Measurement of laser quantum frequency fluctuations using a Pound-Drever stabilization system

Frequency locking of an optical cavity using linear–quadratic Gaussian integral control

“…It can be seen from ( 7) that the transfer function of the optical cavity from to z is a first-order low-pass filter with a corner frequency of κ/2. Physically, this arises from the well-known (see, for example [18,34] and references therein) transfer function of the optical cavity from to a phase shift, which is then measured by the homodyne detector. In the experimental system described herein κ/2 ≈ 10 6 Hz, which is well beyond the frequency range of interest for the integral LQG controller.…”

Parity-time symmetry meets photonics: A new twist in non-Hermitian optics

“…For example, the implications in optics of non-Hermitian degeneracies are know since quite a long time [10], albeit they were not fully exploited in some interesting applications. Nonorthogonality of eigenmodes in laser theory, noticeably in unstable resonators described by a highly non-Hermitian Hamiltonian, is known to increase quantum noise by the so-called excess noise (or Petermann) factor [56][57][58] (the relation between PT symmetry and excess noise factor in a simple model is discussed in [59]). Non-normal dynamics in certain non-Hermitian laser models is known to give rise to transient growth, excitability and turbulence laser behavior [60][61][62].…”

$\mathcal{PT}$ -symmetric quantum oscillator in an optical cavity

“…For typical resonator parameters that realize the PT -symmetric QHO, θ tilt /θ d is smaller that one as discussed above, and the excess noise factor turns out to be modest or even negligible (K 1.023 for the example discussed above). Therefore, unlike lasers with unstable resonators leading to large excess noise factors [36][37][38], in our optical setting non-Hermitian enhancement of the laser linewidth is not a major effect.…”

“…Furthermore, it is able to emulate in a simple setting rather arbitrary non-Hermitian potentials. Optical resonators have been deeply investigated in the context of laser science [35], and non-Hermitian signatures in such systems have been mostly focused to the laser linewidth enhancement factor in certain cavities with non-orthogonal modes (see, for instance, [36][37][38][39][40], and references therein). Recent works have suggested and experimentally demonstrated that beam dynamics in optical cavities and lensguides can effectively simulate the quantum mechanical Schrödinger equation in rather extended forms [41][42][43][44][45][46][47], for example, to emulate a fractional kinetic energy operator [42,43,46], synthetic magnetic fields [44,45], and quantum dissipation [47].…”

“…The eigenfunctions of the PT QHO, given by the ordinary Gauss-Hermite modes of the QHO with complex argument, do not form a set of orthogonal modes. In laser physics, an important consequence of the lack of orthogonality of laser modes is an enhancement of the Schawlow-Townes laser linewidth, which is expressed by the so-called Petermann excess noise factor K (see, for instance [36][37][38][39][40], and references therein). For the laser oscillating in the fundamental transverse mode, the excess noise factor is given by K = ψ 0 , ψ 0 ψ † 0 , ψ † 0 /| ψ 0 , ψ † 0 | 2 , where ψ 0 (x) is given by eq.…”