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Strongly correlated system-reservoir dynamics with quantized pulses: Controlling the atom-photon bound state

Kisa Barkemeyer, Andreas Knorr, Alexander Carmele

Published Nov 7, 2020• 0 citations
OpenAlex

Abstract

Within the matrix product state framework, we study the non-Markovian feedback dynamics of a two-level system interacting with the electromagnetic field inside a semi-infinite waveguide where the formation of an atom-photon bound state is possible. Taking the steady-state excitation of the emitter as a figure of merit, we compare the trapped excitation for an initially excited quantum emitter and an emitter prepared via quantized pulses. In the latter case, we find that for certain feedback delay times, multi-photon pulses yield a significantly higher steady-state excitation than possible with an initially excited emitter. In the system we consider, we find an increase of around 90 percent. Thus, the quantum optical initialization is found to be more efficient due to the self-consistent inclusion of emerging quantum noise. Furthermore, we propose a recursive Heisenberg ansatz which shows good qualitative agreement with the numerically expensive matrix product state method and requires only numerical resources growing quadratically with the number of excitations.

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Within the matrix product state framework, we study the non-Markovian feedback dynamics of a two-level system interacting with the electromagnetic field inside a semi-infinite waveguide where the formation of an atom-photon bound state is possible. Taking the steady-state excitation of the emitter as a figure of merit, we compare the trapped excitation for an initially excited quantum emitter and an emitter prepared via quantized pulses. In the latter case, we find that for certain feedback delay times, multi-photon pulses yield a significantly higher steady-state excitation than possible with an initially excited emitter. In the system we consider, we find an increase of around 90 percent. Thus, the quantum optical initialization is found to be more efficient due to the self-consistent inclusion of emerging quantum noise. Furthermore, we propose a recursive Heisenberg ansatz which shows good qualitative agreement with the numerically expensive matrix product state method and requires only numerical resources growing quadratically with the number of excitations.
Within the matrix product state framework, we study the non-Markovian feedback dynamics of a two-level system interacting with the electromagnetic field inside a semi-infinite waveguide where the excitation of an atom-photon bound state is possible. Taking the steady-state excitation of the emitter as a figure of merit, we compare the trapped excitation for an initially excited quantum emitter and an emitter prepared via quantized pulses containing up to four photons. In the latter case, we find that for large feedback delay times, multiphoton pulses can yield a significantly higher steady-state excitation than possible with an initially excited emitter since the stimulated emission process can enhance the trapping probability in comparison to the spontaneous decay of an initially excited emitter.
The dynamics of waveguide-QED systems involving coherent time-delayed feedback give rise to a hierarchy of multitime correlations within the Heisenberg picture due to the induced non-Markovianity. We propose to perform a projection onto a complete set of states in the Hilbert space to decompose the multitime correlations into single-time matrix elements. To illustrate the procedure, we consider the paradigmatic example of a two-level system that couples to a semi-infinite waveguide and interacts with quantum light pulses. Our approach complements the range of available methods as it allows calculating the dynamics under the inclusion of additional dissipation channels in a numerically exact and efficient manner for multiphoton pulses of arbitrary shape where memory requirements are known in advance.
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.
The calculation of the non-Markovian dynamics of waveguide-QED systems with coherent time-delayed feedback within the Heisenberg picture gives access to the microscopic dynamics and allows the inclusion of dissipation channels. However, typically a hierarchy of multi-time correlations arises. We propose to unravel these multi-time correlations via a projection onto a complete set of states in the Hilbert space. In particular, we consider a two-level system inside a semi-infinite waveguide subjected to quantum light pulses. Our approach makes it possible to calculate the dynamics in a numerically exact and efficient manner for multiphoton pulses of arbitrary shape with memory requirements known a priori.
Squeezed light states have a special place in quantum optics with potentially profound applications in emerging quantum technologies. We present a numerically-exact matrix product states (MPS) approach to model quantum pulses of squeezed light, at the few-photon level, interacting with a two-level system in a waveguide environment. We represent the squeezed state as a coherent superposition of Fock states and explore the nonlinear population dynamics as well as multi-photon correlation functions that emerge. We show how the squeezed pulse can create quantum correlations that are unique to squeezed pulses, including ⟨b(t)b(t+t′)⟩\langle b(t) b(t+t')\rangle⟨b(t)b(t+t′)⟩ for transmitted fields as well as ⟨b†(t)b†(t+t′)b(t+t′)b(t)⟩\langle b^\dagger(t) b^\dagger(t+t') b(t+t') b(t) \rangle⟨b†(t)b†(t+t′)b(t+t′)b(t)⟩. We also demonstrate how ⟨b(t)b(t+t′)⟩\langle b(t) b(t+t') \rangle⟨b(t)b(t+t′)⟩, a first-order correlation function, shows nonlinear photon correlations that are similar to those known and measured for two-photon scattering states. Finally, we also study the squeezed spectra of the pulse before and after interacting with the two-level system, and highlight the role of the spectral bandwidth of the incident pulse. The MPS theory allows the modeling of arbitrary bandwidth squeezing without making any Markov and Born approximations for the light-matter interaction processes, and can easily be extended to waveguide systems with multiple emitters and time-delayed feedback.
Abstract. In this paper, we demonstrate the application of quantum feedback control in creating desired states for atomic and photonic systems utilizing a semi-infinite waveguide coupled with multiple two-level atoms. In this approach, an initially excited atom can emit one photon into the waveguide, and the photon can be reflected by either the terminal mirror of the waveguide or other atoms, establishing various feedback loops through the coherent interactions between the atom and photon. When there are no more than two excitations in the waveguide quantum electrodynamics (QED) system, the evolution of quantum states can be effectively elucidated through the lens of random graph theory. However, this process is influenced by the environment. We propose that the environment-induced dynamics in the coherent feedback loop can be eliminated by measurement-based feedback control or coherent drives. Consequently, in the atom-waveguide interactions in open quantum systems, measurement-based feedback has the potential to modulate the quantum steady states. Additionally, the homodyne detection noise during the measurement process can induce errors upon quantum states, which can be influenced by the coherent feedback parameter designs.