We theoretically investigate the up-conversion process of two entangled photons on a molecule, which is coupled by a cavity or nanoscale metallic structure. Within one-dimensional input-output theory, the propagators of the photons are derived analytically and the up-conversion probability is calculated numerically. It is shown that the coupling with the nanostructure clearly enhances the process. We also find that the enhancement becomes further pronounced for some balanced system parameters, such as the quantum correlation between photons, radiation decay, and coupling between the nanostructure and molecule. The nonmonotonic dependencies are reasonably explained in view of quantum interference between the coupled modes of the whole system. This result indicates that controlling quantum interference and correlation is crucial for few-photon nonlinearity, and provides a new guidance to wide variety of fields, e.g., quantum electronics and photochemistry.
We theoretically investigate the up-conversion process of two entangled photons on a molecule, which is coupled by a cavity or nanoscale metallic structure. Within one-dimensional input-output theory, the propagators of the photons are derived analytically and the up-conversion probability is calculated numerically. It is shown that the coupling with the nanostructure clearly enhances the process. We also find that the enhancement becomes further pronounced for some balanced system parameters, such as the quantum correlation between photons, radiation decay, and coupling between the nanostructure and molecule. The nonmonotonic dependencies are reasonably explained in view of quantum interference between the coupled modes of the whole system. This result indicates that controlling quantum interference and correlation is crucial for few-photon nonlinearity, and provides a new guidance to wide variety of fields, e.g., quantum electronics and photochemistry.
We investigate an efficient two-photon upconversion process in more than one molecule coupled to an optical antenna. In the previous paper [Y. Osaka et al., Phys. Rev. Lett. 112, 133601 (2014)], we considered the two-photon upconversion process in a single molecule within one-dimensional input-output theory and revealed that controlling the antenna-molecule coupling enables the efficient upconversion with radiative loss in the antenna suppressed. In this paper, aiming to propose a way to enhance the total probability of antenna-photon scattering, we extend the model to the case of multiple molecules. In general, the presence of more than one molecule decreases the upconversion probability because they equally share the energy of the two photons. However, it is shown that we can overcome the difficulty by controlling the intermolecule coupling. Our result implies that, without increasing the incident photon number (light power), we can enlarge the net probability of the two-photon upconversion.
We theoretically study nonlinear optical frequency conversion with time-frequency entangled paired photons whose sum frequency is on two-photon resonance of an atomic ensemble. Assisted by a strong coupling laser, two paired photons with wide spectrum are converted into a single monochromatic photon. The on-resonance nonlinear process is made possible due to the electromagnetically induced transparency that not only eliminates the on-resonance absorption but also enhances the nonlinear interaction between the single photons and atoms. Compared to this quantum-nonlinear conversion, the classical corresponding single-photon counts from accidental two-photon coincidence has a wide spectrum and experiences large absorption. As a result, the system can be used as an efficient two-photon quantum correlator in which the classical accidental coincidences can be suppressed. We perform numerical simulations basing on a Rb atomic vapor cell with realistic operating parameters.
The practical development of quantum plasmonic circuits incorporating non-classical interference [1] and sources of entangled states calls for a versatile quantum theoretical framework which can fully describe the generation and detection of entangled photons and plasmons. However, majority of the presently used theoretical approaches are typically limited to the toy models assuming loss-less and nondispersive elements or including just a few resonant modes. Here, we present a rigorous Green function approach describing entangled photon-plasmon state generation through spontaneous wave mixing in realistic metal-dielectric nanostructures. Our approach is based on the local Huttner-Barnett quantization scheme [2], which enables problem formulation in terms of a Hermitian Hamiltonian where the losses and dispersion are fully encoded in the electromagnetic Green functions. Hence, the problem can be addressed by the standard quantum mechanical perturbation theory, overcoming mathematical difficulties associated with other quantization schemes. We derive explicit expressions with clear physical meaning for the spatially dependent two-photon detection probability, single-photon detection probability and single-photon density matrix. In the limiting case of low-loss nondispersive waveguides our approach reproduces the previous results [3,4]. Importantly, our technique is far more general and can quantitatively describe generation and detection of spatially-entangled photons in arbitrary metal-dielectric structures taking into account actual losses and dispersion. This is essential to perform the design and optimization of plasmonic structures for generation and control of quantum entangled states. [1] J.S. Fakonas, H. Lee, Y.A. Kelaita and H.A. Atwater, Nature Photonics 8, 317(2014) [2] W. Vogel and D.-G. Welsch, Quantum Optics, Wiley (2006). [3] D.A. Antonosyan, A.S. Solntsev and A.A. Sukhorukov, Phys. Rev. A 90 043845 (2014) [4] L.-G. Helt, J.E. Sipe and M.J. Steel, arXiv: 1407.4219
Since information has been regarded as a physical entity, the field of quantum information theory has blossomed. This brings novel applications, such as quantum computation. This field has attracted the attention of numerous researchers with backgrounds ranging from computer science, mathematics and engineering, to the physical sciences. Thus, we now have an interdisciplinary field where great efforts are being made in order to build devices that should allow for the processing of information at a quantum level, and also in the understanding of the complex structure of some physical processes at a more basic level. This thesis is devoted to the theoretical study of structures at the nanometer-scale, "nanostructures," through physical processes that mainly involve the solid-state and quantum optics, in order to propose reliable schemes for the processing of quantum information. Initially, the main results of quantum information theory and quantum computation are briefly reviewed. Next, the state-of-the-art of quantum dots technology is described. In so doing, the theoretical background and the practicalities required for this thesis are introduced. A discussion of the current quantum hardware used for quantum information processing is given. In particular, the solid-state proposals to date are emphasised. A detailed prescription is given, using an optically-driven coupled quantum dot system, to reliably prepare and manipulate exciton maximally entangled Bell and Greenberger-Horne-Zeilinger (GHZ) states. Manipulation of the strength and duration of selective light-pulses needed for producing these highly entangled states provides us with crucial elements for the processing of solid-state based quantum information. The all-optical generation of states of the so-called Bell basis for a system of two quantum dots (QDs) is exploited for performing the quantum teleportation of the excitonic state of a dot in an array of three coupled QDs. Theoretical predictions suggest that several hundred single quantum bit rotations and controlled-NOT gates could be performed before decoherence of the excitonic states takes place. In addition, the exciton coherent dynamics of a coupled QD system confined within a semiconductor single mode microcavity is reported. It is shown that this system enables the control of exciton entanglement by varying the coupling strength between the optically-driven dot system and the microcavity. The exciton entanglement shows collapses and revivals for suitable amplitudes of the incident radiation field and dot-cavity coupling strengths. The results given here could offer a new approach for the control of decoherence mechanisms arising from entangled "artificial molecules." In addition to these ultrafast coherent optical control proposals, an approach for reliable implementation of quantum logic gates and long decoherence times in a QD system based on nuclear magnetic resonance (NMR) is given, where the nuclear resonance is controlled by the ground state "magic number" transitions of few-electron QDs in an external magnetic field. The dynamical evolution of quantum registers of arbitrary length in the presence of environmentally-induced decoherence effects is studied in detail. The cases of quantum bits (qubits) coupling individually to different environments ("independent decoherence"), and qubits interacting collectively with the same reservoir ("collective decoherence") are analysed in order to find explicit decoherence functions for any number of qubits. The decay of the coherences of the register is shown to strongly depend on the input states: this sensitivity is a characteristic of both types of coupling (collective and independent) and not only of the collective coupling, as has been reported previously. A non-trivial behaviour - "recoherence" - is found in the decay of the off-diagonal elements of the reduced density matrix in the specific situation of independent decoherence. The results lead to the identification of decoherence-free states in the collective decoherence limit. These states belong to subspaces of the system's Hilbert space that do not become entangled with the environment, making them ideal elements for the engineering of "noiseless" quantum codes. The relations between decoherence of the quantum register and computational complexity based on the new dynamical results obtained for the register density matrix are also discussed. This thesis concludes by summarising and pointing out future directions, and in particular, by discussing some biological resonant energy transfer processes that may be useful for the processing of information at a quantum level.
We investigate theoretically a single-photon frequency conversion with a Sagnac waveguide loop by input-output formalism. The results show that an ultra-wide tunable frequency conversion can be achieved via constructive interference and a flexible adjustment of parameters. For instance, we discuss the generation of ultraviolet photons in detail, which corresponds to the up-conversion process of frequency. We also can obtain entangled states of photons and atoms under suitable parameter conditions. Our calculations prove that a single-photon frequency conversion with high efficiency can be realized, even if effected by spontaneous decay and deviation of parameters.
Nonlinear optical phenomena associated with high-order soliton breakup in photonic crystal fibres and squeezed state generation in three dimensional photonic crystal microcavities are investigated. In both cases, the properties of periodically patterned, high-index contrast dielectric structures are engineered to control the dispersion and local field enhancements of the electromagnetic field. Ultra-short pulse propagation in a polarization-maintaining microstructured fibre (with 1 um core diameter and 1.1 m length) is investigated experimentally and theoretically. For an 80 MHz train of 130 fs pulses with average propagating powers in the fibre up to 13.8 mW, the output spectra consist of multiple discrete solitons that shift continuously to lower energies as they propagate in the lowest transverse mode of the fibre. The number of solitons and the amount that they shift both increase with the launched power. All of the data is quantitatively consistent with solutions of the nonlinear Schrodinger equation, but only when the Raman nonlinearity is treated without approximation, and self-steepening is included. The feasibility of using a parametric down-conversion process to generate squeezed electromagnetic states in 3D photonic crystal microcavity structures is investigated for the first time. The spectrum of the squeezed light is theoretically calculated by using an open cavity quantum mechanical formalism. The cavity communicates with two main channels, which model vertical radiation losses and coupling into a single-mode waveguide respectively. The amount of squeezing is determined by the correlation functions relating the field quadratures of light coupled into the waveguide. All of the relevant model parameters are realistically estimated using 3D finite-difference time-domain (FDTD) simulations. Squeezing up to ~20% below the shot noise level is predicted for reasonable optical excitation levels. To preserve the squeezed nature of the light generated in the microcavity, a unidirectional coupling geometry from the microcavity to a ridge waveguide in a slab photonic crystal structure is studied. The structure was successfully fabricated in a silicon membrane, and experimental measurements of the efficiency for the signal coupled out of the structure are in good agreement with the result of FDTD simulations. The coupling efficiency of the cavity mode to the output channel is ~60%.