Coherent Backscattering of Light Off One-Dimensional Atomic Strings

We present the first experimental realization of coherent Bragg scattering off a one-dimensional system—two strings of atoms strongly coupled to a single photonic mode—realized by trapping atoms in the evanescent field of a tapered optical fiber, which also guides the probe light. We report nearly 12% power reflection from strings containing only about 1000 cesium atoms, an enhancement of 2 orders of magnitude compared to reflection from randomly positioned atoms. This result paves the road towards collective strong coupling in 1D atom-photon systems. Our approach also allows for a straightforward fiber connection between several distant 1D atomic crystals.

Figure 1

Experimental procedure and setup. (a) The standing wave structuring pulse field (orange plane) accelerates atoms (green balls) both axially and radially towards the intensity maxima (bright spots). Since the trapping and structuring fields have incommensurate wavelengths, we depict with blue arrows the positions of atoms starting at the radial equilibrium location and various axial positions after a ballistic flight of 600 ns following the structuring pulse. (b) Experimental setup. In the dipole trap, the atoms arrange themselves into two 1D strings (purple lines) along the TOF (yellow). Each trap site (purple wells in the zoomed-in box) is either empty or contains a single atom prepared in the $|•⟩$ state. A standing wave pulse (SP) (red) is used to imprint a Bragg grating onto the atoms. A probe field (blue) is sent onto the atomic strings; the reflected and transmitted light is mixed with corresponding local oscillator (LO) beams and measured by two photodetectors R and T (heterodyne detection). (c) Level diagram. The probe beam (blue) is tuned close to resonance with the $|•⟩\to |e⟩\equiv (6{}^2{P}_{3/2},F=5)$ transition. The structuring pulse (red) optically exerts both a radial and an axial dipole force and pumps the atoms out of $|•⟩$. (d) Evolution of the axial modulation of the scattering rate, calculated for an atomic ensemble located at the trap potential minimum (green balls in (a) with an initial thermal velocity distribution corresponding to $T=42\mu \mathrm{K}$

Figure 2

Reflectance off the atomic strings within a 2.8 MHz detection bandwidth (3 dB). The probe is tuned 8 MHz above atomic resonance and turned on at $t=0$ with an independently measured rise time of 80 ns. Blue curve: Unstructured atomic ensemble, average of 250 experiments. Red curve: Structured ensemble, average of 200 experiments. The shaded regions signify the $1\sigma$ uncertainty interval with contributions from statistical averaging and a 5% input probe power fluctuation during the measurement. Inset: Zoom on the first reflection peak with a fit to a Gaussian decay (purple) and the theoretical prediction (black) with uncertainty band given by the statistical averaging.

Figure 3

Experimental data. Each point represents the reflectance at $t=0.2\mu \mathrm{s}$ extracted from a Gaussian decay fit to 100–250 consecutive experimental runs with vertical error bars from the uncertainty on the fit parameters. Blue curves show the theoretical predictions with the shaded regions signifying the $1\sigma$ uncertainty interval from the statistical averaging. (a) Reflectance as a function of the power of the structuring pulse $P_{\mathrm{sp}}$ for a probe detuning of $\mathrm{\Delta }=2\pi \times 8\mathrm{MHz}$. For these data, $⟨\tau ⟩=0.89\mu \mathrm{s}$. Horizontal error bars corresponds to a 5% power fluctuation. (b) Variation of the reflectance with the probe detuning. The Bragg grating was created using a structuring power of $0.2\mu \mathrm{W}$. The black triangular point corresponds to the red data trace in Fig. 2. For these data, $⟨\tau ⟩=0.86\mu \mathrm{s}$.