Single-photon scattering on a two-qubit system. Spatio-temporal
structure of the scattered field
- URL: http://arxiv.org/abs/2310.18723v1
- Date: Sat, 28 Oct 2023 14:57:08 GMT
- Title: Single-photon scattering on a two-qubit system. Spatio-temporal
structure of the scattered field
- Authors: Ya. S. Greenberg, A. A. Shtygashev, and A. G. Moiseev
- Abstract summary: We study the photon electric field produced by the scattering of a single photon narrow pulse from a system of two identical qubits coupled to modes in a one-dimensional (1D) open waveguide.
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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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 $t\rightarrow\infty$. 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 $\lambda$, the field energy exhibits temporal
beatings between the qubit frequency $\Omega$ and the photon frequency
$\omega_S$ with the period $T=2\pi/(\omega_S-\Omega)$.
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