Long light storage time in an optical fiber

Light storage in an optical fiber is an attractive component in quantum optical delay line technologies. Although silica-core optical fibers are excellent in transmitting broadband optical signals, it is challenging to tailor their dispersive property to slow down a light pulse or store it in the silica core for a long delay time. Coupling a dispersive and coherent medium with an optical fiber is promising in supporting long optical delay. Here, we load cold Rb atomic vapor into an optical trap inside a hollow-core photonic crystal fiber, and store the phase of the light in a long-lived spin wave formed by atoms and retrieve it after a fully controllable delay time using electromagnetically induced transparency (EIT). We achieve over 50 ms of storage time and the result is equivalent to $8.7\times {10}^{-5}\mathrm{dB}$ $\mu {\mathrm{s}}^{-1}$ of propagation loss in an optical fiber. Our demonstration could be used for buffering and regulating classical and quantum information flow between remote networks.

Figure 1

Details of the experimental setup. NPBS: non-polarizing beam splitter. PBS: polarizing beam splitter. HWP: half-wave plate. QWP: quarter-wave plate. PM fiber: polarization-maintaining fiber. APD: avalanche photodiode. The QWPs are used to adjust the ellipticity of the dipole beams to induce the vector light shift. In order to combine the linearly polarized EIT beams and the elliptically polarized dipole beam, we use a $90\%$ reflection and $10\%$ transmission NPBS. A 50:50 NPBS is then used to separate the EIT beams from the counterpropagating dipole beam. We use a temperature-stabilized solid-state etalon to minimize leakage of the control beam to the APD. The depump light on the $F=3$ to $F^{\prime }=3$ D2 line is used to prepare the atoms in the $F=2$ state. The optical pump beam is resonant on the $F=2$ to $F^{\prime }=2$ D1 line. The first control pulse is for converting the probe pulse into an atomic spin-wave and the second is for retrieving it.

Figure 2

Input, slowed, and delayed light pulses through the hollow-core fiber. (a) Measured slowed light when the control beam is permanently on. The input pulse (black squares) is fitted by a Gaussian function with a FWHM of 304 ns, and the slowed pulse (blue circles) is fitted by a Gaussian function with a FWHM of 415 ns. The peak of the fitted Gaussian function of slowed light is delayed by 173 ns. (b) Numerical calculations of slowed pulses. The blue circles are calculations of the slowed pulse with nonuniform profile of the control beam, the probe beam, and the atom density in the fiber. The green squares are the calculations of the slowed light with uniform EIT beam profiles and atom density distribution. (c) The measured temporal profiles of the leaked and delayed light pulses. The control pulse is switched off when the probe pulse is propagating inside the atomic medium. The bandwidth of the delayed pulse is defined from its FWHM of 160 ns.

Figure 3

Storage efficiency as a function of time. (a) The grey circles are the measurements of the storage efficiency without light shift cancellation. The function $A{[1+{(T/T_{\text{c}})}^2]}^{-3/2}$ is fitted to the data with $T_{\text{c}}=823\left(10\right)\mu \mathrm{s}$, where $A$ is the efficiency at $T=0$. The decay time is limited by the differential ac Stark shift of the dipole potential on the atomic spin coherence. For comparison, the curve in purple represents the 0.03 dB $\mu {\mathrm{s}}^{-1}=0.15\mathrm{dB}{\mathrm{km}}^{-1}$ loss of 1550 nm light propagating in a solid core fiber. The error bars are the standard errors of 40 experimental runs. (b) Measurements of the efficiency with light shift cancellation (orange circles). An exponential decay function is fitted to the data with a $1/e$ time of 20(1) ms. The curve in purple is the same as in (a). The error bars are the standard errors of 40 experimental runs. (c) Measurements of normalized storage efficiency for a free-falling atomic spin-wave with light-shift cancellation. The control and probe pulses are sent when atoms are in motion inside the fiber.

Figure 4

Efficiency versus delay time with different dynamic decoupling (DD) pulse separation times. The black squares represent an average of 40 experimental runs of light delay efficiency and the error bars indicate the standard errors. The red circles are the fit of the simulation to the experimental data. The lines are used to guide the eyes. The efficiencies are normalized to the first points for each $T_{\text{dd}}$. The ratio of the Gaussian waists of the ensemble to the control beam in radial direction $\alpha$ and the frequency difference of the microwave and the EIT two-photon detuning $\mathrm{\Delta }$ are set as free parameters to fit the data. Due to the radial distribution of the EIT beams and atoms, the Rabi frequencies of the control and the probe pulses are set with a Gaussian distribution in the radial direction in the simulation, where their maximum Rabi frequencies excite a $\pi /2$ pulse with 250 ns duration. The duration of the microwave $\pi$ pulses is $37\mu \mathrm{s}$ and the Rabi frequency is assumed uniform across all the atoms. The inset shows the measurement of contrast versus time using microwave Ramsey interferometer with DD sequence. The curve is an exponential fit to the experimental data.