Quantum Study of Information Delay in Electromagnetically Induced Transparency

Using electromagnetically induced transparency (EIT), it is possible to delay and store light in atomic ensembles. Theoretical modeling and recent experiments have suggested that the EIT storage mechanism can be used as a memory for quantum information. We present experiments that quantify the noise performance of an EIT system for conjugate amplitude and phase quadratures. It is shown that our EIT system adds excess noise to the delayed light that has not hitherto been predicted by published theoretical modeling. In analogy with other continuous-variable quantum information systems, the performance of our EIT system is characterized in terms of conditional variance and signal transfer.

Figure 1

(a) Schematic of experimental layout. BS: beam splitter, PBS: polarizing beam splitter, SA: spectrum analyzer, DS: digital storage oscilloscope, $\lambda /4$: quarter-wave plate, $\lambda /2$: half-wave plate, and Pol.: polarizer. (b) Atomic level scheme used in our experiment. $E_p$ is the probe field, $E_c$ is the pump field, $\gamma$ is the spontaneous emission rate, and ${\gamma }_0$ is the ground state dephasing rate. (c) Amplitude quadrature correlation plots. Similar results were observed for the phase quadrature correlation. Cell $\mathrm{\text{temperature}}=62°\mathrm{C}$; probe and pump power densities are $0.32\mathrm{mW}/{\mathrm{cm}}^2$ and $3.2\mathrm{mW}/{\mathrm{cm}}^2$, respectively.

Figure 2

$V_{\mathrm{in}|\mathrm{out}}^{\pm }$ for the amplitude quadrature, optimized for the sideband frequency of 305 kHz. The curves represent the (i) output probe signal, (ii) reference signal with gain $G$ and delay $\tau$, (iii) $V_{\mathrm{in}|\mathrm{out}}^{\pm }$ between the reference and output signals, and (iv) $V_{\mathrm{in}|\mathrm{out}}^{\pm }$ for the beam splitter benchmark. The modulation peaks at 87 kHz and 174 kHz are the laser locking signals. Cell $\mathrm{\text{temperature}}=57°\mathrm{C}$; probe and pump power densities are $9.6\mathrm{mW}/{\mathrm{cm}}^2$ and $96\mathrm{mW}/{\mathrm{cm}}^2$, respectively. Measurements were made with a resolution bandwidth $(\mathrm{RBW})=1\mathrm{kHz}$, video bandwidth $(\mathrm{VBW})=30\mathrm{Hz}$, and 5 averages.

Figure 3

$V_{\mathrm{in}|\mathrm{out}}^{\pm }$ measurements for 2 cell temperatures. (a) Amplitude quadrature, 42 °C; (b) phase quadrature, 42 °C; (c) amplitude quadrature, 57 °C, and (d) phase quadrature, 57 °C. The data point groups represent the (i) EIT $V_{\mathrm{in}|\mathrm{out}}^{\pm }$ and (ii) beam splitter benchmark $V_{\mathrm{in}|\mathrm{out}}^{\pm }$. The shape of the shaded area has been fitted using the passive loss described in Eq. (1). The insets show the zoom-in data points. $\mathrm{RBW}=1\mathrm{kHz}$, $\mathrm{VBW}=30\mathrm{Hz}$, and 10 averages. The 57 °C and 42 °C beam splitter benchmark data points were fitted with ${\gamma }_0=4\mathrm{kHz}$ and ${\gamma }_0=3.5\mathrm{kHz}$, respectively. The probe and pump power densities are $9.6\mathrm{mW}/{\mathrm{cm}}^2$ and $96\mathrm{mW}/{\mathrm{cm}}^2$, respectively, The largest delay for the 57 °C and 42 °C data is $0.48\mu \mathrm{s}$ and $0.18\mu \mathrm{s}$, respectively.

Figure 4

Signal transfer coefficient for the (a) amplitude and (b) phase quadratures. (i) $T=42°\mathrm{C}$ and (ii) corresponding beam splitter benchmark. (iii) $T=57°\mathrm{C}$ and (iv) corresponding beam splitter benchmark. $\mathrm{RBW}=1\mathrm{kHz}$, $\mathrm{VBW}=30\mathrm{Hz}$, and 10 averages. The probe and pump power densities are $9.6\mathrm{mW}/{\mathrm{cm}}^2$ and $96\mathrm{mW}/{\mathrm{cm}}^2$, respectively. The 57 °C and 42 °C beam splitter benchmark data points were fitted with ${\gamma }_0=4\mathrm{kHz}$ and ${\gamma }_0=3.5\mathrm{kHz}$, respectively.