\mid 5^2{P}_{1∕2},F_e=1⟩$ energy levels.

Figure 9

(Color online) (i) Amplitude and (ii) phase quadrature noise results for the $D_2$ line, normalized to the QNL and dark noise subtracted. (a) and (b) correspond to an input beam power of $21\mathrm{mW}$ at sideband frequencies of $3\mathrm{MHz}$ and $6\mathrm{MHz}$, respectively. (c) and (d) are results for an input beam power of $35\mathrm{mW}$ at sideband frequencies of $3\mathrm{MHz}$ and $6\mathrm{MHz}$, respectively. Zero frequency corresponds to the $\mid 5^2{S}_{1∕2},F_g=2⟩$ to $\mid 5^2{P}_{3∕2},F_e=3⟩$ energy level. ResBW: $100\mathrm{kHz}$. VBW: $30\mathrm{Hz}$.

Figure 10

(Color online) Scanned quadrature noise for the $D_2$ line measured in zero span at a sideband frequency of $3\mathrm{MHz}$. The input beam power was $35\mathrm{mW}$, and the laser frequency was $-70\mathrm{MHz}$ from the $\mid 5^2{S}_{1∕2},F_g=2⟩$ to $\mid 5^2{P}_{1∕2},F_e=3⟩$ energy level. All plots are dark noise subtracted. ResBW: $100\mathrm{kHz}$. VBW: $30\mathrm{Hz}$.

Figure 11

(Color online) (i) Amplitude and (ii) phase quadrature noise results for the $D_1$ line, normalized to the QNL and subtracted by the dark noise. (a) and (b) correspond to an input beam power of $21\mathrm{mW}$ at sideband frequencies of $3\mathrm{MHz}$ and $6\mathrm{MHz}$, respectively. (c) and (d) are results for an input beam power of $35\mathrm{mW}$ at sideband frequencies of $3\mathrm{MHz}$ and $6\mathrm{MHz}$, respectively. Zero frequency corresponds to the $\mid 5^2{S}_{1∕2},F_g=2⟩$ to $\mid 5^2{P}_{1∕2},F_e=1⟩$ energy level. ResBW: $100\mathrm{kHz}$. VBW: $30\mathrm{Hz}$.