We present a comprehensive theory and an easy to follow method for the design and construction of a wideband homodyne detector for time-domain quantum measurements. We show how one can evaluate the performance of a detector in a specific time-domain experiment based on electronic spectral characteristic of that detector. We then present and characterize a high-performance detector constructed using inexpensive, commercially available components such as low-noise high-speed operational amplifiers and high-bandwidth photodiodes. Our detector shows linear behavior up to a level of over 13 dB clearance between shot noise and electronic noise, in the range from DC to 100 MHz. The detector can be used for measuring quantum optical field quadratures both in the continuous-wave and pulsed regimes with pulse repetition rates up to about 250 MHz.
The photon creation and annihilation operators are cornerstones of the quantum description of the electromagnetic field. They signify the isomorphism of the optical Hilbert space to that of the harmonic oscillator and the bosonic nature of photons. We perform complete experimental characterization (quantum process tomography) of these operators. By measuring their effect on coherent states by means of homodyne tomography, we obtain their process tensor in the Fock basis, which explicitly shows the "raising" and "lowering" properties of these operators with respect to photon number states. This is the first experimental demonstration of complete tomography of nondeterministic quantum processes.
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