Enhanced intensity-difference squeezing via energy-level modulations in hot atomic media

Narrow-band intensity-difference squeezing (IDS) beams have important applications in quantum metrology and gravitational wave detection. The best way to generate narrow-band IDS is to employ a parametrically amplified (PA) four-wave mixing (FWM) process in high-gain atomic media. Such IDS can be further enhanced by cascading multiple PA FWM processes in separate atomic media. The complicated experimental setup, added losses, and mechanical stability can limit the wide use of such a scheme in practical applications. Here we show that by modulating the internal energy level(s) with an additional laser (or lasers), the degree of original IDS can be substantially increased. With an initial IDS of $\left(-3.6\pm 0.4\right)$ dB using a PA nondegenerate FWM process in a three-level $\mathrm{\Lambda }$-type configuration, the degree of IDS can be enhanced to $\left(-7.0\pm 0.4\right)$ dB or $\left(-9.0\pm 0.4\right)$ dB when we use one (two) laser beam (beams) to modulate the involved ground (excited) state (states). Our results show a low-loss, robust, and efficient way to produce a high degree of IDS and facilitate its potential applications.

Figure 1

(a) Experimental setup: PBS, polarizing beam splitter; SA, spectrum analyzer. (b) Energy-level diagram of the $(\mathrm{\Lambda }$-type $\left(|0\rangle \leftrightarrow |1\rangle \leftrightarrow |2\rangle \right)$ rubidium atomic system with an ${\mathit{E}}_3$ ladder-type dressing (between levels $|2\rangle$ and $|3\rangle )$ and an ${\mathit{E}}_4$ $\mathsf{V}$-type dressing (between levels $|0\rangle$ and $|4\rangle )$ simultaneously. (c) Phase-matching conditions for the spontaneous parametric (c1) spontaneous FWM, (c2) spontaneous SWM1, and (c) spontaneous EWM processes.

Figure 2

(a) Measured probe transmission $\left({\mathit{E}}_{aS}\right)$ and corresponding conjugate $\left({\mathit{E}}_S\right)$ signal versus probe frequency detuning with (a1) and (a3) ${\mathit{E}}_3$ off and (a2) and (a4) ${\mathit{E}}_3$ on, for ${\mathrm{\Delta }}_1=1.12\mathrm{GHz}$ and ${\mathrm{\Delta }}_3=–1\mathrm{GHz}$. (b) Relative intensity noise levels versus spectrum analyzer frequency for (b1) SQL, (b2) FWM, and (b3) dressed FWM (FWM plus SWM1) when ${\mathit{E}}_3$ is applied, and electronic noise. (c) Relative intensity noise power at different total optical power for curve A, SNL (diamonds); curve B, FWM (circles); and curve C, single-dressing FWM (triangles). All three of these noise power curves fit to straight lines. The electronic noise floor and background noise are subtracted from all of the traces and data points.

Figure 3

Same as Fig. 2 but with (a1) and (a3) ${\mathit{E}}_4$ off and (a2) and (a4) ${\mathit{E}}_4$ on, for ${\mathrm{\Delta }}_1=1.12\mathrm{GHz}$ and ${\mathrm{\Delta }}_4=–1\mathrm{GHz}$. (b) Relative intensity noise levels versus spectrum analyzer frequency for (b1) SQL, (b2) FWM, and (b3) dressed FWM (FWM plus SWM2) when field ${\mathit{E}}_4$ is applied. (c) and (d) Same as (a) and (b) but for (c) ${\mathrm{\Delta }}_1=1.15\mathrm{GHz}$ and (d) ${\mathrm{\Delta }}_4=1.15\mathrm{GHz}$, respectively. (e) Relative intensity noise power at different total optical power for SNL (diamonds), FWM (triangles), and enhanced ${\mathit{E}}_4$-dressing FWM (circles). (f) Same as (e) except that it is suppressed ${\mathit{E}}_4$-dressing FWM. All these noise power curves fit to straight lines. The electronic noise floor and background noise are subtracted from all of the traces and data points.

Figure 4

(a) Measured probe transmission signal ${\mathit{E}}_{aS}$ versus the probe detuning with (a1) ${\mathit{E}}_3$ and ${\mathit{E}}_4$ off, (a2) ${\mathit{E}}_3$ on, (a3)${\mathit{E}}_4$ on, and (a4) ${\mathit{E}}_3$ and ${\mathit{E}}_4$ both on, for ${\mathrm{\Delta }}_1=1.12\mathrm{GHz},{\mathrm{\Delta }}_3=–0.9\mathrm{GHz}$, and ${\mathrm{\Delta }}_4=0.95\mathrm{GHz}$. (b1)–(b4) Corresponding conjugate signal ${\mathit{E}}_S$ of (a1)–(a4), respectively. (c) Relative intensity noise levels versus spectrum analyzer frequency for (c1) SQL, (c2) FWM, (c3) ${\mathit{E}}_3$-dressed FWM, (c4) ${\mathit{E}}_4$-dressed FWM, and (c5) ${\mathit{E}}_3$- and ${\mathit{E}}_4$-dressed FWM (FWM plus SWM plus EWM). (d) Relative intensity noise power at different total optical power for curve A, SNL (diamonds); curve B, FWM (triangles); curve C, ${\mathit{E}}_3$-dressing FWM (circles); curve D, ${\mathit{E}}_4$-dressing FWM (pentagons); and curve E, double-dressing FWM (crosses). All five of these noise power curves fit to straight lines. The electronic noise floor and background noise are subtracted from all of the traces and data points.