Phase diffusion and the small-noise approximation in linear amplifiers: Limitations and beyond

Abstract

The phase of an optical field inside a linear amplifier is widely known to diffuse with a diffusion coefficient that is inversely proportional to the photon number. The same process occurs in lasers which limits its intrinsic linewidth and makes the phase uncertainty difficult to calculate. The most commonly used simplification is to assume a narrow photon-number distribution for the optical field (which we call the small-noise approximation). For coherent light, this condition is determined by the average photon number. The small-noise approximation relies on (i) the input to have a good signal-to-noise ratio, and (ii) that such a signal-to-noise ratio can be maintained throughout the amplification process. Here we ask: For a coherent input, how many photons must be present in the input to a quantum linear amplifier for the phase noise at the output to be amenable to a small-noise analysis? We address these questions by showing how the phase uncertainty can be obtained without recourse to the small-noise approximation. It is shown that for an ideal linear amplifier (i.e. an amplifier most favourable to the small-noise approximation), the small-noise approximation breaks down with only a few photons on average. Interestingly, when the input strength is increased to tens of photons, the small-noise approximation can be seen to perform much better and the process of phase diffusion permits a small-noise analysis. This demarcates the limit of the small-noise assumption in linear amplifiers as such an assumption is less true for a nonideal amplifier.1 The semiclassical approximation replaces the bosonic annihilation operatorâ by â + δâ and neglects (δâ) 2 and terms with higher order in δâ, where δâ is the deviation ofâ from its average value.Accepted in Quantum 2019-10-09, click title to verify. Published under CC-BY 4.0.

Synchronization boost with single-photon dissipation in the deep quantum regime

“…As a check for consistency, we note that setting κ = 0 in Eq. (6) gives N 0 = 1/3, which agrees with the well known result for the undriven qvdP in the deep quantum limit: [9,14]. In Fig.…”

“…In practice, many of these processes are noisy, with random noise influencing the dynamical systems. This has given rise to many noise-enhanced, and noise-enabled processes, such as signal amplification [6] and stochastic resonance [7,8]. Studies of synchronization have been taken to the quantum domain and various quantum systems with limit cycles have been studied in recent years, including the weakly nonlinear quantum van der Pol (qvdP) oscillator [9][10][11][12][13][14][15][16], optomechanical systems [17][18][19][20][21][22], and lowdimensional systems [23][24][25][26][27][28].…”

Noise, not squeezing, boosts synchronization in the deep quantum regime

“…As a check for consistency, we note that setting κ = 0 in Eq (6) gives N 0 = 1/3, which agrees with the well known result for the undriven qvdP in the deep quantum limit: lim γ2/γ1→∞ ρ ss = 2 3 |0 0| + 1 3 |1 1| [9,14]. In Fig.…”

“…In practice, many of these processes are noisy, with random noise influencing the dynamical systems. This has given rise to many noise-enhanced, and noise-enabled processes, such as signal amplification [6] and stochastic resonance [7,8]. Studies of synchronization have been taken to the quantum domain and various quantum systems with limit cycles have been studied in recent years, including the weakly nonlinear quantum van der Pol (qvdP) oscillator [9][10][11][12][13][14][15][16], optomechanical systems [17][18][19][20][21][22], and low-dimensional systems [23][24][25][26][27][28].…”

QuISP: a Quantum Internet Simulation Package

“…Unlike classical bits, qubits cannot be copied and resent owing to the no-cloning theorem [65], a fundamental property of quantum mechanics forbidding to deterministically copy arbitrary states of quantum systems. Amplification at the level of single photons becomes ineffective as well [12,13]. This limits the practical length of quantum links to mere tens of kilometers.…”