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arXiv:1706.08028 · Journal of Experimental and Theoretical Physics Letters

Influence of the nonradiative decay of qubits into a common channel on the transport properties of microwave photons

Ya. S. Greenberg, A. N. Sultanov

Published Sep 1, 2017• 4 citations
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Abstract

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.

DOI
10.1134/s0021364017180060

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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.
In this work we calculate the amplitudes of nonradiative decay of the microwave photons for the system of two qubits in a waveguide with energy relaxation to a common bath. The calculations are carried out in the formalism of the effective non-Hermitian Hamiltonian which includes in addition to the local relaxation channels the global relaxation of qubits to a common channel. We showed that for identical qubits the global relaxation can be matched to zero for the certain distances between the qubits. We analyze the contribution of nonradiative decay channels to the detection efficiency of microwave photons by the two-qubit system. We also find the parameters of the system at which the efficiency takes on 100% value.
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 $\mathrm{\ensuremath{\Gamma}}$.
We study the space-time structure of the scattered field induced by the scattering of a narrow single-photon Gaussian pulse on a qubit embedded in a one-dimensional open waveguide. For weak excitation power we obtain explicit analytical expressions for the space and time dependence of reflected and transmitted fields which are, in general, different from plane traveling waves. The scattered field consists of two parts: a damping part which represents spontaneous decay of the excited qubit and a coherent, lossless part. We show that for a large distance xxx from the qubit and at times ttt long after the scattering event our theory provides the result which is well known from stationary photon transport. However, the approach to the stationary limit is very slow. The scattered field decreases as the inverse powers of xxx and ttt as both the distance from the qubit and the time after the interaction increase.
By consistently applying the formalism of quantum electrodynamics, we developed a comprehensive theoretical framework describing the interaction of single microwave photons with an array of superconducting transmon qubits in a waveguide cavity resonator. In particular, we analyze the effects of microwave photons on the array’s response to a weak probe signal exciting the resonator. The study reveals that high quality factor cavities provide a better spectral resolution of the response, while cavities with moderate quality factors allow better sensitivity for a single-photon detection. Remarkably, our analysis showed that a single-photon signal can be detected by even a sole qubit in a cavity under the realistic range of system parameters. We also discuss how the quantum properties of the microwave radiation and electrodynamical properties of resonators affect the response of qubits’ array. Our results provide an efficient theoretical background for informing the development and design of quantum devices consisting of arrays of qubits, especially for those using a cavity where an explicit expression for the transmission or reflection is required.
We study single-photon transport properties in an array of coupled microcavities, coupled to a whispering-gallery-type resonator interacting with a two-level atom. The transmission and reflection coefficients for the single photon propagating in such a coupled system are deduced. We show that the coherent transport properties of the single photon can be well controlled by the intermode backscattering, the resonator–atom coupling and the detuning between the whispering-gallery resonator and the atom. In addition, the influence of the dissipation of the whispering-gallery resonator and the two-level atoms for the realistic physical system on the transport properties are also analysed.