Engineering Frequency-Time Quantum Correlation of Narrow-Band Biphotons from Cold Atoms

Young-Wook Cho, Kwang-Kyoon Park, Jong-Chan Lee, and Yoon-Ho Kim

Phys. Rev. Lett. 113, 063602 – Published 5 August 2014

Abstract

The nonclassical photon pair, generated via a parametric process, is naturally endowed with a specific form of frequency-time quantum correlations. Here, we report complete control of frequency-time quantum correlations of narrow-band biphotons generated via spontaneous four-wave mixing in a cold atomic ensemble. We have experimentally confirmed the generation of frequency-anticorrelated, frequency-correlated, and frequency-uncorrelated narrow-band biphoton states, as well as verifying the strong nonclassicality of the correlations. Our work opens up new possibilities for engineering narrow-band entangled photons for various quantum optical and quantum information applications.

Received 15 April 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.063602

Authors & Affiliations

Young-Wook Cho^*, Kwang-Kyoon Park, Jong-Chan Lee, and Yoon-Ho Kim^†

Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Korea

^*Present address: Centre for Quantum Computation and Communication Technology, Department of Quantum Science, The Australian National University, Canberra ACT 0200, Australia. choyoungwook81@gmail.com
^†yoonho72@gmail.com

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Vol. 113, Iss. 6 — 8 August 2014

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Images

Figure 1
Different types of biphoton frequency-time quantum correlations. The joint spectral intensity plots for (a) frequency-anticorrelated, (b) frequency-uncorrelated, and (c) frequency-correlated biphoton states. Because of the Fourier duality, the correlations are reversed in sign in the time domain. For instance, biphotons with frequency anticorrelation in (a) correspond to positive correlation in the joint temporal intensity plot in (d).
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Figure 2
Schematic of the experimental setup. (a) An ultracold Rb 87 cloud is prepared in a MOT. The pump ( $ω_{p}$ ) and the coupling ( $ω_{c}$ ) lasers create a pair of Stokes ( $ω_{s}$ ) and anti-Stokes ( $ω_{as}$ ) photons via the SFWM process. Each photon is collected into a single mode optical fiber with an objective lens (OL) after polarization filtering with a quarter-wave plate (QWP) and a polarization beam splitter (PBS). To block the strong pump and coupling fields, a solid etalon (F1 and F2) with the full width and half maximum (FWHM) bandwidth of 470 MHz is placed in front of each detector ( $D 1$ and $D 2$ ). (b) SFWM scheme for frequency-anticorrelated and frequency-uncorrelated biphotons. The weak pump is red detuned $Δ_{1} = 2 π \times 63 MHz$ below the $| 1 ⟩ \to | 4 ⟩$ transition (peak power: $75 μ W$ ). (c) SFWM scheme for frequency-correlated biphotons The strong pump is largely blue detuned $Δ_{2} = 2 π \times 6.834 GHz$ above the $| 1 ⟩ \to | 3 ⟩$ so that the Stokes and anti-Stokes photons are frequency degenerate (peak power: 90 mW).
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Figure 3
Experimental results (a)–(d). Color bars represent coincidence counts. (a) JTI for time-correlated or frequency-anticorrelated biphoton state. Experimental parameters are $σ_{p} = 40 ns$ and $τ_{g} = 15 ns$ ( $OD = 15$ , $γ_{13} = 2 π \times 3 MHz$ , $γ_{12} = 2 π \times 0.65 MHz$ , and $Ω_{c} = 2 π \times 36 MHz$ ). (b) JTI for time-uncorrelated or frequency-uncorrelated biphoton state. Experimental parameters are $σ_{p} = 20 ns$ and $τ_{g} = 168 ns$ ( $Ω_{c} = 2 π \times 10.4 MHz$ ). (c) JTI for time-anticorrelated or frequency-correlated biphoton state. Experimental parameters are $σ_{p} = 50 ns$ and $τ_{g} = 178 ns$ ( $OD = 75$ , $γ_{12} = 2 π \times 0.22 MHz$ , and $Ω_{c} = 2 π \times 20 MHz$ ). (d) JTI for time-anticorrelated or frequency-correlated biphoton state. Here, $τ_{g} = 270 ns$ ( $Ω_{c} = 2 π \times 16.2 MHz$ ). Arrows in (c) and (d) indicate biphoton optical precursors having positive time correlation. Numerical simulation of JTI (e)–(f). Color bars represent relative intensities. Experimental parameters given in (a)–(d) are used for the simulation (e)–(h), respectively. The JTA of SFWM biphotons is determined by $χ^{(3)}$ of the medium, the phase matching condition, and pump pulse profile. The numerical simulation also faithfully reproduces the biphoton optical precursor indicated by the arrows in (g) and in (h): see Supplemental Material [29] for the details of the numerical simulation.
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