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QUANTUM INFORMATION EXCHANGE BETWEEN PHOTONS AND ATOMS

Wang Yi-min

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

Quantum information processing tasks have been implemented in various physical platforms. In this thesis, we consider two specific implementations: Part I presents a detailed study of the interaction of a single atom with a light pulse. Part II examines the case of a quantum controlled-phase gate in circuit quantum electrodynamics in the ultrastrong coupling regime. They are both actively pursued by many research groups. In Part I, we first present the framework for a single two-level atom interacting with the quantized electromagnetic field. The effect of temporal and spectral properties of the pulses on atomic excitation is studied for both Fock state and coherent state pulse. The detailed analysis of atomic excited state population is provided for single photon pulse with various temporal shapes. The work is then extended to a more general case with two spatial-modes and multi-photon pulses. The difference between Fock state and coherent state pulse on atomic excitation is further investigated. We find that at few photon levels, the maximum atomic excitation probability is a monotonic function of photon number for the coherent state pulse, but not for the Fock state pulse. Furthermore, we show that the atomic dynamics can be controlled by the initial relative phase between the two counter-propagating coherent state pulses incident on the atom, which is not the case with two Fock state pulses. The theoretical prediction is then compared with an experiment, where a single trapped 87Rb atom interacts with coherent state pulses engineered in temporal shape of rising exponential and rectangular form. Next, we propose a quantum memory setup based on a single two-level atom in a half cavity with a moving mirror. The efficiency of the quantum storage process is studied analytically and

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Quantum information processing tasks have been implemented in various physical platforms. In this thesis, we consider two specific implementations: Part I presents a detailed study of the interaction of a single atom with a light pulse. Part II examines the case of a quantum controlled-phase gate in circuit quantum electrodynamics in the ultrastrong coupling regime. They are both actively pursued by many research groups. In Part I, we first present the framework for a single two-level atom interacting with the quantized electromagnetic field. The effect of temporal and spectral properties of the pulses on atomic excitation is studied for both Fock state and coherent state pulse. The detailed analysis of atomic excited state population is provided for single photon pulse with various temporal shapes. The work is then extended to a more general case with two spatial-modes and multi-photon pulses. The difference between Fock state and coherent state pulse on atomic excitation is further investigated. We find that at few photon levels, the maximum atomic excitation probability is a monotonic function of photon number for the coherent state pulse, but not for the Fock state pulse. Furthermore, we show that the atomic dynamics can be controlled by the initial relative phase between the two counter-propagating coherent state pulses incident on the atom, which is not the case with two Fock state pulses. The theoretical prediction is then compared with an experiment, where a single trapped 87Rb atom interacts with coherent state pulses engineered in temporal shape of rising exponential and rectangular form. Next, we propose a quantum memory setup based on a single two-level atom in a half cavity with a moving mirror. The efficiency of the quantum storage process is studied analytically and
State mapping between atoms and photons, and photon-photon interactions play an important role in scalable quantum information processing. We consider the interaction of a two-level atom with a quantized propagating pulse in free space and study the probability Pe(t){P}_{e}(t)Pe​(t) of finding the atom in the excited state at any time ttt. This probability is expected to depend on (i) the quantum state of the pulse field and (ii) the overlap between the pulse and the dipole pattern of the atomic spontaneous emission. We show that the second effect is captured by a single parameter $\ensuremath{\Lambda}\ensuremath{\in}[0,8\ensuremath{\pi}/3]$, obtained by weighting the dipole pattern with the numerical aperture. Then, Pe(t){P}_{e}(t)Pe​(t) can be obtained by solving time-dependent Heisenberg-Langevin equations. We provide detailed solutions for both single-photon Fock state and coherent states and for various temporal shapes of the pulses.
We describe the interaction of two two-level atoms in free space with propagating modes of the quantized electromagnetic field, using the time-dependent Heisenberg-Langevin method. For single- photon pulses, we consider the effect of the pulse's spatial and temporal profiles on the atomic excitation. In particular, we find the ideal shape for a pulse to put exactly one excitation in any desired state of the bi-atomic system. Furthermore, we analyze the differences in the atomic dynamics between the cases of Fock state pulses and coherent state pulses.
We investigate the dynamics of a single two-level atom, which interacts with pulses propagating in two spatial modes (right and left) and frequency continuum. Using Heisenberg equations of motion, we present the explicit analytical derivations and general formalisms for atomic excitation with two-spatial-mode multiphoton pulses in both the Fock and coherent states. Based on those formalisms, we show that perfect atomic excitation by a single-photon Fock state pulse can only be realized when it is rising exponentially shaped in the even mode, a balanced superposition of the two spatial modes. A single photon from a single spatial mode can only give half of the maximal atomic excitation probability. We also show that the maximum atomic excitation probability with multiphoton pulses in the even mode is a monotonic function of the average photon number for the coherent state, but not for the Fock states. Furthermore, we demonstrate that the atomic dynamics can be controlled by the initial relative phase between the two counterpropagating coherent state pulses incident on the atom, which is not the case with the two Fock state pulses.
We propose a setup for quantum memory based on a single two-level atom in a half cavity with a moving mirror. We show that various temporal shapes of incident photon can be efficiently stored and read out by shaping the time-dependent decay rate $\ensuremath{\gamma}(t)$ between the atom and the light. This is achieved uniquely by an appropriate motion of the mirror without the need for additional control laser or atomic level. We present an analytical expression for the efficiency of the process and study its dependence on the ratio between the incident light field bandwidth and the atomic decay rate. We discuss possible implementations and experimental issues, particularly for a single atom or ion in a half cavity quantum optical setup as well as a superconducting qubit in the context of circuit QED.
We theoretically studied the implementation of a quantum memory and an optical transistor in a system composed by a single atom trapped inside a high finesse cavity. In order to store and map the quantum state of an input pulse onto internal states of the single atom (quantum memory) we employ the electromagnetically induced transparency (EIT) phenomenon (which can work out as an optical transistor) where the information can be transferred to the dark state of the atom modelled by a three-level system in a Λ-type configuration. In our model we consider a suitable temporal shape for the control field that ensures the adiabaticity of the storage process and retrieval of the probe pulse. The dynamic of the field inside the cavity was obtained by master equation approach, while the outside field was calculated by input-output formalism. We have analysed two different setups: i) two-sided and ii) single-sided cavities. While the first setup is the most appropriate and commonly used to observe cavity-EIT in the transmission spectrum, thus the best configuration for the optical transistor, the maximum quantum memory efficiency can not reach reasonable values, being limited to 50% for symmetric cavities. On the other hand, with single-sided cavity the quantum memory efficiency increases considerably and can reach values close to 100% in the strong atom-field coupling regime. However this specific setup is not favourable to observe the cavity-EIT effect in the transmission spectrum and then it is not appropriate to control the transmission of light pulses.
Dynamic coupling of cavities to a quantum network is of major interest to distributed quantum information processing schemes based on cavity quantum electrodynamics. This can be achieved by actively tuning a mediating atom-cavity system. In particular, we consider the dynamic coupling between two coupled cavities, each interacting with a two-level atom, realized by tuning one of the atoms. One atom-field system can be controlled to become maximally and minimally coupled with its counterpart, allowing high fidelity excitation confinement, QQQ switching, and reversible state transport. As an application, we first show that simple tuning can lead to emission of near-Gaussian single-photon pulses that is significantly different from the usual exponential decay in a passive cavity-based system. The influences of cavity loss and atomic spontaneous emission are studied in detailed numerical simulations, showing the practicality of these schemes within the reach of current experimental solid-state technology. We then show that when the technique is employed to an extended coupled-cavity scheme involving a multilevel atom, arbitrary temporal superposition of single photons can be engineered in a deterministic way.