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Quantum control of atomic systems (with applications in nonlinear optics)

Калоян Златанов, Kaloyan N. Zlatanov

Published May 14, 2019• 0 citations
OpenAlex

Abstract

Coherent control is at the core of contemporary quantum physics. Unclassical states of matter, known as "superposition states" are the main building block of modern day experiments. They are at the basis of quantum information, known as Q-bits, they directly regulate the conversion efficiency in nonlinear harmonic waves in the field of nonlinear optics, they improve the precision of atomic clocks etc. The practical need of good and stable control over these states of matter dictate the need of novel generation protocols, which are robust towards unwanted interactions with the environment and imperfections in the control parameters. We investigate the simplest effects of the system-environment interaction and also provide novel robust superposition generation protocols. An emblematic sub-field on nonlinear optics is the nonlinear microscopy field. This type of microscopy has a tremendous success where standard linear microscopy fails, that is in multilayer samples with similar refractive indecies. We investigate contrast improving techniques for nonlinear microscopy based on suppression of the background signal and enhancement of the signal from the sample.

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Coherent control is at the core of contemporary quantum physics. Unclassical states of matter, known as "superposition states" are the main building block of modern day experiments. They are at the basis of quantum information, known as Q-bits, they directly regulate the conversion efficiency in nonlinear harmonic waves in the field of nonlinear optics, they improve the precision of atomic clocks etc. The practical need of good and stable control over these states of matter dictate the need of novel generation protocols, which are robust towards unwanted interactions with the environment and imperfections in the control parameters. We investigate the simplest effects of the system-environment interaction and also provide novel robust superposition generation protocols. An emblematic sub-field on nonlinear optics is the nonlinear microscopy field. This type of microscopy has a tremendous success where standard linear microscopy fails, that is in multilayer samples with similar refractive indecies. We investigate contrast improving techniques for nonlinear microscopy based on suppression of the background signal and enhancement of the signal from the sample.
This paper investigates the application of nonlinear control theory to the precise regulation of quantum systems. Traditional control methods often struggle with the inherent complexities and sensitivities of quantum systems. This work proposes a novel approach leveraging nonlinear control techniques to directly manipulate quantum state evolution. The core claim is that by designing appropriate nonlinear control signals, it is possible to achieve precise control over quantum system dynamics. The central mechanism involves the targeted modulation of quantum motion using these nonlinear signals, ultimately enabling accurate state control. This approach overcomes the limitations of linear control methods and offers a fundamentally new way to interact with and manage quantum systems. We explore the theoretical framework, mathematical formulations, and potential applications of this approach, focusing on the design and implementation of control strategies for quantum systems. The presented methodology provides a robust and adaptable framework for quantum system regulation, promising significant advancements in quantum technologies.
The fields of quantum and nonlinear optics have given rise to a variety of nonclassical states of light that have been proven to surpass certain limitations set by classical physics. Namely, certain squeezed and entangled states have been shown to beat the shot-noise limit when making precision phase measurements in interferometry, as well as write lithographic patterns that are smaller than classically allowed by the Rayleigh diffraction limit. Additionally, single-photon sources and entangled photon pairs have given rise to provably secure quantum key distribution for cryptography. Producing these quantum states of light has proven a difficult task. Nonlinear crystals, when pumped by a laser, produce pairs of single photons via the process of spontaneous parametric down conversion (SPDC). This process is mediated by the second order nonlinear susceptibility of the material. When pumped in a high gain regime, these crystals give rise to optical parametric amplification, which is a viable source of squeezed light. The vast majority of research in this area has focused on crystals that are seeded by vacuum in their two modes. This dissertation concerns the field of quantum nonlinear optics. It is an investigation into the processes that occur when nonlinear materials interact with the electromagnetic field on the single photon level. I have focused on seeding nonlinear crystals with quantum states of light, including single photons and entangled states. This process results in various states directly applicable to interferometry, imaging, and cryptography. Another application investigated is an absolute radiance measurement via stimulated parametric down conversion resulting from non-vacuum seeding of a nonlinear crystal. Additionally, other nonlinear processes, including four-wave mixing, nonlinear magneto-optical effects and coherent population trapping in warm atomic vapor involving quantum states of light are investigated. The process of seeding third-order nonlinear interactions, such as in atomic vapors, gives rise to a variety of interesting, nonclassical phenomena such as entangled image transfer and nonlocal imaging. Strong analogies between SPDC and four-wave mixing are drawn. I also experimentally show an all optical pi-only phase shift of one light beam via another in warm Cesium vapor.
Optical frequency standards with the reference to a narrow electronic transition of a laser-cooled collection of neutral atomic particles are becoming essential tools of research in modern precision physics experiments. In the core of a building block of an optical frequency standard is the optical continuous wave laser that has a good spectral purity of the emitted light. Such a stable optical oscillator is highly desirable in high resolution spectroscopy, if it emits in a good quality beam at a short visible wavelength. This Master thesis explores efficient techniques for building such an optical frequency source intended for use in the cooling and trapping of Calcium atoms scheme. The strong dipole transition at the blue wavelength in the atomic Calcium is needed to reduce the kinetic energy of atoms by nearly six orders of magnitude. A further reduction in the thermal energy of the laser cooled atoms is required to locate with ultra-high precision the 400 Hz narrow clock transition of the stable 40Ca isotope. The experimental methods that achieve this and approach sub-microkelvin temperature of the laser cooled bosonic isotopes of alkaline earths are inspected. The blue laser with a uniform intensity distribution in the beam is useful to maintain the trapped number of cold atoms during these experiments. The spectroscopic properties of the relative transitions in Calcium atom are also reviewed following relevant publications in the area. The constructed blue laser can be used as a primary wavelength source in the lasers network for cooling and trapping of Calcium atoms. These experiments will constitute part of the project to build an optical atom clock referenced to 40Ca narrow linewidth transition. The blue laser is constructed by generating second harmonic in a Potassium Niobate crystal, which is temperature controlled to use a type-I noncritical phase-matching of the optical nonlinear process. The power of the intracavity-generated second harmonic depends on the resonance properties of the optical resonator where this nonlinear crystal is placed. The study is aimed at characterising the designed optical resonator and the experimental parameters that describe it. The formula is derived that relates the resonance power enhancement coefficient with finesse and the power coupling contrast of a passive optical cavity. The obtained relationship is verfied during the experiments. The produced efficiency of the intracavity second harmonic generation is approx. 0.0023 mWblue/(mWred)2. The research work also examines the noise characteristics of the infrared diode laser that is used as a pump source for the intracavity generated second harmonic and determines the spectroscopic precision of the produced blue light. The frequency locking experiment is analysed using the unbalanced scheme of the polarisation stabilisation technique. The designed optical buildup cavity became a part of the unbalanced frequency discriminator in such a scheme. The results demonstrate high gain of frequency noise suppression of the stabilised laser. The unbalanced arrangement of the H}ansch-Couillaud technique has been possible due to a very low amplitude noise of semiconductor lasers.
The controlled generation of entanglement forms the basis for currently emerging ‘quantum technologies’, such as quantum simulation, computation, and metrology. In the field of quantum metrology, multi-particle entangled states, such as spin-squeezed states, are investigated as a means to improve measurement precision beyond the ‘standard quantum limit’. This limit arises from the quantum noise inherent in measurements on a finite number of uncorrelated particles and limits today’s best atomic clocks. Atom chips combine exquisite coherent control of ultracold atoms with a compact and robust setup, suggesting their use for quantum metrology with portable atomic clocks and interferometers. A severe limitation of atom chips, however, is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. In this thesis, I present experiments where we generate for the first time multi-particle entanglement on an atom chip. We achieve this by controlling elastic collisional interactions with a state-dependent potential. We employ this novel technique to generate spin-squeezed states of a two-component Bose-Einstein condensate and show that they are a useful resource for quantum metrology, as they could be used to improve an interferometric measurement by 2.5 dB over the standard quantum limit. The state-dependent potential is created with the help of a coplanar microwave guide, which is integrated on our atom chip. In the vicinity of this waveguide a microwave nearfield is formed. When a Bose-Einstein condensate of 87Rb is brought into this near-field, the hyperfine energy levels of the atoms are shifted differentially due to the AC Zeeman effect. The strong gradients in the field can be used to state-selectively shift the minimum of a static magnetic atom trap and thus coherently split an ensemble of atoms which have been prepared in a superposition of two internal states. During this process, nonlinear atomic interactions lead to the formation of a spinsqueezed state. I tomographically analyze the produced state, reconstruct its Wigner function, and deduce that it is at least four-particle entangled. I compare our results with a dynamical multi-mode simulation which takes not only the atomic motion and internal state dynamics but also particle losses into account and find good agreement. Moreover, I use this comparison to identify technical noise sources in our experiment, which currently limit the achieved amount of squeezing, and make suggestions on how to eliminate them in future experiments. Our method can in principle create a very large amount of squeezing and entanglement and is applicable to a wide variety of atomic systems, in particular to those for which no convenient Feshbach resonance exists. We envisage the implementation of this technique in portable atomic clocks and interferometers operating beyond the standard quantum limit. Furthermore, it is a valuable tool for experiments on many-body quantum physics and could enable quantum information processing on atom chips.
Most phenomena around us can be explained by classical optics since photons interact weakly with atoms. When the interaction is strong enough where one photon affects the properties of other photons, we go to the regime of quantum photon-photon nonlinear optics. The work in this thesis explores this regime of physics. This paves the path to exploring strongly interacting many-body physics with photons which is still a largely unexplored domain. The ability to control strongly interacting photons is also of central importance in quantum science and engineering. We use the approach of Electromagnetically Induced Transparency (EIT) in atomic ensembles to create strong interactions and demonstrate coherent control between single photons. Using EIT, we coherently map single photons onto the atoms which travel as coupled excitations of light and matter called dark-state polaritons. When the medium is optically dense, the polariton propagates as a massive particle with a velocity that is much smaller than the speed of light. These polaritons interact with each other via their atomic component. In this thesis, we show robust symmetry-protected collisions between photons that imprint a large phase of π/2 with little loss and extend the nature of photon-photon interactions to the repulsive regime, which are essential for quantum communication and metrology. We use the technique of photon blockade to make a fast optical detector of Rydberg states, directly demonstrating the use of quantum nonlinear optics for quantum computation. We also study the extensions of the attractive and repulsive photons for three particles shedding light into the formation of bound states and crystals of photons and paving the way to studying many-body physics of photons.