Nonlinear parametric processes involving ultrashort pulses are typically carried out in time domain, which mathematically corresponds to a convolution of their frequency spectra. In contrast, this spectral convolution changes into a multiplication operation when performing the nonlinear interaction in frequency domain. Here, we extend the scope of frequency-domain nonlinear optics by demonstrating its ability to perform a temporal convolution. Through this approach, nonlinear optical operations that are inaccessible in time domain can be realised: specific optical information can be coherently advanced by picoseconds within a pulse sequence-a newly generated second harmonic pulse carries the amplitude and phase information of two input pulses. This central pulse is isolated when using an input field consisting of two cross-polarized input pulses in combination with type-II second harmonic generation. The effects of nonlinear temporal convolution can be viewed from the aspect of signal processing and pulse shaping, where the nonlinear interaction in the parametric crystal plays the role of a dynamic linear optical filter-in contrast to conventional static filters-with a shaping mask instantaneously adapting to the laser field.
Nonlinear parametric processes involving ultrashort pulses are typically carried out in time domain, which mathematically corresponds to a convolution of their frequency spectra. In contrast, this spectral convolution changes into a multiplication operation when performing the nonlinear interaction in frequency domain. Here, we extend the scope of frequency-domain nonlinear optics by demonstrating its ability to perform a temporal convolution. Through this approach, nonlinear optical operations that are inaccessible in time domain can be realised: specific optical information can be coherently advanced by picoseconds within a pulse sequence-a newly generated second harmonic pulse carries the amplitude and phase information of two input pulses. This central pulse is isolated when using an input field consisting of two cross-polarized input pulses in combination with type-II second harmonic generation. The effects of nonlinear temporal convolution can be viewed from the aspect of signal processing and pulse shaping, where the nonlinear interaction in the parametric crystal plays the role of a dynamic linear optical filter-in contrast to conventional static filters-with a shaping mask instantaneously adapting to the laser field.
Creating and controlling well-defined single-photon states is important for many quantum enhanced technologies. Information can be encoded in any degree of freedom associated with a single-photon field excitation, for example in the polarization or transverse spatial mode structure. The ability to encode multiple qubits in these states is desirable for high data transmission rates and increased information processing capacity. The spectral-temporal domain offers a large Hilbert space for encoding information, well suited to integrated optical architectures owing to the low cross-talk between channels. Indeed, time-frequency encoding is an integral component of existing information technologies infrastructure. Thus, complete, coherent control of the spectral-temporal mode structure of light is essential to advancing optical quantum technologies. Arbitrary control of single-photon states has been demonstrated in the polarization and spatial-momentum degrees of freedom however, is yet to be established in the spectral-temporal domain. Recently it was shown that spectral-temporal pulse shaping is experimentally feasible using nonlinear optical methods. However, such techniques can introduce noise photons, are challenging to implement deterministically and require specially prepared auxiliary pump pulses. Furthermore, they are typically only possible at relatively low repetition rates to avoid damage of nonlinear optical materials. Here, we demonstrate deterministic pulse shaping of single-photon wave packets by introducing a time-varying phase. Applying linear or quadratic phase to the wave packet introduces a spectral shift or spectral broadening, respectively. Achieving significant spectral manipulation requires temporal-phase modulation on the order of π. The phase must also vary on the same time scale as the optical pulses, approximately 1 ps in duration here. This relatively rapid phase variation is achieved using a fast electro-optic phase modulator. The modulator is driven by a time-varying voltage that is synchronized with a pulse train of single-photon wave packets for accurate temporal phase control. In this thesis, we experimentally demonstrate control of the spectral-temporal state of single-photon wave packets using this method. Heralded single-photon wave packets are generated by spontaneous parametric down conversion pumped by a frequency-doubled Titanium-Sapphire laser oscillator with 80 MHz repetition rate. To achieve significant modulation of single-photon pulses a 10 V peak-to-peak radio-frequency signal of 40 GHz drives the phase modulator, which requires approximately 3.6 V to achieve a π phase shift. The signal is synchronized with the oscillator pulse train using custom designed electronics. Details of these electronics are presented, resulting in a robust phase and amplitude controllable 40 GHz voltage source, phase locked to the single-photon pulse train. To demonstrate the utility of this pulse-shaping method we experimentally show spectral shearing of almost 1 nm for single-photon wave packets with 830 nm central wavelength and 1 nm bandwidth. Measurement of the second-order intensity correlation before and after the wave-packet manipulation remains constant within uncertainty of the measurement, showing that the quantum nature of the single-photon source is not deteriorated by the modulator. Preservation of the wave-packet coherence is verified by two-photon interference between spectrally sheared and non-modulated single-photons.
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.
Ideally, strong nonlinearities could be used to implement quantum gates for photonic qubits by well-controlled two-photon interactions. However, the dependence of the nonlinear interaction on frequency and time makes it difficult to preserve a coherent pulse shape that could justify a single-mode model for the time-frequency degree of freedom of the photons. In this paper, we analyze the problem of temporal multimode effects by considering the pulse shape of the average output field obtained from a coherent input pulse. It is shown that a significant part of the two-photon state transformation can be derived from this semiclassical description of the optical nonlinearity. The effect of a nonlinear system on a two-photon state can then be determined from the density-matrix dynamics of the coherently driven system using input-output theory. As an example, the resonant nonlinearity of a single two-level atom is characterized. The results indicate that the most efficient nonlinear effect may not be the widely studied single-mode phase shift, but the transfer of one of the photons to an orthogonal mode distinguished by its temporal and spectral properties.
This thesis describes theoretical and experimental aspects as well as potential applications in the field of coherent optics known as Phase Conjugate Optics (PCO). By utilizing nonlinear optical techniques, real-time or wavefront reversal of an arbitrary incident electromagnetic field can be realized. The nonlinear optical interaction gives rise to what is referred to as the phase conjugate (of the incident monochromatic wave) by performing the operation of complex conjugation upon the incident wave's complex spatial amplitude in real time. This conjugate wave, which is also designated as being a wavefront, has the property of exactly retracing the path of the incident field. The ability of the conjugate wave to correct for inhomogeneous linear and nonlinear (intensity-dependent) aberrations as well as polarization distortions is proved. In particular, the theory of a degenerate four-wave nonlinear optical interaction as providing for the conjugator is presented. The effects of linear and nonlinear losses upon this interaction are discussed. The quantum mechanical origin of the third order nonlinear optical susceptibility responsible for the four-wave mixing process is analyzed for both single and two-photon allowed transitions in an atomic (or molecular) system. The analogies of four-wave mixing with that of real-time holography are discussed. The theory of conjugation via four-wave mixing in optical waveguides is presented.
Several of the above characteristics of conjugate fields are verified experimentally where conjugate fields via degenerate four-wave mixing were observed both in the bulk and in waveguide geometries, using carbon disulfide as the nonlinear medium. Amplified time-reversed wavefront generation as well as a mirrorless optical parametric mode of oscillation have been observed, both in agreement with theoretical predictions.
Potential applications of PCO are discussed in three different regimes: spatial-frequency, temporal-frequency, and spatial/temporal frequency domains. In the first category, the ability of PCO to correct for image modal dispersion in optical waveguides as well as the use of PCO to perform real-time coherent image processing and nonlinear microscopy is discussed. Temporal-frequency domain applications of PCO to be analyzed include the use of a nearly degenerate four-wave mixing process as a narrowband, wide field-of-view optical filter, capable of an amplified bandpass. The ability of a PCO interaction to renarrow (transform limited) optical pulses which have been temporally spread due to propagation through (group velocity) dispersive channels is analyzed. A potential application of PCO in the field of nonlinear laser spectroscopy is presented. Specifically, the scattering of a probe photon off a two-photon coherent state (created in a three-level atomic system) is shown to yield a conjugate replica. This conjugate replica is capable of providing sub-Doppler width resolution of the two-photon resonance. Further, in the transient regime, the optical free-induction decay of the conjugate wave is capable of yielding detailed spectral features of the three-level system such as the anharmonic contribution to a (nearly) harmonic potential. This technique, performed in the time domain, is known as [alpha]-beat spectroscopy.
Finally, a detailed theoretical and experimental study is presented of a laser resonator in which one (or both) of the mirror(s) comprising the optical cavity is replaced by a conjugate mirror (PCM). This novel resonator, which is termed a conjugate resonator (PCR), combines many of the spatial- and temporal-frequency aspects of PCO interactions discussed above. The stability criterion, transverse and longitudinal mode spectra, and the PCR output energy, as well as the frequency locking features of the laser modes to the PCM are discussed.
The time-frequency degree of freedom is a powerful resource for implementing high-dimensional quantum information processing. In particular, field-orthogonal pulsed temporal modes offer a flexible framework compatible with both long-distance fibre networks and integrated waveguide devices. In order for this architecture to be fully utilised, techniques to reliably generate diverse quantum states of light and accurately measure complex temporal waveforms must be developed. To this end, nonlinear processes mediated by spectrally shaped pump pulses in group-velocity engineered waveguides and crystals provide a capable toolbox. In this review, we examine how tailoring the phasematching conditions of parametric downconversion and sum-frequency generation allows for highly pure single-photon generation, flexible temporal-mode entanglement, and accurate measurement of time-frequency photon states. We provide an overview of experimental progress towards these goals, and summarise challenges that remain in the field.
The temporal processing operations of convolution and correlation are demonstrated through optical coherent transient techniques, in which two long, low-intensity frequency-chirped pulses replace the single, brief reference pulse of a traditional three-pulse excitation sequence (brief pulse, pattern pulse, and data pulse). Here, a four-pulse excitation sequence is used (two frequency-chirped pulses, pattern pulse, and data pulse) in which the particular order and timing of the chirped pulses with respect to the other waveforms determine the processing operation. An experiment is performed with biphase-coded pattern and data pulses to demonstrate both the correlation and the convolution operations. A new atomic rephasing process that we call delayed rephasing is demonstrated.