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Physics of the Solid State

Effect of the qubit relaxation on transport properties of microwave photons

A. N. Sultanov, Ya. S. Greenberg

Published Nov 1, 2017• 1 citation
Publisher

Abstract

In this work, using the non-Hermitian Hamiltonian method, the transmission of a single photon in a one-dimensional waveguide interacting with the cavity containing an arbitrary number of photons and the two-level artificial atom is studied with allowance for the relaxation of the latter. For transport factors, analytical expressions which explicitly take into account the qubit relaxation parameter have been obtained. The form of the transmission (reflection) coefficient when there is more than one photon in the cavity qualitatively differs from the single-photon cavity and contains the manifestation of the photon blockade effect. The qubit lifetime depends on the number of photons in the cavity.

DOI
10.1134/s1063783417110294

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In this work, using the non-Hermitian Hamiltonian method, the transmission of a single photon in a one-dimensional waveguide interacting with the cavity containing an arbitrary number of photons and the two-level artificial atom is studied with allowance for the relaxation of the latter. For transport factors, analytical expressions which explicitly take into account the qubit relaxation parameter have been obtained. The form of the transmission (reflection) coefficient when there is more than one photon in the cavity qualitatively differs from the single-photon cavity and contains the manifestation of the photon blockade effect. The qubit lifetime depends on the number of photons in the cavity.
We investigate the propagation of microwave photons in a one-dimensional open waveguide interacting with a number of artificial atoms (qubits). Within the formalism of projection operators and a non-Hermitian Hamiltonian approach we develop a one-photon approximation scheme for the calculation of the transmission and reflection factors of the microwave signal in a waveguide which contains an arbitrary number NNN of noninteracting qubits. We considered in detail the resonances and photon-mediated entanglement for two and three qubits in a chain. We showed that in the non-Markovian case the resonance widths, which define the decay rates of the entangled state, can be much smaller than the decay width of an individual qubit. It is also shown that for identical qubits in the long-wavelength limit a coherent superradiant state is formed with the width being equal to the sum of the widths of spontaneous transitions of NNN individual qubits. The results obtained in the paper are of general nature and can be applied to any type of qubits. The specific properties of the qubit are only encoded in the two parameters: the qubit energy $\mathrm{\ensuremath{\Omega}}$ and the rate of spontaneous emission $\mathrm{\ensuremath{\Gamma}}$.
The influence of nonradiative damping of qubits on the microwave transport of photons propagating in a onedimensional microstrip line has been considered. Expressions for the transmission and reflection coefficients for two qubits have been obtained within the non-Hermitian Hamiltonian formalism. The indirect interaction between qubits caused by nonradiative decay into a common channel is explicitly taken into account in these expressions. It has been shown that this interaction leads to results significantly different from known results.
We analyze a photon transport through a one-dimensional open waveguide side coupled to the NNN-photon microwave cavity with embedded an artificial two-level atom (qubit). The qubit state is probed by a weak signal at the fundamental frequency of the waveguide. Within the formalism of projection operators and a non-Hermitian Hamiltonian approach we develop a one-photon approximation scheme to obtain the photon wave function, which allows for the calculation of the probability amplitudes of the spontaneous transitions between the levels of two Rabi doublets in an NNN-photon cavity. We obtain analytic expressions for the transmission and reflection factors of the microwave signal through a waveguide which contains the information of the qubit parameters. We show that for a small number of cavity photons the Mollow spectrum consists of four spectral lines, which is a direct manifestation of the quantum nature of light. The results obtained in the paper are of a general nature and can be applied to any type of qubits. The specific properties of the qubit are only encoded in the two parameters: the energy $\mathrm{\ensuremath{\Omega}}$ of the qubit and its coupling $\ensuremath{\lambda}$ to the cavity photons.
Single-photon transport properties in a one-dimensional coupled resonator waveguide, coupled to a whispering-gallery resonator interacting with two separated two-level atoms, are theoretically investigated. Based on the real-space approach, the transmission and reflection amplitudes of the single photon are deduced. Numerical results demonstrate that the transmission and reflection depend on the resonator–atom coupling, the intermode backscattering, and especially the phase difference between these two separated atoms. Effects of dissipation on single-photon transport properties are also discussed.
The single-photon transport in a single-mode waveguide, coupled to a cavity embedded with a two-level atom, is analyzed. The single-photon transmission and reflection amplitudes, as well as the cavity and the atom excitation amplitudes, are solved exactly via a real-space approach. It is shown that the dissipations of the cavity and of the atom, respectively, affect distinctively on the transport properties of the photons and on the relative phase between the excitation amplitudes of the cavity mode and the atom.
We study single-photon transmission spectra in a waveguide coupled to two cavities embedded with one(two) two-level atom(atoms). When only the left cavity contains a two-level atom, single-photon transmission spectra can be modulated by changing the distance between the two cavities. Phase separation-induced transparency is acquired in such a system when each cavity contains a two-level atom. The influence of the dissipation of cavities and atoms on single-photon transport properties is also analysed. In addition, the experimental design of such an optical system is discussed.