Noiseless phase quadrature amplification via electro-optic feed-forward

The transmission of small optical signals carried by coherent light is fraught with difficulty. Attenuation of the optical power causes degradation of the signal-to-noise ratio as the signal recedes into the quantum noise of the beam. A simple method to rectify this problem would be to amplify the signal. However this is not a trivial exercise as phase insensitive amplifiers, such as laser amplifiers, introduce excess noise [1]. In the limit of high gain, the noise penalty for a phase insensitive amplifier is 3dB, ie a halving of the signal to noise ratio. This is known as the standard quantum limit (SQL) for phase insensitive amplifiers. To overcome this problem, phase sensitive amplification is required [2]. This can entail a non-linear process, as in the case of the optical parametric amplifier, where one observable is amplified while the conjugate is de-amplified. [3]. A far simpler method has been demonstrated by Lam et al. [4] using positive electro-optic feed-forward. In this scheme, a part of the input beam is tapped off using a beamsplitter and detected. The signal is then added back to a modulator further downstream. Using this method with amplitude signals, Lam et al. achieved a signal transfer ratio of Ts = 0.88. In this work we use an analogous feed-forward network to show better-than-SQL amplification of phase quadrature signals. To our knowledge, this is the first demonstration of phase signal amplification superior to the amplifier SQL. In any experiment which generates phase quadrature signals close to the quantum noise limit (QNL) our system could be used to make this signal robust optical loss. Specific suggestions for the application of phase feed-forward include quantum non-demolition measurements [5] and continuous variable teleportation [7,8].