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Coherent Manipulation Of Light In The Classical And Quantum Regimes Via Four-Wave Mixing Bragg Scattering

Alessandro Farsi

Published Aug 17, 2015• 1 citation
OpenAlex

Abstract

Nonlinear (NL) optics differs from its linear counterpart in that it drives interaction between different optical frequencies. In a stimulated parametric process, such as sum/difference frequency generation in in [chi](3) , [chi](2) media or phase conjugation a strong pump drives the interaction with a weaker signal field, and an idler field is generated at a different frequency set by the energy conservation of the process. In this work we focus on a subset of possible interactions, i.e. fre- quency translations, in which, for a generated idler, the signal undergoes depletion and the total energy of the two fields is conserved in the Manley-Row sense (i.e. number of photons is conserved). While for most applications such distinction is not fundamental, it becomes a crucial aspect in the very-low-power and quantum regimes. The focus of this work is Bragg Scattering (BS) in [chi](3) medium, a parametric four wave mixing interaction where two pumps separated by an angular frequency detuning [INCREMENT][omega] drive the interaction between a signal and an idler separated by the same amount. This configuration offers great flexibility with respect to choice of participating fields, enabling translation across both a wide span of wavelength and small detuning within the same frequency bands. We first utilize BS to demonstrate an unusual phenomena known as temporal cloaking : a coherent optical manipulation that hides events from an observer. Using the concept of space-time duality, we implement a novel split time-lens that opens and closes a gap in a continuous wave (CW) probing signal, in which events can happen undetected. The reversibility of frequency translation enables us to do and undo the gap without adding any noise. Successively, we employ BS in the quantum regime: time-reversibility implies the preservation of quantum coherence so that quantum states can be manipulated without affecting their quantum nature. Frequency translation offers a way to connect elements operating at different wavelengths for a large scale quantum system. We use BS to operate on single photon states: we demonstrate high performance implementation using a nonlinear fiber, achieving efficient translation of 94 % while having low-losses and extremely low noise compared to previous demonstrations. With such system, we are able to implement more complex manipulation of the quantum field performing temporal compression and magnification using a time-lens. Since frequency translation provides us with the ability to coherently couple arbitrary pairs of frequencies, it is natural to introduce the concept of chromatic qubits, a frequency encoding that is naturally controlled by BS. We manipulate such qubits using a sequence of two BS interactions in a Ramsey interferometer configuration: by varying the delay between the two stages, we observe fringes of interference between the two possible output frequency states. Finally we propose an extension of BS to control high-dimensional frequency space, and study theoretically the different regimes of BS interaction in densemultiplexed frequency channels in the presence of multiple pumps.

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Nonlinear (NL) optics differs from its linear counterpart in that it drives interaction between different optical frequencies. In a stimulated parametric process, such as sum/difference frequency generation in in chi , chi media or phase conjugation a strong pump drives the interaction with a weaker signal field, and an idler field is generated at a different frequency set by the energy conservation of the process. In this work we focus on a subset of possible interactions, i.e. fre- quency translations, in which, for a generated idler, the signal undergoes depletion and the total energy of the two fields is conserved in the Manley-Row sense (i.e. number of photons is conserved). While for most applications such distinction is not fundamental, it becomes a crucial aspect in the very-low-power and quantum regimes. The focus of this work is Bragg Scattering (BS) in chi medium, a parametric four wave mixing interaction where two pumps separated by an angular frequency detuning [INCREMENT][omega] drive the interaction between a signal and an idler separated by the same amount. This configuration offers great flexibility with respect to choice of participating fields, enabling translation across both a wide span of wavelength and small detuning within the same frequency bands. We first utilize BS to demonstrate an unusual phenomena known as temporal cloaking : a coherent optical manipulation that hides events from an observer. Using the concept of space-time duality, we implement a novel split time-lens that opens and closes a gap in a continuous wave (CW) probing signal, in which events can happen undetected. The reversibility of frequency translation enables us to do and undo the gap without adding any noise. Successively, we employ BS in the quantum regime: time-reversibility implies the preservation of quantum coherence so that quantum states can be manipulated without affecting their quantum nature. Frequency translation offers a way to connect elements operating at different wavelengths for a large scale quantum system. We use BS to operate on single photon states: we demonstrate high performance implementation using a nonlinear fiber, achieving efficient translation of 94 % while having low-losses and extremely low noise compared to previous demonstrations. With such system, we are able to implement more complex manipulation of the quantum field performing temporal compression and magnification using a time-lens. Since frequency translation provides us with the ability to coherently couple arbitrary pairs of frequencies, it is natural to introduce the concept of chromatic qubits, a frequency encoding that is naturally controlled by BS. We manipulate such qubits using a sequence of two BS interactions in a Ramsey interferometer configuration: by varying the delay between the two stages, we observe fringes of interference between the two possible output frequency states. Finally we propose an extension of BS to control high-dimensional frequency space, and study theoretically the different regimes of BS interaction in densemultiplexed frequency channels in the presence of multiple pumps.
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.
By implementing a parametric down-conversion process with a strong signal field injection, we demonstrate that frequency down-conversion from pump photons to idler photons can be a coherent process. Contrary to a common misconception, we show that the process can be free of quantum noise. With an interference experiment, we demonstrate that coherence is preserved in the conversion process. This technique could lead to a high-fidelity quantum state transfer from a high-frequency photon to a low-frequency photon and connect a missing link in quantum networks. Coherent and efficient nonlinear interaction and frequency conversion are of great interest in many areas of quantum optics. Traditionally, the low efficiency of Raman scattering is improved by a high-finesse optical resonator or stimulated Raman conversion. It was recently found that the atomic spin wave initially built through electromagnetically induced transparency or a weak Raman process can actively enhance the Raman frequency conversion. An experimental demonstration of an efficient Raman conversion scheme with coherent feedback of both pump and Stokes fields is presented. The temporal profile of the generated Raman pulse shows that the coherence time of the atomic spin wave is $\sim$1.8 ms. A laser-like power threshold is observed and its low threshold is attributed to the long coherence time of the atomic spin wave. The mechanism of the conversion enhancement process is discussed and the conversion efficiency of a single pass of the beams is compared with that of double passes. Finally, a beat signal is observed between the two Stokes fields and its Fourier transform shows that the frequency difference is caused by the AC Stark effect. Precision phase measurement is traditionally restricted by the standard quantum limit. However, this limit is not as fundamental as the Heisenberg limit and can be circumvented by use of nonclassical quantum states and structure modification of the interferometers. Several examples of nonlinear interferometers are proposed and implemented. The wave propagation equations for the nonlinear interferometers are solved. The interference fringes are measured and compared with that of linear interferometers. The first nonlinear interferometer presented is based on second harmonic generation and degenerate parametric down-conversion. The second nonlinear interferometer is composed of two parametric amplifiers. The idea of nonlinear beam splitters is introduced as an analogy to traditional beam splitters. We show that a nonlinear interferometer can be built alternatively by using only one parametric amplifier. Type II phase-matched crystals can be used to increase the amplification factor. An interferometer based on a Raman amplifier is analyzed for its application to sensitive magnetic field measurement.
The authors consider, experimentally and theoretically, the quantum frequency translation (i.e., noiseless conversion) of quantum states of light, including single-photon states. This process is useful for allowing quantum optical systems (atoms, ions, cavities, fibers, detectors) operating at different wavelengths to communicate with each other. The authors recently developed the process of frequency translation in optical fiber through use of the Bragg scattering four-wave mixing process. The high nonlinearity and the ability to control dispersion in photonic crystal fiber (PCF) enable efficient translation between nearby photon channels within the visible to-near-infrared spectral range, useful in quantum networks. This offers an important advantage compared with frequency translation using second-order nonlinear optical crystals, which limits the translation process to widely separated frequencies only.
Nonlinear effects in fibers with partially coherent pumps have attracted a great interest in view of their potential for polarization insensitive wavelength conversion and the increased resilience to Stimulated Brillouin Scattering [1]. In this work we experimentally study the problem of non-degenerate four-wave-mixing (FWM) by using a pair of partially coherent pumps, and focus our attention on a specific type of FWM, which is generally called “Bragg-Scattering” (BS-FWM). This kind of FWM has attracted a renewed interest because of its intrinsically low-noise nature which makes it potentially applicable for light-by-light manipulation even for very faint signals such as quantum keys [2].
Single photons provide a natural platform for quantum communication and quantum networking, as they can be entangled in many degrees of freedom and maintain coherence over long-distance links. However, while their minimal interactions with the environment isolate them from detrimental noise, it can make them difficult to measure and manipulate. In particular, manipulation on the ultrafast timescale is necessary to fully exploit the energy-time (or spectral) photonic degree of freedom. Full control over the spectral properties of single photons is key to many quantum technologies and opens the door to natural high-dimensional quantum encodings. \n \nIn this thesis, we theoretically and experimentally examine the use of nonlinear optical processes mediated by strong laser pulses as a method to control the spectral properties of ultrafast single photons. By mixing single-photon pulses with strong escort pulses that have been shaped through dispersion in a nonlinear crystal, the shape of the escort is imprinted on the photon, resulting in a custom-tailored upconverted pulse. We theoretically examine this process for quadratic spectral phases and show that it has the potential to be simultaneously effective and efficient for the customization of single-photon spectral waveforms, and can be performed in an entanglement-conserving manner. \n \nWe then experimentally demonstrate the range of this technique through three applications. First, we show that sum-frequency generation with shaped pulses can be used to coherently measure time-bin encoded photons with bin separations on the order of picoseconds, well below the timing resolution of our detectors. Secondly, we show that this technique can be adapted to convert a train of pulses to a frequency comb, which can be read out in a straightforward manner using diffraction-based spectrometry. We also show here that this process can be performed in a polarization-maintaining fashion, and demonstrate that entanglement with a partner photon is conserved with high fidelity. Finally, we show that this process can be viewed as a time lens, which modulates a temporal waveform in an analogous fashion to a lens focusing a beam of light. We apply the time lens to a photon from an energy-time entangled pair, and show negative magnification of the joint spectrum through a reversal of the spectral correlations. Such processes could find application in quantum state engineering and high-speed single-photon measurement.
Optical networks are the leading platform for the transfer of information due to their low loss and ability to scale to many information channels using optical frequency modes. To fully leverage the quantum properties of light in this platform, it is desired to manipulate higher-dimensional superpositions by orchestrating linear, beamsplitter-type interactions between several channels simultaneously. We propose a method of achieving simultaneous, all-to-all coupling between N optical frequency modes via N -way Bragg-scattering four-wave mixing. By exploiting the frequency degree of freedom, additional modes can be multiplexed in an interaction medium of fixed volume and loss while avoiding the introduction of excess noise. We generalize the theory of the frequency-encoded two-mode interaction to N modes under this four-wave-mixing approach, finding that arbitrary unitary transformations are possible through successive four-wave-mixing pump configurations. We experimentally verify the quantum nature of this scheme by demonstrating three-way multiphoton interference. Two input photons are shared among three frequency modes and display interference differing from that of two classical (coherent-state) inputs. These results show the potential of our approach for the scalability of photonic quantum information processing to general N -mode systems in the frequency domain.