The Bridge - February 2018 - 9

of freedom, such as polarization, path, frequency,
time, and angular momentum [2]. In addition,
photon-based qubits are compatible with the wellestablished telecommunications infrastructure,
and exhibit excellent transmission in fiber optics.
However, large and intricate optical quantum states,
which are a key cornerstone for realizing optical
quantum computers, remain difficult to prepare
and entangle.
Optical frequency combs - broadband optical
sources that have equidistantly-spaced coherent
spectral lines - (Fig. 1) provide an elegant solution
to this issue. Due to the lines' precise spectral
locations, frequency combs have served as
extremely precise optical rulers, enabling a revolution
in high-precision metrology and spectroscopy [3].
Recently, the classical frequency comb concept
has been extended to the quantum world for the
preparation of quantum states. This approach brings
about many benefits, especially for the creation
of large quantum states. First, frequency combs
offer many experimentally-accessible frequency
modes within a single spatial mode, where all the
photons of different wavelengths are transmitted
together in a single waveguide. Furthermore, the
intrinsic multi-frequency-mode characteristics
enable the generation of many entangled quantum
states simultaneously, with the density of these
quantum channels controllable via the spectral
mode separation. Finally, the frequency domain
is complementary to other degrees of freedom,
enabling the creation of even larger-scale quantum
states. Many approaches to quantum state
preparation use quantum frequency combs, such
as for the generation of heralded single photons
[4-9], as well as two-photon entangled states via
the time [10-13], energy [14-16], path [17] and
frequency [18] degrees of freedom. In addition, large
and complex states, e.g. high-dimensional (quDit)
entangled states [19-21], cluster states [22-24],
and multipartite entanglement [25, 26], have been
predicted and achieved for applications in quantum

signal processing, including quantum logic gates
[21], boson sampling [27], and spectral linear optical
quantum computation [28].

QUANTUM FREQUENCY COMB
IN BULK SYSTEMS

Fig.2 Schematic of quantum frequency comb generation
in free space optics. (a) Inside an optical parametric
oscillator (where part of the figure is adapted from [29]),
a second-order χ(2)- nonlinear crystal converts the input
pump beam at frequency (ωр) into output signal and
idler beams at frequencies (ωі, ωѕ) through spontaneous
parametric down-conversion (SPDC), satisfying the
relation (ωі+ωѕ=ωр). (b) The quantum frequency comb
is generated on the intra-cavity resonances by spectrally
filtering the broadband SPDC spectrum. When the
input pump is a pulse train, the incident pulse spectrum
(solid lines) has to match perfectly with the cavity
resonances (solid bars), separated by one free spectral
range (FSR) [30].

The first investigations of quantum frequency combs
were based on bulk free-space setups, exploiting
spontaneous parametric down-conversion (SPDC).
In this approach, an optical parametric oscillator
(OPO) in a 2nd order nonlinear crystal, such as
PPKTP [24] or BBO [30], is operated below the
OPO threshold. In this process, a high-energy
pump photon splits into a pair of lower-energy

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