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arXiv:1811.09135 · Physical Review A

Few-photon Fock-state wave packet interacting with a cavity-atom system in a waveguide: Exact quantum state dynamics

E. V. Stolyarov

Published Feb 28, 2019• 20 citations
arXivHTMLPDF

Abstract

In the paper, we employ a wave-function approach to investigate the evolution of a two-photon wave packet propagating in a one-dimensional waveguide coupled to the Jaynes-Cummings (JC) system. We derive and solve, both analytically and numerically, a set of equations of motion governing the quantum state of the system. That allows us to provide real-time analysis of the evolution of the wave packet two-photon joint spectrum (2PJS) and the excitation dynamics of the JC system in the course of its interaction with the two-photon pulse. We demonstrate that the 2PJS and the spectrum of the wave packet scattered from the JC system experience transformation for nonzero atom-cavity couplings. Moreover, using Schmidt decomposition, we show that the scattered photons feature frequency entanglement contrary to the incident ones which are not entangled.

DOI
10.1103/physreva.99.023857

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In the paper, we employ a wave-function approach to investigate the evolution of a two-photon wave packet propagating in a one-dimensional waveguide coupled to the Jaynes-Cummings (JC) system. We derive and solve, both analytically and numerically, a set of equations of motion governing the quantum state of the system. That allows us to provide real-time analysis of the evolution of the wave packet two-photon joint spectrum (2PJS) and the excitation dynamics of the JC system in the course of its interaction with the two-photon pulse. We demonstrate that the 2PJS and the spectrum of the wave packet scattered from the JC system experience transformation for nonzero atom-cavity couplings. Moreover, using Schmidt decomposition, we show that the scattered photons feature frequency entanglement contrary to the incident ones which are not entangled.
Scattering and correlation properties of a two-photon (TP) pulse are studied in a four-terminal waveguide system, i.e., two one-dimensional waveguides connected by a Jaynes-Cummings emitter (JCE). The wave function approach is utilized to exactly calculate the real-time dynamic evolution of the TP transport. When the width of the incident TP Gaussian pulse is much larger than the photon wavelength, the TP transmission spectra approach that of the corresponding single photon cases and are almost independent of the pulse width. On the contrary, as the pulse width is comparable to the photon wavelength, the TP transmission and correlation both show strong dependence on the pulse width. The resonant scattering due to the JCE and the photon interference together determine the TP correlation. When the distance between the TPs is small, the TP correlations between any two terminals for the scattered TP pulse are much different from those for the incident TP pulse and therefore, such a four-terminal waveguide system provides a way to control the TP correlation.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.
Three-level atoms in lambda configuration find diverse applications in quantum information processing, and a promising way to manipulate their quantum states is with single-photon pulses propagating in a waveguide (which can be theoretically regarded as a highly broadband regime of the Jaynes–Cummings model). Here, we analytically find the nonperturbative dynamics of a lambda atom driven by a two-photon wave packet, propagating in a 1D electromagnetic environment. We study the dynamics of a quantum state purification as an application. By comparing our exact model with an approximated model of two cascaded single-photon wave packets, we show how two-photon nonlinearities and stimulated emission affect the purification.
We present a quantum dynamical study of pulsed few-photon scattering from a single artificial atom, consisting of a two-level system (TLS) or qubit, in a waveguide QED system, directly comparing and contrasting two different quantum theoretical simulation methods: (i) an input-output scattering approach that uses frequency-dependent scattering matrices, and (ii) a matrix product states (MPS) approach, which uses quantum noise operators in time bins and a tensor network technique to solve the time-dependent waveguide function for the entire system. Beginning with pulsed excitation using one-photon and two-photon Fock state pulses, we first show how to compute time-dependent observables with the scattering matrix approach, in terms of frequency integrals that encode the pulse spectrum, including how to extract the population dynamics of the excited quantum emitter, as well as the linear and nonlinear contributions. We present solutions for both symmetric and chiral TLS coupling. We then show how to compute the qubit and field observables in a more direct way using MPS, and obtain the characteristic bird-like shape for the two-photon correlation function at two times, which has been observed in recent experiments. We compare and contrast both of these methods, for one and two-photon excitation pulses, and show excellent agreement. We also present a study of the linear and nonlinear contributions, which can easily be calculated using scattering theory, and show the important role of pulse duration. Finally, we demonstrate the clear advantages of MPS by easily going to higher N-photon excitations, and show selected example population dynamics of up to eight-photon Fock-state pulses, manifesting in clear nonlinear population oscillations during the pulse interaction, similar to classical Rabi oscillations, but with quantum input fields that have a vanishing electric field expectation value.