This thesis is mainly devoted to the study of the quantum properties of optical parametric oscillators (OPOs), which are nowadays the sources of the highest-quality quantum-correlated light, apart from fundamental tools in the classical-optics realm, allowing for the conversion of laser light into virtually all regions of the optical spectrum. Regarding its content, the thesis might seem a bit unusual, because two thirds of it are devoted to a self-contained (though dense) introduction to quantum optics, including the quantum physics of harmonic oscillators, the quantization of the electromagnetic field in an open optical cavity and the detection of its output light, as well as the derivation of the basic model and known properties of OPOs. Hence, all the original results of the thesis are contained in the last third, were it is proven that all OPOs can be understood as multi-mode devices whose quantum properties can be explained in terms of three basic phenomena: bifurcation squeezing, spontaneous symmetry breaking, and pump clamping, which are introduced through simple, yet realistic examples.
This thesis is mainly devoted to the study of the quantum properties of optical parametric oscillators (OPOs), which are nowadays the sources of the highest-quality quantum-correlated light, apart from fundamental tools in the classical-optics realm, allowing for the conversion of laser light into virtually all regions of the optical spectrum. Regarding its content, the thesis might seem a bit unusual, because two thirds of it are devoted to a self-contained (though dense) introduction to quantum optics, including the quantum physics of harmonic oscillators, the quantization of the electromagnetic field in an open optical cavity and the detection of its output light, as well as the derivation of the basic model and known properties of OPOs. Hence, all the original results of the thesis are contained in the last third, were it is proven that all OPOs can be understood as multi-mode devices whose quantum properties can be explained in terms of three basic phenomena: bifurcation squeezing, spontaneous symmetry breaking, and pump clamping, which are introduced through simple, yet realistic examples.
This Thesis studies, from a theoretical point of view, the dynamical and quantum properties of a type I degenerate optical parametric oscillator which is synchronously pumped by a mode-locked laser (SPOPO). In recent past, SPOPOs have been used for generating ultra-short optical pulses of tunable wavelength and their temporal properties have been investigated. Having a huge number of degrees of freedom, the output field of a SPOPO needs to be characterized via a multimodal quantum analysis. Then, we first develop a multimode model of the device, obtaining the quantum equations for the intra-cavity field operators. Afterwards, we study the steady state solutions of the average values of the generated fields that are the solutions of an eigenvalue equation. Its spectrum gives information about the “useful” number of modes in which are concentrated almost all the dynamical and quantum properties of the intra-cavity field and which we call “super-modes”.Indeed, we show that not only the super-mode of minimum threshold is (ideally) perfectly squeezed at threshold, but that all the other super-modes have an important non-classical character provided that their thresholds are close enough to the minimum one. This circumstance gives the clear image that a SPOPO is a highly quantum multi-mode system. Finally, the last part of this Thesis is focused on the study of the output of a SPOPO from the point of view of the generation of highly multi-mode entangled states and their optimization by means of specific experimental configurations.
Quantum optics has been, from its beginning, a driving force both for the exploration of fundamental limits of the quantum world and for conceiving seminal ideas and applications of the so-called quantum technologies. The last 20 years have seen a rapid development of ideas and proof-of-principle experiments involving the fields of quantum communication, quantum computation, quantum metrology and quantum simulation. The so called continuous variable (CV) approach to quantum optics, which uses many photon in collective states, and continuous observables like the quadratures of the electric field to encode information, has many interesting properties, especially from a communications perspective. It is inherently broadband and compatible with standard telecom infrastructures. Moreover, in CV, entanglement, one of the fundamental resource of quantum optics, can be generated deterministically. One of the main challenges for all quantum information technologies is scalability, being able to generate and manipulate a large number of quantum resources to achieve practical tasks efficiently. One approach to solve the issue of scalability is to use highly multimode quantum states. The quantum description of the electromagnetic field associate each photon (particle of light) with a mode (way for light to propagate). In a mutlimodal approach, we look at the quantum state bases and optical modes bases conjointly and tailor quantum fields not only in given modes, but also optimize the spatio-temporal shapes of the modes in which the state is defined. This opens wide perspectives for treating complex quantum states. In particular, using ultra-fast pulses of light which contain many temporal/spectral modes, we are able to generate large and complex entangled states of light using simple resources. In this thesis, we used an optical parametric oscillator pumped synchronously (SPOPO) with a frequency comb to generate multimode squeezed vacuum states which can be used to form cluster states: a large collection of modes (the nodes) entangled to each other in a certain way. These state are the basic resource for Measurement Based Quantum Computation (MBQC). This set-up has the advantage to generate entanglement in many mode with a single device. It is also highly tunable. Indeed, by tuning the spectrum of the OPO pump with a pulse shaper, one can tailor the properties of the generated quantum state. In this work, we focus on the optimization of the pump spectral shape to generate specific states. Using simulations based on Machine Learning Algorithms (MLA), we find optimal pump profile for typical target states. We then implement those shapes on the experimental set-up and measure the resulting states using multipixel homodyne detection. We also study intra-cavity dispersion effects. Dispersion inside the SPOPO cavity is indeed one of the main factor that limits the number of entangled modes in the generated quantum states. A systematic study of dispersion effects is therefore necessary to model the SPOPO output accurately. This works paves the way toward a fully tunable device that can be optimized in real time to generate specific quantum resources tailored for specific tasks.
The quantum statistics of a laser result in noise when measurements of the beam are made. This noise sets a classical limit beyond which a laser cannot be used with increasing sensitivity. This quantum noise limit is imposed on many of the uses of lasers currently, especially in power limited devices such as optical communications. The statistics of the laser photon field can be modified to produce a non-classical state resulting in lower noise than the quantum noise limit when detected appropriately. This state, called a squeezed state, has been measured previously from a cavity enhanced optical parametric oscillator (OPO) only at frequency sidebands within the linewidth of the cavity. ¶ This thesis reports measurements of squeezing at microwave frequency sidebands on an optical beam produced by an optical parametric oscillator. This is the first reported measurement of squeezing at frequency sidebands at higher longitudinal modes of the cavity from an OPO. Noise reduction below the quantum noise limit is measured at sideband frequencies of 5 MHz, 1.7 GHz, 3.4 GHz and 5.1 GHz, corresponding to the zeroth, first, second and third longitudinal modes from the squeezed beam. These results are the highest frequency sideband measurements of squeezing to date. In addition to measuring squeezing at different longitudinal modes for the fundamental Gaussian spatial mode, non-classical noise reduction is measured at the same frequencies for a squeezed higher order spatial mode, TEM10. ¶ A single mode theoretical model of the OPO is presented, based on the work of ref. [1]. Computer simulations of the squeezing predicted by this model are developed and compared to the experimental results, showing excellent agreement between the different longitudinal modes for each of the two spatial modes measured.
Coherence properties of light beams generated by optical parametric oscillators (OPOs) are discussed in the region of threshold. Analytic expressions, that are valid throughout the threshold region, for experimentally measurable quantities such as the mean and variance of photon number fluctuations, squeezing of field quadratures, and photon counting distributions are derived. These expressions describe non-Gaussian fluctuations of light in the region of threshold and reproduce Gaussian fluctuations below and above threshold, thus providing a bridge between below and above threshold regimes of operation. They are used to study the transformation of fluctuation properties of light as the OPOs make a transition from below to above threshold. The results for the OPOs are compared to those for the single-mode and two-mode lasers and their similarities and differences are discussed.
Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest quality quantum-correlated light in the continuous variable regime. Being nonlinear systems, they can be driven through critical points in which a solution ceases to exist in favour of a new one, and it is close to these points where quantum correlations are the strongest. The simplest description of such systems consists in writing the quantum fields as the classical part plus some quantum fluctuations, linearizing then the dynamical equations with respect to the latter; however, such an approach breaks down close to critical points, where it provides unphysical predictions such as infinite photon numbers. On the other hand, techniques going beyond the simple linear description become too complicated especially regarding the evaluation of two-time correlators, which are of major importance to compute observables outside the cavity. In this article we provide a regularized linear description of nonlinear cavities, that is, a linearization procedure yielding physical results, taking the degenerate optical parametric oscillator as the guiding example. The method, which we call self-consistent linearization, is shown to be equivalent to a general Gaussian ansatz for the state of the system, and we compare its predictions with those obtained with available exact (or quasi-exact) methods. Apart from its operational value, we believe that our work is valuable also from a fundamental point of view, especially in connection to the question of how far linearized or Gaussian theories can be pushed to describe nonlinear dissipative systems which have access to non-Gaussian states.
The quantum features of ultrashort-pulse optical parametric oscillators (OPOs) are investigated theoretically in the nonlinear regime near and above threshold. Viewing the pulsed OPO as a multimode open quantum system, we rigorously derive a general input-output model that features nonlinear coupling among many cavity (i.e., system) signal modes and a broadband single-pass (i.e., reservoir) pump field. Under appropriate assumptions, our model produces a Lindblad master equation with multimode nonlinear Lindblad operators describing two-photon dissipation and a multimode four-wave-mixing Hamiltonian describing a broadband, dispersive optical cascade, which we show is required to preserve causality. To simplify the multimode complexity of the model, we employ a supermode decomposition to perform numerical simulations in the regime where the pulsed supermodes experience strong single-photon nonlinearity. We find that the quantum nonlinear dynamics induces pump depletion as well as corrections to the below-threshold squeezing spectrum predicted by linearized models. We also observe the formation of non-Gaussian states with Wigner-function negativity and show that the multimode interactions with the pump, both dissipative and dispersive, can act as effective decoherence channels. Finally, we briefly discuss some experimental considerations for potentially observing such quantum nonlinear phenomena with ultrashort-pulse OPOs on nonlinear nanophotonic platforms.