Partially Nondestructive Continuous Detection of Individual Traveling Optical Photons

Mahdi Hosseini, Kristin M. Beck, Yiheng Duan, Wenlan Chen, and Vladan Vuletić

Phys. Rev. Lett. 116, 033602 – Published 19 January 2016

Abstract

We report the continuous and partially nondestructive measurement of optical photons. For a weak light pulse traveling through a slow-light optical medium (signal), the associated atomic-excitation component is detected by another light beam (probe) with the aid of an optical cavity. We observe strong correlations of $g_{s p}^{(2)} = 4.4 (5)$ between the transmitted signal and probe photons. The observed (intrinsic) conditional nondestructive quantum efficiency ranges between 13% and 1% (65% and 5%) for a signal transmission range of 2% to 35%, at a typical time resolution of $2.5 μ s$ . The maximal observed (intrinsic) device nondestructive quantum efficiency, defined as the product of the conditional nondestructive quantum efficiency and the signal transmission, is 0.5% (2.4%). The normalized cross-correlation function violates the Cauchy-Schwarz inequality, confirming the nonclassical character of the correlations.

Received 26 August 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.033602

Physics Subject Headings (PhySH)

Quantum description of light-matter interaction Quantum measurements

Cavity resonators

Atomic, Molecular & Optical

Authors & Affiliations

Mahdi Hosseini, Kristin M. Beck, Yiheng Duan, Wenlan Chen, and Vladan Vuletić^*

Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

^*Corresponding author. vuletic@mit.edu

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Vol. 116, Iss. 3 — 22 January 2016

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Figure 1
(a),(b) The $π$ -polarized signal light travels with slow group velocity through the atoms by means of EIT on the $| g ⟩ \leftrightarrow | c ⟩ \leftrightarrow | d ⟩$ transitions. The associated atomic-excitation component is nondestructively detected via cavity light in the geometric overlap between the atomic ensemble and the cavity mode. Input cavity light is linearly polarized such that, in the absence of signal photons, the probe port of the polarization beam splitter (PBS) ideally remains dark. Whenever a signal photon traverses the atomic medium in the cavity, the transmission of the $σ^{+}$ polarized light through the cavity is blocked. The atomic levels are $| g ⟩ = | 6 S_{1 / 2}; F = 3, m_{F} = 3 ⟩$ , $| c ⟩ = | 6 P_{3 / 2}; 3, 3 ⟩$ , $| d ⟩ = | 6 S_{1 / 2}; 4, 4 ⟩$ , $| e ⟩ = | 6 P_{3 / 2}; 5, 5 ⟩$ , and $| f ⟩ = | 6 P_{3 / 2}; 5, 3 ⟩$ , where $F$ , $m_{F}$ are the hyperfine quantum numbers.
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Figure 2
(a) Signal-probe correlation function $g_{s p}^{(2)}$ is plotted as a function of separation time $τ$ between signal ( $t_{s}$ ) and probe ( $t_{p}$ ) photons. The decay time constant for negative (positive) times $τ_{<} = 1.2 (2) μ s$ [ $τ_{>} = 1.3 (2) μ s$ ] is consistent with the cavity decay time (EIT lifetime) [20]. This measurement is done with mean input cavity photon number $⟨ n_{c}^{in} ⟩ = R_{c}^{s = 0} τ_{c} / q_{c} = 3.7$ , cavity path detection efficiency $q_{c} = 0.2$ , $τ_{c} = (κ / 2)^{- 1} = 2 μ s$ , and Rabi frequency $Ω / 2 π = 1.9 MHz$ . The inset shows the cross-correlation function for signal and $σ^{+}$ -polarized cavity photons, measured for $⟨ n_{c}^{in} ⟩ = 0.1$ and $Ω / 2 π = 2.6 MHz$ . The observed signal-probe anticorrelation is $g_{s σ^{+}}^{(2)} (0) = 0.41 (7)$ . In this and all following figures, statistical error bars are plotted when they are larger than the points and indicate one standard deviation. (b) Normalized detected probe rate $R_{p} / R_{c}^{s = 0}$ , plotted against input signal photon number $⟨ n_{s}^{in} ⟩ = R_{s}^{in} τ_{EIT} / q_{s}$ . The slope of the solid fitted line is 0.20(1). The dashed line represents the maximum possible probe rate with a slope of $ϵ_{i d} = 0.25$ . For this measurement, $⟨ n_{c}^{in} ⟩ = 1.2$ , $q_{s} = 0.3$ , and $Ω / 2 π = 1.3 MHz$ , giving $τ_{EIT} = 1.4 μ s$ .
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Figure 3
(a) The observed conditional nondestructive quantum efficiency $Q$ is plotted against mean cavity photon number $⟨ n_{c}^{in} ⟩$ with mean $R_{s}^{in} = 2.8 \times 10^{5} s^{- 1}$ . The slope of the fitted curves (solid lines) is $d Q / d ⟨ n_{c}^{in} ⟩ = {10 (2), 5 (1), 1.9 (5)} %$ for $Ω / 2 π = {1.8, 2.9, 3.5} MHz$ (top to bottom) and represents the observed detection efficiency per input cavity photon. (b) Signal transmission $T_{s}$ for the same data presented in (a). Exponential fits give $1 / e$ transmission at cavity photon numbers of ${1.2 (1), 1.9 (1), 2.1 (1)}$ for $Ω / 2 π = {1.8, 2.9, 3.5} MHz$ (bottom to top), respectively. The inset displays the nondestructive quantum efficiency $Q$ as a function of signal transmission for the same Rabi frequencies as in (a) and (b).
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Figure 4
Device nondestructive quantum efficiency ( $P_{11} = Q \times T_{s}$ ) and error probability $P_{err}$ for joint detection of signal and probe outputs for $Ω / 2 π = 2.9 MHz$ . $P_{11}$ is calculated assuming one input signal photon. $P_{err}$ represents the false detection of probe photons in the absence of signal photons. The inset displays all four characterizing probabilities $P_{s p}$ with $s$ , $p = {0, 1}$ (see text) and $P_{err}$ under the same conditions.
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