This PhD thesis treats applications of nonlinear optical effects for quantum information processing. The two main applications are four-wave mixing in the form of Bragg scattering (BS) for quantum-state-preserving frequency conversion, and sum-frequency generation (SFG) in second-order nonlinear materials for heralded entanglement. BS is shown to be separable in the input and output modes in the low-conversion regime, the regime of small pump powers or short interaction times. The selective frequency conversion of a signal is found to only depend on one of the pumps, while the temporal output of the converted idler depends on the other pump. This allows for temporal-mode-multiplexing. When the effects of nonlinear phase modulation (NPM) are included, the phases of the natural input and output modes are changed, reducing the separability. These effects are to some degree mediated by pre-chirping the pumps. In the high-conversion regime without the effects of NPM, exact Green functions for BS are derived. In this limit, separability is possible for conversion efficiencies up to 60 %. However, the system still allows for selective frequency conversion as well as re-shaping of the output. One way to obtain a 100 % conversion efficiency is to use multiple stages of frequency conversion, but this setup suffers from the combined effects of NPM. This problem is circumvented by using asymmetrically pumped BS, where one pump is continuous wave. For this setup, NPM is found to only lead to linear phase shifts of the input and output modes, corresponding to shifts of the central frequencies of the fields. The trade-off is that one is only able to select which signals are converted, or change the shape of the output idler. Finally, entanglement swapping using SFG was investigated. Considering two pairs of entangled photons, the process of up-converting one photon from each pair leads to heralded entangled pairs by successful detection of the up-converted photon. It was seen that this was indeed possible in the case of anti-correlated phasematching in the up-conversion crystal. Possible ways of increasing the probability of an up-conversion event were investigated briefly.
This PhD thesis treats applications of nonlinear optical effects for quantum information processing. The two main applications are four-wave mixing in the form of Bragg scattering (BS) for quantum-state-preserving frequency conversion, and sum-frequency generation (SFG) in second-order nonlinear materials for heralded entanglement. BS is shown to be separable in the input and output modes in the low-conversion regime, the regime of small pump powers or short interaction times. The selective frequency conversion of a signal is found to only depend on one of the pumps, while the temporal output of the converted idler depends on the other pump. This allows for temporal-mode-multiplexing. When the effects of nonlinear phase modulation (NPM) are included, the phases of the natural input and output modes are changed, reducing the separability. These effects are to some degree mediated by pre-chirping the pumps. In the high-conversion regime without the effects of NPM, exact Green functions for BS are derived. In this limit, separability is possible for conversion efficiencies up to 60 %. However, the system still allows for selective frequency conversion as well as re-shaping of the output. One way to obtain a 100 % conversion efficiency is to use multiple stages of frequency conversion, but this setup suffers from the combined effects of NPM. This problem is circumvented by using asymmetrically pumped BS, where one pump is continuous wave. For this setup, NPM is found to only lead to linear phase shifts of the input and output modes, corresponding to shifts of the central frequencies of the fields. The trade-off is that one is only able to select which signals are converted, or change the shape of the output idler. Finally, entanglement swapping using SFG was investigated. Considering two pairs of entangled photons, the process of up-converting one photon from each pair leads to heralded entangled pairs by successful detection of the up-converted photon. It was seen that this was indeed possible in the case of anti-correlated phasematching in the up-conversion crystal. Possible ways of increasing the probability of an up-conversion event were investigated briefly.
This thesis deals with applications of nonlinear four-wave mixing in the context of optical quantum information science. By enabling diverse functionalities such as single-photon generation, temporal shaping, and frequency conversion, four-wave mixing is a highly versatile tool for processing optical quantum information. The first part addresses the use of spontaneous four-wave mixing for generating entangled photon pairs with the particular property that the photons are uncorrelated in time and frequency. Two schemes are proposed to achieve this. The first proposal relies on a gradually varying interaction between two orthogonally polarized pump pulses in a birefringent waveguide. It is shown that, if the two pump pulses undergo a complete walk-through, the two generated photons emerge in orthogonal polarizations with uncorrelated- and tailorable time-frequency distributions. The second proposal deals with photon-pair generation in a microring resonator. In this setting, it is shown that a dual-pulse configuration can be used to excite- and subsequently de-excite the resonator on a sub-lifetime timescale. This turns out to strongly diminish time-frequency correlations. The second part considers the four-wave-mixing process Bragg scattering, which is known to enable noise-free frequency conversion. The Bragg-scattering process treated here, which occurs in a birefringent waveguide, is shown to allow for shape-preserving and strongly uni-directional conversion with a large acceptance bandwidth.
In this thesis I study in detail the quantum dynamics of several nonlinear optical processes in microresonator systems. A Heisenberg-picture input-output formalism is developed from first principles that includes the effects of scattering losses and independent quality factors and coupling ratios for different resonances. The task of calculating the device output is then reduced to solving a set of driven, damped, ordinary differential equations for the resonator mode operators alone. This theoretical framework is used to study photon pair generation via spontaneous four-wave mixing in the weakly pumped regime, on which the effects of scattering losses are appraised. A more strongly driven regime is studied for continuous wave pumps, demonstrating when self- and cross-phase modulation and multi-photon pair generation become important, and their effects on the spectral and power scaling properties of the system are examined; A detuning strategy is presented that compensates for some of these effects. The results of the weak-pump regime are applied to study microresonator-based her- alded single photon sources. The impact of scattering losses is studied, revealing that typical systems suffer from low heralding efficiency due to these losses. A technique to improve heralding efficiency is presented through over-coupling the resonator-channel system, and a resultant trade-off between heralding rate and heralding efficiency is un- covered. Limitations to the spectral purity of the heralded single photon output for conventional microresonator systems are also analysed, and a more sophisticated cou- pling scheme presented to overcome the upper bound for spectral purity of 93% that exists in typical systems, permitting the generation of single photons with spectral pu- rity arbitrarily close to 100% without spectral filtering or sophisticated phase-matching techniques. The theory of quantum frequency conversion in microresonators using four-wave mix- ing is then developed in detail, and the spectral conversion probability and conversion efficiency studied. Efficiencies exceeding 90% using less than 100 mW of pump power are predicted to be achievable with current technology. A dressed mode picture is developed to better understand the conversion dynamics. Rabi-like spectral splitting and temporal oscillations of the intraresonator mean photon number are predicted, exhibiting a novel regime of strongly coupled photonic modes.
This thesis presents a study of photon generation and conversion processes in nonlinear optics. Our results extend beyond the first order perturbative regime, in which only pairs of photons are generated in spontaneous parametric down-conversion or four wave mixing. They also allow us to identify the limiting factors for achieving unit efficiency frequency conversion, and to correctly account for the propagation of bright nonclassical photon states generated in the nonlinear material. This is done using the Magnus expansion, which allows us to incorporate corrections due to time-ordering effects in the time evolution of the state, while also respecting the quantum statistics associated with squeezed states (in photon generation) and single photons or coherent states (in photon conversion). We show more generally that this expansion should be the preferred strategy when dealing with any type of time-dependent Hamiltonian that is a quadratic form in the creation and annihilation operators of the fields involved. Using the Magnus expansion, simple figures of merit to estimate the relevance of these time-ordering corrections are obtained. These quantities depend on the group velocities of the modes involved in the nonlinear process and provide a very simple physical picture of the interactions between the photons at different times. These time-ordering effects are shown to be important only when the photons and pump beam overlap within the nonlinear material for a significant amount of time. We also discuss the possibility of preparing Fock states with many photons using parametric down-conversion sources and realistic photon-number-resolving detectors. After discussing photon generation processes, we study photon conversion processes in which a nonlinear material and a classical strong pump field are used modify the frequency of a second incoming low-intensity field. We show that time-ordering effects limit the efficiency of this conversion process, re-examine strategies to get around this problem, and show that it should be possible to have a clear observation of modified upconversion probabilities due to these effects, and thus have an experimental demonstration of time-ordering effects in nonlinear optics.
Single-photon frequency conversion for quantum interface plays an important role in quantum communications and networks, which is crucial for the realization of quantum memory, faithful entanglement swapping and quantum teleportation. In this talk, I will present our recent experiments about single-photon frequency conversion based on quadratic nonlinear processes. Firstly, we demonstrated spectrum compression of broadband single photons at the telecom wavelength to the near-visible window. A positively chirped single-photon-level laser pulse and a negatively chirped classical one are converted to a narrowband single-photon pulse, with a spectrum compression factor of 58, through sum-frequency generation (SFG), marking a critical step towards coherent photonic interface. Secondly, we demonstrated the nonlinear interaction between two chirped broadband single-photon-level coherent states. A high SFG efficiency of 1.06 × 10−7 is realized, which may be utilized to achieve heralding entanglement at a distance. Finally, we theoretically introduced and experimentally demonstrated single-photon frequency conversion in the telecom band, enabling switching of single photons between dense wavelength-division multiplexing channels. Using cascaded quasi-phase matched sum/difference frequency generation, the signal photon of a photon pair from spontaneous down-conversion is precisely shifted to identically match its counterpart, i.e. idler photon, in frequency to manifest a clear non-classical dip in the Hong-Ou-Mandel interference. Moreover, quantum entanglement between the photon pair is maintained after the frequency conversion. Our researches have realized three significant quantum interfaces via single-photon frequency conversion, which hold great promise for the development of quantum communications and networks.
Efficient frequency conversion is crucial for interfacing photons with a variety of quantum systems ranging from matter qubits (color centers, quantum dots, atoms), optical fibers, detectors, that often operate at widely different wavelengths. Frequency conversion is also a resource to process quantum information.1, 2 Parametric processes such as sum frequency generation (SFG) and Bragg scattering four wave mixing (BS-FWM) offer a good versatility for such frequency conversion. It is well understood that those nonlinear processes have to be strong enough and satisfy phase matching to achieve a high conversion efficiency. While it is enough to consider those two aspects for moderate conversion efficiency up to 50%, the analysis is a bit more complicated when targeting efficiencies closely approaching unity. We are reviewing the pitfall that must be avoided to indeed reach near unity frequency transduction.
The temporal shape of single photons provides a high-dimensional basis of temporal modes, and can therefore support quantum computing schemes that go beyond the qubit. However, the lack of linear optical components to act as quantum gates has made it challenging to efficiently address specific temporal-mode components from an arbitrary superposition. Recent progress towards realizing such a "quantum pulse gate," has been proposed using nonlinear optical signal processing to add coherently the effect of multiple stages of quantum frequency conversion. This scheme, called temporal-mode interferometry [D. V. Reddy, Phys. Rev. A 91, 012323 (2015)], has been shown in the case of three-wave mixing to promise near-unity mode-sorting efficiency. Here we demonstrate that it is also possible to achieve high mode-sorting efficiency using four-wave mixing, if one pump pulse is long and the other short - a configuration we call asymmetrically-pumped Bragg scattering.