Homodyne detection

Introduction

Optical homodyne detection is a method for detecting messages transmitted in optical signals, where a frequency or phase modulated signal is compared to what is misleadingly called the "local oscillator" (LO) signal, which is generated from the same source but not modulated with the message. In order to probe quantum effects, it is important to bring the noise of the detector down to the shot-noise limit, where the only fluctuations observed arise from the discrete nature of photons, which can be theoretically modelled as the vacuum-state fluctuations of the quantised electromagnetic field. This project's first objective is to build a homodyne detector from scratch.

Lab Location: S11-02-04 (Optics Lab)

Application: Continuous-variable QKD with Gaussian modulation and coherent states

While the first protocols for quantum key distribution (QKD) involved discrete variables (DV) in finite, small dimensions, QKD can also be done using continuous variables (CV) in infinite dimensions, i.e. the state of an electromagnetic field. Using Gaussian modulation and coherent states makes the QKD system relatively easy to implement and analyse, although getting positive key rates is a different matter. The homodyne detector is an essential component of this setup, but if we have the capacity, we can try to develop other parts of the system, such as the implementation of the QKD protocol itself in software. We want to pay particular attention to the design of the amplifier for the homodyne detector, for which there are stringent requirements and difficult tradeoffs to make.

Christian says this will be more complex that I realised: even getting the detector down to the shot-noise limited regime is tough. Johnkhootf (talk) 02:09, 19 January 2022 (UTC)

Background Reading

Basic background on lasers in Lasers and Electro-Optics, available for download via NUS Library. Chapter 21 briefly touches on coherent homodyne detection.

For DV-QKD theorists who stumbled into this (like me), here's some background reading:

• Review of Gaussian quantum-information processing
• Self-contained tutorial on theory of Gaussian-modulated CV-QKD

Experimental Setup

The basic setup is:

1. Split the laser beam into two, one component will be LO and another will be the signal
2. Frequency-shift the signal beam using an acousto-optical modulator (AOM)
3. Phase-modulate the signal beam using an electro-optical modulator (EOM). This is typically a $\mathrm {LiNbO_{3}}$ crystal, whose birefringence is controlled by the voltage applied to it. For more advanced applications, we can use a transformer to amplify a small change in voltage into a large difference, producing a large change in the birefringence.
4. Recombine the signal and the LO in a 50:50 beam splitter
5. Send the two output beams to two reverse-biased photodiodes, and connect the junction between the photodiodes to a current detector to convert it to a voltage. The signal will be modulated according to the beat frequency.

The noise in the photodiodes tends to be low frequency, so aiming for a signal of frequency $10~\mathrm {MHz}$ or so will help to remove the noise.