Slow light in flight imaging

Slow-light media are of interest in the context of quantum computing and enhanced measurement of quantum effects, with particular emphasis on using slow light with single photons. We use light-in-flight imaging with a single-photon avalanche diode camera array to image in situ pulse propagation through a slow-light medium consisting of heated rubidium vapor. Light-in-flight imaging of slow-light propagation enables direct visualization of a series of physical effects, including simultaneous observation of spatial pulse compression and temporal pulse dispersion. Additionally, the single-photon nature of the camera allows for observation of the group velocity of single photons with measured single-photon fractional delays greater than 1 over 1 cm of propagation.

Figure 1

(a) Experimental setup (not to scale). A fiber-coupled electro-optical modulator (EOM) chops the laser beam into pulses, which propagate through the Rb vapor cell, from left to right along the $z$ axis. The Rb vapor cell is heated and enclosed in a transparent, outer, insulating glass cell (not shown for simplicity). The fast photodiode (PD) is used to measure the transmission spectra shown in (b). The SPAD camera is set up to capture light scattered by the Rb vapor along the $x$ axis. The camera has a 5 cm field of view (resolution of $\delta z=1.6$ mm) and is scanned along the $z$ axis by 4 cm increments. (b) Transmission spectra for the $L=7.18$ cm cell. A temperature of $T\sim 150{}^{\circ }\mathrm{C}$ corresponds to $D\sim 2.5$ at $\delta \sim 0$ GHz, with a group velocity $v_g=c/183$, determined from the SPAD data. The room-temperature transmission spectrum, $T\sim 20{}^{\circ }\mathrm{C}$, is provided for reference.

Figure 2

Pulse compression for varying group velocity. The real time $t$ is given for each pulse, with $t=0$ ns corresponding to the time when the pulse enters the Rb vapor at $z=0$ cm. The white dashed line denotes the position at which the light enters the Rb vapor. (a)–(d) correspond to group velocities of $v_g=c/183,c/81,c/24,$ and $c/2.6$, with temperatures of $T\sim 150$, 130, 106, and $50{}^{\circ }\mathrm{C}$, respectively. (e) Pulse propagating through air to provide a reference for light traveling at $v_g\sim c$. See corresponding video in Supplemental Material [19] for the full pulse propagation. A 7 cm cell was used to obtain the higher temperatures necessary for (a) and (b), while a 30 cm cell was used for (c) and (d).

Figure 3

Pulse compression. Subsequent frames show the pulse (a) propagating through air ($t=2.96$ ns), (b) entering the heated Rb vapor cell ($L\sim 7$ cm) and compressing spatially due to the decrease in group velocity ($t=5.01$ ns), and (c) exiting the cell and decompressing ($t=8.19$ ns).

Figure 4

(a) Representative plots of pulse position along the beam path $z$ vs the scattered photon arrival time $t$, shown for group velocities $v_g\sim c/6$ [(i), red squares], $v_g\sim c/41$ [(ii), blue circles] and $v_g\sim c/139$ [(iii), black diamonds]. Horizontal dashed lines denote the inner edges of the Rb vapor cell, where $z=0$ corresponds to where the pulse enters the Rb vapor. Solid lines are fits $z=v_g(t-t_0)$ to the data. (b) Photon-lag time vs group velocity. Black circles: extrapolated time $t_0$ at which the light entered the Rb vapor vs $v_g$. Red solid line: calculated time lag $t_0=r_{\mathrm{cell}}/v_g$, where $r_{\mathrm{cell}}=1.175$ cm is the inner radius of the vapor cell. Blue dashed line: time lag $t_0=r_{\mathrm{cell}}/c=0.04$ ns that one would expect if the scattered photons traveled out of the medium at $c$. (c) Raw temporal profiles corresponding to each pulse propagation position for $v_g\sim c/183$. Note that the light scattered just after the pulse enters the Rb vapor arrives at the camera approximately 5.3 ns later than the light scattered by the glass window (indicated by white arrows).

Figure 5

Pulse dispersion observed for a pulse propagating through a Rb vapor cell of length $L=30$ cm, with $v_g\sim c/24$ ($T\sim 104{}^{\circ }\mathrm{C}$). (a) Plot of raw pulse temporal profiles (horizontal axis) for increasing propagation distance $z$ (pulse position, vertical axis). (b),(c) Raw histograms and Gaussian fits to the temporal pulse profiles for $z=0$ and $z=17.2$ cm, respectively ($z=0$ cm corresponds to the temporal pulse profile directly after it enters the Rb vapor). Blue traces, labeled R, correspond to a pulse in air for comparison. Relative amplitudes have been scaled (air: $N_{\mathrm{counts}}$/70; Rb: $N_{\mathrm{counts}}$/200) to allow for a comparison of the pulse shape. (d) Representative plot of pulse temporal FWHM $\tau$ vs pulse position $z$ (red circles) for $T\sim 100{}^{\circ }\mathrm{C}, D\sim 0.63$, and $v_g\sim c/13$. Solid black line: data fit with the function $\tau \left(z\right)=\sqrt{{{\tau }_0}^2+{(Bz/{\tau }_0^2)}^2}$, where ${\tau }_0=1.44$ ns is the pulse FWHM at $z=0$ and ${\beta }_3=B/\sqrt{16{[ln\left(2\right)]}^3}=0.035{\mathrm{ns}}^3$/cm (see text). Noisy pixels, corresponding to the repeating line artifacts observed in (a), are set to $\sigma =0$ and excluded from the fit shown in (d).