The purpose of this paper is to study the interaction between a two-level system (qubit) and two continuous-mode photons. Two scenarios are investigated: Case 1, how a two-level system changes the pulse shapes of two input photons propagating in a single input channel; and Case 2, how a two-level system responds to two counterpropagating photons, one in each input channel. The steady-state output field states for both cases are derived analytically in both the time and frequency domains. Numerical simulations demonstrate rich and interesting two-photon scattering phenomena induced by a two-level system.
The purpose of this paper is to study the interaction between a two-level system (qubit) and two continuous-mode photons. Two scenarios are investigated: Case 1, how a two-level system changes the pulse shapes of two input photons propagating in a single input channel; and Case 2, how a two-level system responds to two counterpropagating photons, one in each input channel. The steady-state output field states for both cases are derived analytically in both the time and frequency domains. Numerical simulations demonstrate rich and interesting two-photon scattering phenomena induced by a two-level system.
The problem of photon-photon interaction controlled by a two-level system is studied in this paper. Specifically, we have proposed two scenarios: Case 1, how a two-level system changes the pulse shapes of two initially uncorrelated input photons in a single input channel; and Case 2, how a two-level system entangles two counter-propagating photons, one in each input channel. The steady-state output field states for both cases are derived explicitly. For Case 1, the Wigner spectrum is used to exhibit the interesting properties of the output field state. For Case 2, the nonlinear property of the interaction between the two-level system and the two input photons has been revealed by the probabilities of observing photons in the output channels. In addition, two-photon interference, similar to Hong-Ou-Mandel effect, occurs when the two input photons are chosen with the same pulse shape.
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 purpose of this paper is to study the dynamics of a quantum coherent feedback network composed of two two-level systems (qubits) driven by two counter-propagating photons. The coherent feedback network is a marginally stable system, and the spectral entanglement of photons could be enhanced as a consequence of the continuing two-photon interaction inside the feedback loop. By means of quantum stochastic calculus and the input-output framework, the analytic form of the steady-state output field states are derived in the Heisenberg picture for the first time. Based on the analytic form, significant enhancement of photon-photon interaction can be observed. In particular, we demonstrate that the famous Hong-Ou-Mandel effect can be created using this coherent feedback structure. The proposed framework is also applicable in the single-photon scenario.
In this paper, we study the spatiotemporal distribution of the photon electric field produced by the scattering of a single photon narrow pulse from a system of two identical qubits coupled to continuum modes in a one-dimensional (1D) open waveguide. We derive the time-dependent dynamical equations for qubits' and photon amplitudes which allow the calculation of the photon backward and forward scattering fields in the whole space: before qubits, between qubits, and behind the qubits. The scattered field consists of several contributions that describe a free field of incoming photon, a spontaneous exponential decay of excited qubits, a slowly decaying part that dies out as the inverse powers of t, and a lossless part that represents a steady state solution as t→∞. For our system, we find the transmittance and reflectance fields as both time and distance from the qubits tend to infinity. We show that as the time after the event of scattering tends to infinity, the steady state photon the field is being formed in the whole one-dimensional space. If the distance d between qubits is equal to the integer of the wavelength λ, the field energy exhibits temporal beatings between the qubit frequency Ω and the photon frequency ωS with the period T=2π/(ωS−Ω).
Ideally, strong nonlinearities could be used to implement quantum gates for photonic qubits by well-controlled two-photon interactions. However, the dependence of the nonlinear interaction on frequency and time makes it difficult to preserve a coherent pulse shape that could justify a single-mode model for the time-frequency degree of freedom of the photons. In this paper, we analyze the problem of temporal multimode effects by considering the pulse shape of the average output field obtained from a coherent input pulse. It is shown that a significant part of the two-photon state transformation can be derived from this semiclassical description of the optical nonlinearity. The effect of a nonlinear system on a two-photon state can then be determined from the density-matrix dynamics of the coherently driven system using input-output theory. As an example, the resonant nonlinearity of a single two-level atom is characterized. The results indicate that the most efficient nonlinear effect may not be the widely studied single-mode phase shift, but the transfer of one of the photons to an orthogonal mode distinguished by its temporal and spectral properties.
Non-Gaussian quantum states of light are of paramount importance to quantum computing. Nevertheless, their deterministic generation is challenging problem due to the difficulty to control nonlinearities in physical systems. In this work, we characterize the light stemming from one of the most fundamental quantum optics configurations: the unidirectional scattering of multimode and multiphoton light by a two-level system. We provide an analytic and explicit description of the output light solely in terms of the corresponding input temporal modes which allows a straightforward physical interpretation and is computationally more effective compared to numerical methods. Then, we focus on the specific case of the scattering of two photons in a single mode. By numerically decomposing the output state in terms of its principal modes, we find that it is possible to map single-mode two-photon inputs to be into two-mode entangled output states, i.e., two-photon NOON states, to very good approximation. The latter states, in turn, are known to have more Wigner negativity compared to the associated input, which ultimately suggests a potential application of our considered setup in the deterministic generation of non-Gaussian states.