Quantum Advantage with Seeded Squeezed Light for Absorption Measurement

Fu Li, Tian Li, Marlan O. Scully, and Girish S. Agarwal

Phys. Rev. Applied 15, 044030 – Published 20 April 2021

Abstract

Absorption measurement is an exceptionally versatile tool for many applications in science and engineering. For absorption measurements using laser beams of light, the sensitivity is theoretically limited by the shot noise due to the fundamental Poisson distribution of the photon number in laser radiation. In practice, the shot-noise limit can only be achieved when all other sources of noise are eliminated. Here, we use seeded squeezed light to demonstrate that direct-absorption measurements can be performed with a sensitivity beyond the shot-noise limit. We present a practically realizable scheme, where intensity-squeezed beams are generated by a seeded four-wave mixing process in an atomic rubidium-vapor cell. More than 1.2 dB quantum advantage for the measurement sensitivity is obtained at faint absorption levels ( $\leq 10 %$ ). We also present a detailed theoretical analysis to show that the observed quantum advantage when corrected for optical loss would be equivalent to 3 dB. Our experiment demonstrates a direct sub-shot-noise measurement of absorption that requires neither homodyne or lock-in nor logic coincidence-detection schemes. It is therefore very applicable in many circumstances where sub-shot-noise-level absorption measurements are highly desirable.

Received 5 March 2021
Revised 1 April 2021
Accepted 2 April 2021

DOI:https://doi.org/10.1103/PhysRevApplied.15.044030

Physics Subject Headings (PhySH)

Laser spectroscopy Quantum fluctuations & noise Quantum measurements Quantum optics Quantum states of light Squeezing of quantum noise

Atomic gases

Optical absorption spectroscopy

Atomic, Molecular & Optical

Authors & Affiliations

Fu Li^1,2,*,‡, Tian Li ^1,3,†,‡, Marlan O. Scully^1,4,5, and Girish S. Agarwal^1,2,3

¹Institute for Quantum Science and Engineering, Texas A&M University, College Station, Texas 77843, USA
²Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA
³Department of Biological and Agricultural Engineering, Texas A&M University, College Station, Texas 77843, USA
⁴Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
⁵Quantum Optics Laboratory, Baylor Research and Innovation Collaborative, Waco, Texas 76704, USA

^*fuli@physics.tamu.edu
^†tian.li@tamu.edu
^‡These authors contributed equally to this work.

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Vol. 15, Iss. 4 — April 2021

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Images

Figure 1
(a) The experimental setup, in which a seeded $^{85} Rb$ vapor cell produces strong quantum-correlated twin beams via FWM. The twin beams are separated from the pump by an approximately $2 \times 10^{5} : 1$ polarizer after the cell. The probe beam passes through an absorption “sample” (i.e., a combination of a $λ / 2$ plate and a polarizing beam splitter), while the conjugate beam serves as a reference, before they are focused onto an EMCCD camera. The camera is enclosed in a light-proof box with filters mounted to block ambient light. The AOM in the probe-beam path is used to pulse the twin beams with $2 μ s$ FWHM and a duty cycle of $1 / 12$ . PBS, polarizing beam splitter; PM fiber, polarization-maintaining fiber. (b) The level structure of the $D_{1}$ transition of the $^{85} Rb$ atom. The optical transitions are arranged in a double- $Λ$ configuration, where $ν_{p}$ , $ν_{c}$ , and $ν_{1}$ stand for the probe, conjugate, and pump frequencies, respectively, fulfilling $ν_{p}$ + $ν_{c} = 2 ν_{1}$ . The width of the excited state in the level diagram represents the Doppler-broadened line. $Δ$ is the one-photon detuning, $δ$ is the two-photon detuning, and $ν_{HF}$ is the hyperfine splitting in the electronic ground state of $^{85} Rb$ . (c) The measured intensity-difference noise-power spectrum for the squeezed twin beams (blue line) and for the SNL (red line), obtained with a radio-frequency spectrum analyzer (with a resolution and a video bandwidth of 300 kHz and 100 Hz, respectively). A squeezing of 6.5 dB is achieved.
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Figure 2
The theoretical prediction for the quantum advantage (Qu. Adv.) for absorption $α = 5 %$ as a function of optical transmission in the probe-beam path $η_{p}$ and the conjugate-beam path $η_{c}$ . The squeezing parameter $r = 1.1$ corresponds to 6.5 dB two-mode squeezing.
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Figure 3
(a) The time sequencing of the pump and twin beams. The pulse duration of $2 μ s$ and the duty cycle of 1/12 are realized by pulsing the probe beam with an AOM. The cw pump beam is present all the time. (b) Typical images of the twin beams with absorption $α = 3 %$ captured by the EMCCD camera. This panel is the “real-life” version of panel (a). It is an image of four consecutive pulses with the pulse width and duty cycle shown in panel (a). (c) The temporal photon-count fluctuations of the probe $N_{p} (t)$ and the conjugate $N_{c} (t)$ obtained by integrating the photon counts in the cropped regions in (b). Clear similarities can be observed between the twin beams. (d) The strong noise reduction in the subtraction as opposed to the summation of the $N_{p} (t)$ and $N_{c} (t)$ depicted in (c) showcases strong correlations between them.
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Figure 4
The actual absorption $α$ as a function of the measurement signal $S_{α}$ defined in Eq. (4). The inset is an enlarged view of the data points with absorption $α < 10$ % to illustrate the sizes of the uncertainties on the $x$ axis, $Δ S_{α}$ , and the uncertainties on the $y$ axis, $Δ α$ .
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Figure 5
The temporal quantum noise reduction $σ$ as a function of the absorption $α$ for the intensity-squeezed light (blue squares) and the coherent light (red dots). The dashed blue line is the theoretical prediction with $η_{p} = 0.61$ , $η_{c} = 0.63$ , and $r = 1.1$ .
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Figure 6
The quantum advantage as a function of the absorption $α$ . The dashed blue line is the theoretical prediction with $η_{p} = 0.61$ , $η_{c} = 0.63$ , and $r = 1.1$ . The quantum advantage is only significant ( $> 1$ dB) for small values of $α$ ( $< 20 %$ ) and for $α > 60 %$ there is no quantum advantage.
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Physical Review Applied