Conditional Frequency-Domain Beamsplitters Using Phase Modulators

Abstract

We propose and explore the families of fully tunable, conditional 2 Â 2 frequencydomain beamsplitters that result from sideband coupling in phase modulators. Full tunability is obtained by tailoring the driving voltage feeding the modulators, in a design based on the symmetries of this voltage waveform. The most favorable case in terms of success probability is that of first-sideband coupling, which can be implemented by the use of singletone phase modulation. The use of this device is illustrated by means of several examples based on the use of a wavelength-routed source of pairs of single-photon frequencyentangled states, showing immediate applications as a means of translating to the frequency-domain quantum-processing protocols based on linear optics.

Realization of Single-Photon Frequency-Domain Qubit Channels Using Phase Modulators

“…We define the matrix elements S mn of operator S in the single-photon subspace as S kj ¼ h1 k jSj1 j i [15] so that, for a pure single-photon pure input state jÉi in H I P J S jÉi j0i…”

“…The construction of conditional qubit unitaries in [15] is based on the use of both PM and FBG to mix and filter single-photon wavepackets at two central frequencies ! 0 and !…”

“…1 ¼ ! 0 þ , which is the most favorable situation in terms of probability amplitudes [15]. As described in this reference, current commercial electrooptic modulators feature bandwidths up to several tens of GHz, and therefore, may lie in the microwave or mm-wave range.…”

“…In a recent paper [15], we have shown how phase modulators (PMs) can be operated to conditionally implement qubit unitaries in dual-rail frequency basis. This basis is associated to singlephoton wavepackets of two central frequencies !…”

“…Here, we also study nonoptimal implementations of this construction in terms of success probabilities. In Section 4, we sketch the construction of dual-rail frequency-encoded qubit unitaries presented in [15], which is used to explore the success probability of random unitary channels in Section 5. Finally and using the same techniques as in [15], we present in Section 6 the conditional realization of the archetypal nonunitary qubit channel, the amplitude-damping channel, and end in Section 7 with our conclusions.…”