Squeezed light in an optical parametric oscillator network with coherent feedback quantum control

Abstract

We present squeezing and anti-squeezing spectra of the output from a degenerate optical parametric oscillator (OPO) network arranged in different coherent quantum feedback configurations. One OPO serves as a quantum plant, the other as a quantum controller. The addition of coherent feedback enables shaping of the output squeezing spectrum of the plant, and is found to be capable of pushing the frequency of maximum squeezing away from the optical driving frequency and broadening the spectrum over a wider frequency band. The experimental results are in excellent agreement with the developed theory, and illustrate the use of coherent quantum feedback to engineer the quantum-optical properties of the plant OPO output.

The SLH framework for modeling quantum input-output networks

“…Since our QSDEs are now Itō form, this requires taking differentials to second order, as done in Eq. (37). To aid computations, we write down an Itō table, which prescribes the product of various quantum noise increments.…”

On transfer function realizations for Linear Quantum Stochastic Systems

“…In the case that only the input-output relation of the LQSS is important, we have the problem of transfer function realization. This is the case, for example, in controller synthesis [21], [22], [23].…”

“…controllers that do not perform any measurement on the controlled quantum system, and thus have the potential for increased performance compared to classical controllers, see e.g. [16], [17], [18], [19], [20], [21], [22], [23].…”

Bilinear Hamiltonian interactions between linear quantum systems via feedback

“…controllers that do not perform any measurement on the controlled quantum system, and thus, have the potential to outperform classical controllers, see e.g. [13,14,15,16,17,18,19,8,20].The ways LQSSs can interact are of particular importance to applications such as the synthesis of larger LQSSs in terms of simple ones, the design of coherent quantum observers and controllers for LQSSs, etc. There is, of course, the usual directional signal connection from the output of one system to the input of another.…”

“…5307 13.8692 −7.2157 −5.2280 −4.8396 −3.4451 3.9092 2.8125 −6.7593 3.9878 −0.1884 0.9354 −13.4228 11.8248 −3.5436 2.2052 −3.5366 −15.1783 3.9092 2.8125 −6.7593 3.9878 −0.1884 0Y = P Ỹ P = I 4 , and, hence,X = J −1 Y = −J.Then, from(21) we have thatΣ = (X − I)(X + I) −1 = −(I 4 + J 4 )(I 4 − J 4 ) −1 = −J.Given any Hamiltonian matricesR A andR B for the LQSSsĀ andB, respectively, the corresponding Hamiltonian matrices R A and R B of LQSSs A and B can be computed by(19)-(20). As mentioned in the introduction, this method can work even in the case where the systemsĀ and B are non-linear, provided that a) the additional linear dynamics generated by the Hamiltonians− 1 4 x A J(C A XC A )x A , and − 1 4 x B J(C B XC B )x B can be realized, see (19) -(20), and b) the additional (linear) inputs/outputs can be created in the corresponding systems.…”