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Physical Review A

Wideband photon counting and homodyne detection

Bernard Yurke

Published Jul 1, 1985• 121 citations
Publisher

Abstract

Homodyne detection has been proposed as a means of detecting squeezed coherent radiation. Here the response of a balanced homodyne detector to wideband squeezed coherent states is presented. In order to carry out the analysis the theory of wideband photodetection is reviewed and in order to determine the ultimate performance limits of photoemissive detectors small terms of order \ensuremath{\Delta}\ensuremath{\omega}/${\ensuremath{\omega}}_{0}$ that are usually neglected, where ${\ensuremath{\omega}}_{0}$ is the optical carrier frequency and \ensuremath{\Delta}\ensuremath{\omega} is the electronics bandwidth, have been kept. It is shown that the ultimate noise reduction that can be achieved in the noise-power spectrum of a homodyne detector, detecting squeezed coherent radiation, is a factor of 2 worse when photoemissive detectors are used instead of power flux detectors.

DOI
10.1103/physreva.32.311

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Homodyne detection has been proposed as a means of detecting squeezed coherent radiation. Here the response of a balanced homodyne detector to wideband squeezed coherent states is presented. In order to carry out the analysis the theory of wideband photodetection is reviewed and in order to determine the ultimate performance limits of photoemissive detectors small terms of order \ensuremath{\Delta}\ensuremath{\omega}/\ensuremathω0{\ensuremath{\omega}}_{0}\ensuremathω0​ that are usually neglected, where \ensuremathω0{\ensuremath{\omega}}_{0}\ensuremathω0​ is the optical carrier frequency and \ensuremath{\Delta}\ensuremath{\omega} is the electronics bandwidth, have been kept. It is shown that the ultimate noise reduction that can be achieved in the noise-power spectrum of a homodyne detector, detecting squeezed coherent radiation, is a factor of 2 worse when photoemissive detectors are used instead of power flux detectors.
A photodetector's electronic bandwidth is the frequency range over which beats between different frequencies in the input can be observed in the output. The output of a balanced homodyne detector, the prototypical device for detecting squeezed light, consists of beats between a signal to be measured and a local oscillator. Beats between the signal and quantum local-oscillator fluctuations lead to noise that degrades the observed squeezing. Through wide-band calculations, we show that this noise contains contributions from the entire signal bandwidth, even when this bandwidth is orders of magnitude larger than the detector's electronic bandwidth. This allows us to place an upper limit on the total power that can enter the detector's signal port (both signal and extraneous light) within the detector's optical bandwidth in order for a given level of squeezing to be observable.
Four-wave mixers have been investigated theoretically as potential sources of squeezed-coherent radiation 1,2 and there are a number of experimental efforts underway to demonstrate the production of squeezed-coherent radiation via such devices.3,4,5 Here the results of some wideband calculations of the output of cavity four-wave mixers is presented. The wideband squeezed-coherent radiation generated by such devices may be detected via a wideband homodyne detector.6 Wideband squeezing will manifest itself in the noise-power spectrum of the homodyne detector's output as regions where the noise is reduced below the level that is observed when no light enters the input port of the homodyne detector. Wideband homodyne detection allows one to look for squeezing at frequencies far from d.c. This gives the experimentalist the freedom to look for squeezing in the frequency range where his detector performs best.
Wideband calculations of the response of a homodyne detector to the outputs of various four-wave-mixer configurations are presented. It is shown that the noise-power spectrum of the homodyne detector output can exhibit regions where the noise is greatly reduced below the shot-noise level even at frequencies far from dc. Hence, in the detection of noise squeezing via homodyne detectors, 1/f noise and other low-frequency noise sources may be avoided by observing the homodyne detector's noise power at frequencies far from dc.
This thesis reports the realization and applications of a versatile wideband balanced homodyne detector operating in the time domain and intended for Quantum Optical Tomography. The detector can work with high repetition rate lasers used for the production and measurement of the electric field quadratures of quantum states of light. Full characterization of the detector by shot-noise measurements and by verifying its capability to reconstruct the density matrix and Wigner function of various states of interest is given. By overcoming photodiodes response mismatch, high frequency electronics issues and by choosing an appropriate optical set-up, a high level of common mode suppression (52.4dB) and a low electronic noise gave a shot-to-electronic noise ratio of I3dB for a Local Oscillator with 6.2 x 108 photons-per-pulse on a ~ 100MHz bandwidth. Results for the characterization of a single-photon Fock state are presented. An average efficiency of 56% was obtained for the generation/detection of the state.
A homodyne detector was constructed for use in the balanced homodyne detection of light. In the frequency domain, the detector had an approximately 95 MHz 3 dB bandwidth and showed a 10 dB difference with regard to the electronic noise level at a local oscillator power of approximately 14 mW. With the detector, mean photon numbers in the signal light were measured in the time domain. The minimum mean photon number was about a few photons during the detector’s integration time of approximately 5.3 ns.
Homodyne detection is a phase-sensitive measurement technique, essential for the characterization of continuous-variable (CV)-encoded quantum states of light. It is a key component to the implementation of CV quantum-information protocols and benefits from operating, by design, at room temperature. However, performing high-speed quantum information processing remains a major challenge, as conventional homodyne detectors often fail to sustain pulsed operation at high repetition rates due to electronic limitations. We present wideband homodyne detectors operating at near-infrared (NIR) and telecom wavelengths, with optimized performance at repetition rates up to 150 MHz. We demonstrate their performance by resolving the pulse-by-pulse structure of squeezed states of light at telecom wavelengths while preserving their spectral multimode properties.