Abstract The temporal dynamics of absorption of a single-photon pulse by two qubits interacting with a microwave field of a one-dimensional waveguide have been studied. The theory, which allows one to use arbitrary shapes of the input single-photon wave packet as an initial condition, as well as investigate the excitation dynamics of each qubit, has been developed. The numerical calculation is performed for the packet of a Gaussian shape, at different parameters of frequency detuning and duration of the input pulse. The excitation dynamics of both identical and nonidentical qubits have been studied. It has been specifically shown that it is possible to form symmetric and antisymmetric entangled states for identical qubits.
Abstract The temporal dynamics of absorption of a single-photon pulse by two qubits interacting with a microwave field of a one-dimensional waveguide have been studied. The theory, which allows one to use arbitrary shapes of the input single-photon wave packet as an initial condition, as well as investigate the excitation dynamics of each qubit, has been developed. The numerical calculation is performed for the packet of a Gaussian shape, at different parameters of frequency detuning and duration of the input pulse. The excitation dynamics of both identical and nonidentical qubits have been studied. It has been specifically shown that it is possible to form symmetric and antisymmetric entangled states for identical qubits.
AbstractThe temporal dynamics of absorption of a single-photon pulse by two qubits interacting with a microwave field of a one-dimensional waveguide have been studied. The theory, which allows one to use arbitrary shapes of the input single-photon wave packet as an initial condition, as well as investigate the excitation dynamics of each qubit, has been developed. The numerical calculation is performed for the packet of a Gaussian shape, at different parameters of frequency detuning and duration of the input pulse. The excitation dynamics of both identical and nonidentical qubits have been studied. It has been specifically shown that it is possible to form symmetric and antisymmetric entangled states for identical qubits.
In the present paper, we have proposed the experimentally achievable method for the characterization of the collective states of qubits in a linear chain. We study a temporal dynamics of absorption of a single-photon pulse by three interacting qubits embedded in a one-dimensional open waveguide. Numerical simulations were performed for a Gaussian-shaped pulse with different frequency detunings and interaction parameters between qubits. The dynamic behavior of the excitation probability for each qubit is investigated. It was shown that the maximum probability amplitudes of excitation of qubits are reached when the frequency of external excitation coincides with the frequency of excitation of the corresponding eigenstate of the system. In this case, the magnitude of the probability amplitude of each qubit in the chain unambiguously correlates with the contribution of this qubit to the corresponding collective state of the system, and the decay of these amplitudes is determined by the resonance width arising from the interaction of the qubit with the photon field of the waveguide. Therefore, we show that the pulsed harmonic probe can be used for the characterization of the energies, widths, and the wave functions of the collective states in a one dimensional qubit chain.
Abstract We study the dynamics of a single-photon pulse traveling through a linear qubit chain coupled to continuum modes in a one-dimensional (1D) photonic waveguide. We derive a time-dependent dynamical theory for qubits’ amplitudes and for transmitted and reflected spectra. We show that the requirement for the photon-qubit coupling to exist only for positive frequencies can significantly change the dynamics of the system. First, it leads to the additional photon-mediated dipole-dipole interaction between qubits which results in the violation of the phase coherence between them. Second, the spectral lines of transmitted and reflected spectra crucially depend on the shape of the incident pulse and on the initial distance between the pulse center and the first qubit in the chain. We apply our theory to one-qubit and two-qubit systems. For these cases we obtain the explicit expressions for the qubits’ amplitudes and for the photon radiation spectra as time tends to infinity. Specific calculations are performed for superconducting qubits operating in GHz frequency range. For the incident Gaussian wave packet we calculate the line shapes of transmitted and reflected photons.
We present a detailed quantum theory and simulations of few-photon Fock state pulses interacting with a two-level system (TLS) in an open waveguide-QED system. For a rectangular pulse shape, we present an exact temporal scattering theory to derive analytical expressions for the TLS population, using one-photon and two-photon pulses, for both chiral and symmetric emitters. We also derive the stationary (long-time) and time-dependent spectra for one-photon excitation, and show how these differ at a fundamental level when considering TLS population effects. Numerically, we also present matrix product state (MPS) simulations, which allow us to compute more general photon correlation functions for arbitrary quantum pulses, and we use this approach to also show results for Gaussian quantum pulses and to confirm the accuracy of our analytical solutions. In the case of a chiral TLS, we show how a one-photon pulse, of any temporal shape, yields a transmitted long-time spectrum that is identical to the input pulse, despite significant TLS population effects. However, the dynamical spectra and spectral intensity show rich population effects, allowing for their detection in spectroscopic experiments. We also show the striking differences between one-photon and two-photon excitation, where the latter shows clear signatures of nonlinear saturation effects. In addition, we demonstrate how significant population TLS dynamics also occur for pulses that are relatively long compared to the radiative decay time (showing that a weak excitation approximation, which neglects finite TLS population effects, cannot be made) and investigate the population signatures, nonlinear features and dynamical behavior as a function of quantum pulse length.
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.
We study the dynamics of a single-photon pulse travelling through a linear qubit chain coupled to continuum modes in a one-dimensional (1D) photonic waveguide. We derive a time-dependent dynamical theory for qubit amplitudes and for transmitted and reflected spectra. We show that the requirement for the photon-qubit coupling to exist only for positive frequencies can significantly change the dynamics of the system. First, it leads to an additional photon-mediated dipole-dipole interaction between qubits which results in the violation of the phase coherence between them. Second, the spectral lines of transmitted and reflected spectra crucially depend on the shape of the incident pulse and the initial distance between the pulse center and the first qubit in the chain. We apply our theory to one-qubit and two-qubit systems. For these two cases, we obtain the explicit expressions for the qubits' amplitudes and the photon radiation spectra as time tends to infinity. For the incident Gaussian wave packet we calculate the line shapes of transmitted and reflected photons.