Quantum 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). 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. The primary advantage of Q-OCT over OCT is insensitivity to even-order dispersion in multi-layered and scattering media.
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). 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.
Theory.
The principle of Q-OCT is fourth-order interferometry. The optical setup is based on a Hong ou mandel (HOM) interferometer with a source. Twin-photons travel into and recombined from reference and sample arm and the coincidence rate is measured with time delay.
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 (formula_1) 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.
The twin-photon source is characterized by the frequency-entangled state:
formula_2
where formula_3 is the angular frequency deviation about the central angular frequency formula_4 of the twin-photon wave packet, formula_5 is the spectral probability amplitude.
A reflecting sample is described by a transfer function:
formula_6
where formula_7 is the complex reflection coefficient from depth formula_8,
The coincidence rate formula_9 is then given by
formula_10 
where
formula_11,
and
formula_12
represent the constant (self-interference) and varying contributions (cross-interference).
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:
Applications.
Similar to FD-OCT, Q-OCT is able to provide 3D imaging of biological samples with a better resolution due to the photon entanglement. Q-OCT permits a direct determination of the group-velocity dispersion (GVD) coefficients of the media. 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.