Quantum optical coherence tomography explained

See also: Optical coherence tomography.

Quantum optical coherence tomography (Q-OCT) is an imaging technique that uses nonclassical (quantum) light sources to generate high-resolution images based on the Hong-Ou-Mandel effect (HOM).^[1] Q-OCT is similar to conventional OCT but uses a fourth-order interferometer that incorporates two photodetectors rather than a second-order interferometer with a single photodetector.^[2] The primary advantage of Q-OCT over OCT is insensitivity to even-order dispersion in multi-layered and scattering media.^{[3] [4] [5]}

Several quantum sources of light have been developed so far. An example of such nonclassical sources is spontaneous parametric down-conversion that generates entangled photon pairs (twin-photon).^[6] The entangled photons are emitted in pairs and have stronger-than-classical temporal and spatial correlations. The entangled photons are anti-correlated in frequencies and directions. However, the nonclassical light sources are expensive and limited, several quantum-mimetic light sources are developed by classical light and nonlinear optics, which mimic dispersion cancellation and unique additional benefits.^[7]

Theory

The principle of Q-OCT is fourth-order interferometry. The optical setup is based on a Hong ou Mandel (HOM) interferometer with a nonclassical light source. Twin photons travel into and recombined from reference and sample arm and the coincidence rate is measured with time delay.^[8]

The nonlinear crystal is pumped by a laser and generates photon pairs with anti-correlation in frequency. One photon travels through the sample and the other through a delay time before the interferometer. The photon-coincidence rate at the output ports of the beam splitter is measure as a function of length difference (

c\tau _{q} ) by a pair of single-photon-counting detectors and a coincidence counter.

Due to the quantum destructive interference, both photons emerge from the same port when the optical path lengths are equal. The coincidence rate has a sharp dip when the optical path length difference is zero. Such dips are used to monitor the reflectance of the sample as a function of depth.^[9]

The twin-photon source is characterized by the frequency-entangled state:

\left | \psi \right\rangle = \int d \Omega \zeta (\Omega) \left | \omega _{0} + \Omega \right\rangle _{1} \left | \omega _{0} - \Omega \right\rangle _{2,}

where

\Omega is the angular frequency deviation about the central angular frequency \omega _{0} of the twin-photon wave packet, \zeta (\Omega) is the spectral probability amplitude.

A reflecting sample is described by a transfer function:

H(\omega) = \int\limits ^{inf ty} _{0} d z r(z,\omega)e ^{i2\phi(z,\omega)} ,

where

H(\omega) = r(z,\omega) is the complex reflection coefficient from depth z ,

The coincidence rate

C(\tau _{q)} is then given byC(\tau _{q)} \propto Λ _{0} - Re{ Λ ( 2 \tau _{q)},}

where

Λ _{0} = \int d\Omega |H(\omega _{0} + \Omega)| ^{2} S(\Omega) ,

and

Λ (\tau _{q)} = \int d\Omega H(\omega _{0} + \Omega) H ^{\ast} (\omega _{0} - \Omega) S(\Omega)e ^{- i\Omega\tau _{q}} ,

represent the constant (self-interference) and varying contributions (cross-interference).^[10]

Dips in the coincidence rate plot arise from reflections from each of the two surfaces. When two photons have equal overall path lengths, the destructive interference of the two photon-pair probability amplitude occurs.

Advantages

Compared with conventional OCT, Q-OCT has several advantages:

• greater signal-to-background ratio;^[11]
• intrinsic resolution enhancement by a factor of two for the same source bandwidth;^[12]
• interferogram components that are insensitive to even-order dispersion of the medium;^[13]
• interferogram components that are sensitive to the dispersion of the medium^[14]

Applications

Similar to FD-OCT, Q-OCT can provide 3D imaging of biological samples with a better resolution due to the photon entanglement.^[15] Q-OCT permits a direct determination of the group-velocity dispersion (GVD) coefficients of the media.^[16] The development of quantum-mimetic light sources offers unique additional benefits to quantum imaging, such as enhanced signal-to-noise ratio, better resolution, and acquisition rate. Although Q-OCT is not expected to replace OCT, it does offer some advantages as a biological imaging paradigm.

Notes and References

1. Hong. C. K.. Ou. Z. Y.. Mandel. L.. 1987-11-02. Measurement of subpicosecond time intervals between two photons by interference. Physical Review Letters. 59 . 18 . 2044–2046. 10.1103/PhysRevLett.59.2044. 10035403 . 1987PhRvL..59.2044H .
2. Gilgen. H. H.. Novak. R. P.. Salathe. R. P.. Hodel. W.. Beaud. P.. August 1989. Submillimeter optical reflectometry. Journal of Lightwave Technology. 7. 8. 1225–1233. 10.1109/50.32387. 1989JLwT....7.1225G . 1558-2213.
3. Franson. J. D.. 1992-03-01. Nonlocal cancellation of dispersion. Physical Review A. 45 . 5 . 3126–3132. 10.1103/PhysRevA.45.3126. 9907348 . 1992PhRvA..45.3126F . 36542368 .
4. Steinberg. A. M.. Paul Kwiat. Raymond Chiao. Kwiat. P. G.. Chiao. R. Y.. 1993-08-02. Measurement of the single-photon tunneling time. Physical Review Letters. 71 . 5 . 708–711. 10.1103/PhysRevLett.71.708. 10055346 . 1993PhRvL..71..708S . 31009201 .
5. Larchuk. Todd S.. Teich. Malvin C.. Saleh. Bahaa E. A.. 1995-11-01. Nonlocal cancellation of dispersive broadening in Mach-Zehnder interferometers. Physical Review A. 52 . 5 . 4145–4154. 10.1103/PhysRevA.52.4145. 9912731 . 1995PhRvA..52.4145L .
6. Book: Klyshko. D. N.. 1988-01-01. Photons Nonlinear Optics. CRC Press. 978-2-88124-669-2 . en.
7. Lavoie. J.. Kaltenbaek. R.. Resch. K. J.. 2009-03-02. Quantum-optical coherence tomography with classical light. Optics Express. 17 . 5 . 3818–3826. EN. 10.1364/OE.17.003818. 19259223 . 8115209 . free. 0909.0791. 2009OExpr..17.3818L .
8. Teich. Malvin Carl. Saleh. Bahaa E. A.. Wong. Franco N. C.. Shapiro. Jeffrey H.. 2012-08-01. Variations on the theme of quantum optical coherence tomography: a review. Quantum Information Processing. 11 . 4 . 903–923. en. 10.1007/s11128-011-0266-6. 254985458 .
9. Nasr. Magued B.. Saleh. Bahaa E. A.. Sergienko. Alexander V.. Teich. Malvin C.. 2003-08-22. Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography. Physical Review Letters. 91 . 8 . 083601. en. 10.1103/PhysRevLett.91.083601. 14525237 . quant-ph/0304160 . 2003PhRvL..91h3601N . 7206765 . 2021-04-14.
10. Abouraddy. Ayman F.. Nasr. Magued B.. Saleh. Bahaa E. A.. Sergienko. Alexander V.. Teich. Malvin C.. 2002-05-08. Quantum-optical coherence tomography with dispersion cancellation. Physical Review A. 65 . 5 . 053817. 10.1103/PhysRevA.65.053817. quant-ph/0111140 . 2002PhRvA..65e3817A . 15047941 .
11. Abouraddy. Ayman F.. Nasr. Magued B.. Saleh. Bahaa E. A.. Sergienko. Alexander V.. Teich. Malvin C.. 2002-05-08. Quantum-optical coherence tomography with dispersion cancellation. Physical Review A. 65 . 5 . 053817. 10.1103/PhysRevA.65.053817. quant-ph/0111140 . 2002PhRvA..65e3817A . 15047941 .
12. Web site: 2002-11-26. Quantum optical coherence tomography data collection apparatus and method for processing therefor. en.
13. Nasr. Magued B.. Saleh. Bahaa E. A.. Sergienko. Alexander V.. Teich. Malvin C.. 2003-08-22. Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography. Physical Review Letters. 91 . 8 . 083601. 10.1103/PhysRevLett.91.083601. 14525237 . quant-ph/0304160 . 2003PhRvL..91h3601N . 7206765 .
14. Nasr. Magued B.. Saleh. Bahaa E. A.. Sergienko. Alexander V.. Teich. Malvin C.. 2004-04-05. Dispersion-cancelled and dispersion-sensitive quantum optical coherence tomography. Optics Express. 12 . 7 . 1353–1362. EN. 10.1364/OPEX.12.001353. 19474956 . free. 2004OExpr..12.1353N .
15. 2009-03-15. Quantum optical coherence tomography of a biological sample. Optics Communications. 1154–1159. en. 10.1016/j.optcom.2008.11.061. Nasr . Magued B. . Goode . Darryl P. . Nguyen . Nam . Rong . Guoxin . Yang . Linglu . Reinhard . Björn M. . Saleh . Bahaa E.A. . Teich . Malvin C. . 282 . 6 . 0809.4721 . 2009OptCo.282.1154N . 931548 .
16. Nasr. Magued B.. Saleh. Bahaa E. A.. Sergienko. Alexander V.. Teich. Malvin C.. 2004-04-05. Dispersion-cancelled and dispersion-sensitive quantum optical coherence tomography. Optics Express. 12 . 7 . 1353–1362. EN. 10.1364/OPEX.12.001353. 19474956 . free. 2004OExpr..12.1353N .